An Updated Numerical Simulation of the Ground-Water 

Flow System for the Castle Lake Debris Dam, Mount 

St. Helens, Washington, and Implications for Dam 

Stability Against Heave 

U.S. GEOLOGICAL SURVEY 

Water-Resources Investigations Report 94-4075 

An Updated Numerical Simulation of the Ground-Water 

Flow System for the Castle Lake Debris Dam, Mount 

St. Helens, Washington, and Implications for Dam 

Stability Against Heave 

By Evelyn A. Roeloffs 

U.S. GEOLOGICAL SURVEY 

Water-Resources Investigations Report 94-4075 

Vancouver, Washington 

1994 
U.S. DEPARTMENT OF THE INTERIOR 

BRUCE BABBITT, Secretary 

For additional information 

write to: 

John E. Costa 

U.S. Geological Survey 

5400 MacArthur Blvd. 

Vancouver, WA 98661 

U.S. GEOLOGICAL SURVEY 

GORDON P. EATON, Director 

ii 

Copies of this report can be 

purchased from: 

U.S. Geological Survey 

Earth Science Information Center 

Open-File Reports Section 

Box 25286, MS 517 

Denver Federal Center 

Denver, CO 80225 
CONTENTS 

Abstract ................................................................................................. 1 

Introduction ................................................................................................ 1 

Previous Investigations .................................................................................. 2 

Scope and Methods oflnvestigation ....................................................................... .4 

Acknowledgments .................................................................................... .4 

Description of the Debris Dam ................................................................................ .4 

Topography and Geology ................................................................................ 4 

Drillhole Data and Pre-1980 Materials ..................................................................... 12 

1983 Drillholes ................................................................................. 12 

1990 Drillholes ................................................................................. 12 

SiteDH1 ................................................................................. 12 

Site DH2A, B ............................................................................. 12 

SiteDH3 ................................................................................. 12 

Site DH4A, B, C, D ......................................................................... 13 

Site DH5A, B ............................................................................. 13 

SiteDH6 ................................................................................. 14 

Vegetation .......................................................................................... 14 

The Ground-water Flow System .............................................................................. 14 

Alternative Conceptual Models of the Flow System ......................................................... 14 

Hydraulic and Engineering Properties ..................................................................... 14 

Precipitation ......................................................................................... 15 

Water Levels in Piezometers ............................................................................ 15 

Seep Discharge ....................................................................................... 17 

Evapotranspiration .................................................................................... 17 

Castle Creek ......................................................................................... 27 

Hydraulic Head Gradients and Factors of Safety .............................................................. 27 

Factors of Safety: Gradient Method ................................................................. 27 

Factors of Safety: Overburden Method ............................................................... 31 

Numerical Simulation of the Ground-water Flow System .......................................................... 31 

Approach ........................................................................................... 32 

General Features of the Model. .......................................................................... 32 

Model Geometry ............................................................................... 32 

Boundary Conditions ............................................................................. 32 

Upper and Lower Boundaries ................................................................... 34 

Castle Lake ............................................................................... 34 

Castle Creek and Spillway .................................................................... 34 

Western Boundary .......................................................................... 35 

Northern Boundary ......................................................................... 36 

Natural Conditions to be Simulated by the Model. ..................................................... 36 

Precipitation .............................................................................. 36 

Evapotranspiration ......................................................................... 36 

Seep Discharge ............................................................................ 38 

Seep Locations and Conductances ........................................................... 38 

Correction of Seep Discharge Measurements for the 

1991 Water Year ....................................................................... 38 

Piezometer Water Levels ...................................................................... 41 

Free Parameters and Calibration .................................................................... 41 

Uniform Model. ...................................................................................... 42 

Modifications Tested for the Uniform Model. ............................................................... 44 

Permeable Material Beneath the 1980 Deposits ........................................................ 44 

Vertical Anisotropy ............................................................................. 47 

Decrease of Hydraulic Conductivity with Depth ....................................................... 48 

iii 
Evapotranspiration Parameters .................................................................... 48 

Variation of Recharge with Surface Slope ............................................................ 48 

Nonuniform Calibrated Model .......................................................................... 49 

Large-scale Hydraulic Conductivity Variations ........................................................ 49 

The Area Around Piezometers DH4A, B, C, D .................................................... 49 

Crest Conductance .............................................................................. 51 

Other Local Conductivity Changes .................................................................. 51 

Creekbed Conductance .......................................................................... 61 

Drain Conductances and Elevations ................................................................. 61 

Fit to Observations .............................................................................. 62 

Hydraulic Conductivity Distribution ................................................................. 62 

Water Budget .................................................................................. 62 

Limitations on the Use of the Numerical Models ............................................................. 64 

Stability of the Debris Dam Against Heave ...................................................................... 64 

Factors of Safety ..................................................................................... 64 

Effect of Lowering Castle Lake .......................................................................... 65 

Effect of Artificially Draining the Dam Crest. ............................................................... 65 

Conclusions ............................................................................................. 79 

References Cited ............................................................................................. 80 

FIGURES 

1. Map showing location and general features of the study area ................................................. 2 

2. Map showing topography of the Castle Lake area before the 1980 eruption of Mount St. Helens ................ 5 

3. Map showing topography of the Castle Lake debris dam ..................................................... 6 

4. Map showing thickness of the debris avalanche deposit. ..................................................... 7 

Sa-b. Cross sections of the Castle Lake debris dam: 

Sa. Cross-sections A-A', B-B' ........................................................................... 8 

5b. Cross-sections C-C', D-D' .......................................................................... 9 

5c. Cross-sections E-E', F-F', G-G' ...................................................................... 10 

5d. Cross-sections H-H', J-J', K-K', M-M' ......................................................... .11 

6a-e. Graphs showing monthly precipitation at the Castle Lake debris dam and 

water levels in piezometers, 1983-1993: 

6a. Water levels in piezometers 14, P3A, and P3B .......................................................... 18 

6b. Waterlevels in piezometers DH3, P2A, P2B and DHl. .................................................. 19 

6c. Water levels in piezometers II, PI, 12, and 13 .......................................................... 20 

6d. Water levels in piezometers DH6, P4A, DH2A and DH2B ................................................ 21 

6e. Water levels in piezometers DH4A, B, C, D and DH5A,B ............................................... 22 

7. Map showing seep discharge exit points ................................................................ 23 

8a-c. Graphs showing monthly precipitation at the Castle Lake debris dam and 

discharge from seeps, 1983-1993: 

8a. Seeps I and 3 ................................................................................... 24 

8b. Seeps 5, 6, and 7 ................................................................................. 25 

8a. Seep 8 and combined flow of seeps 9 and 10 .......................................................... 26 

9. Map showing the channel of Castle Creek in 1989 and in September, 1991 

and the thalweg of Castle Creek in June, 1991. ......................................................... 28 

10. Graphs showing the elevation of Castle Creek's channel: 

A. Channel elevations .............................................................................. 29 

B. Differences between channel elevations and uniformly sloping beds .................................. 29 

11. Graphs showing results of cross-section surveys at Castle Creek: 

A. Cross-section CA205 ............................................................................. 30 

B. Cross-section CA210 ............................................................................. 30 

iv 
12. Graphs showing factors of safety corresponding to water level observations on the Castle Lake debris dam: 

A. Factors of safety calculated using the gradient method .................................................. 31 

B. Factors of safety calculated using the overburden method ............................................... 31 

13. Map view of the numerical model grid .................................................................. 33 

14. Map showing percentage of vegetative cover ............................................................. 37 

15. Graphs showing seep discharge versus water level ........................................................ 40 

16. Graph showing differences between average water levels in piezometers 

during the 1991 and 1992 water years ................................................................. 41 

17 A. Observed and calculated water levels for the uniform and nonuniform calibrated models .................... .45 

17B. Observed and model calculated seep discharge for the uniform and 

nonuniform calibrated models ...................................................................... 45 

18. Map showing water levels in the highest active model layer as simulated by the 

uniform model for the 1992 water year ............................................................... 46 

19. Graph showing water budget summary for the uniform and nonuniform calibrated models ................... 47 

20. Map of the model grid showing division into higher and lower conductivity quadrants ....................... 50 

21a-e. Map showing horizontal hydraulic conductivity distribution for the nonuniform calibrated model: 

21a. Layer 1 ................................................................................ 52 

21b. Layer 2 ................................................................................ 53 

21c. Layer 3 ................................................................................ 54 

21d. Layer 4 ................................................................................ 55 

21e. Layer 5 ................................................................................ 56 

22a-d. Map showing the distribution of vertical hydraulic conductivity 

for the nonuniform calibrated model: 

22a. Between layer 1 and layer 2 ................................................................ 57 

22b. Between layer 2 and layer 3 ................................................................ 58 

22c. Between layer 3 and layer 4 ................................................................ 59 

22d. Between layer 4 and layer 5 .............................................................. , . 60 

23. Map showing the hydraulic head in the highest active layer as simulated by the nonuniform 

calibrated model ................................................................................. 63 

24a-c. Map showing factors of safety against heave calculated using the nonuniform 

calibrated model for the 1992 water year: 

24a. Overburden method ....................................................................... 66 

24b. Gradient method, top active layer .............................................................. 67 

24c. Gradient method, cells below the top active layer ................................................. 68 

25a-b. Map showing factors of safety against heave calculated using the uniform 

model for the 1992 water year: 

25a. Overburden method ....................................................................... 69 

25b. Gradient method, top active layer ............................................................ 70 

26. Map showing the simulated hydraulic head in the highest active layer assuming 

Castle Lake has been lowered by 40 ft ............................................................. 71 

27a-c. Map showing factors of safety against heave when Castle Lake has been lowered 40 feet: 

27a. Overburden method ....................................................................... 72 

27b. Gradient method, top active layer ............................................................ 73 

27c. Gradient method, cells below the top active layer ................................................. 74 

28. Map showing the simulated hydraulic head in the highest active layer assuming 

drains have been installed .......................................................................... 75 

29a-c. Map showing factors of safety against heave when the crest is artificially drained: 

29a. Overburden method ....................................................................... 76 

29b. Gradient method, top active layer ............................................................ 77 

29c. Gradient method, cells below the top active layer ................................................. 78 

v 
TABLES 

1. Locations, elevations and depths of piezometers .......................................................... 13 

2. Hydraulic conductivity measured by falling head tests ..................................................... 15 

3. Monthly precipitation at Castle Lake ................................................................... 16 

4. Wells used to compensate for recharge from outside of the model boundaries .................................. 35 

5. Linear regression relations between seep discharges and water levels ......................................... 39 

6. Averages of measured and estimated seep discharge ....................................................... 39 

7. Summary of the uniform and fully calibrated Castle Lake ground-water models ................................. 43 

8. Vertical hydraulic head differences in the Castle Lake debris dam ............................................ 44 

9. Summary of the hydraulic conductivity distribution for the nonuniform calibrated model. ....................... 61 

vi 
CONVERSION FACTORS AND VERTICAL DATUM 

Multiply By To obtain 

inch (in.) 25.4 millimeter 

foot (ft) 0.3048 meter 

mile 1.609 kilometer 

square foot ( ft2

) 0.0929 square meter 

acre-foot (acre-ft) 1233 cubic meter 

cubic foot per second (ft3

/s) 0.02832 cubic meter per second 

foot per day (ft/day) 0.3048 meter per day 

Sea level: In this report "sea level" refers to the National Geodetic Vertical Datum of 1929-a geodetic datum derived from a general 

adjustment of the first-order level nets of the United States and Canada, formerly called Sea Level Datum of 1929. 

State plane coordinates: In this report, positions in the study area are given using the Washington State Plane Coordinate System 

South Zone. This state coordinate system relates longitude and latitude to plane-rectangular (easting and northing) coordinates using the 

Lambert Conformal Conic projection. Eastings and northings are given in feet. 

vii 

An Updated Numerical Simulation of the Ground-Water 

Flow System for the Castle Lake Debris Dam, 

Mount St. Helens, Washington, and Implications for Dam 

Stability Against Heave 

By Evelyn A. Roeloffs 

Abstract 

A numerical simulation of the ground-water 

flow system in the Castle Lake debris dam, calibrated to data from the 1991 and 1992 water 

years, was used to estimate factors of safety 

against heave and internal erosion. The Castle 

Lake debris dam, 5 miles northwest of the summit 

of Mount St. Helens, impounds 19,000 acre-ft of 

water that could pose a flood hazard in the event 

of a lake breakout. 

A new topographic map of the Castle Lake 

area prior to the 1980 eruption of Mount St. 

Helens was prepared and used to calculate the 

thickness of the debris avalanche deposits that 

compose the dam. Water levels in 22 piezometers 

and discharges from seeps on the dam face measured several times per year beginning in 1990 

supplemented measurements in 11 piezometers 

and less frequent seep discharge measurements 

made since 1983. Observations in one group of 

piezometers reveal heads above the land surface 

and head gradients favoring upward flow that correspond to factors of safety only slightly greater 

than 2. 

The steady-state ground-water flow system in 

the debris dam was simulated using a threedimensional finite difference computer program. 

A uniform, isotropic model having the same 

shape as the dam and a hydraulic conductivity of 

1.55 ft/day simulates the correct water level at 

half the observation points, but is in error by 10 ft 

or more at other points. Spatial variations of 

hydraulic conductivity were required to calibrate 

the model. The model analysis suggests that 

ground water flows in both directions between 

the debris dam and Castle Lake. 

Factors of safety against heave and internal 

erosion were calculated where the model simulated upward flow of ground water. A critical 

gradient analysis yields factors of safety as low 

as 2 near the piezometers where water level 

observations indicate low factors of safety. Low 

safety factors are also computed near Castle 

Creek where slumping was caused by a storm in 

January, 1990. If hydraulic property contrasts are 

present in areas of the debris dam unsampled by 

piezometers, then low safety factors may exist 

that are not evident in the numerical model analysis. Numerical model simulations showed that 

lowering Castle Lake by 40 feet increases many 

factors of safety by 0.1, but increases greater 

than 1 are limited to the area of 1990 slumping. 

INTRODUCTION 

When Mount St. Helens erupted in May, 1980, 

the debris flow that swept down the Toutle River 

blocked South Fork Castle Creek, impounding Castle 

Lake (fig. 1). In order to prevent the rising lake from 

overtopping the debris dam, a spillway was constructed in 1981 to stabilize the elevation of the lake, 

which now contains approximately 19,000 acre-feet 

(acre-ft) of water. If the natural dam were to fail, the 
123°00' 45' 

46°15' 

0 2 4 6 MILES 

I I 11 1

1 I I 

0 2 4 6 8 KILOMETERS 

Figure 1. Location and general features of the study area. 

ensuing breakout of Castle Lake might seriously affect 

communities downstream along the Toutle River. 

Although the dam and spillway have performed well 

to date, piezometers in the dam reveal hydraulic heads 

30 ft or more above lake level in the dam crest. In this 

respect, the hydraulic head distribution in the natural 

dam does not resemble that in an engineered embankment dam. This report describes the results of a U.S. 

Geological Survey study to characterize the groundwater flow system in the debris dam so that its influence on the dam's stability can be evaluated. 

2 

EXPLANATION 

Debris avalanche deposits 

from May 18, 1980 eruption 

Previous Investigations 

122°00' 

The stability of the Castle Lake debris dam and the 

destructive potential of a lake breakout have been considered by the U.S. Army Corps of Engineers (USACE) and the U.S. Geological Survey, as well as 

consultants hired by the Weyerhauser Company, 

which owns timber-producing land that might be affected by a dam failure. 

Meyer and others (1985) used water level measurements in 11 piezometers installed in 1983 to draw 

contours of hydraulic head in the debris dam. This in-
ferred hydraulic head distribution was in tum used to 

estimate the possibility that slope failures on the debris 

dam could take place under gravitational forces or 

stronger loading by earthquake shaking. They concluded that the dam slopes were stable with respect to static 

gravitational forces for the ground-water levels observed in September, 1983, and that even if retrogressive slope failures took place at higher ground-water 

levels, the damaged dam would remain capable of impounding Castle Lake. They pointed out, however, that 

when the debris dam is fully saturated, localized slope 

failures on both its upstream and downstream faces 

would be expected in response to a nearby earthquake 

of magnitude 6.0 or greater. In addition to the static and 

dynamic slope stability analyses, this report contains 

basic data on the geologic materials composing the debris dam and their engineering properties. 

Another scenario by which the natural dam could 

fail is seepage erosion caused by relatively rapid 

ground-water flow. A specific type of seepage erosion 

called "heave" results when the upward seepage force 

exerted by exiting ground water is great enough to 

overcome the overburden weight of the dam material. 

Assessment of the potential for heave or other types of 

seepage erosion requires knowledge of ground-water 

flow rates and hydraulic gradients, but data on the these 

quantities, in the form of seep discharge rates and measurements of water levels in collocated piezometers 

sampling different depths, were available for only a 

few points on the debris dam. Thus Meyer and Sabol 

(1989) used the available data to calibrate a numerical 

model of the ground-water flow system in the debris 

dam; the model was in tum used by Meyer and others 

( 1994) to simulate the hydraulic head distribution in the 

parts of the debris dam where data were not available. 

They concluded that, at places in the toe of the Castle 

Lake debris dam, simulated hydraulic heads suggested 

that the upward seepage force was as much as one-fifth 

of the overburden weight. This situation corresponds to 

a factor of safety against heave of about 5, a value that 

they considered to be "marginally stable". 

The U.S. Army Corps of Engineers (1988) also 

prepared a report considering the long-term stability of 

the debris dam. In this report, they emphasized the concept of the "minimum embankment section", which is 

the part of the debris dam necessary to safely impound 

Castle Lake. They concluded that an embankment dam 

with a crest 10 ft higher than the lake level over a distance no less than 50 ft thick in the downstream direction met this criterion, so that slope failure and erosion 

3 

in other parts of the debris dam should not contribute 

to a lake breakout. They agreed that some areas of the 

debris dam could be unstable, as Meyer and others 

(1994) had suggested, but held that these areas were 

outside of the minimum embankment section. Nonetheless, they presented a list of alternatives that could 

be used to reduce the hazard, including lowering or 

draining of Castle Lake or artificial draining of the debris dam. 

Kienle and Coombs (unpublished report, 1988) 

evaluated the studies described above, some of which 

were in draft form, at the request of the Weyerhauser 

Company. They concurred that the possibility of seepage erosion was cause for concern, and raised some issues whose resolution would require further analysis. 

Among these issues was an incorrect elevation scale 

on figure 20 of the report by Meyer and others ( 1985), 

as well as uncertainty as to the location of the preeruption surface. Kienle and Coombs also suggested 

that the potential for two other types of seepage erosion referred to by Meyer and others (1994), piping 

and internal erosion, be evaluated using the same 

methods as the heave analysis. 

Subsequent to Kienle and Coombs' evaluation, a 

series of meetings took place between representives 

from the U.S. Geological Survey, USACE, the U.S. 

Forest Service (USFS), and local governments. No decision was reached as to whether the likelihood of the 

debris dam eventually failing by seepage erosion was 

great enough to warrant mitigation measures, and further questions about the previous analyses emerged. It 

was questioned whether the numerical model presented by Meyer and Sabol (1989) was the only possible 

interpretation of the ground-water flow regime. Analternative hypothesis is that the high ground-water levels might represent a "perched" water table that is not 

in significant hydraulic communication with groundwater at depths critical to the stability of the dam. 

Meyer and Sabol (1989) had assumed the base of the 

debris dam to be impermeable, but the actual nature of 

the material beneath the debris dam remained unknown. The consensus that emerged was that additional data and further analysis were required, in 

particular of the potential for seepage erosion. A new 

data collection effort was begun when the USFS funded the installation of 11 new piezometers at six sites in 

the debris dam during fall, 1990, in which water levels 

have been periodically measured. 
Scope and Methods of Investigation 

The primary subject of this report is the groundwater flow system in the Castle Lake debris dam as it 

pertains to the potential for seepage erosion. The general approach was to compile the hydrologic and geologic data that had previously been collected, to 

supplement them where necessary and practical with 

additional data, to develop conceptual and numerical 

models of the ground-water flow system, and to use 

these models to evaluate the potential for seepage erosion. 

Water level measurements made in 22 piezometers by the Survey and USACE personnel were 

merged into computer files maintained at the Survey. 

In April, 1991, a survey was made to determine the 

locations of all points at which water was seeping 

from the debris dam; most of this seep discharge is 

measured in one of seven drainages near the debris 

dam toe. In June, 1991, the elevation and location of 

Castle Creek's thalweg were surveyed. In July, 1992, 

the USACE installed weirs to facilitate more frequent 

seep discharge measurements. 

Earlier studies of the debris dam were open to criticism because the thickness of the debris dam was not 

well known. For this study, aerial photography from 

1978 was used to prepare a 5-ft contour interval topographic map of the area under part of Castle Lake and 

the debris dam before the 1980 eruption of Mount St. 

Helens. Three control points for this map were established by setting targets in summer, 1991, on bedrock 

sites where no debris avalanche material is present. 

New aerial photographs were made in September, 

1991 and the phototargets were transferred from these 

photographs to the 1978 photographs; a fourth control 

point was obtained along a section line. The pre-eruption topography is shown in figure 2, which was prepared from elevations digitized at 100 ft intervals from 

this contour map. This map confirms that the pre-eruption topography assumed by Meyer and Sabol (1989) 

and Meyer and others (1994) was essentially correct. 

Acknowledgments 

J.E. Christensen and W. Leeman of the USACE 

Portland District helped plan the new pre-eruption 

map and provided access to the USACE's information 

about the debris dam. 

