Prepared in cooperation with the U.S. Army Corps of Engineers

Geophysical Investigations at Hidden Dam, Raymond, 

California—Flow Simulations

By Burke J. Minsley and Scott Ikard

Open-File Report 2010–1153

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2010

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Minsley, B.J., and Ikard, Scott, 2010, Geophysical investigations at Hidden Dam, Raymond, California—Flow 

simulations: U.S. Geological Survey Open-File Report 2010–1153, 64 p.

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Geophysical investigations at Hidden Dam—Flow simulations iii

Contents

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

Background ................................................................................................................................................................... 2

Location and Geology ................................................................................................................................................ 2

Summary of Previous Work ....................................................................................................................................... 3

Hidden Dam Flow Simulations....................................................................................................................................... 3

Description of Model .................................................................................................................................................. 3

Scenario 1: Baseline Model, Profile A........................................................................................................................ 6

Scenario 2: Baseline Model, Profile B........................................................................................................................ 8

Scenario 3: Profile A, No Horizontal Drainage Fill.....................................................................................................10

Scenario 4: Profile A, Baseline Model with Near-Surface Sediment Layer ...............................................................11

Scenario 5: Profile A, Baseline Model with Deep Sediment Channel........................................................................12

Comparison with Selected Observation-Well Data .......................................................................................................13

Conclusions..................................................................................................................................................................14

Acknowledgments ........................................................................................................................................................16

References Cited..........................................................................................................................................................16

Appendix.......................................................................................................................................................................18

Governing Variably Saturated Flow Equations..........................................................................................................18

Determination of Variably Saturated Model Input Parameters ..................................................................................18

Electrokinetic Coupling to Determine the Self-Potential Response...........................................................................19

Figures..........................................................................................................................................................................21
iv Geophysical investigations at Hidden Dam—Flow simulations

Figures

Figure 1. Location (inset) and aerial photo of Hidden Dam ....................................................................................... 2

Figure 2. Inverted sections for DC resistivity (A) line 1 and (B) line 2........................................................................ 4

Figure 3. Geometry of Hidden Dam and downstream topography along profile A in figure 1 .................................... 5

Figure 4. Geometry of Hidden Dam and downstream topography along profile B in figure 1 .................................... 5

Figure 5. Flow model results for the profile A baseline model and reservoir elevation of 485 ft

(flow scenario 1) .......................................................................................................................................................... 21

Figure 6. Flow model results for the profile A baseline model and reservoir elevation of 510 ft 

(flow scenario 1) .......................................................................................................................................................... 22

Figure 7. Flow model results for the profile A baseline model and reservoir elevation of 540 ft 

(flow scenario 1) .......................................................................................................................................................... 23

Figure 8. Seepage (foot per second) through the downstream embankment and ground surface as a 

function of distance for the three different reservoir elevations illustrated in figures 5–7 (flow scenario 1).................. 24

Figure 9. Volumetric flow (gallons per minute) through the downstream embankment (blue) and ground

surface (red) per foot along the length of the dam as a function of reservoir elevation (flow scenario 1) .................... 25

Figure 10. Predicted water levels in observation wells 15 feet (left) and 90 feet (right) from the downstream 

toe for flow scenario 1.................................................................................................................................................. 26

Figure 11. Self-potential (millivolts) values predicted along the downstream embankment and ground 

surface for the three different reservoir elevations illustrated in figures 5–7 for flow scenario 1 .................................. 27

Figure 12. Electrical resistivity (ohm-meters) predicted for flow scenario 1 at a reservoir elevation of 510 feet ...... 28

Figure 13. Flow model results for the profile B baseline model and reservoir elevation of 485 ft 

(flow scenario 2) .......................................................................................................................................................... 29

Figure 14. Flow model results for the profile B baseline model and reservoir elevation of 510 ft 

(flow scenario 2) .......................................................................................................................................................... 30
Geophysical investigations at Hidden Dam—Flow simulations v

Figure 15. Flow model results for the profile B baseline model and reservoir elevation of 540 ft 

(flow scenario 2) .......................................................................................................................................................... 31

Figure 16. Seepage (foot per second) through the downstream embankment and ground surface as a 

function of distance for the three different reservoir elevations illustrated in figures 13–15 (flow scenario 2).............. 32

Figure 17. Volumetric flow (gallons per minute) through the downstream embankment (blue) and ground 

surface (red) per foot along the length of the dam as a function of reservoir elevation for flow scenario 2.................. 33

Figure 18. Predicted water levels in observation wells 15 feet (left) and 300 feet (right) from the downstream 

toe for flow scenario 2.................................................................................................................................................. 34

Figure 19. Self-potential (millivolts) values predicted along the downstream embankment and ground 

surface for the three different reservoir elevations illustrated in figures 13–15 for flow scenario 2 .............................. 35

Figure 20. Flow model results for the profile A model with no horizontal-drainage fill and reservoir 

elevation of 485 ft (flow scenario 3)............................................................................................................................. 36

Figure 21. Flow model results for the profile A model with no horizontal-drainage fill and reservoir 

elevation of 510 ft (flow scenario 3)............................................................................................................................. 37

Figure 22. Flow model results for the profile A model with no horizontal-drainage fill and reservoir 

elevation of 540 ft (flow scenario 3)............................................................................................................................. 38

Figure 23. Seepage (foot per second) through the downstream embankment and ground surface as a 

function of distance for the three different reservoir elevations illustrated in figures 20–22 (flow scenario 3).............. 39

Figure 24. Volumetric flow (gallons per minute) through the downstream embankment (blue) and ground 

surface (red) per foot along the length of the dam as a function of reservoir elevation for flow scenario 3.................. 40

Figure 25. Predicted water levels in observation wells 15 feet (left) and 90 feet (right) from the downstream 

toe for flow scenario 3.................................................................................................................................................. 41

Figure 26. Self-potential (millivolts) values predicted along the downstream embankment and ground 

surface for the three different reservoir elevations illustrated in figures 20–22 for flow scenario 3 .............................. 42
vi Geophysical investigations at Hidden Dam—Flow simulations

Figure 27. Saturated hydraulic-conductivity values for scenario 4 are identical to scenario 1 (figure 3), 

with the addition of a higher conductivity near-surface layer in the downstream portion of the model......................... 43

Figure 28. Flow model results for the profile A baseline model with an additional near-surface sediment 

layer and reservoir elevation of 485 ft (flow scenario 4)............................................................................................... 44

Figure 29. Flow model results for the profile A baseline model with an additional near-surface sediment 

layer and reservoir elevation of 510 ft (flow scenario 4)............................................................................................... 45

Figure 30. Flow model results for the profile A baseline model with an additional near-surface sediment 

layer and reservoir elevation of 540 ft (flow scenario 4)............................................................................................... 46

Figure 31. Seepage (feet per second) through the downstream embankment and ground surface as a 

function of distance for the three different reservoir elevations illustrated in figures 28–30 (flow scenario 4).............. 47

Figure 32. Volumetric flow (gallons per minute) through the downstream embankment (blue) and ground 

surface (red) per foot along the length of the dam as a function of reservoir elevation for flow scenario 4.................. 48

Figure 33. Predicted water levels in observation wells 15 feet (left) and 90 feet (right) from the downstream 

toe for flow scenario 4.................................................................................................................................................. 49

Figure 34. Self-potential (millivolts) values predicted along the downstream embankment and ground 

surface for the three different reservoir elevations illustrated in figures 28–30 for flow scenario 4 .............................. 50

Figure 35. Electrical resistivity (ohm-meters) predicted for flow scenario 4 at a reservoir elevation of 510 feet ...... 51

Figure 36. Saturated hydraulic-conductivity values for scenario 5 are identical to scenario 1 (figure 3), 

with the addition of a higher conductivity channel that extends to several hundred feet depth and connects 

the upstream and downstream portions of the model.................................................................................................. 52

Figure 37. Flow model results for the profile A baseline model with an additional deep sediment channel

and reservoir elevation of 485 ft (flow scenario 5) ....................................................................................................... 53

Figure 38. Flow model results for the profile A baseline model with an additional deep sediment channel 

and reservoir elevation of 510 ft (flow scenario 5) ....................................................................................................... 54
Geophysical investigations at Hidden Dam—Flow simulations vii

Figure 39. Flow model results for the profile A baseline model with an additional deep sediment channel 

layer and reservoir elevation of 540 ft (flow scenario 5)............................................................................................... 55

Figure 40. Seepage (feet per second) through the downstream embankment and ground surface as a 

function of distance for the three different reservoir elevations illustrated in figures 37–39 (flow scenario 5).............. 56

Figure 41. Volumetric flow (gallons per minute) through the downstream embankment (blue) and ground 

surface (red) per foot along the length of the dam as a function of reservoir elevation for flow scenario 5.................. 57

Figure 42. Predicted water levels in observation wells 15 feet (left) and 90 feet (right) from the downstream 

toe for flow scenario 5.................................................................................................................................................. 58

Figure 43. Self-potential (millivolts) values predicted along the downstream embankment and ground 

surface for the three different reservoir elevations illustrated in figures 37–39 for flow scenario 5 .............................. 59

Figure 44. Historical record of reservoir elevation (top) and water levels relative to ground surface 

(negative values are below ground) for observation wells OW-22 and OW-7.............................................................. 60

Figure 45. Detailed view of reservoir elevation and observation-well data for OW-22 and OW-7 

from 2001–2004 .......................................................................................................................................................... 61

Figure 46. Crossplots of reservoir elevation and observation-well water level data for OW-22 (A) 

and OW-7 (B), along with model-predicted results from the various flow scenarios in this study ................................ 62

Figure 47. Gradation curves for primary Hidden Dam model units .......................................................................... 63

Figure 48. Soil-water retention curves for primary Hidden Dam model units........................................................... 64
viii Geophysical investigations at Hidden Dam—Flow simulations

Tables

Table 1. Baseline parameters for each Hidden Dam unit used in the variably saturated flow model ......................... 6

Table 2. Summary of gradation and soil-water retention data for Hidden Dam model units..................................... 19
Geophysical investigations at Hidden Dam—Flow simulations ix

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

acre 4,047 square meter (m2)

acre 0.004047 square kilometer (km2)

square mile (mi2) 2.590 square kilometer (km2) 

Volume

gallon (gal) 0.003785 cubic meter (m3) 

acre-foot (acre-ft) 1,233 cubic meter (m3)

Flow rate

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

cubic foot per day (ft3/d) 0.02832 cubic meter per day (m3/d)

gallon per minute (gal/min) 0.06309 liter per second (L/s)

gallon per day (gal/d) 0.003785 cubic meter per day (m3/d)

Mass

pound, avoirdupois (lb) 0.4536 kilogram (kg) 

Pressure

pound-force per square foot (lb/ft2) 0.04788 kilopascal (kPa) 

Density

pound per cubic foot (lb/ft3) 16.02 kilogram per cubic meter 

(kg/m3)

Acceleration

foot per square second (ft/s2) 0.3048 meter per square second (m/s2)

Hydraulic conductivity

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

Vertical coordinate information is referenced to North American Vertical Datum of 1988 (NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Elevation, as used in this report, refers to distance above the vertical datum.
x Geophysical investigations at Hidden Dam—Flow simulations

Electrical Conductivity and Electrical Resistivity

Multiply By To obtain

Electrical conductivity

siemens per meter (S/m) 1,000 millisiemens per meter (mS/m)

siemens per meter (S/m) 10,000 microsiemens per meter (μS/cm)

Electrical resistivity

ohm-meters (ohm-m) 0.001 kiloohm-meters (kohm-m)

Electrical conductivity σ in siemens per meter (S/m) can be converted to electrical resistivity ρ in ohm-meters (ohm-m) as 

follows: ρ = 1/ σ.

Electrical resistivity ρ in ohm-meters (ohm-m) can be converted to electrical conductivity σ in siemens per meter (S/m) as 

follows: σ = 1/ ρ.
Geophysical Investigations at Hidden Dam, Raymond, 

California—Flow Simulations

By Burke J. Minsley and Scott Ikard

Introduction 

Numerical flow modeling and analysis of 

observation-well data at Hidden Dam are 

carried out to supplement recent geophysical 

field investigations at the site (Minsley and 

others, 2010). This work also is complementary 

to earlier seepage-related studies at Hidden Dam 

documented by Cedergren (1980a, b). Known 

seepage areas on the northwest right abutment 

area of the downstream side of the dam was 

documented by Cedergren (1980a, b). 

Subsequent to the 1980 seepage study, a 

drainage blanket with a sub-drain system was 

installed to mitigate downstream seepage. Flow 

net analysis provided by Cedergren (1980a, b)

suggests that the primary seepage mechanism 

involves flow through the dam foundation due 

to normal reservoir pool elevations, which 

results in upflow that intersects the ground 

surface in several areas on the downstream side 

of the dam. In addition to the reservoir pool 

elevations and downstream surface topography,

flow is also controlled by the existing 

foundation geology as well as the presence or 

absence of a horizontal drain in the downstream 

portion of the dam. 

The current modeling study is aimed at 

quantifying how variability in dam and 

foundation hydrologic properties influences

seepage as a function of reservoir stage. Flow 

modeling is implemented using the COMSOL 

Multiphysics software package, which solves 

the partially saturated flow equations in a twodimensional (2D) cross-section of Hidden Dam 

that also incorporates true downstream 

topography. Use of the COMSOL software 

package provides a more quantitative approach 

than the flow net analysis by Cedergren (1980a, 

b), and allows for rapid evaluation of the 

influence of various parameters such as 

reservoir level, dam structure and geometry, and 

hydrogeologic properties of the dam and 

foundation materials. Historical observationwell data are used to help validate the flow 

simulations by comparing observed and 

predicted water levels for a range of reservoir 

elevations. The flow models are guided by, and 

discussed in the context of, the geophysical 

work (Minsley and others, 2010) where 

appropriate. 
2 Geophysical investigations at Hidden Dam—Flow simulations

Background

Location and Geology

Hidden Dam is located on the Fresno River 

in the Sierra Nevada foothills, approximately 15 

miles northeast of Madera, California (figure 1). 

Detailed information regarding the dam 

construction and local geology and hydrology, 

summarized below, is provided by the U.S. 

Army Corps of Engineers (1977) as well as 

Cedergren (1980a, b). Hidden Dam is a rolled 

earthfill dam constructed between 1972 and 

1975, with a crest length of approximately 

5,700 ft, a maximum height above streambed of 

184 ft, and a crest elevation of 561 ft. At gross 

pool (elevation of 540 ft), the impounded lake 

has a surface area of about 1,570 acres and a 

storage capacity of 90,000 acre-feet. Relief at 

the dam site is approximately 180 ft with 

elevations ranging between about 400 ft at the 

streambed to approximately 580 ft on the right 

and left abutments. This topography is 

characterized by gently rolling, rounded hills 

with scattered rock outcrops.

Figure 1. Location (inset) and aerial photo of Hidden Dam. Colored lines indicate topographic profiles that are used 

in the flow modeling study. Observation wells discussed in this report are labeled.

The area in the vicinity of Hidden Dam is 

underlain by what is generally described as 

granitic and associated metamorphic rocks 

derived from the Sierra Nevada batholith, 

though there is some variability in composition, 

texture, and color (U.S. Army Corps of 

Engineers, 1977). Granitic rocks are overlain 

by residual soil, slope wash, and alluvium, 

ranging in thickness from zero to approximately 

30 ft and varying in composition between sands, 
Geophysical investigations at Hidden Dam—Flow simulations 3

silts, and clays. Beneath the overburden, to 

total depths of up to 60 ft, the granite is 

decomposed such that it is easily crumbled or 

broken. Fresh rock occurs below the 

decomposed granite, though decomposed 

materials are occasionally interspersed up to 

depths of 140 ft. Jointing was observed 

throughout the foundation area during 

excavation, though the profusion of joints and 

the extent to which they are clay-filled varies 

throughout the site.

Summary of Previous Work

Studies carried out by Cedergren (1980a, b)

highlighted the right, or northwest, side of the 

dam as the primary area of seepage concern. 

Part of these studies included several flow net 

calculations based on different characteristic 

sections of the dam that capture variability in 

downstream topography and horizontal drainage 

in the downstream portion of the dam. Initial 

estimates of hydraulic conductivity for the 

foundation and core materials resulted in 

seepage rates that did not match observed 

values, and revised hydraulic conductivity 

values were determined that provided a match 

between observed and predicted seepage 

(Cedergren, 1980a). A second set of flow net 

calculations were calibrated to new observationwell data, and predicted substantially higher 

water levels in several downstream locations for 

gross pool (540 ft) conditions. All of the flow 

net calculations were presented for gross pool 

conditions and did not incorporate any effect of 

the grout curtain located beneath the dam 

foundation.

More recently, geophysical surveys 

conducted in May 2009 at Hidden Dam focused 

on (1) assessing seepage through the use of selfpotential measurements and (2) characterizing 

heterogeneity in the subsurface that might 

influence seepage patterns using direct current 

(DC) resistivity measurements (Minsley and 

others, 2010). The reservoir elevation at the 

time of the self-potential survey was 

approximately 490 ft, resulting in significantly 

less seepage than expected when the reservoir is 

at or near gross pool. The self-potential data 

highlighted several diffuse seepage areas on the 

right side of the dam that were consistent with 

the areas of previously known seepage. 

Additionally, one area of potentially focused 

seepage was identified above the outlet works. 

There was no evidence for significant amounts 

of seepage on the left side of the dam, which is 

also consistent with previous observations from 

the site (Cedergren, 1980a). 

The DC resistivity data showed a resistive 

feature at approximately 0- to 80- ft depths 

along most of the right side of the dam, which 

was interpreted to be relatively unweathered and 

low-porosity granitic bedrock (figure 2). In 

general, this bedrock is expected to have 

relatively low hydraulic conductivity, but it is 

possible that there are localized seepage 

pathways in this unit due to the presence of 

joints. At the surface, lower resistivity values 

were interpreted as a combination of alluvial 

overburden and decomposed, or weathered, 

granitic bedrock that likely have higher 

hydraulic conductivity. One notable feature in 

the resistivity data is the presence of a wide 

(300–400 ft), intermediate-resistivity channel on 

the right side of the dam, which may be a 

significant pathway for increased flow 

underneath the dam. This feature is coincident 

with the broad self-potential anomaly in the 

low-topography area on the right side of the 

dam, which lends further evidence to the fact 

that this is an area of enhanced seepage.

Hidden Dam Flow Simulations

Description of Model

Two-dimensional (2D) numerical models of 

variably saturated flow at Hidden Dam were 

constructed using the COMSOL Multiphysics 

3.5a finite element modeling software. The 

models simulate pressure head and flow 

distributions in the dam and surrounding 

foundation materials by solving the steady-state 
4 Geophysical investigations at Hidden Dam—Flow simulations

Richards equation (Freeze and Cherry, 1979), 

where the van Genuchten (1980)

parameterization is used to describe the 

saturation-dependent hydraulic properties (see 

Appendix). The models are used to assess the 

potential for seepage at the dam for several

scenarios that include variability in the reservoir

Figure 2. Inverted sections for DC resistivity (A) line 1 and (B) line 2 (from Minsley and others, 2010) at 1:1 scale. 