4 

DESCRIPTION OF THE DEBRIS DAM 

Before the May 18, 1980 eruption, South Fork 

Castle Creek flowed to the north between two bedrock 

ridges. With the eruption, debris avalanche material 

filled the two-thousand foot wide space between the 

ridges, damming South Fork Castle Creek and 

impounding Castle Lake. 

Topography and Geology 

The topography of the post-eruption surface, as 

mapped by the USACE from 1989 aerial photography 

and incorporating lake bathymetry obtained from 

Embrey and Dion (1988), is shown in figure 3. The 

bathymetry is not as precisely known as the post-eruption topography outside of the lake. The debris avalanche deposit is as much as 260 ft thick above the 

former channel of South Fork Castle Creek (figs. 4, 5). 

The thinnest area of the deposit is at the western edge, 

as shown in figure 4 and in the cross-sections. 

The thickness distribution shown in figure 4 does 

not differ greatly from that shown in figure 4 of Meyer 

and others (1985), which was derived from a less 

detailed pre-eruption map. 

The bedrock ridges are Eocene or Oligocene Ohanopecosh Formation, consisting of andesitic and dacitic lava flows, breccias, and volcaniclastic rocks that 

have undergone zeolite facies alteration (Meyer and 

others, 1985). 

Meyer and others (1985) give a complete description of the debris dam, which consists of unconsolidated material ranging from clay and sand to boulders 

tens of feet across, as well as some wood debris. 

These materials can be divided into the modem undifferentiated unit, the older dacite unit, and the blast 

deposit. More than 90 percent of the debris dam consists of the modem undifferentiated unit, which is 

overlain in places by the blast deposit. The blast 

deposit is less than 1 ft thick over most of the debris 

dam but is as thick as 15ft in some isolated locations. 

There is less than 1 in. of ash from 1980 eruptions of 

Mount St. Helens on the debris dam. 

Both the modem undifferentiated unit and the 

older dacite unit are unsorted and mostly unstratified, 

containing particles from silt-clay size to boulders 

several feet across. The modem undifferentiated unit 

consists of fragments of dacite, andesite, and basalt 

less than 2,500 years old that were part of the Mount 
122°16'45" 122°16'15" 

345000 

344000 

343000 

46°15'30" 

Unpublished base from 1550000 1551000 1552000 

U.S. Geological Survey, o 500 1000 FEET 

1 :24000, 1991 h-'-r-/--.',--'---'---,----.' 

0 100 200 300 METERS 

CONTOUR INTERVAL 20 FEET 

Figure 2. Topographic contour map of the Castle Lake area before the 1980 eruption of Mount St. Helens. Locations of 

cross-sections refer to figure 5. Eastings and northings, according to the Washington State Plane Coordinate System, in 

feet, are given below and at the right. 

5 
122°16'45" 122°16'15" 

Spillway 

Debris avalanche deposit 

46°16' 

Piezometer 

345000 

344000 

343000 

46°15'30" 

Unpublished base 1550000 1551000 1552000 

from U.S. Army Corps 

of Engineers, 1 :1200, 1989 0 500 1000 FEET 

0 100 200 300 METERS 

CONTOUR INTERVAL 20 FEET 

Figure 3. Topographic contour map of the Castle Lake debris dam. Locations of cross-sections refer to figure 5. Eastings and 

northings, according to the Washington State Plane Coordinate system, in feet, are given below and at the right. 

6 
122°16' 45" 

46°16' 

46°15'30" 

1550000 

0 

0 

122°16'15" 

100 

Spillway 

Debris avalanche deposit 

Bedrock 

Alluvium 

1551000 1552000 

500 1 000 FEET 

200 300 METERS 

CONTOUR INTERVAL 20 FEET 

345000 

344000 

343000 

Figure 4. Thickness of the debris avalanche deposit in the Castle Lake area, obtained by subtracting the elevations contoured in figure 2 from those shown in figure 3. Locations of cross-sections refer to figure 5. Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are given below and at the right. 

7 
(10 

cl cl c 

FEET A ~~ 0. or :;::;:>.:: :;::;~ A' ~...!, al~ al~ I- ....I 2,800 I (/) (/) (/) 

ww 

w> 

u..w 2,700 

Z...J 

--<( 

zw 2,600 

ocn 

i=w 2,500 <(> >O 

wm 2,400 u:j<( 

2,300 

1- 2,800 

w...J 

ww u.. > 2,700 

zw _....I 

;;i <( 2,600 

om i= w 2,500 

<(> >O 

~ m 2,400 

w<( 

2,300 

EXPLANATION 

c::=J Debris avalanche deposit ... J ... Bottom of model layer 

0 500 1000 FEET 

Undifferentiated (Pre-1980) material S7 Seep n . 0 250 500 METERS 

-?- Contact- queried where uncertain ~ Simulated potentiometric surface a.. Piezometer - horizontal line indicates 

t average water level, 1992 water year 

VERTICAL EXAGGERATION X 1.5 

Figure 5. Cross-sections of the Castle Lake debris dam. Cross-section locations are shown in figures 2, 3, and 4. Piezometers are projected to the nearest cross-section. Ground-water table shown is calculated by the nonuniform calibrated steady-state model for the 1992 water year, described in a later section. Ground water model 

layers are indicated at right of each cross-section. 
10 

FEET C 

f-...J 2,800 

ww 

~> 2,700 

~~ 

-~ 2,600 

zw 

oen 

i=w 2,500 

~> >O 

WOJ 

u:l~ 

2,400 

2,300 

FEET D 

2,800 ~ 

f-...J 

ww 

w> 2,700 

I LLw 

Z...J 

-:~ 2,600 

zw 

oen 

i=w 

~> 

2,500 

>0 

WOJ 2,400 u:l~ 

2,300 

c: 

21;;., 

~~ 

en 

:;::::.<: §I_ 

~~ en 

<(CO 

C\IC\1 

J:J: 

..... ss.9..0 ••••••• ,. .'jr·;·.·~·;· 

···········l···l ...... . 

~~;;., c:l 0 - :;::::.<: (.) . ~...., ~~ en 

10 _, I I II 

,... "" 0:::1:: S10 

0 500 1000 FEET 

0 250 500 METERS 

VERTICAL EXAGGERATION X 1.5 

C' 

J: Spillway 

0 / 1 

r ·.·----··-·--·- ·--···············2·· • •••• .:............. ••••••••••••••-•••w• 

§-

:;;I~ ~::i1 D' 

en 

I Spillway 

Figure 5. Cross-sections of the Castle Lake debris dam. Cross-section locations are shown in figures 2, 3, and 4. Piezometers are projected to the nearest cross-section. Ground-water table shown is calculated by the nonuniform calibrated steady-state model for the 1992 water year, described in a later section. Ground water model 

layers are indicated at right of each cross-section--Continued. 
.... 

0 

FEET 

2,800 

1-...J 

ww If> 2,700 

z~ -_ <( 2,600 

zw 

0CI) 

i=w <C> 2,500 

>O 

Will u:l <( 2,400 

2,300 

FEET 

2,800 

1-...J 

ww If> 2,700 

z~ 

--<( 2,600 

zw 

0CI) 

i= w 2,500 <C> >O 

ww u:l <( 2,400 

2,300 

1- 2,800 

w...J 

ww 

u. GJ 2,700 

z...J 

;- i;5 2,600 

0(/) i= w 2,500 

<(> 

>0 

~ ~ 2,400 

w 2,300 

0 500 1 000 FEET 

0 250 500 METERS 

VERTICAL EXAGGERATION X 1.5 

Figure 5. Cross-sections of the Castle Lake debris dam. Cross-section locations are shown in figures 2, 3, and 4. Piezometers are projected to the nearest cross-section. Ground-water table shown is calculated by the nonuniform calibrated steady-state model for the 1992 water year; described in a later section. Ground water model 

layers are indicated at right of each cross-section--Continued. 
..... 

..... 

FEET 

1- 2,800 

w...J 

ww 

LL G:i 2,700 

z....l 

-_ ~ 2,600 

zw 0(/) 

i= w 2,500 

~> 

>0 w al 2,400 ..... ~ 

w 2,300 

I- ....I tl:Jw LL > 2,700 

z~ ;t ~ 2,600 

0(J) 

i= w 2,500 

~> >0 

~ ~ 2,400 

w 2,300 

1- 2,800 w...J 

ww 

LL G:i 2,700 

Z...J 

;t ~ 2,600 

0(J) 

i= w 2,500 ~> >O 

~ al 2,400 w~ 

2,300 

§I_ :o::Q 

0 ' QlC) 

(/) 

c ·gill 

~\,) 

§I_ :o::Q 

0• QlC) 

(/) 

2,800 

I- ....I tl:Jw LL > 2,700 

;?;~ ~ 2,6oo 

Q~ !;;: w 2,500 

>e5 

~ al 2,400 

w~ 

M' 

2,300 

0-cl c 0-

:;::: 0•0' \..) ·-1<1::1 Q) \..) Q) <1::1 (/) (/) 

.§I~ (j, 

~--.:: 

500 1000 FEET 

0 250 500 METERS 

VERTICAL EXAGGERATION X 1.5 

c 

,gl~ 0• 

Q)--.:: 

(/) 

Figure 5. Cross-sections of the Castle Lake debris dam. Cross-section locations are shown in figures 2, 3, and 4. Piezometers are projected to the nearest cross-section. Ground-water table shown is calculated by the nonuniform calibrated steady-state model for the 1992 water year, described in a later section. Ground water model 

layers are indicated at right of each cross-section--Continued. 
St. Helens edifice before the 1980 eruption. The older 

dacite unit originated in the core of Mount St. Helens 

exposed in the 1980 crater, which is material more 

than 2,500 years old. It is more homogeneous in composition than the modem undifferentiated unit. 

The blast deposit is present only over a limited 

part of the debris dam. It is also poorly sorted, but 

unlike the other deposits, contains few clasts more 

than several inches in diameter, especially on the 

higher areas of the debris dam. It contains all pre-1980 

Mount St. Helens rock types, as well as possibly some 

juvenile material from the 1980 eruption. 

Drillhole Data and Pre-1980 Materials 

The debris avalanche deposit rests on unconsolidated volcaniclastic debris of unknown thickness, cut 

by the 130-ft deep channel of South Fork Castle 

Creek. For this study, it is important to consider the 

location of the bottom of the 1980 deposit as well as 

the hydraulic properties of the material below the 1980 

deposit. 

Eleven holes were drilled into the debris dam in 

1983 and eleven more holes were drilled in October, 

1990. The hole locations are shown in figure 3, and 

their locations, elevations and depths are listed in table 

1. The holes are also projected to the nearest cross-sections in figure 5. Piezometers have been installed in all 

of these holes. 

1983 Drillholes 

Little information is available about stratigraphy 

from the drilling in 1983. On the basis of the pre-eruption map, all of the drillholes except for I4 and possibly P3B bottom within the 1980 debris avalanche 

deposits. According to the pre-eruption topographic 

map (fig. 2), I4 bottoms at least 30ft beneath the 1980 

material, and appears to penetrate the western bedrock 

ridge. Water levels in I4 have the largest seasonal variations of any of the piezometers, consistent with the 

idea that the material in the interval sampled by this 

piezometer is too impermeable to allow recharge to 

quickly dissipate to other parts of the debris dam. On 

the other hand, the hole was reportedly drilled using an 

auger that would not penetrate bedrock. For the purpose of this study, it was assumed that I4 does not 

sample the ground-water flow system in the debris 

dam. 

12 

1990 Drillholes 

Drilling logs for all of the 1990 drillholes are 

included in the report by the U.S. Army Corps of 

Engineers (1992). During drilling, a geologist on site 

attempted to discern the base of the 1980 deposits, 

and these observations can be compared with preeruption elevations from the new map. 

Site DH1 

At DH1, no significant stratigraphic break was 

observed to the total depth of 115ft, consistent with 

the pre-eruption elevation from the map, which is 

about 20 ft below the bottom of the hole. 

Site DH2A,B 

The shallower piezometer at this site, DH2B, certainly bottoms in 1980 debris. Geologist's notes on 

the drilling at DH2A suggested that pre-1980 alluvium may have been encountered at elevations of 

2,501 to 2,491 ft (72 to 82ft below the surface); the 

pre-eruption map shows this drillhole overlying a 

slope on the pre-eruption surface with elevations this 

high about 75 feet south of the drillhole. While the 

exact elevation at site DH2A as read from the preeruption map is lower than the pre-1980 horizon possibly noted during drilling, it is conceivable that the 

pre-eruption topography on this slope is inaccurate. 

Consequently it is questionable whether DH2A bottoms in 1980 debris or pre-1980 alluvium. It does not, 

however, appear to bottom in material that is impermeable relative to the debris dam. It is assumed here 

that DH2A is completed within the ground-water system of the debris dam, which is not necessarily limited to the 1980 deposits. 

Site DH3 

Drilling ofDH3 was terminated at a depth of74 

ft with a fairly positive identification of the base of 

the 1980 debris avalanche, marked by an avalanche 

deposit of possible Pine Creek age, wood fragments, 

and iron staining. This observation gives a pre-eruption elevation of 2,555 ft, consistent with the new preeruption map. Here also, there seems to be no abrupt 

change in hydraulic material properties at the base of 

the 1980 deposits. The open interval in DH3 is the 

bottom 5 ft of the 1980 deposits. 
Table 1. Locations, elevations and depths of holes drilled in the Castle Lake debris dam 

[Names beginning with the the letter "I" denote holes drilled in 1983 in which inclinometer measurements have been made; "P", other holes drilled in 1983; 

and "DH", holes drilled in 1990. Letters A,B,C, and Dare used to indicate piezometers at different depths at the same location. In USACE publications, sites 

DH5A and DH5B are referred to as DH6AZ and DH6BZ, while site DH6 is referred to as site DH5AZ. Locations of holes are shown in figure 3.] 

Site Easting Northing Land 

(ft) (ft) elevation 

(ft) 

I1 1,550,135 343,231 2,656 

12 1,549,942 343,295 2,655 

I3 1,550,277 343,429 2,653 

14 1,549,846 343,539 2,661 

PI 1,550,147 343,219 2,655 

P2A 1,550,600 343,093 2,628 

P2B 1,550,607 343,093 2,629 

P3A 1,551,139 342,589 2,629 

P3B 1,551,155 342,585 2,628 

P4A 1,551,375 343,135 2,584 

P4B 1,551,370 343,155 2,584 

DH1 1,551,668 342,673 2,600 

DH2A 1,551,097 343,386 2,573 

DH2B 1,551,097 343,376 2,575 

DH3 1,551,000 342,478 2,629 

DH4A 1,550,637 344,051 2,503 

DH4B 1,550,659 344,035 2,503 

DH4C 1,550,675 344,016 2,503 

DH4D 1,550,645 344,042 2,503 

DH5A 1,550,205 343,851 2,569 

DH5B 1,550,211 343,866 2,569 

DH6 1,549,970 343,872 2,572 

Site DH4A,B,C,D 

At the sites of piezometers DH4A,B,C, and D, the 

drillers' and geologists observations are inconclusive, 

noting that the clasts found between depths of 88 to 

110ft could represent either pre-1980 alluvium or 

1980 debris avalanche deposits. At this site, the preeruption topographic map suggests that 123-ft deep 

piezometer DH4A bottoms approximately at the base 

13 

Total Open Completed 

depth interval in 

(ft) (ft) 

83 2,573 1980 Debris 

86 2,569 1980 Debris 

97 2,556 1980 Debris 

62 2,599 Pre-1980 

190 2,465 1980 Debris 

51 2,577 1980 Debris 

45 2,584 1980 Debris 

50 2,579 1980 Debris 

93 2,535 Pre-1980? 

76 2,508 1980 Debris 

24 2,560 1980 Debris 

115 2,485-2,490 1980 Debris 

85 2,489-2,494 1980 Debris? 

57 2,518-2,523 1980 Debris 

74 2,555-2,560 1980 Debris 

123 2,381-2,384 Pre-1980 

85 2,419-2,424 1980 Debris 

40 2,463-2,468 1980 Debris 

7 2,495-2,501 1980 Debris 

82 2,504-2,509 Bedrock at 67.9' 

23 2,547-2,552 1980 Debris 

21 2,552-2,557 Bedrock at 8.1' 

of the 1980 deposits, while the shallower piezometers DH4B,C, and Dare within 1980 debris. 

Site DHSA,B 

At DH5A, the observed depth to bedrock of 67.9 

ft agrees well with the map. The hole was drilled 13.9 

ft further in andesite, and the piezometer screen was 

installed to sample water pressure in a 5-ft interval 
just above the bottom of the 1980 deposits. The shallower piezometer DH5B is entirely within the 1980 

deposits. At this site, it does appear appropriate to 

consider the material beneath the 1980 debris avalanche deposit to be relatively less hydraulically conductive. 

Site DH6 

At piezometer DH6, the depth to bedrock encountered during drilling (8.1 ft) agrees with the elevation 

on the new pre-eruption map. 

In summary, several of the 1990 drillholes appear 

to have penetrated the base of the 1980 deposit. Bedrock encountered at sites DH5A and DH6 suggests 

that material below the 1980 deposits is relatively 

impermeable in that vicinity. Alluvium encountered at 

other sites suggests that the base of the 1980 deposit 

may not be a significant hydrologic boundary elsewhere. 

Vegetation 

Except for willow and alder growing along the 

drainage channels, the debris dam remains sparsely 

vegetated in 1993. Grass seed dropped from aircraft 

in 1980 as an erosion-prevention measure failed to 

take hold on the steep and unstable slopes of the hummocky surface. The alluvial plain of Castle Creek also 

remains sparsely vegetated, probably because the 

active stream channel has continued to move within 

the plain, as described below. The plants that are 

growing on the debris dam are 60-70 percent willow 

of various species and 30-40 percent trees, primarily 

Red Alder and Sitka Alder (P. Frenzen, USFS, oral 

commun., 1993). Unless ash layers from future eruptions of Mount St. Helens interfere, a conifer forest of 

Silver Fir, Noble Fir, and Douglas Fir can be expected 

to establish itself on the debris dam in about 200 years 

(T. Beckman, USFS, oral commun., 1993). As forest 

covers the debris dam, its canopy will intercept 

recharge currently available to the ground-water 

regime and its large trees will transpire more shallow 

ground water, lowering ground-water levels in the 

debris dam. Interception, however, is negligible at 

present. 

14 

THE GROUND-WATER FlOW SYSTEM 

In the crest of the debris dam, ground-water levels as much as 45 ft above the lake level have been 

recorded. These ground-water levels are maintained 

by downward recharge of infiltrating precipitation 

through the debris dam. Two possible interpretations 

of this observation have different implications for the 

stability of the dam. 

Alternative Conceptual Models of the 

Ground-water Flow System 

In the first interpretation, ground-water flow in 

the debris dam moves downward from the crest and 

then horizontally both toward the lake and toward the 

toe, discharging in seeps on the dam's downstream 

face and in the lake bed. The alternative interpretation is that the high ground-water levels represent 

"perched" water rather than the water table surface, 

and that the true water table declines monotonically 

from the lake surface to the toe of the dam. Ground 

water in the debris dam would then flow downstream 

only, with water flowing from the lake into the debris 

dam, not vice versa. The absence of seeps on the 

upstream dam face above the lake could be interpreted as evidence for this flow configuration. If this 

interpretation is correct, then ground-water levels in 

the part of the debris dam that impounds Castle Lake 

are controlled by the lake level, and could be lowered 

to a safe level by lowering the lake. If the "groundwater mound" interpretation is correct, however, then 

high ground-water levels might not be eliminated 

even if the lake level were lowered. Moreover, seepage erosion could occur if the currently submerged 

locations where water flows from the dam into Castle 

Lake were exposed. 

Hydraulic and Engineering Properties 

The hydraulic conductivity of the debris dam 

material is primarily a function of its grain size and 

texture. Median grain diameters for seven samples 

from the debris dam surface range from 0.02 to 0.14 

in. (0.5 to 3.5 mm; Meyer and others, 1985), and 

porosities range from 24 to 46 percent. The modem 

undifferentiated unit, which composes most of the 

debris dam, is 42 to 56 percent gravel, 37 to 49 percent sand, and 13 percent or less silt and clay. 
The U.S. Army Corps of Engineers (1992) 

describes testing performed on samples recovered during drilling in 1990. These samples were found to consist of 13 to 88 percent gravel, 12 to 66 percent sand, 

and 1 to 30 percent fines. The coarsest samples were 

from the upstream edge of the dam, and the finest 

from the downstream edge. Based on samples 

obtained during drilling in 1990, the pre-eruption 

materials were found to have similar grain size distributions and shear strength to the post-eruption materials, but to be of higher density. 

Seven falling head permeability tests in five of the 

1990 drillholes yielded hydraulic conductivities of 6.2 

to 110.5 ft/day (table 2; U.S. Army Corps of Engineers, 1992). In contrast, slug tests conducted in piezometers in the debris-avalanche deposit several miles 

north of Castle Lake gave horizontal hydraulic conductivities of 2.4 to 5.0 ft/day (Meyer and others, in 

press). These hydraulic conductivities should be close 

to those of the debris dam, which consists of essentially identical material. These values are close to 

those arrived at by Meyer and Sabol (1989) in calibrating their ground-water model, but are lower than 

those measured during the falling head tests. As will 

be described below, this study also finds that hydraulic 

conductivities lower than those measured in the falling 

head tests are necessary to model the observed heads 

and seep discharges. 

Precipitation 

Precipitation data, recorded every 15 minutes by a 

tipping bucket rain gage, are available from a station 

near the spillway outlet and are given in table 3. Typically, the area receives 8 to 12 in. of rain per month 

from November through February, and 5 in. or less 

each month from May through September. Monthly 

precipitation is shown in figures 6a-6e. 

Water levels in Piezometers 

Water levels in the 22 piezometers in the debris 

dam have been measured as frequently as nine times 

per year since 1990 (figs. 6a-6e). For most piezometers, the amplitude of the annual variation in water 

level is between 7 and 15ft, lowest water levels each 

year are in late summer or early fall, and highest 

annual water levels are in spring. In I4, which is in 

pre-1980 material, the annual difference between high 

15 

Table 2. Hydraulic conductivity measured by falling head 

tests in 1990 drillholes, Castle Lake debris dam (U.S. 

Army Corps of Engineers, 1992) 

Drillhole 

DH1 

DH1 

DH2A 

DH2A 

DH2A 

DH2B 

DH3 

Depth 

(ft) 

50 

95 

31 

65 

75 

57 

84 

Hydraulic 

conductivity 

(ft/day) 

8.5 

6.2 

19.6 

110.5 

21.3 

44.2 

69.4 

and low water levels is typically 30 ft, and highest 

water levels are reached in December. 

The hydrographs shown in figure 6b illustrate the 

difficulty of distinguishing between the two conceptual models for the ground-water flow system. The 

hydrograph from piezometer DH3 supports the 

hypothesis that water in the debris dam flows into the 

lake. This piezometer is close to the northern boundary of the lake, and is open in an interval20-25 ft 

below the lake level. Yet its lowest recorded water 

level is higher than the lake level, which could not be 

the case if the water whose pressure were measured at 

this piezometer were corning from the lake. On the 

other hand, in the absence of an impediment to vertical flow, water levels in the shallower piezometer P3A 

would be expected to fluctuate more than those in the 

deeper piezometer P3B (fig. 6a). While the relative 

water levels in this piezometer pair are consistent with 

downward flow, the larger fluctuations in the deeper 

piezometer suggest that its primary connection to a 

recharge area is not through the material directly overlying it and that it may be completed in a fractured, 

confined, unit. Alternative interpretations are that P3A 

may not have been well developed when installed, or 

is screened in a zone of low hydraulic conductivity, 

resulting in sluggish response to seasonal precipitation. 

In contrast, at piezometer pair Il, Pl (fig. 6c), 

water levels track each other well, with water level in 

Pl remaining 2 to 3ft below Il, although Pl is more 

than 100ft deeper than Il. Water levels at DH2A and 

DH2B (fig. 6d) are nearly identical, although DH2A is 

28ft deeper than DH2B. At piezometer pair P4A,B, 
.... 

en 

Table 3. Monthly precipitation, in inches, recorded by a tipping bucket rain guage at Castle Lake 

[Monthly values are given in parentheses when data were recorded on fewer than 24 days of that month; those months are not included in the monthly averages. 

Water year (W.Y.) totals are given in parentheses when data were recorded on fewer than 300 days of the year. Data from 1981 to 1986 are from Uhrich(1990).] 

Water Year 

Month 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 

October 13.7 9.5 0.2 7.1 8.9 4.5 ---- ---- 7.1 14.2 3.4 

November 5.4 10.4 18.5 15.3 4.6 7.2 ---- ---- (9.0) 13.9 16.5 

December 12.5 13.8 6.3 3.6 2.5 7.1 ---- ---- (0.8) 5.9 8.9 

January 12.8 12.9 8.0 0.7 12.0 ---- ---- ---- 17.3 8.0 15.1 

February 15.1 10.9 6.6 0.5 9.6 ---- ---- ---- 8.7 12.4 (8.1) 

March 7.3 13.5 8.8 1.7 7.7 ---- ---- ---- 5.2 8.9 1.4 

April 8.0 2.5 5.3 2.8 4.1 ---- ---- ---- 7.8 14.4 10.9 

May 2.8 2.4 8.9 2.8 4.3 ---- ---- ---- 5.6 5.7 1.0 

June 1.5 4.8 5.4 4.6 1.2 ---- ---- ---- 5.2 4.5 1.5 

July 1.1 4.5 0.0 0.0 ---- ---- ---- ---- 0.8 0.1 1.3 

August 1.3 2.0 0.5 0.2 ---- ---- ---- 1.1 2.5 2.1 (1.0) 

September 5.4 2.5 3.5 4.4 ---- ---- ---- 0.4 (0.2) 0.1 (6.0) 

W. Y. total: 86.9 89.7 72.1 43.7 (55.0) (18.8) ---- (1.4) (70.1) 90.1 75.1 

Days w/ data: 365 365 365 366 273 92 0 55 287 353 310 

1993 Monthly 

average 

5.7 7.4 

11.4 11.5 

6.9 I 7.5 

5.2 I 10.2 

0.5 I 8.0 

9.4 I 7.1 

14.5 7.8 

7.2 I 4.5 

2.4 I 3.5 

1.7 1.2 

(0.4) I 1.4 

o.o I 2.3 

(65.2) 

294 
there is a constant 2 to 3 ft difference over a 52 ft 

depth range (fig. 6d), and the difference favors upward 

flow. 

The data from piezometers DH4A,B,C, and D are 

complex (fig. 6e). Pressure at the three deeper piezometers here (DH4A,B, and C) is artesian; pressure at 

DH4D is sometimes artesian. Pressure in piezometer 

DH4C varies more than at any other level at this site. 

In DH4B, the next deepest piezometer, pressure is 

lower and annual variations are smaller than in DH4C, 

consistent with downward flow between these two 

levels. Water at the level of DH4C, however, must 

come from higher elevations, because the water level 

is higher than the ground surface elevation at this site. 

Water level in the deepest piezometer, DH4A, is 

higher than at any of the shallower levels, but has 

steadily declined. The U.S. Army Corps of Engineers 

(1992) describes hydrostratigraphy at this site as 108 

ft of overburden over a 6-ft-thick confining layer, 

which would be between DH4A and DH4B. The 

declining head in DH4A may represent the natural 

behavior of ground water at this site, but could also be 

caused by leakage into material above the confining 

layer if the hole is not perfectly sealed. As discussed 

below, ground-water model calibration suggests that 

such a confining layer can partially explain the 

observed heads, but a ground-water model driven by 

seasonal precipitation and evaporation cannot reproduce the steadily falling water level observed at piezometer DH4A. 

In summary, at piezometer sites P2AB, 11 and P1, 

P4AB, and DH2AB, there appears to be good hydraulic connection between piezometers at different levels. 

At the sites of P3AB and DH4ABCD, the water level 

records suggest that relatively impermeable layers 

may be present. Water level above the lake level in 

piezometer DH3 near the northern shore of the lake is 

evidence that at least some of the ground-water in the 

debris dam flows into the lake. 

Seep Discharge 

Numerous seeps have developed that drain the 

debris dam on its downstream side. Channels have 

developed in the debris dam's surface that collect the 

seep discharge and carry it overland to Castle Creek. 

Discharge measurements have been made in the most 

important of these drainages since 1984. 

Most seep discharge measurements include discharge from a fairly large area of the debris dam. On 

17 

April 30 and May 1, 1991, a survey was made to 

locate places where water was exiting from the debris 

dam. Figure 7 shows these points grouped according 

to the identification number of the seep discharge 

measurement. 

Seep discharge measurements were made approximately every six months until July 1991, after which 

weirs were installed, facilitating more frequent measurements. The data are shown in figures 8a-8c. Discharge from most of the seeps varies seasonally. 

Insofar as can be determined given the infrequent 

measurements from 1985 to 1989, the peak seep discharge has remained constant with time except at 

seeps 3 and 7, where discharge has decreased. 

Seeps 9 and 10 were measured separately through 

October, 1991, but it had become increasingly difficult 

to meaningfully separate the two sources because the 

area near the measuring points had coalesced into a 

single marshy area. After October, 1991, the sum of 

the two seeps was measured. The sources of both 

seeps were resurveyed in April, 1992. 

Evapotranspiration 

Presently, vegetation draws water from the drainage channels along which it is concentrated, as well as 

shallow ground water. The gradually increasing transpiration from the drainage channels might be 

expected to decrease seep discharge measured downstream of heavily vegetated reaches. This effect may 

explain the observed discharge decrease at seep 7, 

where transpiration could be a significant proportion 

of the small total discharge. Seep 3 has also displayed 

a decrease of discharge with time, but the measurement point is not downstream of a vegetated drainage. 

Seeps 5, 6, 8, 9, and 10 are measured downstream of 

vegetated reaches but their relatively larger discharges 

probably mask any effect of increased transpiration. 

Evaporative losses occur from the bare surface of 

the debris avalanche deposit. No measurements have 

been made of evaporation or evapotranspiration on the 

debris dam, but an estimate of maximum rates can be 

made. Kohler and others (1959) prepared an evaporation map for the United States; according to this map, 

mean annual lake evaporation at the study area is 24-

26 in. Evaporation from bare wet soil is approximately 0.9 times the lake evaporation, with evaporation ceasing when the upper 0.25-0.5 in. (5-10 mm) of 

the soil are dry (Dunne and Leopold, 1978). 

There are insufficient data to precisely estimate a 
....I 

LU 

> LU 

....I 

<( 

LU 

(/) 

LU 

> 

0 

co 

<( 

2,630 

2,610 

~ 2,590~-L--~-L--~-L---L-L---LJ-__ -L~---L~--_L~ __ J_L_ __ J_L_~ LU 

u.. 

z 

....I 

LU 

> LU 

....I 

a: 

LU 

1-

<( 

$: 

z 

Q(f) 

-LU 

I-I 

~() -z C..-

Uz 

LU0: 

c.. 

2,610 

2,590 

o P3A (Shallower) 

• P3B (Deeper) 

0 

• I 

I 

tlO 

I 

I 

1 1 Lake 1 

Elevation 

2,570~-L---L~---L~--~L---~--~-L--~-L---L~--J-L---~--~ 

20 

15 

10 

5 

0 

1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 

Figure Ga. Monthly precipitation at the Castle Lake debris dam and water levels in piezometers 14, P3A, and P38, 1983-1993. 

Water level measurements made more than three months apart are not connected. 

18 
2,610 

2,590 

....I 

w 

> 

w 

....I 

<( 2,570 

w 

(/) 

w 

> 2,610 0 

OJ 

<( 

1-

w 

w 

LL. 

z 2,590 

....I 

w 

> 

w 

....I 

a: 2,570 

w 

1-

<( 

~ 2,610 

2,590 

2,570 

20 

z 

QCI) 15 -w 

I-I 

~0 10 

-z a__ 

oz 

w 

5 

a: 0 a_ 

1984 

I I 

:<water..,: 

1 Year 1 

Q 

I 0 DH31 

Lake 1 

Elevation 

o P2B (Shallower) 

• P2A (Deeper) 

; Q I 

I 

I 

~ ~ I 

I 

1 Lake 

Elevation 

I 

I 

I 0 DH1 I 

Lake 1 

Elevation 

I 

o D a tal------7 I 

1985 1986 1987 1988 1989 

' 

I 

I 

I 

v 

1990 1991 1992 1993 

Figure 6b. Monthly precipitation at the Castle Lake debris dam and water levels in piezometers DH3, P2A, P2B and DH1, 1983-

1993. Water level measurements made more than three months apart are not connected. 

19 
2,610 

2,590 

...1 

w 2,570 > 

w 

...1 

<( 

w 2,600 en 

w 

> 

0 

lil 

<( 

Iw 2,580 

w 

u. 

z 

...1 

w 2,560 > 

w 

...1 

a: 

w 2,600 I-

<( 

$: 

2,580 

2,560 

20 

z 

ocn 15 -w 

I-I 

~() 10 

Q._ -z 

oz 

w5 

a: 0 a. 

1984 

I I 

:<water>: 

Year 

0 

• 

0 

0 

• 

o 11 (Shallower) 

e P1 (Deeper) 

I 

I 

i Lake 

I 

~ Elevation 

~ 

0 

Lake 1 

Elevation 

I 

I 

~ 

0 0 

o Lake 

Elevation 

I I 

0 

' 

1985 1986 1987 1988 1989 1990 1991 1992 1993 

Figure 6c. Monthly precipitation at the Castle Lake debris dam and water levels in piezometers 11, P1, 12, and 13, 1983-1993. 

Water level measurements made more than three months apart are not connected. 

20 
.....1 

w 

2,590 

2,570 

I I 

:<water,: 

1 Year 1 o DH6 

I 

1 Lake 1 

Elevation 

> 2,550~-L---L~---L~--~L---~--~_L--~-L---L~--~L_--~--~ 

w 

.....1 

<{ 

w 

(/) 

w 

> 

0 

CD 

<{ 

1-

w 

w 

LL 

z 

2,590 

2,570 'f'V i I e 

I I 

o P4B (Shallower) 

• P4A (Deeper) 

1 Lake 1 

Elevation 

I 

:e 

I :-\: I I : I 

I I I 

I 

:~1: I I 

I 

I I I 

.....1 

w > 2,550 L-L-'-----'--'-----'--'-----'--'----L-'-------'--'---__j_-'----L-'----~L_--~ __ ___J 

w 

.....1 

a: 

w 

I-

< s; 

z 

Q(J) 

-w 

1-J: ;::o 

-z c__ 

Oz 

w 

a: 

c.. 

2,590 

2,570 

0 

• 

1 Lake 1 

Elevation 

\ 2,550~-L---L~--~--~_L __ _L~--~L---~--~....JL __ .....IL~--~--___J 

20 

15 

10 

5 

0 

1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 

Figure 6d. Monthly precipitation at the Castle Lake debris dam and water levels in piezometers DH6, P4A, DH2A, DH2B, 

1983-1993. Water level measurements made more than three months apart are not connected. 

21 
2,590 

I I 

1 Lake 1 

Elevation 

2,570 

....I 

> 

LU 

....I 

LU 

2,550 

~ <( 

LU 

en o DH4B (Shallower) I 

I 

LU 2,520 e DH4A (Deeper) > 

0 ~ m 

<( 

1-

LU 

LU 

~ 

u.. 2,500 

z 

....I 

LU 

> 

LU 

....I 2,480 

a: 

LU 

1-

<( 

~ 2,520 I 

(\ 

00 I 

2,500 I 

I 

2,480 

20 

z 

ocn 15 

-w 

1-:c 

~() 10 

-z Q.._ 

oz 5 

LUa: 0 

a.. 

1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 

Figure 6e. Monthly precipitation at the Castle Lake debris dam and water levels in piezometers DH4A, B, C, D and DH5A, B, 

1983-1993. Water level measurements made more than three months apart are not connected. 

22 
Unpublished base 1550000 1551000 

from U.S. Army Corps 

of Engineers, 1:1200, 1989 0 500 

0 100 200 

CONTOUR INTERVAL 20 FEET 

Spillway 

Debris avalanche deposit 

Bedrock 

Alluvium 

Seep discharge point 

1000 FEET 

300 METERS 

345000 

344000 

343000 

1552000 

Figure 7. Contour map of the post-eruption surface showing seep discharge exit points surveyed in April, 1991. Eastings 

and northings, according to the Washington State Plane Coordinate System, in feet, are given below and at the right. 

23 
0.4 I 

:<water": I 

0 Year 

z I 0 S1 I 

0 0.3 {) 

w 

en 

a: 0.2 w 

a.. 

1-

w 

w 0.1 

u.. 

{) 

::::> 

co 0.0 0 

I ~ {) 0.4 I I I 

z lo S3 

w 

<!' 0.3 

a: 

<( 

:r: 

{) 0.2 en 

0 \ a.. 

w 0.1 0 - w 

en 

0 00 9 0 ~ ~Q.,...~.,., 

0.0 I -~~-v~ 

20 

z 

oen 15 -w 1-:r: 

~{) 10 

-z 0..- I 

uz 5 Datal-----7 

w- I 

a: 0 a.. 

1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 

Figure Sa. Monthly precipitation at the Castle Lake debris dam and discharge from seeps 1 and 3, 1983-1993. Seep discharge measurements are not connected if they were made more than three months apart. 

24 
0.4 I I 

1 Water 1 

;c Year>; 0 ss 

0.3 

0 

0.2 I 

\ 0 

0 

z 0.1 0 \l. 0 0 0 

() I I 

w :o I 

(/) ,0 

0.0 

a: 

w 0.4 I I 

a.. :"water>: I 

I- 1 Year 1 /o ss/ 

w 

w 

LL. 

0.3 

() 

Ill 

::J 0.2 

() 

z 

w 0.1 I I 

(!J I 

() 

:r: 

<( 

a: 

0.0 

0.4 

o\! 0 

0 I 

I 

'O 

0 

(j 

I 

0 01 

I 

~~ (/) 

0 I 

a.. I 0 S7 I 

w 

w 

(/) 

0.0 

20 

z 

QC/) 15 -w 1-:r: 

~() 10 

-z a__ 

uz 5 

wa: 0 a.. 

1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 

Figure 8b. Monthly precipitation at the Castle Lake debris dam and discharge from seeps 5, 6, and 7, 1983-1993. Seep discharge measurements are not connected if they were made more than three months apart. 

25 
Figure Be. Monthly precipitation at the Castle Lake debris dam and discharge from seep 8 and seeps 9 and 1 0 (combined 

flow), 1983-1993. Seep discharge measurements are not connected if they were made more than three months apart. 

26 
maximum transpiration rate for vegetated areas, but a 

typical figure of 35 in/year is probably appropriate. 

Vegetation rooting depths of 7.5 ft would be expected 

for the type and size of the plants growing on the 

debris dam. The present willow and alder dominated 

plant population can grow in areas with some standing 

water; thus they do not cease to transpire water when 

the water table rises to the ground surface. 

Castle Creek 

The reach of Castle Creek flowing past the debris 

dam toe is an important control on the ground-water 

flow system. A ground-water divide presumably 

extends downward from the creek channel because 

ground water from higher elevations north of the creek 

would not be expected to flow under the creek and into 

the debris dam. The ground-water table in the debris 

dam toe must tend toward equality with the stage in 

Castle Creek. 

The creek and spillway thalweg elevation was surveyed in June, 1991, and this survey revealed that the 

course of the river and its bed elevation had changed 

since 1989. Figure 9 compares the course of the thalweg as surveyed in June, 1991 with the outline of Castle Creek as it appears on the 1989 post-eruption map 

and on September, 1991 aerial photographs, and figures lOA and lOB compare the 1989 and 1991 creek 

bed elevations. The 1991 channel is closer to the dam 

toe in some places and further from it in others, as 

compared to the 1989 channel. In particular, it is closer 

to the dam toe just downstream of the confluence of 

the spillway with Castle Creek. In the first 1,700 ft 

downstream from the lake, the creek bed elevation was 

as much as 7ft lower in 1991 than in 1989, while the 

reverse holds between 2,800 and 4,000 ft downstream. 

Figure 11 shows repeated cross-section surveys of 

Castle Creek which show that significant downcutting 

occurred in 1990, probably the result of a storm during 

January of that year. 

In the future, any significant changes in the channel of Castle Creek may be expected to affect the 

ground-water flow system in the debris dam and perhaps debris dam stability. 

On September 22, 1993, discharge in the sr,illway 

was measured at 0.97 cubic feet per second (ft /s) and 

discharge in Castle Creek below its confluence with 

the spillway was 32.0 ft3

/s. The most recent previous 

discharge measurement in Castle Creek was 36.8 ft3

/s 

on June 14, 1991. 

27 

Hydraulic Head Gradients and Factors of 

Safety 

Upward flow of ground water exerts an upward 

force on the solid material above it. If this force 

exceeds the submerged weight of the overlying material, then the exiting ground water will lift and possibly erode it. This process is referred to as "heave", 

and is only one of several types of seepage erosion. 

Such erosion would reduce the stability of the debris 

dam, especially if it were followed by concentration 

of flow in the area and progressive erosion were to 

result. 

Heave requires upward flow of ground water, 

which is indicated when two or more water level 

measurements made at different depths beneath the 

same point on the surface show the hydraulic head to 

be greater at depth. On the Castle Lake debris dam, 

measurements of water level at different depths 

beneath the same point are made at sites P2A,B, 

P3A,B, P4A,B, DH2A,B, DH4A,B,C,D, and 

DH5A,B. Sites 11 and Pl can also be considered to 

measure water level at different depths beneath the 

same point on the surface. Figure 12A illustrates the 

differences in water levels at different depths at these 

locations. 

At DH5A, B,and at Pl-11, which are near the 

crest of the debris dam, ground-water flow is always 

downward. This downward flow represents recharge 

traveling down from the surface, and at DH5AB, possibly flow from the lake through the debris dam. At 

all of the other sites, there is upward flow during at 

least part of the year. Flow is always upward, and gradients are largest, at P4A, B, and between DH4A and 

B and DH4C and D. These sites are near the dam toe, 

where ground water is exiting. The potential for 

heave must also be considered where the creek 

traverses the dam toe, where ground-water flow 

through the debris dam presumably discharges 

upward into the creekbed. 

Factors of Safety: Gradient Method 

Heave is not possible until the rate of increase of 

hydraulic head with depth reaches a "critical gradient". At the critical gradient, the upward force due to 

ground-water seepage equals the weight of the overlying material. Heave refers to uplift of material at the 

soil surface, so it requires the hydraulic gradient to 

exceed the critical gradient at the surface and for 

some distance below that. Internal erosion, however, 
Unpublished base 1550000 

Spillway 

Debris avalanche deposit 

Bedrock 

Alluvium 

Castle Creek Channel 

- June 1991 survey 

- - September 1991 airphoto 

1551000 1552000 

from U.S. Army Corps 0 500 1000 FEET 

of Engineers, 1 :1200, 1989 1--r-'-r-/-o'-,--l.--..JL.....-,------r 

0 100 200 300 METERS 

CONTOUR INTERVAL 20 FEET 

345000 

344000 

343000 

Figure 9. Contour map of the post-eruption surface showing the channel of Castle Creek as it appears on a map by the U.S. 