Location E, observed on both lines, is interpreted to be a deep alluvial valley between bedrock highs; locations F 

are highly resistive features that may represent competent granitic highs with complex geometry; and locations G 

illustrate high near-surface resistivity associated with large granite outcrops.

elevation, internal dam structure, and 

foundation structure. The DC resistivity survey 

results (Minsley and others, 2010) are used to 

help inform likely scenarios for subsurface 

hydraulic conductivity variability. 

Additionally, self-potential signals are predicted 

for the various flow models by incorporating 

electrokinetic coupling in COMSOL, as 

described in the Appendix.

The basic model geometry was constructed 

to match the dam design specifications (U.S. 

Army Corps of Engineers, 1977; Cedergren, 

1980a) as closely as possible, and downstream 

topographic profiles were extracted from a 30-ft 

resolution digital elevation model (DEM) of the 

surrounding terrain. The model geometries 

shown in figure 3 and 4 correspond to profiles 

A and B shown in figure 1, where the elevation 

at the downstream toe is approximately 450 and 

470 ft, respectively. Each model includes 

subdomains representing bedrock (BR), the 

central impervious core (IC), the outer shell 

comprising random fill materials (RF), 

transition and outer shell zones comprising

select fill materials (SF), the vertical chimney 

drain comprising drainage fill materials (DF), 

and the impervious grout curtain (GC) beneath 

the dam foundation. 

The model geometries in figure 3 and 4 and 

the hydrologic parameters for each unit 

summarized in table 1 are used as the ‘baseline’ 

models for this study. Saturated hydraulic 

conductivity values were taken from Cedergren 

(1980a), with the exception of the grout curtain, 

which was not incorporated in previous studies. 

The saturated and residual moisture content, as 

well as parameters a (related to the air entry 

pressure head and desorption behavior of the 

soil) and n (related to the pore-size distribution 

of the soil), were derived according to the 
Geophysical investigations at Hidden Dam—Flow simulations 5

procedure discussed in the Appendix from 

information in the foundation report (U.S. Army 

Corps of Engineers, 1977) and Cedergren 

(1980a) for all units except for the bedrock and 

grout curtain, which did not have the necessary 

input data. Default values have been used for 

the hydrologic parameters where no information 

was available. Results from these baseline 

models, as well as several variations on the 

geometry and hydrologic properties, are 

discussed in the following sections. For 

convenience, the figures from all of the 

scenarios have been placed together at the end 

of this report..

Figure 3. Geometry of Hidden Dam and downstream topography along profile A in figure 1. Color scale indicates 

the baseline saturated hydraulic conductivity values used in this study.

Figure 4. Geometry of Hidden Dam and downstream topography along profile B in figure 1. Color scale indicates 

the baseline saturated hydraulic conductivity values used in this study.
6 Geophysical investigations at Hidden Dam—Flow simulations

Table 1. Baseline parameters for each Hidden Dam unit used in the variably saturated flow model.

Saturated 

hydraulic 

conductivity, Ks

(ft/day)

Saturated 

moisture 

content, θs

(volume 

fraction)

Residual 

moisture 

content, θr

(volume 

fraction)

a

(1/ft) n

Water 

density, ρ 

(lb/ft3)

Fluid 

source, Qs

(1/s)

Bedrock (BR) 0.1 0.150 0.050 0.2000 2.000

62.42 0

Impervious 

core (IC) 0.02 0.418 0.210 0.2013 1.9923

Random fill 

(RF) 1.0 0.372 0.015 0.2399 3.9218

Select fill (SF) 2.0 0.375 0.014 0.2453 3.3088

Drainage fill 

(DF) 8,000.0 0.425 0.020 0.7165 3.5952

Grout curtain 

(GC) 0.01 0.05 0.005 0.2000 2.0000

Scenario 1: Baseline Model, Profile A

This first scenario illustrates the difference 

in flow for the baseline model along profile A at 

reservoir elevations between 480 and 540 ft. 

The baseline models have identical material 

properties for the various dam and bedrock units 

(table 1), but differ in downstream topography 

profiles. The elevation at the downstream toe 

on profile A is 450 ft, and there is a lowtopography area approximately 100 ft from the 

toe of the dam, or at about 350 ft downline 

distance on the model. This geometry and 

parameters for this scenario are similar to flow 

net number 2 produced by Cedergren (1980a).

Figure 5–7 show the flow model results for 

profile A with reservoir elevations 485, 510, 

and 540 ft. Increasing saturation and flow 

through the dam are evident as the reservoir 

elevation increases. In each of these figures, the 

length of the white arrows represent relative 

variations in flow velocity in a model, but do 

not indicate absolute differences in flow 

velocity between models. The effectiveness of 

the high-hydraulic-conductivity horizontaldrainage fill on the downstream side of the dam 

is evident in these figures, as the drainage fill 

prevents increased water levels and redirects 

upward flow in the foundation materials out 

toward the toe. Saturation in the hightopography areas downstream of the dam can 

also be seen to increase as the reservoir 

elevation increases. Focused seepage is also 

evident in the low-topography area at 

approximately 350 ft downline distance , and 

becomes more enhanced at higher reservoir 

elevations. This observation of focused seepage 

in the low-topography area is consistent with 

observations of seepage at Hidden Dam 

(Cedergren, 1980a).

Seepage through the downstream 

embankment and ground surface is quantified in 

figure 8, which shows the rate of seepage (ft/s) 

along the surface model boundary as a function 

of distance for the models shown in figure 5–7. 

The sharp spike at a distance of approximately 

260 ft corresponds to the outward flow through 

the conductive drainage-fill material at the toe 

of the dam. Discrete zones of seepage are 

evident in the low-topography areas from 300–

400 ft, as well as 900–1,000 ft. This latter 

seepage zone is another low-topography area, 

which can be seen in figure 3. As expected, the 

rate of seepage increases with reservoir 

elevation. In some cases (just past 400 ft, for 

example), seepage only begins at the higher 

reservoir elevations.

Further quantification of seepage for this 

model is shown in figure 9, which shows 

volumetric flow (gal/min) through the 
Geophysical investigations at Hidden Dam—Flow simulations 7

downstream embankment (blue) and ground 

surface (red) per foot along the length of the 

dam as a function of reservoir elevation. The 

volumetric flow is calculated by integrating the 

seepage along both the downstream 

embankment and ground surface boundaries in 

the model. An increasing proportion of flow 

through the dam can be seen with increasing 

reservoir elevation, to a maximum of 

approximately 0.055 gal/min per ft of total 

seepage at gross pool. This is consistent with, 

but slightly greater than, the approximately 0.04 

gal/min per ft for flow net number 2 produced 

by Cedergren (1980a). 

Figure 10 illustrates simulated observationwell data that can be obtained from the flow 

model results. Each panel shows the predicted 

water level in an observation well relative to the 

ground surface, where positive values are higher 

than the ground surface, for different reservoir 

elevations and any well depth between zero and 

50 feet. That is, for a given observation well 

depth and reservoir elevation, the predicted 

water level in the well can be found on one of 

the curves in the figure. The panel on the left is 

for an observation-well approximately 15 ft 

from the downstream toe, which is a typical 

location for a number of observation wells at 

Hidden Dam. The panel on the right is for an 

observation well approximately 90 ft from the 

downstream toe, which corresponds to a lowtopography area of focused seepage.

The model-predicted water levels are 

consistent with observation-well data reported 

in the 1980 seepage study (Cedergren, 1980b). 

Although the observed and model-predicted 

water levels are consistent, some discrepancy 

can be expected due to (1) the fact that the 

ground surface elevations for the flow model do 

not exactly match the observation wells, (2) 

hydrogeologic heterogeneity is not captured in 

the flow model, and (3) the three-dimensional 

nature of flow is not captured in the twodimensional flow model. 

For example, water levels in observation 

wells OW-9 and OW-10, which are located in 

areas of relatively low topography away from 

the downstream toe (figure 1), were 2–5 ft 

above ground surface at the reservoir elevation 

of approximately 484 ft (see table 1 in 

Cedergren, 1980b). Given the well depth of 

approximately 22 ft for these wells, the modelpredicted water level on the right panel in figure 

10 is around 4 ft above the ground surface for 

the curve that corresponds to a reservoir 

elevation of 485 ft. Observed water levels in 

wells OW-7A/B and OW-8A/B, which are close 

to the downstream toe, were approximately 2 ft 

and –2ft with respect to the ground surface, 

respectively. The model-predicted water level 

for wells close to the downstream toe at a 

reservoir elevation of 485 ft is less than 1 ft 

below ground surface (figure 10, left panel), 

which is consistent with the observed values. A 

key benefit of the flow modeling is that water 

levels can be predicted for any reservoir 

elevation or observation-well depth. As can be 

seen in figure 10, the maximum expected water 

level for this model geometry is approximately 

8 ft above the ground surface for a 50-ft-deep 

well located 90 ft from the downstream toe.

Figure 11 shows the self-potential values 

predicted along the ground surface and 

downstream embankment for the flow depicted 

in figure 5–7 (reservoir elevations 485, 510, and 

540 ft). The self-potential values are calculated 

by incorporating electrokinetic coupling into the 

COMSOL model, as described in the Appendix. 

The self-potential values depend on the flow 

velocity, electrical resistivity structure, and 

excess charge in the pore space. The latter two 

values are automatically calculated using 

empirical relationships that are also discussed in 

the Appendix. The self-potential values 

displayed in figure 11 are relative to an arbitrary 

reference location, which was chosen at the 

crest of the dam (distance equals 0 ft).

There are four main components to the selfpotential signal that can be attributed to details 

in the flow model:

1. General trend of increasing potentials with 

distance: This trend represents the expected 
8 Geophysical investigations at Hidden Dam—Flow simulations

response of increasing self-potentials in the 

direction of flow (Morgan and others, 1989; 

Minsley and others, 2010). 