Army Corps of Engineers based on 1989 aerial photography, the position of the thalweg as surveyed in June, 1991, and the 

position of the channel as it appears on September, 1991 aerial photography. Locations of the channel cross-sections shown in 

figure 11 are also indicated. Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are 

given below and at the right 

28 
....J 

w 

iii 

....J 

i1i 

(/) 

w 

~ 

~ 

tu 

w 

lL 

~ 

;i 

0 

....J 

~ w 

::.:: 

w 

w 

a: 

() 

2,600 

2,550 

2,500 

2,450 

2,400 

30 

25 

20 

15 

10 

5 

0 

-5 

-10 

-15 

A 

B 

0 1,000 2,000 3,000 

o 1991 Survey 

"1989 U.S. Army Corps of 

Engineers map 

o 1991 Survey 

"1989 U.S. Army Corps of 

Engineers map 

4,000 5,000 6,000 

DISTANCE FROM CASTLE LAKE, IN FEET 

Figure 10. A. Elevation of Castle Creek thalweg as read from the 1989 U.S. Army Corps of Engineers map and as surveyed 

in June, 1991. B. Differences between channel elevations and a uniformly sloping bed. 

can take place at depth when the critical gradient is 

exceeded, even if the critical gradient does not extend 

to the surface. In this study, factors of safety are computed wherever there is upward flow, whether it 

extends to the surface or not. 

The seepage force per unit area, cr s ,on the bottom 

of a soil column can be expressed mathematically as 

cr = Iy s w (1) 

where I = aptaz is the rate of increase of piezometer 

water level with piezometer depth, z, and 'Yw is the 

unit weight of water (Van Zyl, 1979). The downward 

29 

force per unit area is equal to the submerged weight, 

"fsus• of the solid particles in the same depth range of 

the column, 

'Ysus = (1- n) (~:- 1 )rw (2) 

where 'Ys and 'Yw are the unit weights of the solid particles and water, respectively, and n is porosity. Thus 

the critical gradient, I crit• is defined by equating (1) 

and (2) to obtain 

(3) 
...J 

w 

(ij 

...J 

UJ 2,580 (/) 

w 

6 

III 

<( 

Iii 2,570 w 

u. 

z 

z 

0 

~ 2,560 

...J 

w 

A 

········· Aug. 19, 1988 

- ·- June 7, 1989 

-- July 10, 1990 

2,550 '------'-------'-------'------'-------' 

1,200 1,300 1 ,400 1,500 1,600 1, 700 

...J 

w 

~ 2,570 

<( 

w 

(/) 

w 

6 

III 

<( 2,550 

Iii 

w 

u. 

~ 

z 

0 

~ 2,530 

> w 

...J 

w 

B 

········ June 19, 1986 

---- Sept. 18, 1987 

- ·- June 7, 1989 

-- July 10, 1990 

HORIZONTAL DISTANCE, IN FEET, FROM LEFT MONUMENT 

VERTICAL EXAGGERATION X 10 

Figure 11. Cross-section surveys on Castle Creek. Cross-section locations are shown in figure 9. A. Cross-section CA205. 

B. Cross-section CA21 0. 

Equation (3) shows that in order to calculate the 

critical gradient, the weight of the grains in the material and its porosity must be known. These quantities 

cannot be measured everywhere in the debris dam, but 

for 'Ys lyw between 2.5 and 2.6 and porosity of 24 to 40 

percent, the critical gradient is between 0.9 and 1.2 

(Meyer and others, 1994; U.S. Army Corps of Engineers, 1992). This range of gradients corresponds in 

figure 12a to the area in which the "factor of safety", 

FS=l. The "factor of safety" is the factor by which the 

critical gradient exceeds the existing gradient. Figure 

12a shows that even between piezometers DH4A and 

30 

B, the observed upward gradient is subcritical and 

that the lowest factor of safety that has been recorded 

at site DH4 is about 2, for the two depth intervals 

showing upward flow. In the report by the U.S. Army 

Corps of Engineers (1992), the same conclusion is 

reached with respect to the factor of safety in the 

deeper of these two intervals (DH4A to DH4B). 

Since the water pressure in piezometer DH4A has 

declined steadily, the present factor of safety between 

DH4A and DH4B is greater than 2. For the 1992 

water year, the average factor of safety between 
DH4A and DH4B was 3.6 and the average factor of 

safety between DH4C and DH4D was 4.7. 

At site DH4, the two intervals with upward flow 

are separated by an interval of downward flow. Consequently, while the upward flow between piezometers 

DH4A and DH4B might be expected to foster internal 

erosion, heave would be limited to the surface interval 

between piezometers DH4C and DH4D. 

Factors of Safety: Overburden Method 

Another way to estimate factors of safety against 

heave is to compare the weight of the soil column 

above a particular depth, z, with the hydraulic head 

above the land surface at depth z. A critical state for 

heave occurs when the head above land surface is 

given by 

PcRIT(z) = (1- n) (~: -1} (4) 

Equation 4 can be obtained by integrating equation 3 over the depth range from 0 to z and using p(O) 

= 0. Equation 4 is a meaningful criterion for incipient 

heave only at locations where there is upward flow. 

Figure 12B illustrates equation 4 for site DH4, 

which is the only group of piezometers where head is 

above the land surface and flow is upward. The lowest 

factors of safety are about 5, for the two shallowest 

piezometers, DH4C and DH4D. For DH4A and 

DH4B, the factors of safety calculated using equation 

4 are greater than 5, and greater than those calculated 

for the piezometer pair DH4A-B using equation 3. 

Meyer and others (1994) discuss the issue of what 

factor of safety should be accepted as indicative of 

long-term stability of the debris dam. Their discussion 

points out that even if factors of safety as low as 1.5 

are acceptable, in poorly characterized materials a 

margin of error is required in order to be sure that 

lower factors of safety do not exist anywhere in the 

dam. For the Castle Lake debris dam, a ground-water 

model can be used to infer factors of safety at locations where no measurements are available. But as 

will be discussed below, calibration of a ground-water 

model for the Castle Lake debris dam requires the 

assumption of material properties that vary spatially, 

and underestimates the head gradients favoring 

upward flow at site DH4. Thus the ground-water 

model can offer no assurance that factors of safety as 

low, or lower, than those present at site DH4 do not 

exist elsewhere in the debris dam. 

31 

A 2o.----,~.--~~~---.------­

15 

1-

tiJ 10 u. 

~ 

uj 

() 5 z 

w 

a: 

w 

u. 

u. 0 

i5 

....J 

w 

> w -5 ....J 

a: 

w 

!;;:-10 

s: 

-15 

-20 

0 

30 

tu 25 

w 

u. 

z 

;;s 20 

() 

u: 

~ 15 en 

Cl 

z ::5 10 

w 

> 0 

aJ 

<( 5 ....J 

w 

> w 

....J 0 a: 

w 

!;;: 

s: -5 

-10 

0 

, .... , i It, :!!: 

DH2A- H2B .j, P4A-P4B 

FS = Critical Gradient 

Observed Gradient 

+i2ft:-P2:- -- --- --- --- -- ----- - tP1-11 

DH4B-DH4C 

DH5A-DH5B 

P3B-P3A Water Level 

Differences 

I Maximum 

Average 

Minimum 

ro ~ oo oo 100 1ro 

DIFFERENCE IN DEPTH OF PIEZOMETERS, IN FEET 

B 

' ' ' ' ',_ t 

,' IJ,' ·If· ' ' ' ' ' ' ' ' ' ' ' ' ' ' / / /~ ' ' I I I i ,' 

I I .t: 'I ' I I r I: I 

'• '• '• :· 

t DH4B 

FS = Critical Head Above Land Surface 

Observed Head Above Land Surface 

20 40 60 80 100 

PIEZOMETER DEPTH, IN FEET 

~M~M Average 

Minimum 

120 140 

Figure 12. A. Differences in water levels for piezometers at 

different depths below the same point on the surface of the 

Castle Lake debris dam. A positive difference is a gradient 

favoring upward flow. The average, maximum, and minimum 

values have been determined over the period October 1, 

1990, through September 30, 1992. B. Water level above the 

land surface vs. piezometer depth at site DH4 on the Castle 

Lake debris dam. 

NUMERICAL SIMULATION OF THE 

GROUND-WATER FLOW SYSTEM 

A numerical simulation of the ground-water flow 

system in the debris dam can be used to calculate 

hydraulic heads at locations where there are no pie-
zometers and to predict how ground-water levels 

might change in response to greater amounts of precipitation, increased evapotranspiration due to reforestation of the debris dam, or mitigation measures such 

as lowering of the lake level. If the results of such simulations are to be meaningful, the numerical model 

must be calibrated so that it can reproduce the existing 

data acceptably well. The procedure is to construct a 

gridded numerical model having the same shape as the 

debris dam and to adjust the hydraulic properties of 

the model within reasonable limits until observed 

water levels and seep discharges agree satisfactorily 

with observations. Once the hydraulic properties have 

been adjusted in this way, they may be held fixed and 

the model's response to different scenarios can be 

tested. This section describes the development and calibration of such a simulation. 

Approach 

The simulation uses the finite-difference groundwater model Modflow (McDonald and Harbaugh, 

1988). It is calibrated to approximately reproduce the 

average seep discharges and piezometer water levels 

for the 1991 and 1992 water years. 

The simulation is steady state, calibrated under the 

assumption that on average, over a one-year period, 

the volume of water entering the debris dam, either as 

precipitation or as inflow from Castle Lake, equals the 

sum of the volumes discharged to Castle Creek, to 

Castle Lake, from seeps on the dam itself, and evaporated. Equivalently, it is assumed that there is no longterm change in the volume of water stored in the 

ground-water system. In accordance with this assumption, most of the piezometer hydrographs (fig. 6) and 

seep discharge records (fig. 8) change seasonally with 

precipitation and evapotranspiration and vary about a 

long-term average value. In piezometers DH4A and 

B, however, there has been a long-term decline of 

water level that is less consistent with the steady-state 

assumption. The steady-state numerical model cannot 

reproduce this feature. 

General Features of the Model 

Model Geometry 

The ground-water model is contained in the rectangular area shown in figures 2 thru 4, with the active 

32 

part of the model including all of the material 

between the pre-eruption elevation and the post-eruption elevation, except in areas on the western bedrock 

ridge where this material is less than 20 ft thick. The 

model grid, shown in figure 13, divides the area into 

cells that are 100ft on each side in the east-west and 

north-south directions. Although layered geologic 

units do not exist in the debris dam, the model is 

divided into five layers in order to determine the 

hydraulic head as a function of depth. The bottoms of 

the layers are nominally at elevations of2,575, 2,525, 

2,450, 2,400, and 2,250 ft, respectively, as shown in 

the cross-sections in figure 5. In each cell, however, 

if the nominal layer bottom elevation is below the 

pre-eruption surface elevation, then the cell bottom is 

instead set to the elevation of the pre-eruption surface. At the edges of each layer, the bottom or top 

may be defined by the pre- or post-eruption surface. 

At layer edges, cells thinner than 2.5 ft were eliminated from the model, and cells between 2.5 and 5.0 

ft thick were increased to a thickness of 5.0 ft. Thus 

the bottom of the active model is everywhere within 

2.5 feet of the elevation of the pre-eruption surface. 

Each cell's top is specified as the average of the 

elevations at the four cell corners. Cell bottom elevations are computed in an analogous fashion. The 

numerical model calculates hydraulic head at the center of each cell. 

The water surface in layer 1 is unconfined, but all 

the lower layers are capable of converting between 

confined and unconfined behavior depending on 

whether the hydraulic head is above or below the 

layer top. Confined/unconfined layers must be used in 

this simulation because the upper four layers intersect 

the water table, a free surface, in some areas. 

This model grid occupies approximately the same 

area as the model developed by Meyer and Sabol 

(1989), which will be referred to as the "MS" model. 

The MS model has a coarser grid, with cells 200 ft on 

each side and three layers. The layers in the MS 

model divide the thickness of the debris dam into 

thirds, instead of having horizontal bottoms. An earlier finite difference code (Trescott, 1975) was 

employed in the MS model, but the use of a different 

numerical code should have little, if any, effect on the 

results. 

Boundary Conditions 

The boundary conditions on the numerically 

modeled area were chosen to coincide with the natu-
C/) 

;: 

0 

a: 

41 

40 

39 

38 

37 

36 

35 

34 

26 

25 

24 

23 

Inactive 

Area II 

1551000 

D 

D . 

~ 

w 

3 

c 

L 

122° 

16'15"1552000 

EXPLANATION 

Debris avalanche deposit 

Bedrock 

Alluvium 

Well simulating recharge 

Drain simulating seep 3 46° 16' 

River cell simulating 

Castle Creek /Spillway 

Constant head cell 

simulating Castle Lake 345000 

344000 

343000 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

Figure 13. Map of grid for the numerical model of Castle Lake debris dam. Creek, constant head, and well cells are not necessarily in the top layer. Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are 

given above and at the right. 

33 
ral boundaries of the ground-water flow system wherever possible. These natural boundaries include Castle 

Creek, the spillway, Castle Lake, and the western bedrock ridge where it abuts or underlies the debris dam. 

Some estimates were required of the amount of 

recharge entering the debris dam from its western 

boundary. To the north and south of the debris dam, 

there are no natural features that provide a distinct 

boundary to the ground-water flow system. In these 

areas, the boundary was placed far enough away so 

that the simulated heads in piezometers in the debris 

dam were insensitive to its exact position. The choices 

made in assigning all of the boundary conditions are 

described below. 

Upper and Lower Boundaries 

Cells with bottoms that are above the top of the 

debris dam are required to be inactive; that is, flow is 

not permitted through them. 

The bottom of the model is also a no-flow boundary, which is equivalent to assuming that the material 

beneath the model is much less hydraulically conductive than the material within the model. As an initial 

working hypothesis, the bottom of the model was 

placed at the bottom of the 1980 debris avalanche 

deposit as in the MS model. Additional model runs 

were made to investigate how this assumption affected 

the simulated ground-water flow field. 

Castle Lake 

In each vertical column of cells beneath Castle 

Lake, the uppermost active cell is a specified head cell 

and the cell below it has its top at the lake-lakebed 

interface. If there is a cell above the specified head 

cell, then it is assumed to be inactive. Where head is 

specified, it is set to 2,580 ft except when simulating a 

lowered lake level. 

Castle Creek and Spillway 

The spillway and Castle Creek bound the groundwater system to the east, and along part of its northern 

edge. Cells in the model's uppermost active layer 

simulate these features by using the Modflow "river" 

package. These cells are represented by a "C" in figure 

13. Flow is not permitted into cells across the spillway 

or creek from the debris dam. This assumption is 

appropriate at the shallow depths included in the 

active model, although at greater depth, ground-water 

34 

flow on a more regional scale could pass beneath the 

creek. 

Modflow requires that riverbed conductance, Cri~ 

be specified at each cell containing a river reach. Thi~ 

conductance can be calculated as 

KLW 

criv = -x:r- (5) 

where Land Ware the length and width, respectively, 

of each river reach, M is the thickness of the riverbed 

material, and K is its hydraulic conductivity. In addition to the conductance, Modflow requires bed elevation and stage in each river reach. In each cell, 

discharge, QriV' from the river reach into the groundwater system is calculated by Modflow as 

Qriv = Criv (Hriv- Hi,j, k) (6) 

where Hriv is the head (stage) in the river and H i,j,k is 

the head at the center of the cell containing the river 

reach. In the present study, Qriv always represents 

flow from the debris dam into the creek or spillway, 

and thus is always negative. 

The length and width of each reach of the spillway and creek were measured from the topographic 

map prepared by the USACE from December, 1989 

aerial photography, but the horizontal position and the 

elevation of each reach were as determined in the 

1991 thalweg survey. A stage of 1ft above the creek 

bed elevation was used for all reaches, which was the 

average depth measured 200 ft below Castle Lake in 

the spillway, in June, 1991. The spillway is excavated 

from the debris dam and its banks are constructed 

from the excavated material (U.S. Army Corps of 

Engineers, 1988). Consequently the bed conductivity 

of the spillway should be similar to that of the natural 

channel of Castle Creek. Thus the bed conductivity 

over the entire length of the creek and spillway was 

initially set equal to the vertical hydraulic conductivity between the cell containing the reach and the cell 

below it. The thickness of the bed was set equal to the 

distance from the creek or spillway bed to the center 

of the cell containing it. These choices are equivalent 

to assuming that there is no difference between the 

creekbed material and the material composing the rest 

of the cell containing the creek reach. These values 

were modified, however, during model calibration. 
Table 4. Wells used to compensate for recharge from outside of the model boundaries 

[Note. ET = evapotranspiration, assumed to be 25 in/year on the ridge, which is vegetated, and 22.5 in/year 

on the debris dam, which is sparsely vegetated] 

1991 Water Year 1992 Water Year 

Layer, Estimated Recharge 

row, draininage no ET 

column area 

(tt2) (ft3/day) 

1,14,5 90,000 1,917 

1,15,3 110,000 2,343 

1,16,1 90,000 1,917 

1,17,1 30,000 639 

2,18,9 27,143 217 

2,19,9 27,143 217 

2,22,12 27,143 108 

2,22,12 27,143 108 

3,23,11 27,143 217 

3,24,11 27,143 217 

Western Boundary 

Along its western edge, the debris avalanche 

deposit pinches out as the bedrock rises to a ridge. In 

order to improve the numerical stability of the model, 

active cells were not included to represent material 

less than 20 ft thick overlying the western bedrock 

ridge. This material does not play a role in containing 

Castle Lake, so it is not necessary to simulate the 

ground-water flow within it. Precipitation that falls on 

that area and drains to the debris dam, however, must 

be estimated and accounted for in the model. 

The area west and northwest of Castle Lake 

labeled "Inactive Area I" in figure 13 is excluded from 

the model because debris avalanche deposits are thin 

or not present. Precipitation from most of this area will 

drain into Castle Lake, whose level is modeled as fixed 

regardless of overland flow into the lake. Consequently, it is not necessary to compensate for the 

recharge falling on the inactive cells that drain 

directly to the lake. 

In model rows 14 thru 17, precipitation draining 

from the west can enter the ground-water system in the 

debris dam. The area of the bedrock ridge that can 

drain, either by overland or by shallow subsurface 

flow, to the ground-water system extends west of the 

boundary of figure 13. The recharge that is neglected 

in the model by not including these areas is compensated for by constant flux boundaries in layer 1, indicated by W in figure 13. The maximum amount of 

recharge that should be introduced into each cell was 

estimated as the area draining to the boundary cell 

35 

Recharge Recharge Recharge 

corrected no ET corrected 

for ET for ET 

(ft3/day) (tt3

/day) (tt3/day) 

1,169 1,818 1,109 

1,429 2,222 1,355 

1,169 1,818 1,109 

390 606 370 

1,120 1,472 265 

1,120 1472 265 

1,120 1,472 133 

1,120 1,472 133 

1,120 1,472 265 

1,120 1,472 265 

times the average daily precipitation rate and is listed 

in table 4. It was simply assumed that evapotranspiration on the ridge takes place at the maximum rate of 

35 in/year (0.0080 ft/day). 

During model calibration, it was observed that 

the recharge amounts listed in table 4 did not always 

maintain head above the bottom of the cell; at these 

cells, the hydraulic conductivity was reduced and/or 

the recharge was increased in an effort to raise head 

above the cell bottom. 

The boundary of the areas labeled "Inactive Area 

II" and "Inactive Area III" in figure 13 approximates 

part of the 20 ft thickness contour of the debris avalanche deposit (see fig. 4). In Inactive Area II, precipitation flowing overland or at shallow depths reemerges at seeps 9 and 10. The recharge falling on 

this area approximately equals the discharge of seeps 

9 and 10 if22.5 in/year (0.0051 ft/day) of evaporation 

are assumed, equal to the potential rate for bare soil 

used elsewhere in this model. Thus exclusion of Inactive Area II from the model is approximately balanced by removal of the discharge of seeps 9 and 10 

from the water budget to be matched by the model. 

Inactive Area III includes some cells surveyed as 

part of seep 8. During a field visit in February, 1992, 

the area that comprises these cells provided approximately 20 percent of seep 8's total discharge. To calculate the amount of recharge to be introduced into 

the ground-water flow system to compensate for 

exclusion of Inactive Area III from the active model, 

the recharge falling on it was first reduced to account 
for evapotranspiration under vegetated conditions (35 

in/year; 0.008 ft/day) and then further reduced by 20 

percent of seep 8's total discharge. The remaining 

amount was introduced at constant flux boundary cells 

in rows 18, 19, 22, 23, and 24. Also, the discharge 

from seep 8 was reduced by 20 percent before comparing it with the simulated seep discharge. 

In model rows 28 through 41, recharge presumably drains from the west into the ground-water system in the 1980 debris, but there is no available map 

from which to determine the drainage areas. In lieu of 

accurate information, it was assumed that up to 0.012 

ft3/s (1,000 ft3/day) entered each column of cells, 

which is slightly larger than the amount estimated for 

each western edge cell in rows 14, 15, and 16. This 

amount can be increased by 50 percent without changing the fit of the model to the data. However, this 

amount of recharge led to unrealistically high heads 

near the constant flux boundary cells; therefore, the 

hydraulic conductivity of each cell was increased and/ 

or the amount of recharge was reduced until the head 

at the boundary was approximately at the land surface. 

Northern Boundary 

Flow from beyond the western edge of the model 

in rows 28 to 41 causes ground-water flow in the 

northwestern comer of the model to be subparallel to 

the northern boundary of the model grid. Because 

there is little flow across it, the northern boundary can 

be assumed to be impermeable. An alternate treatment 

for the northern boundary would be to add a constant 

flux boundary approximating ground-water flow 

toward North Fork Toutle River, approximately two 

miles to the north. The elevation drop between the 

reach of Castle Creek in row 41 and the point directly 

to the north on the North Fork Toutle River is about 

930 ft, and the average hydraulic conductivity of the 

debris avalanche material is near 1.55 ft/day, yielding 

a flux of 0.016 ft3

/s (1360 ft3/day) through each ofthe 

cells in row 41, which can be removed from these 

cells by a constant flux boundary. Either this treatment 

or the impermeable boundary provides the same fit of 

the model to the observations, so the simpler impermeable boundary was used. 

Natural Conditions to be Simulated by the Model 

1991 and 1992 are the water years for which the 

most complete hydrologic data are available. The 

36 

model was calibrated to simulate conditions during 

these water years. 

Precipitation 

Precipitation data are available for 353 days during the 1991 water year, and total precipitation 

recorded was 90.1 in., for an average of 0.0213 ft/day. 

Of the 12 days when no precipitation data were available, 3 were during stormy periods when precipitation 

may have been missed. Assuming the missing days 

experienced average precipitation rates, then the total 

precipitation for the 1991 water year is complete to 

within about 1 percent. 

For the 1992 water year, precipitation data are less 

complete. Data are available for 310 days, during 

which 75.1 in. of precipitation were recorded. The 

nearest other rain gage, at Spirit Lake, was nonfunctional at the same times as the Castle Lake rain gage. 

Another gage, at Coldwater Lake, records a much 

lower amount of precipitation than Castle Lake. Consequently, data from other nearby rain gages were not 

available to complete the 1992 water year precipitation record. In lieu of better information, it was 

assumed that the missing 56 days experienced average 

precipitation, yielding total precipitation for the 1992 

water year of 88.7 in., averaging 0.0202 ft/day. 

Evapotranspiration 

Modflow allows simulated evapotranspiration to 

occur at a specified maximum rate when the water 

table is above a specified depth, and to cease altogether when the water table is below a specified 

"extinction" depth. Between these two depths, evapotranspiration decreases linearly with depth to the 

water table. The maximum rate, as well as the two 

depths, can vary spatially over the model. 

As discussed above, most of the debris dam experiences evaporative water loss from its bare surface, at 

a maximum rate of approximately 22.5 in/year 

(0.0051 ft/day), which is 0.9 times the lake evaporation rate. For the areas in which there is no vegetation, 

the extinction depth was set to 1 ft. 

In addition, there may be increased water use by 

willow and alder, growing primarily in drainage channels. Using a grid placed over a September, 1991 

aerial photograph of the debris dam, the approximate 

percentage of vegetative cover in each model grid 

square was estimated by quartile, as shown in figure 

14. In cells that were not completely free of vegeta-
(/) 

3: 

0 

a: 

37 

36 

35 

34 

33 

32 

31 

27 

26 

25 

24 

23 

21 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

122° 

1551000 16'15'{552000 

EXPLANATION 

D Bedrock 

Vegetation Coverage 

• 75-100% 

50-75% 

D 25-50% 46°16' 

D . 0-25% 

345000 

344000 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000 FEET 

0 100 200 300 METERS 

Figure 14. Percentage of vegetative cover as estimated from a September, 1991, aerial photograph. Blank cells within the 

active model grid are completely unvegetated. Eastings and northings, according to the Washington State Plane Coordinate 

System, in feet, are given above and at the right. 

37 
tion, the extinction depth was set to 7.5 ft. The maximum evapotranspiration rate was 35 in/day (0.0080 ft/ 

day) in completely vegetated cells. For cells that had 

some vegetation coverage, the evapotranspiration rate 

varied linearly between the "bare soil" value and the 

"fully vegetated" value. 

Seep Discharge 

Seep Locations and Conductances 

In the Modfiow finite difference model, seeps are 

simulated by drain cells. Each drain is characterized 

by the area through which draining can occur, the 

thickness of the material through which draining takes 

place, the hydraulic conductivity of this material, and 

the elevation of the drain. The drain is inactive until 

head in the drain cell becomes equal to or greater than 

the drain's elevation. 

Every cell containing at least one surveyed seep 

point was simulated as a drain cell. Because the cell 

bottom and top elevations are averages of elevations at 

the cell comers, six seep elevations turned out to be 

higher than the elevation of the top of the uppermost 

active cells. The existence of a seep indicates that the 

ground-water system extends to at least that elevation, 

so the tops of these cells were redefined to equal the 

highest surveyed seep elevation plus 1 ft. These 

adjustments are at most 8 ft. In all cases but one, the 

new elevation is no higher than at least one comer of 

the cell. The exception is seep 3, which has deposited 

a mound around its vent, presumably composed of 

material eroded from within the debris dam. 

As a preliminary estimate of seep conductance, 

each seep was assumed to occupy the entire surface 

area of its cell. The length of the flow path from the 

node to the seep and a weighted average of the vertical 

and horizontal hydraulic conductivities was used to 

calculate the seep conductance. Where there were 

several seep points surveyed in a cell, the highest elevation seep was used. As model calibration was 

refined, seep conductances were adjusted to improve 

the fit to the observed discharges. In most cases, conductances were adjusted downward, which is reasonable considering that most seeps do not occupy an area 

as large as one cell. 

Most seep discharge measurements include discharge from an area larger than one model cell, as 

shown in figure 7. The discharges from all cells that 

drain to a single discharge measuring point were 

38 

summed and compared to the observed discharges. 

Figure 13 shows the locations of the drain cells in the 

model grid; each drain cell is labeled with the number 

of the corresponding discharge measurement. Some 

of the surveyed seep locations do not drain to measurement points. These include two new seeps at the 

heads of slumps that formed during a storm in January, 1990. Discharge at these two seeps, designated 

"11" and "12", was visually estimated to be at most 

0.01 ft3/s (864 ft3/day). The seeps on the northeast 

face of the dam crest denoted "13" do not drain to a 

measuring point, and during a field visit in February, 

1992, they were observed to be dry. Consequently, 

during model calibration it was required that no discharge emerge from these seeps. Finally, the drain 

cell denoted "14" was introduced to prevent head in 

the corresponding cell from rising above the land surface. The necessity to introduce a drain cell at this 

point suggests that there is a submerged discharge 

exit point just below the edge of Castle Lake. 

Correction of Seep Discharge Measurement for the 1991 Water 

Year 

During the 1991 water year, seep discharges were 

measured less frequently than water levels, and more 

measurements were made during the drier part of the 

year than during the wetter part. In an effort to 

improve the estimate of the average seep discharge 

during the 1991 water year, linear relations between 

seep discharge measurements, Qi , and well water 

levels, hi> were sought. For each seep, linear regression was used to estimate the best values of h0 and A , 

such that 

(7) 

approximated the measured discharges. In equation 

(7), A is the coefficient between measured discharge 

and observed water level for a particular seep-piezometer pair and h0 is the head below which discharge ceases. Except at seep 8, the linear relation 

was fit to all pairs of seep-well level measurements 

with time differences less than 4 days that were available prior to May, 1992. For seep 8, a better relation 

was obtained by excluding two measurements for 

which the wells and seeps had been measured more 

than two days apart. Only the piezometers installed in 

1983 were considered as possible predictors of seep 
Table 5. Linear regression relations between seep discharges and water levels 

[R is the linear correlation coefficient.] 

Seep Best Number R2 Slope Intercept Other 

predictor of Wls predictors 

measurements ft (ft) R2

20.S 

12 8 0.96 0.00382 2,577.3 All But P3A 

3 P3A 15 0.83 0.01227 2,602.6 None 

5 12 16 0.77 0.02029 2,581.1 P3B, PI, II 

6 P2A 16 0.47 0.00187 2,572.8 None 

7 P3B 16 0.52 0.00053 2,592.7 PI 

8 12 14 0.74 0.01300 2,580.8 11 ,I3,Pl ,P2A,P2B,P3B 

9+ 10 I2 16 0.61 0.02449 2,579.2 PI, P3B 

TableS. Averages of measured and estimated seep discharge for the 1991 water year 

Seep Actual average discharge 

(W/s) 

0.027 

3 0.032 

5 0.042 

6 0.038 

7 0.002 

8 0.036 

Subtotal 0.176 

9 + 10 0.145 

Total 0.321 

discharge, since only a few data points were available 

for the piezometers installed in 1990. 

For each seep, the piezometer having the strongest 

linear relation with seep discharge was chosen. The 

piezometer levels are correlated with each other, and 

the number of measurements is small, so no attempt 

was made to estimate seep discharge as a linear combination of the water levels in more than one piezometer. Table 5 lists the piezometers whose heads best 

predict the discharge in each seep, together with the 

correlation coefficient and the coefficients in the linear 

relation. The fits of the data to these relations are 

shown in figure 15. The data points collected since the 

Estimated average discharge Estimated/actual 

(W/s) 

0.029 1.11 

0.030 0.95 

0.079 1.90 

0.036 0.93 

0.004 1.77 

0.055 1.53 

0.233 1.33 

0.141 0.97 

0.374 1.17 

analysis was done are shown in black, and generally 

fit the same regression lines. 

39 

These linear relations were used to estimate the 

seep discharge on days when water levels were measured, but seepage was not. These estimates were then 

averaged for the calibration period. Table 6 lists the 

average discharge from each of the seeps as calculated 

from discharge observations during the period October 1, 1990 thru September 30, 1991, as well as the 

average calculated from the discharges estimated 

using the linear relations with water level. At seeps 3, 

6 and 9+10, the simulated average is close to the average of the observations, while at the other seeps the 
SEEP 1, PIEZOMETER 12 

0.4 

0.3 

0.2 

0.1 

0.4 ,...s_E_E_P,5.:.., _P_IE,Z_O_M_E,T_E_R_I,2_--..,-~-~-~-~ 

0 

z 0.3 

0 

0 

w 

rn 0.2 a: 

w 

a. 

1- 0.1 w 

w 

1.1.. 

0 

' ' 

' ' 

0 0.0 L__.L.l!!:::..::_...J_ _ _L_ _ _j_ _ _J_ _ _.l. _ __j __ L__J 

Ill 

::::> 

0 

z 

0.4 

w 0.3 

(!) 

a: 

<( 

:c 

0 0.2 rn 

0 

ft 0.1 

w 

rn 

SEEP 7, PIEZOMTER P3B 

0.0 L__...J__...l..__eJG·.t ....... diBIIH>-4!iiiW...,.IliLflt1-::c:...c.{E!:...;-::..J:..;-:_-:_-:_· "':L:...-=--:._:-

o.

4 ,S_E_E_P,9_+_1 O-',,_P_I_E_Z,O_M_E_T,E_R_I2--r-----.-----.-----.---, 

0.3 

0.2 

0.1 

0 

' ' 

' ' 

0 ,

0 0 

Q'o o q' 

. ' ' 

' ' 0 GO ,;_oo 0 

o, ~~-, • . 

' ' 

/tie •• 0.0 L--~~..JIL _ _j_ _ _L _ _J_ _ __j __ L__.L.._____J 

2,575 2,580 2,585 2,590 2,595 2,600 2,605 2,610 2,615 2,620 

PIEZOMETER WATER LEVEL, IN FEET ABOVE SEA LEVEL 

SEEP 3, PIEZOMETER P3B 

SEEP 6, PIEZOMETER P2A 

SEEP 8, PIEZOMETER 12 

2,575 2,580 2,585 2,590 2,595 2,600 2,605 2,610 2,615 2,620 

PIEZOMETER WATER LEVEL, IN FEET ABOVE SEA LEVEL 

0 

EXPLANATION 

Best fitting linear relationship 

Measured before May 1992 

Measured after May 1992 

Figure 15. Seep discharge as a function of water level for the Castle Lake debris dam. 

40 
_j 0 

w eDH4D > w -1 

....J 

DH5Be e P1._li _eD~~--------------------ffi•-------------- 812 

8 DH4C eP48 eDHa 8 P2 a: A 8 P3A w -2 -------------- -oH5,4;8-8-p-4A------ -CDP-2!3------- --

~ ~ 8P3B - - - - - - - - - - - - - - - - - - - - OH2A- - - - - - - - - - - - - - - - --

DH288 814 

-3 ..-I- mw 

~w _JlL -4 DH1 -- ----------------------- -·------- ----- -- wz 

>-

w -5 - - - - - - - - -- - - -- - - - - - - -- - - - - - - - - - - - - - - - -- -- ....J eDH4A 

a: 

w - - - - - - - - - - - - - - - - - - - - - - - - - - - lD- - - - - - - - - - - -- DH3 

-6 1-

<( 

~ 

C\1 -7 ----------------------------------------- 0> 

0> 

-8 ~------~------~------~------J_ ______ _L ______ ~-~ 

2,500 2,520 2,540 2,560 2,580 2,600 2,620 

1992 WATER LEVEL, IN FEET ABOVE SEA LEVEL 

Figure 16. Differences between average water levels in piezometers at Castle Lake debris dam during the 1991 and 

1992 water years. 

simulated average is between 11 and 77 percent larger 

than the average of the observations. The estimated 

total of all the seep discharges except for seeps 9+ 10 is 

33 percent larger than the measured total. 

Discharge from seep 3 decreased between 1984 

and 1986. Water level in piezometer P3A also 

decreased during this time period. Consequently, there 

is a strong relation between discharge from seep 3 and 

water level in piezometer P3A when all data since 

1984 are considered. For data since 1986, however, 

there is no significant relation between discharge from 

seep 3 and water level in any of the piezometers. Discharge from seep 6 is also poorly correlated with any 

of the water levels. Thus for these two seeps, the average of the discharges measured during the 1991 water 

year was used instead of the estimated value. 

During the 1992 water year, seep discharges were 

measured as often as water levels, so the water level 

information could not be used to provide additional 

information about seep discharges. Consequently, for 

the 1992 data set, the model was calibrated to the average of the actual seep discharge measurements for that 

water year. 

Piezometer Water Levels 

Because piezometers I4 and DH6 are in areas 

where less than 20 ft of 1980 debris overlies bedrock, 

they are not included in the active part of the groundwater model and data from these sites were not used to 

41 

calibrate the model. Water levels in all 20 other piezometers were used in model calibration. For each 

piezometer, the average of the water level observations was determined for each of the 1991 and 1992 

water years. In addition, the elevations of two ponds, 

which will be referred to as Pond 1 and Pond 2 (fig. 3) 

were compared with the model-calculated water levels in the corresponding cells. 

Recharge in the 1992 water year was estimated to 

be 5 percent less than in the 1991 water year, and the 

average 1992 heads are all lower than those in 1991 

(fig. 16). Most of the differences are 4ft or less. At 

piezometer DH4A, however, the difference is larger 

because the water level there has been falling monotonically since measurements began in fall, 1990. As 

will be discussed in more detail below, this groundwater model cannot reproduce the monotonically falling behavior. The decision was made to calibrate the 

model to the 1992 head in DH4A, and to allow it to 

be lower than the 1991 head at that site. Piezometer 

DH3 also has a much lower value in 1992 than in 

1991; figure 6b reveals that no measurements were 

made here for the first two months of the 1991 water 

year, so that the 1992 average value is more nearly 

representative. 

Free Parameters and Calibration 

The preceding discussion shows that many features of the model are only approximately known and 
can be adjusted during calibration to help the model fit 

the data. Of these features, the horizontal and vertical 

hydraulic conductivities are the least well known and 

are therefore the primary parameters to be adjusted. 

The horizontal hydraulic conductivity is required for 

each of the 1560 active cells in the model. The vertical 

hydraulic conductivity is specified between each cell 

and the active cell below it, wherever there is such an 

active cell. In addition, it is important to evaluate 

whether the heads and discharges can be better modeled if some flow is permitted beneath the 1980 debris. 

The drain and creekbed conductances and the distribution of recharge were also varied to achieve a calibrated model. Seep elevations were adjusted as well, 

but by no more than 2 ft. 

Although they are not precisely known, the maximum evapotranspiration rates, the evapotranspiration 

extinction depths, the 1991 seep discharges, the 1992 

total precipitation, and the creekbed elevation were 

not varied during model calibration. Neither was the 

amount of recharge introduced via wells to represent 

inflow from west of the active model, except as 

needed to maintain the head in these cells between the 

top and bottom of the corresponding cell. The degree 

to which these choices affect the model calculated 

heads and seep discharges was evaluated over a range 

of plausible values and found to be small, typically 

less than 1 ft at all 20 piezometers and at both ponds. 

To assess the fit of the model to the data, simulated heads were interpolated horizontally and vertically from the centers of the cells to the locations of 

the piezometers. Simulated discharges from each drain 

cell were summed over all cells contributing to each 

measuring point, and compared with the observations. 

One measure of how well the model fits the data is 

the root-mean-squared (rms) misfit, equal to the 

square root of the sum of the squares of the differences 

between the annual average water level in each piezometer and the model-calculated water level. 

Because the rms misfit can in general be small when 

all simulated heads are either too high or too low, it is 

also important to maintain the average head misfit 

close to zero. Consequently, adjustments to the model 

were made so as to maintain a small average misfit, 

minimize the rms misfit, and approximate the correct 

total seep discharge. 

Calibration goals were to minimize the rms misfit 

between the observed and simulated piezometer and 

pond water levels, and to obtain a model-predicted 

head within 5 ft of the observed value at each individual piezometer, which is approximately 5 percent of 

42 

the total head variation across the debris dam. The 

individual seep discharges were matched to their measurement precision of approximately 0.01 ft3 /s (864 

ft3/day). Finally, an effort was made to match the sign 

and magnitude of the head difference at each pair of 

piezometers sampling water level at different depths 

beneath the same point on the surface. 

The data sets from both the 1991 and 1992 water 

years were used to calibrate the model, bearing in 

mind that the seep discharges are somewhat uncertain 

for 1991 and the total amount of precipitation is somewhat uncertain for 1992. Also, as described above, 

the decision was made to match the heads at piezometers DH4A, DH4B, and DH3less well for the 1991 

water year than for the 1992 water year. 

The model contains many more free parameters 

than there are data values, so there is more than one 

way to adjust the model such that the simulated heads 

and seep discharges agree with the observations. In 

order to distinguish model features that are essential in 

order to fit the data from features that represent only 

one arbitrary choice of many ways to fit the data, the 

following calibration strategy was adopted. First, a 

model with uniform, isotropic hydraulic conductivity 

was calibrated such that the average difference 

between the observed and modeled heads was as small 

as possible and such that the total seep discharge was 

approximately equal to the observed value. Then, 

plausible refinements, such as variation of recharge 

rate with surface slope, were tested and added to the 

uniform model if they helped meet the calibration 

goals or if they made little difference but were judged 

to improve the realism of the model. When all plausible refinements were exhausted, the remaining discrepancies between the model and the observations 

were removed by adjusting hydraulic properties in the 

vicinity of piezometers where simulated heads failed 

to agree with observations. 

Uniform Model 

In the uniform model, the vertical and horizontal 

hydraulic conductivities are assumed to be equal, and 

the single best-fitting such value for the entire debris 

dam was sought. Recharge was distributed uniformly 

over the active area of the model except that no 

recharge is applied on the spillway or on Castle Creek. 

No flow was permitted beneath the pre-eruption surface. The creekbed conductances and the seep eleva-
Table 7. Summary of the uniform and fully calibrated 

Castle Lake groundwater models 

Uniform Nonuniform 

model calibrated 

model 

Horizontal conductivity, 1.55 0.01-490 

(ftlday) 

Vertical conductivity, 1.55 0.00006-60.7 

(ft/day) 

Recharge distribution 

Creekbed conductivity 

1991 Water Year: 

Average misfit, (ft) 

Rms misfit, (ft) 

Minimum misfit, (ft) 

Maximum misfit, (ft) 

Calculated/observed 

seep discharge, percent 

Maximum discharge misfit, 

(ft3/s) 

1992 Water Year: 

Average misfit, (ft) 

Rms misfit, (ft) 

Minimum, misfit, (ft) 

Maximum misfit, (ft) 

Calculate/observed 

seep discharge, percent 

Maximum discharge misfit, 

(ft3/s) 

Uniform 

Equal to 

vertical 

conductivity 

0.7 

7.2 

-12 

17 

96 

+0.04 

-0.4 

7.1 

-13 

16 

120 

+0.04 

tions and conductances were all set to their 

preliminary values as described earlier. 

0 near DH4 

Higher 

upstream, 

lower 

downstream 

0.8 

2.4 

-3 

5 

82 

-0.03 

0.04 

2.3 

-4 

5 

101 

O.QI 

It was determined that the best fitting value of 

hydraulic conductivity was 1.55 ft/day, which yielded 

average head misfits of -2.2 and -0.2 ft for the 1991 

and 1992 data sets, respectively. Table 7 describes the 

uniform model and how it fits the observations for 

both water years. For the 1992 water year, table 8 

43 

describes the fit to the hydraulic head differences for 

piezometers sampling different depths beneath the 

same location. The solid circles in figures 17 A and 

17B show the head and discharge misfits for this 

model for the 1992 water year, and figure 18 shows 

the water level in the uppermost active layer throughout the active model. 