2. Trend of increasing potentials with 

increasing reservoir level: Because the selfpotentials are proportional to flow, as 

described in equation (6) in the Appendix, 

increased flow due to higher reservoir 

elevations leads to increased self-potentials

3. Positive “kicks” superimposed on the 

general trend: Seepage outflow areas are 

expected to result in positive self-potential 

anomalies. This is related to item (1) above, 

as the seepage areas represent localized flow 

terminations and, correspondingly, 

maximum self-potentials at those locations.

4. Sharp trend in self-potentials between 0–100 

ft, increasing with reservoir elevation, and a 

negative center at the highest reservoir

elevation: This trend near the dam crest is 

due to the increasing downward component 

of flow as seepage passing through the 

impervious core is rapidly transported 

through the drainage fill. In contrast with 

the seepage outflow areas that generate a 

positive anomaly, this downward flow-zone 

generates a negative anomaly. Because the 

flow magnitude increases with increasing 

reservoir elevation, the strength of the 

negative self-potential anomaly increases 

proportionally.

The self-potential data collected at Hidden 

Dam (Minsley and others, 2010) clearly indicate 

localized positive anomalies on the order of 30–

70 mV in the low-topography seepage areas, 

which is consistent with the coupled flow 

modeling result. The data do not clearly 

indicate an overall trend of increasing potentials 

in the downstream direction, though this is 

difficult to identify due to the location of survey 

lines, which were primarily in the dam-parallel 

direction. Additionally, there is clearly a threedimensional component to the flow and 

corresponding self-potentials due to variations 

in the ground-surface topography both along 

and perpendicular to the dam strike.

An example of the electrical resistivity 

structure determined from the flow model at a 

reservoir elevation of 510 ft is shown in figure 

12. The resistivity values are calculated using 

equation (7) in the Appendix, where a constant 

water resistivity of 20 ohm-m and cementation 

factor, m, of 1.7 are assumed. The bedrock 

resistivity of 500 ohm-m is similar to the values 

observed during the geophysical surveys at 

Hidden Dam (Minsley and others, 2010), 

though the field data suggest a primarily twolayer model with lower near-surface resistivity, 

which is investigated in modeling scenarios 4 

and 5. Very high resistivities (greater than 

10,000 ohm-m) are observed in the unsaturated 

portions of the dam. The resistivity information 

is an important part of calculating self-potential 

values, but could also be used to guide future 

geophysical investigations at the site.

Scenario 2: Baseline Model, Profile B

This flow scenario follows the same 

modeling procedures as with the previous 

example, but uses the model geometry for 

profile B (figure 4) along with the baseline 

model parameters (table 1). Profile B is located 

closer to the right abutment than profile A 

(figure 1), and therefore has higher ground 

surface elevations (470 ft at the downstream 

toe) than profile A. A second difference with 

this profile is the details of the downstream 

topography. Along profile B, the ground 

surface dips only slightly near the downstream 

toe, then rises again over one of the rounded 

hills found in the right abutment area before 

dropping approximately 20 ft to a lowtopography area that coincides with the area 

covered by the drainage blanket. As with 

scenario 1, the low-topography areas are 

significant factors in the distribution of seepage.

Figure 13–15 show results from the flow 

model at 485-, 510-, and 540-ft-reservoir 

elevations. As with scenario 1, the 

effectiveness of the horizontal drainage fill is 

evident as it redirects upward seepage beneath 
Geophysical investigations at Hidden Dam—Flow simulations 9

the dam toward the downstream toe rather than 

into the dam structure. The main difference 

with this flow scenario is the distribution of 

seepage in low-topography areas; particularly 

between 450–650 ft, but also somewhat near the 

downstream toe. Additionally, the uppermost 

part of the hill between 250–450 ft remains 

unsaturated at the lower reservoir elevations, 

but becomes almost entirely saturated at gross 

pool.

Seepage through the downstream 

embankment and ground surface is quantified in 

figure 16, which shows the rate of seepage (ft/s) 

along the surface model boundary as a function 

of distance for the models shown in figure 13–

15. The sharp spike at a distance of 

approximately 220 ft corresponds to the 

outward flow through the conductive drainagefill material at the toe of the dam. Discrete 

zones of seepage are evident on either side of 

the hill area from 220–280 ft and 450–600 ft, as 

well as another low-topography area farther 

downstream at 900–1,000 ft. As expected, the 

rate of seepage increases with reservoir 

elevation. 

Figure 17 shows the volumetric flow 

(gal/min) through the downstream embankment 

(blue) and ground surface (red) per foot along 

the length of the dam as a function of reservoir 

elevation. As with scenario 1, an increasing 

proportion of flow through the dam can be seen 

with increasing reservoir elevation, to a 

maximum of approximately 0.0425 gal/min per 

ft at gross pool. This is also very consistent 

flow net number 2 produced by Cedergren 

(1980a), which predicted approximately 0.04 

gal/min per ft. The reduced seepage compared 

with scenario 1 is due to the higher downstream 

elevation in this case. For the lowest reservoir 

elevation (480 ft), virtually all of the seepage is 

through the downstream ground surface.

Figure 18 illustrates simulated observationwell data that can be obtained from the flow 

model results. Each panel shows the predicted 

water level in an observation well relative to the 

ground surface, where positive values are higher 

than the ground surface (that is, artesian 

conditions), for different reservoir elevations 

and any well depth between 0 and 50 ft. That 

is, for a given observation-well depth and 

reservoir elevation, the predicted water level in 

the well can be found on one of the curves in 

the figure. The panel on the left is for an 

observation well approximately 15 ft from the 

downstream toe, which is a typical location for 

a number of observation wells at Hidden Dam. 

The panel on the right is for an observation well 

approximately 300 ft from the downstream toe, 

which corresponds to a low-topography area of 

focused seepage.

The simulated observation-well results are 

similar to those for scenario 1, with a few minor 

differences. For example, the water level 

predicted for any well depth at the location 15 ft 

downstream from the toe is approximately 2 ft 

below ground surface for the 480-ft reservoir 

elevation in scenario 2, whereas it is much 

closer to the ground surface in scenario 1. 

Additionally, at a reservoir elevation of 485 ft, 

the predicted water level on the left panel of 

figure 18 is above the ground surface, whereas 

the corresponding curve in figure 10 indicates a 

water level slightly below ground surface. This 

is somewhat counterintuitive as one might 

expect the lower topography scenario (scenario 

1) to have the higher predicted water levels, and 

highlights the nonlinearity in predicted water 

level as a function of model geometry.

Figure 19 shows the self-potential values 

predicted along the ground surface and 

downstream embankment for the flow depicted 

in figure 13–15 (reservoir elevations 485, 510, 

and 540 ft). The self-potential values displayed 

in figure 19 are relative to an arbitrary reference 

location, which was chosen at the crest of the 

dam (distance equals 0 ft).
10 Geophysical investigations at Hidden Dam—Flow simulations

Scenario 3: Profile A, No Horizontal Drainage 

Fill

This flow scenario is identical to scenario 1, 

with the exception that there is no horizontal 

drainage-fill material along the downstream 

base of the dam, and is similar to flow net 1 

produced by Cedergren (Cedergren, 1980a). 

Absence of the high-hydraulic-conductivity 

horizontal-drainage fill results in elevated water 

levels in the downstream portion of the dam, 

which can be seen in the flow model results in 

figure 20–22. This increased flow through the 

dam, as well as elevated hydraulic pressure 

relative to the baseline models, could be a 

mechanism for internal erosion over long 

periods of time.

Although there is clearly a larger region of 

seepage in the dam and downstream 

embankment, the seepage pattern along the 

downstream topography is not significantly 

different. This is quantified in figure 23, which 

shows the rate of seepage (ft/s) along the model 

boundary as a function of distance for the 

models shown in figure 20–22. In this scenario, 

the increased seepage face along the 

downstream embankment is evident as a 

broader zone of flow between 240–260 ft in 

figure 23, compared with the very sharp outflow 

spike at the downstream toe in figure 8. 

Discrete zones of seepage are evident in the 

low-topography areas from 300–400 ft, as well 

as 900–1,000 ft, and are similar in magnitude to 

scenario 1. One interesting feature is the 

increased seepage areas between 400–500 ft 

compared with scenario 1. This is likely due to 

the fact that the net hydraulic conductivity of 

the dam is reduced with the removal of the 

drainage-fill material, which partitions a greater 

amount of seepage into the foundation below 

the dam that exits further downstream.

Figure 24 shows the volumetric flow 

(gal/min) through the downstream embankment 

(blue) and ground surface (red) per foot along 

the length of the dam as a function of reservoir 

elevation. As with scenario 1, an increasing 

proportion of flow through the dam can be seen 

with increasing reservoir elevation, to a 

maximum of approximately 0.0425 gal/min per 

ft at gross pool. It is interesting that the total 

seepage in scenario 3 is less than scenario 1 at 

all reservoir elevations (0.055 gal/min at gross 

pool for scenario 1 versus 0.0425 gal/min at 

gross pool for scenario 3). Additionally, a 

much greater proportion of seepage in scenario 

3 flows through the ground surface instead of 

the downstream embankment compared with 

scenario 1. This can be explained by the fact 

that, while the seepage face along the 

downstream embankment is wider in scenario 3, 

the high-hydraulic conductivity drainage-fill 

material in scenario 1 drains significantly more 

water through the dam.