The best-fitting uniform hydraulic conductivity is 

well determined by the data. For the 1992 water year, 

lowering it from 1.55 ft/day to 1.35 ft/day causes the 

average head misfit to change from -0.2 to +3.3 ft 

and increases the rms head misfit by 2 ft. This 15 percent decrease in conductivity raises the simulated 

heads by 6 to 10ft at piezometers DH5A, Band 

DH4A, B, C, D. Thus the uniform numerical model 

requires a hydraulic conductivity much lower than 

any of the values determined in falling head tests, and 

slightly lower than the values from slug tests in other 

parts of the debris avalanche deposit. The uniform 

model cannot be made to approximate the observations using the values measured in the tests. For 

example, using a hydraulic conductivity of 2.4 ft/day, 

the lowest slug test value, leads to an rms misfit of 

10.5 ft and an average head misfit of -3.3 ft. 

Figure 19 illustrates the water budget for the uniform model. Of the total budget of 1.3 ft3 Is, 97 percent derives from recharge either falling on the debris 

dam or entering from the western boundary. Water 

flows in both directions between the lake and the 

debris dam, with the net flow being from the debris 

dam into the lake. Almost 2/3 of the ground water 

leaving the debris dam flows into Castle Creek. This 

outflow is only 0.8 ft3

/s, which is small compared to 

the total discharge of Castle Creek (30 to 37 ft3

/s). 

Thus this important component of the water budget 

cannot be verified by field measurements. Evapotranspiration accounts for slightly less than one-fifth 

of the water budget. 

The flow of ground-water in both directions 

between Castle Lake and the debris dam is plausible, 

because infiltrating precipitation presumably reaches 

the lake along the northern part of the lake basin, but 

farther south beneath the lake seepage from the lake 

bottom into the subsurface should predominate. 

There is about twice as much flow into Castle Lake 

from the debris dam as from the lake to the dam. Thus 

the natural situation has features of both conceptual 

models outlined earlier. If the model were extended 

farther south and deeper, additional flow from the 

lake into the ground-water system would be included 

in the water budget. 
Table 8. Vertical hydraulic head differences in the Castle Lake debris dam, as observed, and as simulated by the uniform and nonuniform calibrated models for the 1992 water year 

[A positive value indicates higher head in the deeper piezometer] 

Deeper 

piezometer 

P3B 

P1 

DH4A 

DHSA 

DH2A 

P2A 

P4A 

DH4B 

DH4C 

Shallower 

piezometer 

P3A 

11 

DH4B 

DH5B 

DH2B 

P2B 

P4B 

DH4C 

DH4D 

Depth 

difference, 

(ft) 

44 

108 

35 

38 

24 

7 

52 

45 

33 

The ground-water flow system to some degree 

reflects the debris dam's irregular shape. The uniform 

model incorporates this irregular shape, but calculates 

a hydraulic head distribution that differs significantly 

from the observed values in many places. The complicated shape of the debris dam cannot fully explain its 

hydraulic head distribution. 

Modifications Tested for the Uniform Model 

The uniform model is not an acceptable fit to the 

observations, primarily because several model-predicted water levels disagree with the observations by 

more than 10 ft. The distribution of differences 

between the model-calculated and observed heads is 

complex. For example, for the 1992 water year, 

model-calculated heads are too low by 7 and 13ft at 

P3A and B, but 2ft too high at DH3, only 200ft away. 

The model fits the observed heads acceptably at I1 and 

P1, but 200 ft west at I2, the model-predicted heads 

are 8 ft too high, and 200 ft to the northeast at I3 they 

are 5 ft too low. Individual seep discharges range 

from 0.4 to 12 times their observed values for the 

1992 water year. 

Several modifications to the model, representing 

plausible features of the natural ground-water flow 

system, were tested to determine whether they could 

44 

Hydraulic Head Differences 

Observed, Uniform Nonuniform 

(ft) model, calibrated 

(ft) model, 

(ft) 

-6.5 -0.9 -8.8 

-2.1 -1.4 -4.0 

9.7 -1.7 4.4 

-7.3 -1.6 -6.4 

0.2 -0.3 -0.4 

-0.9 0.0 -0.1 

2.2 2.5 1.8 

-4.1 -0.7 4.5 

7.1 0.1 0.0 

improve the fit of the model to the observations. The 

tests are described below, with reference to the 1992 

data set. 

Permeable Material Beneath the 1980 Deposits 

Alluvial material in the former drainage of South 

Fork Castle Creek presumably has hydraulic conductivity comparable to that of the debris avalanche. 

Drilling in 1990 showed that in several locations, 

material beneath the debris avalanche deposit should 

not differ hydraulically from the debris avalanche 

itself. Thus several runs were made to investigate 

whether a better fit to the observed heads and discharges might result if flow were permitted beneath 

some part of the debris dam. These experiments were 

performed with the 1992 data set. The lower boundary 

of the model was lowered at selected cells, which 

added permeable material to the deepest layer, assigning it the same hydraulic conductivity as that layer. It 

is not possible to infer both the thickness and the 

hydraulic conductivity of the material beneath the 

debris dam from the configuration that best fits the 

data because the simulated ground-water flow 

depends only on the product of these two quantities. 

The first experiment was to lower the bottom of 

the active model by 20 ft everywhere except within 

200 ft of the western bedrock ridge. This change 

resulted in an average head misfit of 0.9 ft and 
tu 

w 

u.. 

20 

15 

A 

DH4D l Uniform ~ Nonuniform 

_j 

w 

> 

w 

...J 

a: 

w 

~ Cl 

w 

10 

5 

> 0 

a: 

DH4B Calibrated 

I DH:~~::---- -----~--rr:--- --;: t:;~ ------- w Pond 2• DHSA 

DH2Bt 

____ Ji_ h-- rJ) _____________________ Q~2~-

-- Ill 

0 -5 

6 

w 

~ -10 ::::> 

~ 

Ci5 -15 

DH5B DH1 P2B P3B 

Pond 1 

P3A 

2,500 2,520 2,540 2,560 2,580 2,600 

B 

OBSERVED WATER LEVEL, IN FEET ABOVE SEA LEVEL 

Cl 0.25 

z 

0 

() 

w 

rJ) 

a: 

w 

a. 

tu 

~ 

() 

co 

::::> 

() 

~ 

u.i 

(.!:) 

a: 

0.20 

0.15 

0.10 

~ 0.05 

() 

rJ) 

iS 

Uniform 

Nonuniform 

Calibrated 

S1 S3 S5 S6 S7 SB S11 S12 TOTAL 

SEEP NUMBER 

Figure 17. A. Observed and calculated water levels for the uniform and nonuniform calibrated models of the Castle Lake 

debris dam. B. Observed and model-calculated seep discharge for the uniform and nonuniform calibrated models. 

increased the rms misfit by 1 ft. Simulated heads both 

rose and fell, with the largest changes being increases 

of 8 ft at piezometer DH5A, B. Total seep discharge 

decreased slightly to 111 percent of the observed 

value. This modification did change the simulated 

ground-water flow field, but the changes resulted in a 

poorer fit to the data. 

In a second experiment, the bottom of the active 

model was lowered by 50 ft except within 300 ft of the 

western bedrock ridge, and the optimal uniform 

hydraulic conductivity was sought for the new lower 

boundary. Because the material added beneath the 

1980 deposits raises the debris dam's transmissivity, a 

45 

lower hydraulic conductivity should be needed to 

maintain the average head misfit near zero. The optimal conductivity, however, still appears to be 

between 1.35 ft/day (average misfit 0.3 ft) and 1.75 ft/ 

day (average misfit -1.4 ft). Throughout this range, 

the rms misfit was between 9 and 10 ft, and no pattern 

of improved fit to the observations was noted. 

Further model runs were made in which the lower 

boundary was deepened in limited areas, but these 

changes did not help the uniform model to match the 

observed water levels more closely in the areas where 

the largest differences existed between the simulated 

and observed heads. 
41 

40 

39 

38 

37 

36 

35 

34 

33 

2 

122° 

EXPLANATION 

D Debris avalanche deposit 

D Bedrock 

Alluvium 

-2560- Hydraulic head contour 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000 FEET 

0 100 200 300 METERS 

CONTOUR INTERVAL 10 FEET 

46°16' 

343000 

46° 

15'30" 

Figure 18. Water levels in the highest active model layer as simulated by the uniform model for the 1992 water year. Eastings 

and northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the right. 

46 
1.6 ,-----------------------------------------------------------------------

1.4 UNIFORM NONUNIFORM 

CALIBRATED 

LAKE LOWERED 

40 FEET 

0 

z 

0 

1.2 

0 1 w 

(f) 

a: 

w 

a.. 0.8 

tu 

w 

LL 

0 0.6 

m 

::> 

0 

0.4 

0.2 

IN OUT IN OUT IN OUT 

Figure 19. Water budget summary for the uniform and nonuniform calibrated model of the Castle Lake debris dam, and for the 

nonuniform calibrated model when the lake has been lowered 40 ft. W.B denotes recharge entering at the western boundary 

of the model. 

It seems contradictory for the material beneath the 

1980 deposits to have hydraulic properties similar to 

the deposits themselves, while the water level measurements match the model more closely when no 

flow is permitted through this material. A possible 

explanation is that the boundary between the debris 

avalanche deposit and the pre-1980 materials parallels 

streamlines in the ground-water flow field. Flow 

beneath this boundary could enter the ground-water 

system from the bed of Castle Lake farther south than 

the model extends. To properly include flow through 

the material beneath the 1980 deposits, it would be 

necessary to also incorporate the additionallakebed 

area that supplies it with ground-water. There is little 

information, however, to constrain properties of the 

additional material that would need to be incorporated. 

In particular, it is unclear whether this deeper flow 

47 

would exit to the surface at Castle Creek, or would 

pass beneath the creek. 

If the bottom of the 1980 material does approximately parallel streamlines, then it is an appropriate 

lower boundary for the ground-water model. It would 

be fortuitous for this interface to coincide exactly with 

streamlines, so there are presumably localized areas in 

which flow through the pre-1980 materials should be 

permitted in the model. These changes, however, 

appear too small to detect relative to the uniform 

model. 

Vertical Anisotropy 

The vertical hydraulic conductivity of unconsolidated deposits can be lower than the horizontal 

hydraulic conductivity, even in the absence of distinct 

layering or preferred orientation in the texture. The 
MS model fit the data more closely with a vertical 

hydraulic conductivity 10 times smaller than the horizontal conductivity in most areas. To test whether vertical anisotropy would improve the fit of the present 

model to the data, the uniform model was perturbed by 

lowering the vertical hydraulic conductivity to 0.5 ftl 

day and raising the horizontal hydraulic conductivity 

to 2.0 ft/day. Head changes from the uniform run were 

-4 to + 10 ft, with an average head misfit of 1.4 ft and 

an rms misfit of 10 ft. The sign of the head difference 

between DH4C and DH4D changed to disagreement 

with observations. 

The introduction of anisotropy produces the largest head changes at piezometers DH4A,B,C, and D, 

which did not exist when the MS model was calibrated. With the present more complete data set, 

assuming the entire debris dam to be anisotropic does 

not improve the model's fit to the data. It will be 

shown below, however, that significant vertical 

anisotropy in localized areas does help the model 

match the observations. 

Decrease of Hydraulic Conductivity with Depth 

Compaction of the debris avalanche material 

under its own weight might be expected to cause 

hydraulic conductivity to decrease with depth. This 

feature cannot be included by varying the conductivity 

from layer to layer because the layers are not at uniform depth beneath the surface. A variation with depth 

of the form 

hc(z) = hc(O)exp(-z/z0) (8) 

was chosen, where z is the depth of the node beneath 

the surface and zo is the depth where the hydraulic 

conductivity is reduced to l!e times its surface value, 

where e = 2.718. The average hydraulic conductivity 

of the debris dam is well-determined for the uniform 

model, so including a decrease with depth requires 

assumption of a higher conductivity near the surface. 

After some experimentation, it was found that setting 

zo to 350ft while raising both the vertical and horizontal conductivities to 2.0 ft/day at the surface maintained an acceptable average misfit of -0.3 ft, but 

raised the rms misfit to 9.0 ft. Simulated heads both 

rose and fell, with the largest change being +5 ft at 

DH5A, B. There was little change in the simulated 

head differences at piezometer pairs, but the total seep 

discharge decreased from 120 percent to 97 percent of 

48 

the observed value, chiefly because simulated seepage from seeps 7 and 8 dropped. The improvement in 

seep discharge, however, was not judged sufficient 

reason to incorporate this feature into the model, 

because, as will be shown below, adjusting the seep 

conductances can achieve as good a fit to the observations without adversely affecting the fit to the heads. 

Evapotranspiration Parameters 

Because the evapotranspiration parameters are 

unmeasured, it is important to evaluate how the 

model behaves over a range of plausible values. 

Lowering the maximum evapotranspiration rate 

for the bare soil areas of the debris dam from 22.5 in/ 

year (0.0051 ft/day) to 15 in/year (0.0034 ft/day) 

raises the simulated head at most of the observation 

points, with the maximum changes being 0.5 to 0.7 ft 

at DH4A,B. These values gave an rms misfit of7.3 ft; 

total seep discharge increased by 10 percent. 

Raising the evapotranspiration rate to 35 in/year 

everywhere on the debris dam, and deepening the 

extinction depth to 7.5 ft, lowers heads, with the maximum changes being -0.9 to -1.2 ft at DH4A,B,C and 

D. All other head changes are -0.2 ft or smaller. This 

simulation has an rms misfit of 7.0 ft, slightly better 

than the uniform model. These evapotranspiration 

parameters, however, are appropriate for an area 

much more heavily vegetated than the debris dam, so 

this marginally better fit to the observations was not 

judged sufficient reason to use them in the model. 

These experiments show that varying the evapotranspiration parameters throughout the range of 

plausible values affects simulated heads at the observation points by at most 1 ft, which is small compared 

with the precision to which the model can be matched 

to the observations. The model is relatively insensitive to the choice of evapotranspiration parameters. 

Variation of Recharge with Surface Slope 

It seems plausible that the percentage of precipitation entering the ground-water system might 

decrease as the slope of the cell's surface increases. 

To test the effect of such an assumption, the recharge 

assigned to each non-drain cell was multiplied by 

cos28, where e is the angle the cell surface makes 

with the horizontal. This run was otherwise the same 

as the uniform model. This modification caused 

some cells to receive as little as 62 percent of the total 

precipitation falling on them as infiltration, but the 
total recharge was still 97 percent of its value prior to 

introducing this change. Reducing recharge in this 

manner lowered all of the simulated heads, with the 

greatest change being -0.7 ft at piezometer 13. There 

was no change in the rms head misfit. Total seep discharge decreased by 12 percent. Overall, reducing 

recharge on the surface slopes changed the simulated 

heads by amounts small relative to their disagreement 

with the observations, so this feature was not incorporated into the model. 

Nonuniform Calibrated Model 

None of the tested modifications resulted in a 

model that fit the data appreciably better than the uniform model. Moreover, the experiments show that 

plausible spatial variations in recharge distribution or 

evapotranspiration parameters do not change the 

model-calculated heads by amounts large enough to 

bring them into agreement with the observations. 

Permitting flow through the material beneath the 1980 

deposits is also ineffective at matching the simulated 

and observed heads and discharges. 

In order to obtain a good fit between the model 

and the observations, the hydraulic conductivity distribution was made nonuniform. Insofar as possible, this 

was done by varying conductivity over large areas in 

order to improve the fit at several points simultaneously. The final calibration was achieved, however, 

by changing the model in the immediate vicinity of 

the individual observation points. This technique is 

unappealing because it is unreasonable to assume that 

the observation points preferentially sample the volumes of the debris dam with distinctive properties. On 

the other hand, the observation points are the locations 

where there is the most information to constrain the 

hydraulic property distribution. Where large changes 

are required in order to fit an individual observation 

point, it should be recognized that equally large 

hydraulic property variations may exist in other parts 

of the debris dam that are unsampled by seeps or piezometers. 

Large-scale Hydraulic Conductivity Variations 

The first changes to the hydraulic conductivity 

distribution were small changes over large areas. The 

model was divided into "halves" along the line X-X' 

shown in figure 20, which follows the southeastern 

edge of South Fork Castle Creek's pre-eruption channel. All simulated heads more than ten ft too high are 

49 

northwest of X-X', while the one location where simulated heads were more than ten ft too low is southeast of X-X'. Increasing the horizontal and vertical 

hydraulic conductivities by a factor of 1.45 northwest 

of X-X' and decreasing them by a factor of 0.7 to the 

southeast both raised and lowered simulated heads, 

with the largest change being +6ft at P3A,B. The rms 

misfit dropped to 6.3 ft, total seep discharge remained 

about the same, and there was no overall improvement 

in the fit to the head differences at piezometer pairs. 

As a further modification, the debris dam was 

divided parallel to its crest along the line Y-Y' shown 

in figure 20. Both the vertical and horizontal conductivities were multiplied by 1.1 northeast of this line, 

and by 0.9 southwest of it. The resulting head distribution has an even lower rms misfit of 5.6 ft. There is 

little change to the simulated seep discharge or vertical head differences between collocated piezometers. 

At this stage, the simulated heads are within 5 ft of the 

observations at 13 of the 22 locations where there are 

data; only at DH4B and DH4D are simulated and 

observed heads different by more than 10 ft. 

The existence of a conductivity contrast across YY' may reflect differences in the way the debris avalanche came to rest. As it was being deposited, the 

part of the debris dam northeast of Y-Y' appears to 

have kept moving longer than the southwestern part, 

which became wedged between the bedrock ridges 

(U.S. Army Corps of Engineers, 1993). On the other 

hand, the contrast that improves the fit to the data is 

not in the direction that would be expected, given that 

samples from the upstream edge of the debris dam are 

in general coarser than those from the downstream 

edge. 

Although the line X-X' is approximately the 

southeastern limit of South Fork Castle Creek's preeruption drainage, and the debris dam is thicker northwest of this line than southeast of it, there is no 

mapped geologic or textural contrast to explain why a 

hydraulic conductivity contrast across this line helps 

the model to fit the data. 

The Area Around Piezometers DH4A,B,C,D 

With the incorporation of large-scale hydraulic 

conductivity variations, the largest discrepancy 

remaining in the model is its calculation of head 14 ft 

too high at DH4D and 10ft too high at DH4B. Moreover, an upward flow gradient is observed between the 

two deepest piezometers, DH4A and DH4B, as well 

as between the two shallowest piezometers, DH4C 
4 1 

4 0 

3 9 

3 8 

3 7 

3 6 

3 5 

3 4 

3 3 

3 2 

3 1 y 

3 

0 " 

2 9 

2 8 

27 

2 6 

2 5 

24 

2 3 

122° 

16 • 45 ;·550ooo 

I \ 

~ ~ 

r":: "-

~ 

f\ 

I 

~\ 

\\ 

!"' 

1"-

~E (~ 

1\\ 

1551000 

I 

EXPLANATION 

D Bedrock 

122° 

16'15'{552000 

I' 

XX' Line of hydraulic 

conductivity contrast 

0 Piezometer 

- 345000 

- 344000 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000 FEET 

0 100 200 300 METERS 

Figure 20. Model grid showing the lines dividing the model into higher as opposed to lower conductivity "quadrants". Eastings 

and northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the right. 

50 
and DH4D, but the model calculates downward flow 

gradients for all pairs of piezometers at this site. All 

the modifications tested to the uniform model change 

heads by about the same amount at all four DH4 piezometers, so that they cannot reproduce the upward 

gradient. The upward gradient at this site is an important feature of the natural ground-water flow system, 

so local hydraulic conductivity variations were introduced to reproduce it as well as possible. Figures 21 

and 22 show the horizontal and vertical hydraulic conductivity distributions in the calibrated model. 

The first change was to eliminate recharge near the 

DH4 piezometers because the upward flow gradient, 

with water level above the surface in the shallowest 

piezometer, would prevent infiltration. This change 

was made over 44 grid squares, reducing total 

recharge by 0.1 ft3 Is (9 percent) for the 1992 water 

year. Eliminating recharge in the vicinity of 

DH4A,B,C,D lowers heads there by 3.6 ft at DH4D to 

3.9 ft at DH4A, reducing the overall rms misfit to 5.5 

ft. The total seep discharge decreases to 95 percent of 

the observations. 

To simulate the observed confining layer between 

the depths of the two deepest piezometers, vertical 

conductivity was lowered by a factor of 200 between 

layers 4 and 5. This change alone does not reproduce 

the increasing hydraulic head with depth from DH4B 

to DH4A; it is also necessary to provide a flow path 

for higher pressure water to reach DH4A, which is in 

layer 5. Consequently, upstream ofDH4, vertical conductivity from layer 4 to layer 5 was increased by a 

factor of 10, and horizontal conductivity by a factor of 

5, relative to their respective values for the uniform 

model. This modification increases heads at all 4 levels of DH4, but the increase is only 2ft in the shallower piezometers, increasing to 4ft in DH4B and 6ft 

in DH4A. 

Changes to the horizontal hydraulic conductivity 

in the shallower layers near DH4 were imposed to 

lower simulated head in the shallower piezometers. In 

particular, hydraulic conductivity was decreased by a 

factor of 200 in layer 3 and increased by a factor of 

200 in layer 4. These changes lower heads by 7 ft in 

the upper 3 piezometers, but only by 2 ft in DH4A. 

The combination leaves head in DH4A 4ft above head 

in DH4B, bringing the sign of the hydraulic head gradient into agreement with observation. 