The predicted observation-well water levels

in figure 25 are elevated with respect to the 

predicted water levels for scenario 1 (figure 10), 

and this difference becomes more pronounced 

as the well depth and/or reservoir elevation 

increases. Significant pressures at depth 

corresponding to water levels of 10–12 ft above 

the ground surface are predicted for the highest 

reservoir elevations. This observation is 

consistent with the argument that the reduced 

net-hydraulic conductivity of the dam due to the 

lack of horizontal-drainage fill causes more 

seepage to be partitioned into the subsurface 

beneath the dam, contributing to increased 

pressure at depth. It is possible that an analysis 

of observation-well data could be used to assess 

the effectiveness of the horizontal drain along 

the length of the dam, though it is important to 

note that other factors such as local 

hydrogeologic heterogeneity can influence these 

observations. 

Figure 26 shows the self-potential values 

predicted along the ground surface and 

downstream embankment for the flow depicted 

in figure 20–22 (reservoir elevations 485, 510, 

and 540 ft). The self-potential values displayed 

in figure 26 are relative to an arbitrary reference 
Geophysical investigations at Hidden Dam—Flow simulations 11

location, which was chosen at the crest of the 

dam (distance equals 0 ft).

The self-potentials for scenario 3 are very 

similar to scenario 1 (figure 11), with a few 

exceptions. First, the magnitude of the seepagerelated self-potential anomalies between 250–

450 ft are more pronounced in scenario 3, again 

reflecting the increased amount of subsurface 

flow relative to scenario 1. Second, the shape 

of the self-potential curves from 0–250 ft are 

different for the two scenarios, reflecting the 

difference in internal flow patterns in the dam 

structure and shallow foundation. 

Measurements in this area could be very 

diagnostic about flow in the dam structure, 

though good measurements are difficult to make 

over the dam structure due to the difficulty in 

obtaining good electrical contact over riprapcovered surfaces (Minsley and others, 2010).

Scenario 4: Profile A, Baseline Model with 

Near-Surface Sediment Layer

Flow scenario 4 uses the profile A baseline 

model as in scenario 1, but with the addition of 

a variable-thickness layer in the near-surface on 

the downstream portion of the model that has a 

higher saturated hydraulic conductivity than the 

bedrock (figure 27). Justification for the 

addition of this layer comes from the known 

presence of residual soil, slope wash, alluvial 

sediments, and decomposed granite that overlie 

bedrock (U.S. Army Corps of Engineers, 1977; 

Cedergren, 1980a), as well as the two-layer 

resistivity model observed over the downstream 

portion of the dam foundation (Minsley and 

others, 2010) that is consistent with higher 

hydraulic conductivity sedimentary overburden. 

Hydraulic parameters used for this sediment 

layer are: Ks = 0.5 ft/day, s = 0.25, r = 0.015, 

a = 0.2399 1/ft, n = 3.9218.

The flow modeling results in figure 28–30

are similar to those in scenario 1 (figure 5–7) 

with a few minor exceptions. Although the 

drainage-fill material still serves as an effective 

cutoff for upward flow coming from the 

foundation, an increased amount of 

downstream-oriented seepage is focused in the 

sediment layer due to its elevated hydraulic 

conductivity with respect to the bedrock. 

Additionally, the elevated hydraulic 

conductivity and saturated moisture content of 

the sediment layer limits the saturation in some 

of the high-topography hill areas downstream of 

the dam, even at gross pool.

The rate of seepage (ft/s) along the model 

boundary as a function of distance for the 

models shown in figure 28–30 is illustrated in 

figure 31. Compared with the corresponding 

image for scenario 1 (figure 8), it is clear that 

the impact of the high-hydraulic-conductivity 

sediment layer has not significantly altered the 

distribution of seepage, but the seepage rate has 

increased by a factor of 2–3.

Figure 32 shows the volumetric flow 

(gal/min) through the downstream embankment 

(blue) and ground surface (red) per foot along 

the length of the dam as a function of reservoir 

elevation. The maximum of approximately 

0.057 gal/min at gross pool is close to the 

scenario 1 value of 0.055 gal/min (figure 9), and 

the total rate of seepage at other reservoir 

elevations are also comparable between the two 

models. In scenario 4, however, it is apparent 

that a greater amount of the volumetric seepage 

occurs through the downstream ground surface 

rather than the embankment when compared 

with scenario 1. This is again consistent with 

the observation that the elevated hydraulic 

conductivity of the sediment layer directs an 

increased amount of flow in the downstream 

direction away from the dam.

The predicted observation-well water levels 

for scenario 4 are illustrated in figure 33. The 

water levels are significantly reduced with 

respect to scenario 1 (figure 10), with a 

maximum predicted water level of 

approximately 4 ft above ground surface at 

gross pool for a 50-ft-deep well. The ‘kink’ in

the curves at approximately 40-ft depth 

corresponds to the transition from the sediment 
12 Geophysical investigations at Hidden Dam—Flow simulations

layer to bedrock. The reduced water levels 

predicted for scenario 4 are a direct result of the 

elevated hydraulic conductivity, which acts to 

reduce hydraulic pressure in the subsurface.

Figure 34 shows the self-potential values 

predicted along the ground surface and 

downstream embankment for the flow depicted 

in figure 28–30 (reservoir elevations 485, 510, 

and 540 ft). The self-potential values are 

relative to an arbitrary reference location, which 

was chosen at the crest of the dam (distance 

equals 0 ft). The self-potential response for 

scenario 4 is very similar to scenario 1 (figure 

11), both in character and magnitude, though 

the self-potential values in flow scenario 4 are 

slightly smaller. This is somewhat non-intuitive 

due to the increased seepage rate with respect to 

scenario 1 (figure 31), but results from the fact 

that the elevated hydraulic conductivity 

sediment layer leads to reduced excess charge in 

equation (8) and the elevated saturated moisture 

content of the sediment layer leads to reduced 

electrical resistivity according to equation (7), 

both of which lead to reduced self-potential 

values as described in the Appendix.

The electrical resistivity profile for this flow 

model derived using equation (7) and a 

reservoir elevation of 510 ft is shown in figure 

35. The resistivity of the near-surface sediment 

layer is approximately 200 ohm-m, which is 

consistent with the values reported from the 

geophysical field survey (Minsley and others, 

2010). One important factor that is not 

accurately accounted for in this flow model is 

the thickness profile of this sediment layer. 

Because the resistivity surveys were oriented 

parallel to the dam, this information could not 

be incorporated into the flow models beyond the 

use of a ‘typical’ thickness observed from the 

resistivity profiles.

Scenario 5: Profile A, Baseline Model with 

Deep Sediment Channel

Flow scenario 5 uses the profile A baseline 

model as in scenario 1, but with the addition of 

a thick (several hundred feet) sediment channel 

that extends from the upstream to downstream 

portions of the model (figure 36). Justification 

for the addition of this deep channel comes 

from the resistivity survey at Hidden Dam 

(Minsley and others, 2010) that identified a 

wide (300–400 ft), low-resistivity channel that 

extends to depths of several hundred feet over a 

portion of the low-topography area downstream 

of the dam (figure 2). Hydraulic parameters 

used for this sediment channel are the same as 

those used in scenario 4: Ks = 0.5 ft/day, s = 

0.25, r = 0.015, a = 0.2399 1/ft, n = 3.9218.

The flow modeling results in figure 37–39

are more similar to those in scenario 1 (figure 

5–7) than to the sediment layer case in scenario 

4 (figure 28–30). In scenario 5 the hydraulic 

conductivity in the foundation is controlled 

mainly by the sediment channel (Ks = 0.5 

ft/day), compared with scenario 1, where the 

foundation is bedrock (Ks = 0.1 ft/day). One 

similarity with scenario 4, however, is the 

reduced saturation in the high-topography hill 

area downstream of the dam due to the elevated 

hydraulic conductivity.

The rate of seepage (ft/s) along the model 

boundary as a function of distance for the 

models shown in figure 37–39 is illustrated in 

figure 40. The seepage pattern is similar to 

scenario 1 (figure 8), but the magnitude of the 

rate of seepage is similar to (but somewhat 

larger than) scenario 4 (figure 31). The highhydraulic-conductivity sediment channel that 

extends to the upstream side of the dam results 

in seepage rates that are approximately 3–4 

times greater than the baseline case in 

scenario 1.

Figure 41 shows the volumetric flow 

(gal/min) through the downstream embankment 

(blue) and ground surface (red) per foot along 
Geophysical investigations at Hidden Dam—Flow simulations 13

the length of the dam as a function of reservoir 

elevation. The maximum of approximately 

0.162 gal/min at gross pool is significantly 

larger than the scenario 1 or scenario 5 values of 

approximately 0.055 gal/min (figure 9 and 32). 

This increased volumetric rate of seepage is 

consistent with the value of 0.108 gal/min 

reported by Cedergren (1980a, table 6) for a 

slightly lower foundation hydraulic conductivity 

of 0.25 ft/day. 

The predicted observation-well water levels 

for scenario 5 are illustrated in figure 42. The 

water levels are very similar to those predicted 

in scenario 1 (figure 10), with a maximum 

predicted water level of approximately 7 ft 

above ground surface at gross pool for a 50-ftdeep well. Although the seepage rate is much 

higher than in scenario 1, the effect of the 

elevated hydraulic conductivity reduces 

pressures at depth and results in similar 

predicted water levels.

Figure 43 shows the self-potential values 

predicted along the ground surface and 

downstream embankment for the flow depicted 

in figure 37–39 (reservoir elevations 485, 510, 

and 540 ft). The self-potential values are 

relative to an arbitrary reference location, which 

was chosen at the crest of the dam (distance 

equals 0 ft). The self-potential response for 

scenario 5 is very similar to scenario 1 (figure 

11) and scenario 4 (figure 34), both in character 

and magnitude, though the self-potential values 

in flow scenario 5 are slightly smaller. This is 

due to the same effect discussed in scenario 4, 

where the reduced excess charge in equation (8)

and the reduced electrical resistivity according 

to equation (7) counteract the increased seepage 

rate and leads to reduced self-potential 

magnitudes as described in the Appendix.