With the hydraulic conductivity and recharge distributions just described, simulated heads at 16 of the 

22 observation points, including all4 DH4 piezometers, are within 5 ft of the observed values for the 1992 

51 

water year. Overall, the model has an rms misfit of 

4.8 ft, and the simulated total seep discharge is 96 

percent of the observed value. Despite the complexity of the hydraulic conductivity variations imposed 

near DH4, the fit to the data there is not perfect, in 

that it underestimates the increases in head with depth 

from DH4D to DH4C and from DH4B to DH4A. 

Crest Conductance 

Changes to the hydraulic conductivity distribution were also required in the vicinity of piezometers 

DH3 and P3A,B. With the conductivity distribution 

described to this point, simulated head agrees perfectly with the observation at P3B (in layer 2), but is 

6ft too low at P3A (in layer 1) and 7ft too high in 

DH3 (also in layer 3, 200ft southwest of P3A,B). 

In order to match the observed water level at 

P3A, vertical conductivity was lowered by a factor of 

500 between layers 1 and 2 near that site, and horizontal hydraulic conductivity was lowered by a factor 

of 2.5 in layer 1. Thus the data seem to require a partial impediment to vertical flow beneath the dam 

crest. 

Simulated head in piezometer DH3 can be 

brought to agreement with data by lowering the vertical conductance between specified-head cells representing the lake and the active cells beneath them by a 

factor of 3 and raising the horizontal hydraulic conductivity of these cells by a factor of 3. Making these 

changes in a small area south of DH3 accounts for 

most of the improvement in the fit to the data, but a 

marginally better overall fit is obtained by extending 

the changes to the entire area under the lake. With 

these modifications, the rms misfit to the head observations is 4.5 ft. 

Other Local Conductivity Changes 

The remaining four locations where the simulated 

heads differ by more than 5 ft from the observed 

heads are at piezometers DH5B and 13, where heads 

are 9 ft too low, and piezometers P4A,B, where heads 

are 8 ft too high. Horizontal hydraulic conductivity 

was raised by a factor of 10 in the nine cells surrounding P4A,B. Vertical hydraulic conductivity was 

lowered by a factor of 25 within a 3-cell radius of 

DH5A,B, and by a factor of20 near 13. These vertical 

conductance changes resulted in a good fit to the data 

at DH5B and 13, but increased the misfit at 12. To 

compensate, within a 1-cell "radius" ofl2, horizontal 
41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

~~-4--+--+--~4--+--~~-4--~~-4~~~ 

r-+-4-~-+~~~~+-4-~-+-+~--~ 

31r-4-~-+~--~+-4--+-4--r-+-4-~-+~ 

30 r-+-4-~-+~~~~+-4-~-+-+~~r-~ 

29r-4--+-4--~4--+-4--~+--+-+~r-+-4--+~ 

28 

27 

26 

25 

24 

23 

17 

15 

14 

13 

~-L~--~_L~L-~-L--~4--+--+-4--4--+-~~ 

1551000 

Model layer 1 

EXPLANATION 

Hydraulic conductivity 

(horizontal), in feet/day 

D 

D 

till 

Inactive in layer 1 

0.1-1.0 

1.0-10.0 

10.0-100.0 

Bedrock 

0 Piezometer 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

46°16' 

345000 

344000 

46° 

15'30" 

Figure 21a. Horizontal hydraulic conductivity distribution for layer 1 of the nonuniform calibrated model. Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the right. 

52 
(/) 

~ 

0 

a: 

41 

40 

39 

38 

37 

36 

27 

26 

25 

24 

23 

4 

2 

1551000 

122° 

16'15 '{552000 

Model layer 2 

EXPLANATION 

Hydraulic conductivity 

(horizontal), in feet/day 

D Inactive in layer 2 

D 0.1-1.0 

D 1.0-10.0 

10.0-100.0 

B Bedrock 

0 Piezometer 

46°16' 

345000 

344000 

343000 

46° 

15'30" 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

Figure 21 b. Horizontal hydraulic conductivity distribution for layer 2 of the nonuniform calibrated modeL Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the right 

53 
(/) 

3: 

0 

a: 

40 

39 

38 

37 

36 

35 

34 

31 

26 

25 

24 

23 

21 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1551000 

Model layer 3 

EXPLANATION 

Hydraulic conductivity 

(horizontal), in feet/day 

D Inactive in layer 3 

D 0.01-0.1 

D 0.1-1.0 

D 1.0-10.0 

10.0-100.0 

Bedrock 

Piezometer 

122° 

16'15 '{552000 

46°16' 

345000 

344000 

343000 

46° 

15'30" 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

Figure 21 c. Horizontal hydraulic conductivity distribution for layer 3 of the nonuniform calibrated model. Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the right. 

54 
en 

$: 

0 

a: 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

9 

7 

4 

3 

2 

122° 

1551000 16'15'1.552000 

Model layer 4 

EXPLANATION 

Hydraulic conductivity 

(horizontal), in feet/day 

D Inactive in layer 4 

D 0.1-1.0 

~ 1.0-10.0 

10.0-100.0 

~ > 100.0 

D / Bedrock 

0 Piezometer 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300METERS 

46°16' 

345000 

344000 

Figure 21d. Horizontal hydraulic conductivity distribution for layer 4 of the nonuniform calibrated model. Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the right. 

55 
122° 

1551000 16'15 ,1,552000 

41 

40 

39 Model layer 5 

38 

37 EXPLANATION 

36 

35 Hydraulic conductivity 

(horizontal), in feet/day 

34 

33 D Inactive in layer 5 

32 1.0-10.0 46°16' 

31 10.0-100.0 

30 D Bedrock 345000 / 

29 0 Piezometer 

28 

27 

26 

25 

24 

23 

en 22 

3: 21 0 

a: 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

0 500 1000FEET 

0 100 200 300 METERS 

Figure 21 e. Horizontal hydraulic conductivity distribution for layer 5 of the nonuniform calibrated model. Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the right. 

56 
41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

(/) 22 

$: 21 0 

a: 20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

122° 

16'45'155oooo 

I \' 

~ ~ 

. 

1/ 

~ -- 0DH6 'D 

0~ l~fll ~ //// ::--,._, 

--- //// 

//////// "'\ //////// ·~a 

//////// 

////////t_t....., 

//////// 

/////////L:L- '1 /////////// 

/////// /~ //////// 

//////// 7 

~///////~ //////// 

//////// 

//////// 

////////; 

////// 

////// 

k////// 

////// 

/////// 

/////// 

/////// 

/////// 

/////// 

/////// -castl4 Lak~ /////// 

/////// 

~/ ///// 1// / / / / / / 

I !/ ~/ ///// 

~ 1'\. 

"\ 

~ 

H5 ~B 

'~i! 1'1:': ~ ~ \:' 

:-: 

:-: 

......... 

122° 

1551000 16 '15 .1.552000 

I F 

Model layers 1 and 2 

EXPLANATION 

Hydraulic conductivity 

(vertical), in feet/day 

0 Inactive in layer 1 or 2 

~ ~ 0.001-0.01 

~ 1:::::1 0.01-0.1 -

\\ D o.1-1.o 

\ I :: I 1.o-1o.o 

~ - 345000 

10.0-100.0 

!) U Bedrock 

~ 0 Piezometer 

1\~ '\~ 

I)J 

(?: 

~"2 I~ E' 

'DH.4ABCD ~ 0. ~ 

~ - E'..f: 

344000 

IT 

~ 

·"- 'II= i 

·>: ''o1 ~ 

'~.c :~~ ::;v \\. 

:-: :~~> ,:;{~t ~;e P4AB ~ 

l;~~l 'P~AE 

343000 

~ 

\ 

~ 

~ 

~ % 

% ~ 

~l :~! 

~ 

~B ~ ~ !'---~ ....... ~I?J _ ~~~· ~ j 

I\ /,'(/ -1 

'/ ~~ 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

Figure 22a. Vertical hydraulic conductivity between layer 1 and layer 2 for the nonuniform calibrated model. Eastings and 

northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the right. 

57 
(/) 

41 

40 

39 

38 

37 

36 

35 

29 

28 

27 

26 

25 

24 

23 

~ 21 

0 

a: 

19 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

1 2 3 4 

122° 

16' 45'1550000 1551000 

122° 

16'15'{552000 

Model layers 2 and 3 

EXPLANATION 

Hydraulic conductivity 

(vertical), in feet/day 

D 

f'":-':-'1 

L:..:.:.:.J 

D 

~ 

~ 

0 

Inactive in layer 2 or 3 

0.01-0.1 

0.1-1.0 

1.0-10.0 

Bedrock 

0 Piezometer 

46°16' 

345000 

344000 

343000 

46° 

15'30" 

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

Figure 22b. Vertical hydraulic conductivity between layer 2 and layer 3 for the nonuniform calibrated model. Eastings and 

northings, according to the Washington State Plane Coordinate System, in feet, are given below and at the right. 

58 
41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

(J) 

$; 

0 

a: 

122° 

16'45'155oooo 1551000 

122° 

16'15'1'552000 

Model layers 3 and 4 

EXPLANATION 

Hydraulic conductivity 

(vertical), in feet/day 

Inactive in layer 3 or 4 

0.01-0.1 

10.0-100.0 

Bedrock 

Piezometer 

46° 16' 

345000 

344000 

343000 

46° 

15'30" 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

Figure 22c. Vertical hydraulic conductivity between layer 3 and layer 4 for the nonuniform calibrated model. Eastings and 

northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the right. 

59 
41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

3: 21 

00

221b 

~ 20 L. 

19 

18 

17 

16';;.1, 

:-:· 

122° 

16 • 45 ;·55oooo 

J :·:~ 

:-: 

:- . . . . .· -:: ::: :-:. .'( 

:.· <· :.: ·:·1·: 

•· 1·:~ 

1·>. :-: :-: 

<· :-:-::-: 

.-: ·:· .·. ::! 

:·· 

1551000 

I 

122° 

16'15 '1552000 

Model layers 4 and 5 

EXPLANATION 

Hydraulic conductivity 

(vertical), in feet/day 

D 

~ 

D 

D 

0 

Inactive in layer 4 or 5 

< 0.001 

0.01-0.1 

0.1-1.0 

1.0-10.0 

10.0-100.0 

Bedrock 

Piezometer 

II 

- 46°16' 

- 345000 

- 344000 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

Figure 22d. Vertical hydraulic conductivity between layer 4 and layer 5 for the nonuniform calibrated model. Eastings and 

northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the right. 

60 
Table 9. Summary of the hydraulic conductivity distribution for the nonuniform calibrated model-of the Castle 

Lake debris dam 

Layer Average Maximum 

(ftlday) (ftlday) 

Horizontal: 1.915 0.200E+02 

Vertical: 1-2 1.362 0.607E+02 

Horizontal: 2 2.512 0.200E+02 

Vertical: 2-3 0.781 0.303E+Ol 

Horizontal: 3 2.410 0.200E+02 

Vertical: 3-4 2.419 0.124E+02 

Horizontal: 4 16.833 0.490E+03 

Vertical: 4-5 0.516 0.247E+02 

Horizontal: 5 3.127 0.120E+02 

All Layers: Average Maximum Lay 

(ft/day) (ft/day) 

Horizontal: 5.254 0.490E+03 4 

Vertical 1.469 0.607E+02 

hydraulic conductivity was raised by a factor of 10 and 

vertical conductivity by a factor of 30. 

Creekbed Conductance 

In the uniform model, the bed of Castle Creek was 

treated as having conductivity equal to that of the 

debris dam as a whole. A better simulation of the 

observed discharges at seeps 1 and 3, however, was 

obtained when creekbed conductance was lowered by 

a factor of 10 for reaches upstream of row 21 and 

raised by a factor of 10 for reaches further downstream. This modification improves the fit to the data 

at other sites as well; the largest change it produces is 

an increase of 5 ft in simulated head at DH1. The 

lower conductivity reaches are those for which the 

creek thalweg elevation as surveyed in 1991 is below 

the elevation read from the USACE 1989 map, suggesting that loose material with relatively high conductance has been eroded from these reaches and 

deposited further downstream. 

Drain Conductances and Elevations 

Drain conductances in the uniform model were 

calculated assuming that each drain occupied the full 

61 

Row Col Minimum Row Col 

(ftlday) 

11 6 0.310E+OO 11 5 

11 7 0.195E-02 4 17 

11 7 0.980E+OO 2 23 

11 8 0.244E-Ol 11 12 

11 8 0.120E-Ol 19 13 

18 14 0.108E-Ol 15 16 

20 14 0.980E+OO 13 13 

17 15 0.597E-04 19 17 

17 15 0.120E+Ol 20 17 

Row Col Minimum Lay Row Col 

(ft/day) 

20 14 0.120E-Ol 3 19 13 

11 7 0.597E-04 4 19 17 

area of the cell containing it and that the conductivity 

of the material between the center of the cell and the 

drain vent equaled the conductivity of the cell. Drain 

conductances calculated in this manner ranged from 

274 to 374 ft2

/day. As a final step in model calibration, drain conductances and elevations were adjusted 

to provide a better fit to the discharges observed at the 

individual seeps. Adjustments were limited to those 

required to fit the individual seep discharges within 

0.01 ft3/s. 

For all but seep 3, satisfactory simulation of seep 

discharge could be achieved by lowering the drain 

conductances and changing the elevations by 1 ft. 

Elevations of the drain cells composing seeps 1 and 8 

were raised by 1 ft while those composing seeps 5, 

11, and 12 were lowered by 1 ft. At seeps 6 and 7, 

simulated discharges were too high, but raising elevations had no effect, so calibration was carried out by 

lowering the seep conductances. The largest reduction in drain cell conductance was by a factor of 20 

in seep 7. Reductions in drain cell conductances are 

plausible because most of the drains do not cover an 

area as large as a 100 by 100 ft model grid cell. 

Compared with the other seeps, greater changes 

were required to simulate the discharge at seep 3. 
Seep 3 emerges from a single vent about three feet 

across situated at the top of a mound of material that 

has presumably been eroded from within the debris 

dam. The vent is within the alluvial plain of Castle 

Creek, which is essentially flat there. These conditions suggest not only that there is some resistance to 

flow into Castle Creek from the vicinity of seep 3, but 

also that the conduit feeding seep 3 is highly conductive relative to its immediate vicinity. Elevation of 

seep 3 was lowered by 2 ft and conductance was raised 

by a factor of 8. In addition, vertical conductivity was 

divided by 50 within a 4-cell radius of seep 3, and horizontal conductivity was multiplied by 1.5. 

Relative to the final nonuniform model, omitting 

the adjustments to drain elevation and conductance 

and to conductivity near seep 3 increases the simulated seep discharge by 20 percent, significantly overestimates discharge at seeps 1, 6, and 7, and 

significantly underestimates discharge at seep 3. Simulated heads at most measurement points are changed 

by 1 ft or less, but heads drop by 9 ft at DH5A, B, by 4 

ft at P4B, and by 3 ft at DH4A, B ,C, D. 

Fit to Observations 

The arrowheads in figures 17 A and 17B show how 

the nonuniform calibrated model fits the observed 

heads and discharges and table 7 summarizes how the 

model fits the data. The seep discharge is close to the 

observed value for the 1992 water year, but is underestimated for the 1991 water year. The water level in the 

highest active layer is shown in figure 23. 

Hydraulic Conductivity Distribution 

The horizontal and vertical hydraulic conductivity 

distributions for the nonuniform calibrated model are 

shown in figures 21 and 22 and summarized in table 9. 

With respect to the uniform model, the average vertical hydraulic conductivity is about the same, while the 

average horizontal hydraulic conductivity is about 3.4 

times larger. Horizontal hydraulic conductivities range 

from 0.012 to 490ft/day and vertical hydraulic conductivities from 0.00006 to 61ft/day. Most of these 

conductivities are within the range typical of silty sand 

and clean sand (0.003 to 3,000 ft/day; Freeze and 

Cherry, 1979, p. 29), but vertical conductivities below 

this range seem to be required near seep 3. The locations where the highest hydraulic conductivity values 

are required are not near DH2 or DH3, where high 

conductivities were measured. This suggests that the 

62 

high measured values are due to disturbance of the 

soil during drilling. 

For the MS model, the average horizontal 

hydraulic conductivity was 2.7 ft/day and vertical 

hydraulic conductivity was approximately 10 times 

smaller over most of the debris dam. There were also 

variations in hydraulic properties in the MS model, 

but they were no more than a factor of 10 in either 

direction. There are three reasons why calibration of 

the present model requires larger variations in 

hydraulic properties. First, the model attempts to fit 

more piezometer water levels. In particular, the largest variations are required to fit the data at 

DH4ABCD, which did not exist when the MS model 

was developed, and near P3A,B and DH3. Second, 

the total amounts of recharge entering from the bedrock ridge or falling on the debris dam were not 

adjusted during calibration of this model; the only 

change in a uniform recharge distribution is near site 

DH4. Third, this model attempts to fit individual 

seep discharges in addition to the total seep discharge, 

and a closer fit to the total seep discharge was sought. 

Water Budget 

Figure 19 summarizes the water budgets for the 

uniform and nonuniform calibrated models. The total 

water budget is smaller for the calibrated model 

because recharge is not permitted in a 440,000 ft2 

area surrounding piezometers DH4. The relative proportions among the different water sources are close 

to those for the uniform model, however. 

The water budgets for the uniform and nonuniform calibrated models differ from the budget of the 

MS model. The MS model period was the 1984 water 

year, which received 72.1 in. of precipitation; thus the 

total recharge was 82 percent of that in the 1992 

water year. In the MS model, recharge from precipitation plus inflow from the western boundary was 

adjusted during model calibration; the final amount of 

recharge entering approximately balanced the simulated seep discharge of 1.0 ft3 Is. This simulated seep 

discharge was approximately equal to their calibration goal of 0.7 ft3

/s, the highest value measured in 

the 1984 water year. In contrast, the calibration goal 

for this study was the average seep discharge of 0.2 

ft3 /s for the 1992 water year. The seep discharge figure used to calibrate the MS model is higher than that 

used here not only because it is a maximum for the 

year but also because it includes discharge from seeps 

9 and 10 and because maximum discharge from seep 
41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

27 

26 

25 

24 

23 

(/) 22 

$: 21 0 

a: 20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

122° 

1551000 16'15 "1552000 

EXPLANATION 

0 Debris avalanche deposit 

0 Bedrock 

k,,l Alluvium 

- 2460 - Hydraulic head contour 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000 FEET 

0 100 200 300 METERS 

CONTOUR INTERVAL 10 FEET 

344000 

343000 

460 

15'30" 

Figure 23. Hydraulic head in the highest active layer as simulated by the nonuniform calibrated model for the 1992 water 

year. Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are given above and at 

the right. 

63 
3 was 0.1 ft3 Is greater during the 1984 water year than 

at any time since measured. The MS model predicts no 

flow from Castle Lake into the debris dam, possibly 

because that model does not extend quite as far south 

as the model developed here. The main difference in 

the two water budgets is in the relative outflows to 

Castle Creek as opposed to the seeps. In the MS 

model, the seeps account for 81 percent of the outflow, 

whereas in the models presented here, the seep discharge is at most 17 percent of the outflow. 

Limitations on the Use of the Numerical 

Models 

In order to fit the model to the data, adjustments to 

the conductivities were made in the vicinity of measurement points. This procedure demonstrated that 

large conductivity variations in the model are required 

to fit the actual data. The spacing of piezometers, 

however, is not dense enough to constrain conductivity 

everywhere in the debris dam. Additional zones with 

large conductivity contrasts could exist in areas 

unsampled by piezometers. 

With the available data, it is not possible to prove 

or disprove that flow takes place beneath the 1980 

debris avalanche deposit. Because the few samples 

that have been taken of this material show no marked 

contrast in hydraulic properties at the base of the 1980 

deposits, it is likely that such flow does take place. 

But including such material in the model does not 

improve the fit to the observations. The proper way to 

add material beneath the debris dam would be to 

include more of the southern portion of Castle Lake 

and to refine the boundary condition beneath Castle 

Creek. Subsurface information, however, does not 

permit this to be done with certainty, and it appears 

that water levels in the existing piezometers do not 

give much information about heads in this material. 

Redefinition of the boundary condition beneath Castle 

Creek could affect model-calculated heads in the toe 

region of the debris dam. 

The model does not perfectly reproduce the vertical head distribution near piezometer DH4. This is one 

of the areas known to have a low factor of safety 

against heave; field observations must be given more 

weight than the model simulations. 

The hydraulic conductivity distribution arrived at 

is nonunique. Moreover, the model could also be calibrated with different evapotranspiration parameters or 

64 

amounts of recharge entering from the western 

boundary. 

The nonuniform model does a reasonably good 

job of reproducing the historical data set for the 1991 

and 1992 water years. Further validation of the 

model, however, can only be obtained by comparing 

its predictions with future data sets not considered in 

the calibration procedure. 

STABILITY OF THE DEBRIS DAM 

AGAINST HEAVE 

Factors of Safety 

Hydraulic heads and gradients computed by the 

ground-water model can be used to calculate factors 

of safety against heave in the debris dam. Factors of 

safety were calculated for the 1992 water year. Both 

of the two approaches discussed earlier were used. 

For the "overburden" method of calculating factors of safety, model cells were identified in which the 

hydraulic head in the shallowest active layer was 

higher than the land surface, and in which higher 

head at a lower cell showed that upward flow was 

occurring. The ratio of the buoyant overburden 

weight to the excess fluid pressure at the center of the 

cell was calculated. The excess fluid pressure is the 

pressure corresponding to the amount by which the 

hydraulic head exceeds the land surface elevation. 