Comparison with Selected 

Observation-Well Data

Historical reservoir elevation data, along 

with measurements from observation wells, 

piezometers, and weirs, were obtained for the 

Hidden Dam site (K. Hazleton, written 

commun., 2009). These records provide useful 

information regarding the connection between 

reservoir elevation and downstream water levels 

and seepage at the site. Here, we focus on the 

records for two observation wells on the right 

abutment drainage blanket area with elevations 

that are comparable to the surface elevations on 

the two profiles used in this study (figure 1). 

OW-22 has an elevation of approximately 450 

feet, with a screened depth between 15–20 feet. 

OW-7 has an elevation of approximately 470 

feet, with a screened depth interval between 30–

40 feet. Figure 44 shows the historical record 

of reservoir elevation (top panel) as well as 

water levels relative to the ground surface 

(negative values are below ground) for these 

wells (lower panels) since 1980. 

A more detailed view of these curves is 

provided in figure 45, which overlays the 

reservoir elevation and observation-well records 

for the years 2001–2004. Water levels in the 

observation wells are a damped version of the 

forcing produced by variations in the reservoir 

elevation, with a clear time-shift between the 

two curves that indicates a characteristic 

reaction time for seepage through the dam. 

In figure 46, the reservoir elevation data are 

cross-plotted with the observation-well water 

levels for OW-22 (A) and OW-7 (B) for the 

entire available historical record. As expected, 

there is a positive correlation between reservoir 

elevation and observed water level, with a slope 

of approximately 0.1 and 0.2 in OW-22 and 

OW-7, respectively (that is, a 1-ft increase in 

reservoir elevation leads to approximately 0.2-ft 

increase in observation-well levels in OW-7). 

The large number of zero-values and absence of 
14 Geophysical investigations at Hidden Dam—Flow simulations

positive water levels in the OW-22 data indicate 

the inability to record water levels that are 

higher than the ground surface. Values 

extrapolated to gross pool using the slope of 0.2 

are approximately 8 ft above ground. In OW-7, 

above-ground water levels are measured with 

pressure transducers. 

Superimposed on the observation-well data 

are the model-predicted water levels from the 

various flow scenarios in this study taken from 

the appropriate well depths in figure 10

(scenario 1), figure 18 (scenario 2), figure 25

(scenario 3), figure 33 (scenario 4), and figure 

42 (scenario 5). There is a reasonably good 

agreement between the observation-well data 

and model-predicted water levels, suggesting 

that the flow models in this study provide a 

good representation of seepage at Hidden Dam, 

though the flow models tend to predict water 

levels that are slightly elevated for specific 

reservoir elevations. This discrepancy may be 

related to inaccuracies in the details of the 

model geometry or hydrologic properties, as 

well as the fact that there is a 3D component of 

flow that is not captured in the 2D models. One 

notable feature in the simulated water-level data 

is the nonlinear aspect that is apparent as a 

decrease in slope at higher reservoir elevations, 

which is also apparent in the historical record 

data in figure 46B.

In figure 46A, it is evident that the 

predictions for the scenario 4 model, which 

involves the thin sediment (higher hydraulic 

conductivity) layer over bedrock (figure 27), 

correspond most closely with the historical 

record. The lack of historical data for positive 

water levels, however, makes it impossible to 

validate this observation for reservoir elevations 

above 510 ft. Agreement with the historical 

data, along with the fact that scenario 4 is 

consistent with the hydrogeologic knowledge of 

the site as well as the general character observed 

in the DC resistivity models (figure 2) over 

much of the right abutment area, suggests that 

this is a reasonable model for flow through the 

portion of the dam in the vicinity of OW-22.

Conclusions

Quantitative information about seepage and 

flow patterns at Hidden Dam is provided by this 

numerical modeling study. The flow model 

scenarios, dam geometry, and hydrologic 

parameters were guided by the foundation 

report and initial flow net studies (U.S. Army 

Corps of Engineers, 1977; Cedergren, 1980a), 

with additional information about subsurface 

structural properties inferred from more recent 

geophysical work (Minsley and others, 2010). 

Implementation of the variably saturated flow 

equations in COMSOL allows for quantitative 

predictions of seepage rates or volumes, water 

levels, and degree of saturation anywhere in the 

model as a function of changing reservoir 

elevation. This provides a valuable framework 

for studying different hydrogeologic or damstructure scenarios. The modeling results are 

consistent with both the initial flow net studies 

(Cedergren, 1980a) as well as data from 

observation wells at the site. 

Additionally, we have provided a 

methodology for coupling the flow results to 

geophysical properties investigated by Minsley 

and others (2010). The predicted electrical 

resistivity model for any flow scenario is 

determined through a petrophysical relationship 

that incorporates the calculated total moisture 

content. This electrical resistivity model is 

subsequently used in a second set of equations 

that describe the self-potential response to the 

various flow scenarios based on electrokinetic 

coupling. Predicting the geophysical response 

to various hydrogeologic models helps to 

validate the field data already acquired, but also 

provides useful information for guiding future 

geophysical studies. The expected geophysical 

response to different flow scenarios can be used 

to guide survey locations and acquisition 

parameters that will be most sensitive to 

subsurface changes of interest.

Several of the main insights gained from 

this study are outlined below:
Geophysical investigations at Hidden Dam—Flow simulations 15

• Low-topography areas act to focus seepage, 

which is consistent with historical 

observations at the site. Low-topography 

areas can also result in seepage at significant 

distances downstream of the dam (for 

example, 900–1,000 ft in figure 8). 

Cedergren (1980a) identified one such area 

approximately 700 ft downstream on the left 

side of the dam.

• Predicted water levels are near or above the 

ground surface for reservoir elevations 

above 480 ft in all of the scenarios studied. 

The maximum value in this study is 

approximately 12 ft above ground surface 

for scenario 3 (no horizontal drainage fill, 

figure 25). Water levels do not, however, 

reach the extremely high values up to 40 

feet above the ground surface at gross pool 

predicted in the revised flow net study by 

Cedergren (1980b)

• Absence of the horizontal drainage-fill 

material in the downstream part of the dam 

(scenario 3) results in a broader area of 

seepage on the downstream embankment 

(figure 20–22), but reduced volumetric 

seepage compared with the case where the 

drainage fill is present. This is because the 

absence of the drainage fill reduces the net 

hydraulic conductivity of the dam, which 

partitions a greater amount of seepage into 

the subsurface (compare figure 24 with 

figure 9). None the less, this enhanced area 

of flow in the dam may lead to increased 

long-term erosion under elevated reservoir 

levels.

• The presence of a thin (tens of feet) 

sedimentary layer with higher hydraulic 

conductivity than the underlying bedrock 

results in moderately increased seepage in 

the downstream area (compare figure 23

with figure 8) as well as a greater proportion 

of seepage in the sediment and bedrock 

(compare figure 24 with figure 9), but also 

results in lower water levels in observation 

wells (compare figure 25 with figure 10). 

• The presence of a deep (hundreds of feet) 

sedimentary channel under the dam 

foundation, suggested by the resistivity 

survey carried out by Minsley and others 

(2010), leads to substantial increases in 

volumetric seepage under the dam (compare 

figure 41 with figure 9), though water levels 

predicted in observation wells are 

comparable to the case without a highconductivity channel (compare figure 42

with figure 10). This observation of 

increased seepage, but unchanged water 

level (pressure), is predicted from normal 

Darcy flow (Freeze and Cherry, 1979): the 

increased hydraulic conductivity in the 

sediment channel leads to increased flow, 

but the pressure gradient (defined by the 

ratio of flow to hydraulic conductivity) 

remains unchanged. This suggests that 

water-level data alone may not be a good 

indicator of relative amounts of seepage 

along the dam if the wells are located in 

different geologic structures.

• For a given scenario, the predicted selfpotential response scales with seepage due 

to increased flow. However, increased 

seepage at one location with elevated 

hydraulic conductivity does not necessarily 

lead to larger self-potentials than an area 

with lower hydraulic conductivity and 

reduced seepage (compare figure 43 with 

figure 11) due to the counteracting role of 

electrical resistivity and excess charge in the 

self-potential response. It is clear, however, 

that for the same bedrock hydraulic 

conductivity, increased self-potentials are 

observed when the horizontal-drainage fill is 

absent because of increased seepage beneath 

the dam (compare figure 26 with figure 11). 

• The self-potential response over the 

downstream embankment for the case with 
16 Geophysical investigations at Hidden Dam—Flow simulations

no horizontal drainage fill (figure 26) is 

different than when the drainage fill is 

present (figure 11) and becomes more 

apparent at higher reservoir elevations. 

While this could be a useful indicator of 

locations with effective drainage fill, selfpotential measurements on riprap are 

difficult and would likely require dedicated 

holes into dam material to make good 

electrical contact.

• One limiting factor in this study is that 2D 

models are used, which assumes that all 

flow is perpendicular to the dam. While this 

is a reasonable modeling assumption, the 

true downstream topography likely produces 

a component of flow that is directed toward 

the outflow axis of the dam. Additionally, 

variability in internal dam structure (for 

example, the presence or absence of 

drainage fill) and subsurface heterogeneity 

(such as the influence of a deep sediment 

channel) may also lead to 3D flow patterns 

not captured in this study.

Acknowledgments

This work was carried out with the support 

of the U.S. Army Corps of Engineers, 

Sacramento District, under the supervision of 

Lewis Hunter. We thank Lewis Hunter, Kevin 

Hazleton, Beth Burton, and Martin Fahning for 

their reviews of the manuscript.

References Cited

Archie, G.E., 1942, The electrical resistivity log 

as an aid in determining some reservoir 

characteristics: Trans. Amer. Inst. Mining 

Metallurgical and Petroleum Engineers, v. 

146, p. 54–62.

Cedergren, H.R., 1980a, Seepage study of 

Hidden Dam, Fresno River, California: 

Prepared for Department of the Army, 

Sacramento District, Corps of Engineers, 

210 p.

Cedergren, H.R., 1980b, Seepage study of 

Hidden Dam, Fresno River, California: 

Analysis of data from observation wells put in 

right abutment seepage areas in 1980: 

Prepared for Department of the Army, 

Sacramento District, Corps of Engineers, 

31 p.

Freeze, R.A., and Cherry, J.A., 1979, 

Groundwater: Englewood Cliffs, New Jersey, 

Prentice Hall, 604 p.

Ishido, T., and Mizutani, H., 1981, 

Experimental and theoretical basis of 

electrokinetic phenomena in rock-water 

systems and its applications to geophysics: 

Journal of Geophysical Research, v. 86, no. 

NB3, p. 1763–1775.

Jardani, A., Revil, A., Boleve, A., and Dupont, 

J.P., 2008, Three-dimensional inversion of 

self-potential data used to constrain the 

pattern of groundwater flow in geothermal 

fields: Journal of Geophysical Research-Solid 

Earth, v. 113, B09204.

Lesmes, D.P., and Friedman, S.P., 2005, 

Relationships between the electrical and 

hydrogeological properties of rocks and soils, 

in Rubin, Y., and Hubbard, S.S., eds., 

Hydrogeophysics: Netherlands, Springer, 

p. 87–128.

Minsley, B.J., Burton, B.L., Ikard, S., and 

Powers, M.H., 2010, Geophysical 

investigations at Hidden Dam, Raymond, CA: 

Summary of fieldwork and preliminary data 

analysis U.S. Geological Survey Open-File 

Report 2010-1013, 25 p.

Morgan, F.D., Williams, E.R., and Madden, 

T.R., 1989, Streaming potential properties of 

Westerly Granite with applications: Journal of 

Geophysical Research-Solid Earth and 

Planets, v. 94, no. B9, p. 12449–12461.

Revil, A., Pezard, P.A., and Glover, P.W.J., 

1999, Streaming potential in porous media 1. 

Theory of the zeta potential: Journal of 

Geophysical Research-Solid Earth, v. 104, 

no. B9, p. 20021–20031.
Geophysical investigations at Hidden Dam—Flow simulations 17

Saxton, K.E., and Rawls, W.J., 2006, Soil water 

characteristic estimates by texture and organic 

matter for hydrologic solutions: Soil Science 

Society of America Journal, v. 70, no. 5, 

p. 1569–1578.

U.S. Army Corps of Engineers, 1977, 

Foundation report: Hidden Dam project, 

Hensley Lake, Fresno River, California, 

Madera County: USACE, Sacramento 

District.

van Genuchten, M.T., 1980, A Closed-form 

Equation for Predicting the Hydraulic 

Conductivity of Unsaturated Soils: Soil 

Science Society of America Journal, v. 44.
18 Geophysical investigations at Hidden Dam—Flow simulations

Appendix

Governing Variably Saturated Flow Equations

The formulation of the steady-state Richards 

equation solved by COMSOL Multiphysics is 

( )   ∇⋅ − ∇ + ∇ =    

s r

s

K k p gz Q

g





(1)

where Ks is the saturated hydraulic conductivity 

(ft/s);  is the water density, which is set to a 

constant 62.42 lb/ft3; g is the acceleration due to 

gravity, equal to 32.2 ft/s2; p is the state variable 

that describes water pressure (lbf/ft2

) throughout 

the model; z is elevation (ft), and Qs represents 

imposed fluid sources or sinks (1/s). The van 

Genuchten equations (van Genuchten, 1980) are 

used to describe the relative permeability, kr, 

effective saturation, Se, and liquid volume, θ, as 

a function of pressure head, which is defined as 

H pg p =  (ft). 

( ( ) )

2

1/ 1 1 0

1 0

m m

p

r

p

Se Se H

k

H



 − − < = 

 ≥ 

(2)

( )

1 0

1

1 0

m p n

p

p

H

Se aH

H

 < 

 =  +



 ≥ 

(3)

( ) 0

0

r sr p

s p

Se H

H

 +− <  = 

 ≥ 

 



 (4)

1

m 1

n = − (5)

Liquid volume ranges from user-specified small 

residual value, r, to the total porosity, s. 

These bounds, as well as the constants a and n 

depend on material properties. The constant a 

(1/ft) is related to the air entry pressure head 

and desorption behavior of the soil, and n is 

related to the pore-size distribution of the soil. 

A detailed description of how these values were 

determined for the Hidden Dam model is 

provided below.

Determination of Variably Saturated Model 

Input Parameters

The model input parameters were obtained 

from the seepage studies conducted by 

Cedergren (1980a, b) and the Soil Plant Air 

Water (SPAW) soils database developed by 

Saxton and Rawls (2006) and available through 

the USDA-NRCS 

(http://www.wsi.nrcs.usda.gov/products/W2Q/w

ater_mgt/Water_Budgets/SPAW_Model.html, 

last accessed January 2010). Estimates of the 

saturated hydraulic conductivity (table 1) and 

gradation curves (figure 47) corresponding to 

each sub-domain of the dam were provided by 

Cedergren (1980a) and the foundation report 

(U.S. Army Corps of Engineers, 1977). Grain 

size distributions were summarized in terms of 

percent gravel, sand, silt and clay, by employing 

a standardized grain scale. 

Soil-water retention curves (figure 48) and 

saturated and residual moisture contents (table 

1) for each sub-domain were estimated using 

the graphical user interface of Saxton and Rawls 

(2006) and the available gradation data. 

Percentages were entered into the SPAW 

database to obtain estimates of textural 

classification (table 1) and statistically based 

estimates of soil-water retention curves for each 

sub-domain. The retention curves relate matric 

suction (Hp < 0) to volumetric moisture content 

(volume fraction), and are a key component of 

the unsaturated flow models. Soil-water 

retention curves were created for matric 

suctions ranging between 1,500 kPa (31,328 

lbf/ft2

), corresponding to absorbed soil moisture 

at the residual moisture condition, and 

atmospheric pressure, corresponding to soil 

moisture at the saturated condition. The curves 
Geophysical investigations at Hidden Dam—Flow simulations 19

were produced under the assumption that the 

effects of organic matter and osmotic pressures 

were negligible. Soil compaction in the SPAW 

model was specified as “normal,” implying that 

no unnatural changes in soil bulk density had 

occurred.

Table 2. Summary of gradation and soil-water retention data for Hidden Dam model units.

Impervious Core Random Fill Select Fill Drainage Fill

Saturated hydraulic

conductivity (ft/day) 0.02 1.0 2.0 8000.0

Gravel

(weight fraction) 0.10 0.25 0.30 1.00

Sand

(weight fraction) 0.45 0.10 0.50 0.00

Silt

(weight fraction) 0.10 0.63 0.18 0.00

Clay

(weight fraction) 0.35 0.02 0.02 0.00

Textural classification Sandy clay Silty loam Sandy loam Sandy gravel

Residual moisture

(volume fraction) 0.21 0.02 0.01 0.02

Saturated moisture

(volume fraction) 0.42 0.37 0.38 0.43

a (1/ft) 0.2013 0.2399 0.2453 0.7165

n 1.9923 3.9218 3.3088 3.5952

The soil-water retention curves are 

incorporated into the flow model by 

determining the parameters a and n in equations 

(3) and (4) that fit each retention curve 

produced by the SPAW model. These 

parameters define the relative permeability as a 

function of saturation in equation (2), which is 

incorporated in the variably saturated flow 

equation (1). Nominal values a = 0.2 / ft and n

= 2.0 are used for the grout curtain and bedrock 

as the necessary input parameters were not 

available for these units.

Electrokinetic Coupling to Determine the SelfPotential Response

Electrokinetic coupling is the mechanism by 

which fluid flow in porous media generates 

measurable electrical potentials in the earth, 

called self-potentials (Ishido and Mizutani, 

1981; Morgan and others, 1989; Revil and 

others, 1999). The basic concept, summarized 

by Minsley and others (2010), involves a small 

amount of excess positive charge that is 

transported along with fluid flow in porous 

materials, generating a “streaming” electric 

current density. Because the total electric 

current density in the earth must be conserved, 

this streaming current density generates a 

balancing conduction current density that flows 

throughout the earth. As this conduction 

current traverses the subsurface electrical 

resistivity structure, it results in measurable 

electrical potential differences between various 

locations, which are called self-potentials.

Mathematically, this phenomenon is written 

( ) ( ) 0 sc V ∇⋅ + =∇⋅ − ∇ = j j Qu V  (6)

where js and jc represent the streaming and 

conduction currents (A/ft2

), respectively. The 

streaming current can be defined as the excess 

charge density QV in coulombs per cubic foot 

(C/ft3) times the fluid velocity u (ft/s). The 

conduction current is defined as the negative of 

the electrical conductivity (S/m) times the 

electrical potential gradient (V/ft). The 

difference in electrical potential, V, between two 

locations is the self-potential value (V). By 
20 Geophysical investigations at Hidden Dam—Flow simulations

coupling the electrical problem to the variably 

saturated flow problem, the self-potential 

response can be calculated for any flow 

scenario.