For cells beneath the lake, the excess head was based 

on the lake elevation, rather than the land surface elevation, but the presence of the lake does not increase 

the buoyant weight of the overburden. 

The "gradient" method is based on differences in 

fluid pressures at different depths. The simulated 

hydraulic gradient is the difference in hydraulic head 

between the center of a cell and the center of the cell 

directly beneath it, divided by the difference in elevation of these two points. The factor of safety is the 

ratio by which the critical gradient exceeds the calculated gradient. Here, a critical gradient of 1 is 

assumed; critical gradients in place are believed to 

range from 0.9 to 1.2. These factors of safety are 

meaningful only where the hydraulic gradient favors 

upward flow. They can be calculated for model layers beneath the surface; low factors of safety in subsurface layers suggest the possibility of internal 

erosion, but erosion in the form of heave requires the 

factor of safety to be low in the uppermost active 

model layers. 
All factor of safety calculations were made for the 

1992 water year. Figures 24a-24c show the factors of 

safety for the nonuniform calibrated model. Only factors of safety less than 10 are shown. 

Figure 24a shows the factors of safety using the 

overburden method. Low factors of safety exist 

beneath Castle Creek near the location of active 

slumping during a January, 1990 storm as well as in 

one reach near seep 3. Low factors of safety also exist 

just north of the DH4 piezometers. 

Using the gradient method (fig. 24b), the lowest 

factor of safety in the uppermost active layer is 3.4, 

beneath the bed of Castle Creek near site DH4. Low 

safety factors also exist beneath Castle Creek in rows 

13 and 14, near the slumps that formed in 1990. 

Below the top active layer, the lowest factor of safety 

is 2.1 near site DH4. Although this low factor of safety 

is not in the top active layer of the model, factors of 

safety only slightly greater than 2 have been observed 

near the surface above this point, between piezometers 

DH4C and DH4D, although the model fails to reproduce them. Factors of safety almost as low are calculated along much of the creekbed north of DH4, but 

they are distant from the material that impounds Castle 

Lake. 

It is interesting to compare the factors of safety 

from the calibrated model with those from the uniform 

model (figs. 25a-25b). Using the overburden method, 

only 1 cell beneath Castle Creek has a factor of safety 

less than 10. Using the gradient method, low factors 

of safety for the uniform model exist near the 1990 

slumping, but 7. 7 is the smallest value, compared to 

5.3 for the calibrated model in the same area. There 

are no factors of safety less than 10 in layers below the 

top active layer. The uniform model does not produce 

upward flow near site DH4, so it would suggest infinite factors of safety in that area. This comparison 

shows that most of the low factors of safety in the Castle Lake debris dam result from its nonuniform composition. 

Effect of Lowering Castle lake 

The level of Castle Lake, which is controlled by 

the spillway elevation, has some effect on groundwater levels. A numerical experiment was performed 

to test the potential effect of lowering Castle Lake 40 

ft on the factors of safety. 

The model was modified by reducing the area of 

the lake to include only those cells whose top eleva65 

tions were lower than 2,540 ft and lowering the exit 

channel linearly over its first 1,400 feet. Reducing 

the lake area "exposed" cells in the lakebed in layer 2. 

Because layer 2 behaves as a confined layer when the 

head within it exceeds its surface elevation, drains 

were placed in the newly exposed lakebed cells, with 

elevations equal to the ground surface elevation; 17 

of these drains turned out to be active. An active 

seepage face can absorb no recharge, so recharge was 

then set to zero on these cells, which had a negligible 

effect on the calculated heads, but did modify the 

water budget. The final water budget is shown in figure 19. The increased recharge relative to the calibrated model is infiltrating to the newly exposed 

lakebed. The increased seepage is due to seeps in the 

exposed lakebed, which discharge 0.16 ft3/s, more 

than half the total seep discharge from the debris dam 

with the lake at its present level. 44 percent of the 

additional seep discharge is from the cell in row 7, 

column 6. 

The head in the highest active layer is shown in 

figure 26. The highest water levels in the debris dam 

crest are 15 feet lower than calculated by the nonuniform calibrated model. The head decrease is smaller 

to the north, and is only 3 feet at the DH4 piezometer 

site. 

Factors of safety calculated with the lower lake 

level are shown in figure 27. Almost all factors of 

safety are higher by at least 0.1, when compared with 

the nonuniform calibrated model. The overburden 

method yields larger increases in the area near piezometer DH4 (fig. 27a). For the gradient method, factors of safety in the top active layer increase by 0.5 to 

0.8 under Castle Creek near the 1990 slump (fig. 27b) 

but safety factors as low as 2.2 still remain near DH4 

(fig. 27c). Figure 27b shows that the factor of safety 

in the exposed lakebed cell with the greatest seep discharge is 6.6. Thus lowering the lake raises the possibility that the southern dam face could be destabilized 

by seepage erosion. 

Effect of Artificially Draining the Dam Crest 

Because recharge entering the debris dam at high 

elevations on the dam crest elevates heads, it is plausible that factors of safety might increase if this 

recharge could be diverted before it entered the 

ground-water system. Diversion might be accomplished with drain pipes in the debris dam crest running back into the debris dam. All of the trial drains 
25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

122° 

16'45'1550000 

Overburden Method 

122° 

16'15"1552000 

EXPLANATION 

D Debris avalanche 

deposit 

D Bedrock 

4.0 Safety factors < 10 

~1--+--~4--+~~4-~~--+-~-4--~4--+--~4-~~--+-~~ 

343000 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000 FEET 

~~~~~--L--,-------. 

0 1 00 200 300 METERS 

Figure 24a. Factors of safety against heave overburden method calculated using the nonuniform calibrated model for the 

1992 water year. The factors of safety assume a critical gradient of 1.0 and only factors of safety less than 10 are shown. 

Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the 

right. 

66 
25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

CJ) 14 

$: 13 

0 

a: 12 

11 

10 

9 

8 

122° 

16'45"1550000 

Gradient Method 

Top Active Layer 

1551000 

122° 

16'15"1552000 

EXPLANATION 

D Debris avalanche 

deposit 

l:J Bedrock 

4.0 Safety factors < 10 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000 FEET 

0 100 200 300 METERS 

Figure 24b. Factors of safety against heave in the top active layer, calculated using the gradient method and the nonuniform 

calibrated model for the 1992 water year. The factors of safety assume a critical gradient of 1.0 and only factors of safety 

less than 10 are shown. Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are 

given above and at the right. 

67 
25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

(/) 14 

s: 13 0 

a: 12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

122° 

16 '45 "1550000 

Gradient Method 

Lower Layers 

1551000 

122° 

16'15"1552000 

EXPLANATION 

D Debris avalanche 

deposit 

D Bedrock 

4.0 Safety factors < 10 

344000 

46° 

15'45" 

343000 

46° 

15'30" 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

Figure 24c. Factors of safety against heave below the top active layer, calculated using the gradient method and the nonuniform calibrated model for the 1992 water year. The factors of safety assume a critical gradient of 1.0 and only factors of safety 

less than 10 are shown. Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are 

given above and at the right. 

68 
25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

(J) 14 

~ 13 0 

a: 12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

122° 

16'45"1550000 

Overburden Method 

1551000 

122° 

16'15"1552000 

EXPLANATION 

~ 

Debris avalanche 

deposit 

LL._.d Bedrock 

I 

4.0 Safety factors < 10 

344000 

46° 

15'45" 

343000 

46° 

15'30" 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

Figure 25a. Factors of safety calculated using the overburden method and the uniform model for the 1992 water year. The 

factors of safety assume a critical gradient of 1.0 and only factors of safety less than 1 0 are shown. Eastings and northings, 

according to the Washington State Plane Coordinate System, in feet, are given above and at the right. 

69 
25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

en 14 

$: 13 

0 

a: 12 

11 

10 

9 

8 

122° 

16'45"1550000 1551000 

122° 

16'15"1552000 

Gradient Method 

Top Active Layer 

EXPLANATION 

D Debris avalanche 

deposit 

~ 

L...:..J Bedrock 

4.0 Safety factors < 10 

~~~--~1--+--~1-~-4--+-~-+--~1--+-4~+-~-+--+-~~~· 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

344000 

46° 

15'45" 

343000 

46° 

15'30" 

Figure 25b. Factors of safety in the top active layer, calculated using the gradient method and the uniform model for the 

1992 water year. The factors of safety assume a critical gradient of 1.0 and only factors of safety less than 10 are shown. 

Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the 

right. 

70 
41 

40 

39 

38 

37 

36 

35 

34 

33 

31 

28 

27 

26 

25 

24 

23 

(J) 22 

3: 21 

0 

a: 20 

19 

1551000 

D 

[ZJ 

D 

122° 

EXPLANATION 

Debris avalanche deposit 

Bedrock 

Alluvium 

-2560- Hydraulic head contour 

~+-*-~~-+--~~-~~~~~~ s 

~L-L-~~~~-4~-+-+~~~~R\ 

Active seep in present 

lake bed 

Constant head cell 

18 ~--.-4--*-+-.--.-+-~~~~~~-=~~ 

17~~i-~~~~~r+~~~\r-t~~==~~+-9==F=t~~<< 16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

fL-<"-l.C'>-<d--+--1--

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000 FEET 

0 100 200 300 METERS 

CONTOUR INTERVAL 10 FEET 

46° 16' 

345000 

344000 

343000 

46° 

5'30" 

Figure 26. Contour map of the simulated hydraulic head in the highest active layer assuming that Castle Lake has been lowered 40 ft. Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are given above 

and at the right. 

71 
(f) 

25 

24 

23 

14 

3i: 13 

0 

a: 12 

9 

8 

7 

6 

5 

4 

3 

122° 

16 '45 "1550000 1551000 

Overburden Method 

122° 

16 '15 "1552000 

EXPLANATION 

0 Debris avalanche 

deposit 

D Bedrock 

4.0 Safety factors < 1 0 

343000 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

Figure 27a. Factors of safety in the top active layer, calculated using the overburden method when Castle Lake has been 

lowered 40ft. The factors of safety assume a critical gradient of 1.0 and only factors of safety less than 10 are shown. Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the right. 

72 
25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

CJ) 

5: 13 

0 

0: 12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

122° 

16 '45 "1550000 

Gradient Method 

Top Active Layer 

1551000 

122° 

16'15 "1552000 

EXPLANATION 

0 Debris avalanche 

deposit 

U Bedrock 

4.0 Safety factors < 10 

343000 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

Figure 27b. Factors of safety in the top active layer, calculated using the gradient method, when Castle Lake has been lowered 40ft. The factors of safety assume a critical gradient of 1.0 and only factors of safety less than 10 are shown. Eastings 

and northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the right. 

73 
25 

24 

23 

(/) 14 

~ 13 

a: 

12 

11 

10 

9 

8 

122° 

16 '45 "1550000 

Gradient Method 

Lower Layers 

1551000 

122° 

16'15 "1552000 

EXPLANATION 

D Debris avalanche 

deposit 

c=J Bedrock 

4.0 Safety factors< 10 

344000 

46° 

15'45" 

343000 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

Figure 27c. Factors of safety in cells below the top active layer, calculated using the gradient method when Castle Lake has 

been lowered 40 ft. The factors of safety assume a critical gradient of 1.0 and only factors of safety less than 10 are shown. 

Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the 

right. 

74 
en 

41 

40 

39 

38 

37 

36 

35 

34 

33 

28 

27 

26 

25 

24 

23 

3: 21 

0 

a: 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

122° 

1551000 16 '15 "1552000 

r-~~-L-L~~--L-+-~-r-Fi~~ 

D 

EXPLANATION 

Debris avalanche deposit 

Bedrock 

Alluvium 

-2560- Hydraulic head contour 

D Artificial drain 

2 3 4 5 6 7 8 9 1 0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000 FEET 

0 100 200 300 METERS 

CONTOUR INTERVAL 10 FEET 

46°16' 

345000 

344000 

343000 

460 

15'30" 

Figure 28. Simulated hydraulic head in the highest active layer assuming drains have been installed at an elevation of 2,580 

feet in the cells marked "D". Eastings and northings, according to the Washington State Plane Coordinate System, in feet, 

are given above and at the right. 

75 
25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

(/) 14 

$: 13 0 

a: 12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

122° 122° 

16 '45 "1550000 1551000 16 '15 "1552000 

Overburden Method 

EXPLANATION 

D Debris avalanche 

deposit 

D Bedrock 

4.0 Safety factors < 10 

D Constructed drain 

2 3 4 5 6 7 8 9 10 11 12 13 14 1. 5 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

344000 

46° 

15'45" 

343000 

46° 

15'30" 

Figure 29a. Factors of safety calculated using the overburden method when the crest of Castle Lake debris dam is artificially 

drained. The factors of safety assume a critical gradient of 1.0 and only factors of safety less than 10 are shown. Eastings 

and northings, according to the Washington State Plane Coordinate System, in feet, are given above and at the right. 

76 
122° 122° 

16 '45 "1550000 1551000 16 '15 "1552000 

25 

24 

23 

21 

19 

Gradient Method 

Top Active Layer 

EXPLANATION 

D Debris avalanche 

deposit 

U Bedrock 

4.0 Safety factors< 10 

D Constructed drain 

18 

~---.--~4--+~r-~~~--+-~-+--~4--+~~+-~-+--~~~ 

17 D 

16 ~~~--~4--+~~+-~~--+-~-+--~4--+~~+-~-+--~~~~ 

15 

(f) 14 

5: 13 

0 

a: 12 

11 

10 

9 

8 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

344000 

343000 

Figure 29b. Factors of safety in the top active layer, calculated using the gradient method, when the crest of Castle Lake 

debris dam is artificially drained. The factors of safety assume a critical gradient of 1.0 and only factors of safety less than 10 

are shown. Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are given above 

and at the right. 

77 
(/) 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

$: 13 

0 

a: 12 

11 

10 

9 

8 

122° 

16'45"1550000 

Gradient Method 

Lower Layers 

D 

D 

D 

1551000 

D 

D 

122° 

16'15 "1552000 

EXPLANATION 

D Debris avalanche 

deposit 

[J Bedrock 

4.0 Safety factors < 10 

D Constructed drain 344000 

343000 

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 

COLUMNS 

0 500 1000FEET 

0 100 200 300 METERS 

Figure 29c. Factors of safety below the top active layer, calculated using the gradient method, when the crest of Castle Lake 

debris dam is artificially drained. The factors of safety assume a critical gradient of 1.0 and only factors of safety less than 10 

are shown. Eastings and northings, according to the Washington State Plane Coordinate System, in feet, are given above 

and at the right. 

78 
were installed at an elevation of 2,580 ft, and were 

assigned conductances of 300 ft2

/day, approximately 

the conductance of a natural seepage face covering the 

area of an entire model cell. If actual drains were to be 

installed, their conductances would depend on the 

details of their construction. 

The locations of the drains on the crest of the 

debris dam, as well as the resulting head distribution, 

are shown in Figure 28. Heads are about ten feet lower 

in the vicinity of the drains, which remove about 0.06 

ft3/s from the debris dam. The factors of safety are 

shown in figure 29. 

Draining the crest raises almost all factors of 

safety beneath Castle Creek by at least 0.1. The overburden method give increases of up to 4.8 (fig. 29a) 

just downstream of the spillway, while the gradient 

method predicts smaller increases. Draining has little 

effect, however, on the low factors of safety calculated 

using the gradient method in layers below the top 

active layer near site DH4. 

Although artificial draining may have some potential to improve the factors of safety, the amount of 

improvement that could be obtained needs to be studied for particular drain construction methods. A possible problem with draining is that the concentration of 

flow in their vicinity may encourage internal erosion. 

CONCLUSIONS 

The primary goal of this study was to develop a 

numerical simulation of the ground-water flow system 

in the Castle Lake debris dam that could be used to 

evaluate the potential for seepage erosion and to estimate the effects of hypothetical mitigation measures. 

General conclusions of the study are as follows. 

1. A calibrated ground-water model was developed that fits the available hydrologic data. These 

data, however, do not constrain the lower boundary of 

the model. Moreover, large variations in hydraulic 

properties required to fit the data suggest that equally 

large variations could exist in parts of the debris dam 

unsampled by piezometers. Thus the ground-water 

model presented here should not be regarded as 

unique. 

2. The average hydraulic conductivity of the Castle Lake debris dam is of the order of 1 to 5 ft/day. 

These values are substantially smaller than those measured during falling head tests in piezometers in the 

debris dam, but are comparable to the results of slug 

tests in similar material and to values inferred in cali79 

bration of a previous ground-water model. Tests 

showing higher conductivities may have been made 

in material disturbed by drilling. 

3. The simulation does not predict substantially 

different water levels in the observation wells if flow 

is permitted beneath some or all of the material 

beneath the debris dam. Though such flow may take 

place, it is not required in order to fit the data, and 

does not provide a way to explain the observations 

with smaller material property variations. 

4. The results of this simulation show that some 

features of both conceptual models for the groundwater flow system are correct, in that the dam crest 

has low vertical conductivity, and there is flow in 

both directions between the dam and the lake. Within 

the boundaries used in this simulation, net flow is 

from the debris dam into the lake. 

5. While the updated model differs from an earlier model, the implications for debris dam stability 

are similar and are now supported by field data. 

6. The nonuniform calibrated model predicts 

factors of safety between 2 and 3 near piezometers 

DH4A, B, C, and D, and very low factors of safety 

near Castle Creek in an area that slumped during a 

storm in January, 1990. The known low factor of 

safety at site DH4, as obtained from water level 

observations, and the fact of the slumping are consistent with the low model-calculated factors of safety. 

7. Either lowering Castle Lake by 40 ft or installing drains in the debris dam crest increases factors of 

safety slightly, but factors of safety below 5 remain. 

Other drain configurations besides the one assumed 

here can be tested using the numerical model. Lowering the lake level or draining the crest can increase 

factors of safety where they are presently low, but 

may increase the risk of seepage erosion on the south 

face of the dam or on the crest. 

8. When choosing an appropriate factor of safety, 

the accuracy with which the factors of safety are 

known needs to be considered. Near DH4, the introduction of nonuniform properties in order to make the 

model fit the data changes a downward flow area, 

with an infinite factor of safety, to one with a factor of 

safety below 3. Low factors of safety in the Castle 

Lake debris dam are "predicted" by the calibrated 

ground-water model in areas where piezometer data 

and active slumping have already shown that they 

exist. It is prudent to assume that low safety factors 

could exist elsewhere in the debris dam where there 
are no piezometers. Also, because factors of safety 

computed here are for average conditions, factors of 

safety could be lower during some parts of the year. 

REFERENCES CITED 

Dunne, T., and L.B. Leopold, 1978, Water in Environmental 

Planning: San Francisco, W.H. Freeman and Co., 818 

p. 

Embrey, S.S., and Dion, N.P, 1988, Effects of the 1980 

eruption of Mount St. Helens on the limnological characteristics of selected lakes in western Washington: 

U.S. Geological Survey Water-Resources Investigations Report 87-4263, 60 p. 

Freeze, R.A., and J.A. Cherry, 1979, Groundwater: Englewood Cliffs, N.J., Prentice-Hall, 604 p. 

Kienle, C.F., Jr., and H.A. Coombs, Review ofU.S.G.S. and 

U.S.A.C.E. evaluations of Castle Creek debris dam: 

unpublished report, Northwest Geological Services, 

Inc., Portland, Oregon, 1988. 

Kohler, M.A., Nordenson, T.J., and Baker, D.R., 1959, 

Evaporation maps for the United States: U.S. Weather 

Bureau Technical Paper 37. 

McDonald, M.G., and Harbaugh, A.W., 1988, A modular 

three-dimensional finite-difference ground-water flow 

model: Techniques of Water-Resources Investigations 

of the United States Geological Survey, Chapter A1 of 

Book 6, Modeling Techniques, 576 p. 

Meyer, William, Sabol, M.A., Glicken, H. X., and Voight, 

Barry, 1985, The effects of ground water, slope stability, and seismic hazard on the stability of the South 

Fork Castle Creek blockage in the Mount St. Helens 

area, Washington: U.S. Geological Survey Professional Paper 1345, 42 p. 

Meyer, William, and Sabol, Martha, 1989, Hydrology of the 

Castle Lake blockage, Mount St. Helens, Washington: 

U.S. Geological Survey Water-Resources Investigations Report 87-4272, Tacoma, Wash., 25 p. 

Meyer, William, Schuster, R.L., and Sabol, M.A., 1994, 

Potential for seepage erosion of a landslide dam, Journal of Geotechnical Engineering, American Society of 

Civil Engineers v. 120, n.7, p.1211-1229. 

Trescott, P.C., 1975, Documentation of finite-difference 

model for simulation of three-dimensional groundwater flow: U.S. Geological Survey Open-File Report 

75-438, 102 p. 

Uhrich, M.A., 1990, Precipitation data for the Mount St. 

Helens area, Washington-- 1981-1986: U.S. Geological Survey Open-File Report 90-117, Vancouver, 

Washington. 

U.S. Army Corps of Engineers, 1988, Castle Lake: Engineering analysis and alternative evaluation: Portland, 

Ore., 33 p., I 0 figs. 

80 

U.S. Army Corps of Engineers, 1992, Castle Lake: Criteria and performance report: Portland, Ore., 28 p., 9 

figs., 10 pis. 

van Zyl, D.J., 1979, Seepage erosion of geotechnical structures subjected to confined flow -- a probabilistic 

design appraoch: West Lafayette, Indiana, Purdue 

University, Ph.D. dissertation, 244 p.