Equation (6) can be solved in COMSOL by 

coupling directly to the flow velocity, u, that is 

calculated in the solution of Richards equation 

discussed previously. The subsurface electrical 

conductivity structure () is calculated 

dynamically as a function of the liquid volume 

content, , in equation (4) using Archie’s law 

(Archie, 1942; Lesmes and Friedman, 2005), m   = w (7)

where w is the electrical conductivity of the 

pore water, and is fixed at a value of 0.05 S/m 

(20 ohm-m) for this study. The cementation 

exponent, m, is fixed at 1.7. An example of the 

electrical resistivity (inverse of conductivity) 

structure for one flow model is shown in figure 

12. The excess charge density, QV, is also 

calculated dynamically as a function of the 

saturation-dependent hydraulic permeability, k, 

using the relationship provided by Jardani and 

others (2008):

log 9.2349 0.8219log (Q k V ) =− − ( ) (8)
Geophysical investigations at Hidden Dam—Flow simulations 21

Figures

Figure 5. Flow model results for the profile A baseline model and reservoir elevation of 485 ft (flow scenario 1). Background colors represent the 

effective saturation, contours indicate hydraulic head (feet), and white arrows show flow directions and relative magnitude.
22 Geophysical investigations at Hidden Dam—Flow simulations

Figure 6. Flow model results for the profile A baseline model and reservoir elevation of 510 ft (flow scenario 1). Background colors represent the 

effective saturation, contours indicate hydraulic head (feet), and white arrows show flow directions and relative magnitude.
Geophysical investigations at Hidden Dam—Flow simulations 23

Figure 7. Flow model results for the profile A baseline model and reservoir elevation of 540 ft (flow scenario 1). Background colors represent the 

effective saturation, contours indicate hydraulic head (feet), and white arrows show flow directions and relative magnitude.
24 Geophysical investigations at Hidden Dam—Flow simulations

Figure 8. Seepage (foot per second) through the downstream embankment and ground surface as a function of 

distance for the three different reservoir elevations illustrated in figure 5–7 (flow scenario 1).
Geophysical investigations at Hidden Dam—Flow simulations 25

Figure 9. Volumetric flow (gallons per minute) through the downstream embankment (blue) and ground surface 

(red) per foot along the length of the dam as a function of reservoir elevation (flow scenario 1).
26 Geophysical investigations at Hidden Dam—Flow simulations

Figure 10. Predicted water levels in observation wells 15 feet (left) and 90 feet (right) from the downstream toe for 

flow scenario 1. The predicted water level relative to ground surface (positive upwards) is shown for different 

reservoir elevations and any well depth between 0 and 50 feet.
Geophysical investigations at Hidden Dam—Flow simulations 27

Figure 11. Self-potential (millivolts) values predicted along the downstream embankment and ground surface for the 

three different reservoir elevations illustrated in figure 5–7 for flow scenario 1.
28 Geophysical investigations at Hidden Dam—Flow simulations

Figure 12. Electrical resistivity (ohm-meters) predicted for flow scenario 1 at a reservoir elevation of 510 feet.
Geophysical investigations at Hidden Dam—Flow simulations 29

Figure 13. Flow model results for the profile B baseline model and reservoir elevation of 485 ft (flow scenario 2). Background colors represent the 

effective saturation, contours indicate hydraulic head (feet), and white arrows show flow directions and relative magnitude.
30 Geophysical investigations at Hidden Dam—Flow simulations

Figure 14. Flow model results for the profile B baseline model and reservoir elevation of 510 ft (flow scenario 2). Background colors represent the 

effective saturation, contours indicate hydraulic head (feet), and white arrows show flow directions and relative magnitude.
Geophysical investigations at Hidden Dam—Flow simulations 31

Figure 15. Flow model results for the profile B baseline model and reservoir elevation of 540 ft (flow scenario 2). Background colors represent the 

effective saturation, contours indicate hydraulic head (feet), and white arrows show flow directions and relative magnitude.
32 Geophysical investigations at Hidden Dam—Flow simulations

Figure 16. Seepage (foot per second) through the downstream embankment and ground surface as a function of 

distance for the three different reservoir elevations illustrated in figure 13–15 (flow scenario 2).
Geophysical investigations at Hidden Dam—Flow simulations 33

Figure 17. Volumetric flow (gallons per minute) through the downstream embankment (blue) and ground surface 

(red) per foot along the length of the dam as a function of reservoir elevation for flow scenario 2.
34 Geophysical investigations at Hidden Dam—Flow simulations

Figure 18. Predicted water levels in observation wells 15 feet (left) and 300 feet (right) from the downstream toe for 

flow scenario 2. The predicted water level relative to ground surface (positive upwards) is shown for different 

reservoir elevations and any well depth between 0 and 50 feet.
Geophysical investigations at Hidden Dam—Flow simulations 35

Figure 19. Self-potential (millivolts) values predicted along the downstream embankment and ground surface for the 

three different reservoir elevations illustrated in figure 13–15 for flow scenario 2.
36 Geophysical investigations at Hidden Dam—Flow simulations

Figure 20. Flow model results for the profile A model with no horizontal-drainage fill and reservoir elevation of 485 ft (flow scenario 3). Background 

colors represent the effective saturation, contours indicate hydraulic head (feet), and white arrows show flow directions and relative magnitude.
Geophysical investigations at Hidden Dam—Flow simulations 37

Figure 21. Flow model results for the profile A model with no horizontal-drainage fill and reservoir elevation of 510 ft (flow scenario 3). Background 

colors represent the effective saturation, contours indicate hydraulic head (feet), and white arrows show flow directions and relative magnitude.
38 Geophysical investigations at Hidden Dam—Flow simulations

Figure 22. Flow model results for the profile A model with no horizontal-drainage fill and reservoir elevation of 540 ft (flow scenario 3). Background 

colors represent the effective saturation, contours indicate hydraulic head (feet), and white arrows show flow directions and relative magnitude.
Geophysical investigations at Hidden Dam—Flow simulations 39

Figure 23. Seepage (foot per second) through the downstream embankment and ground surface as a function of 

distance for the three different reservoir elevations illustrated in figure 20–22 (flow scenario 3).
40 Geophysical investigations at Hidden Dam—Flow simulations

Figure 24. Volumetric flow (gallons per minute) through the downstream embankment (blue) and ground surface 

(red) per foot along the length of the dam as a function of reservoir elevation for flow scenario 3.
Geophysical investigations at Hidden Dam—Flow simulations 41

Figure 25. Predicted water levels in observation wells 15 feet (left) and 90 feet (right) from the downstream toe for 

flow scenario 3. The predicted water level relative to ground surface (positive upwards) is shown for different 

reservoir elevations and any well depth between 0 and 50 feet.
42 Geophysical investigations at Hidden Dam—Flow simulations

Figure 26. Self-potential (millivolts) values predicted along the downstream embankment and ground surface for the 

three different reservoir elevations illustrated in figure 20–22 for flow scenario 3.
Geophysical investigations at Hidden Dam—Flow simulations 43

Figure 27. Saturated hydraulic-conductivity values for scenario 4 are identical to scenario 1 (figure 3), with the addition of a higher conductivity 

near-surface layer in the downstream portion of the model.
44 Geophysical investigations at Hidden Dam—Flow simulations

Figure 28. Flow model results for the profile A baseline model with an additional near-surface sediment layer and reservoir elevation of 485 ft 

(flow scenario 4). Background colors represent the effective saturation, contours indicate hydraulic head (feet), and white arrows show flow 

directions and relative magnitude.
Geophysical investigations at Hidden Dam—Flow simulations 45

Figure 29. Flow model results for the profile A baseline model with an additional near-surface sediment layer and reservoir elevation of 510 ft 

(flow scenario 4). Background colors represent the effective saturation, contours indicate hydraulic head (feet), and white arrows show flow 

directions and relative magnitude.
46 Geophysical investigations at Hidden Dam—Flow simulations

Figure 30. Flow model results for the profile A baseline model with an additional near-surface sediment layer and reservoir elevation of 540 ft (flow 

scenario 4). Background colors represent the effective saturation, contours indicate hydraulic head (feet), and white arrows show flow directions 

and relative magnitude.
Geophysical investigations at Hidden Dam—Flow simulations 47

Figure 31. Seepage (feet per second) through the downstream embankment and ground surface as a function of 

distance for the three different reservoir elevations illustrated in figure 28–30 (flow scenario 4).
48 Geophysical investigations at Hidden Dam—Flow simulations

Figure 32. Volumetric flow (gallons per minute) through the downstream embankment (blue) and ground surface (red) 

per foot along the length of the dam as a function of reservoir elevation for flow scenario 4.
Geophysical investigations at Hidden Dam—Flow simulations 49

Figure 33. Predicted water levels in observation wells 15 feet (left) and 90 feet (right) from the downstream toe for 

flow scenario 4. The predicted water level relative to ground surface (positive upwards) is shown for different 

reservoir elevations and any well depth between 0 and 50 feet.
50 Geophysical investigations at Hidden Dam—Flow simulations

Figure 34. Self-potential (millivolts) values predicted along the downstream embankment and ground surface for the 

three different reservoir elevations illustrated in figure 28–30 for flow scenario 4.
Geophysical investigations at Hidden Dam—Flow simulations 51

Figure 35. Electrical resistivity (ohm-meters) predicted for flow scenario 4 at a reservoir elevation of 510 feet.
52 Geophysical investigations at Hidden Dam—Flow simulations

Figure 36. Saturated hydraulic-conductivity values for scenario 5 are identical to scenario 1 (figure 3), with the addition of a higher conductivity channel 

that extends to several hundred feet depth and connects the upstream and downstream portions of the model.
Geophysical investigations at Hidden Dam—Flow simulations 53

Figure 37. Flow model results for the profile A baseline model with an additional deep sediment channel and reservoir elevation of 485 ft 

(flow scenario 5). Background colors represent the effective saturation, contours indicate hydraulic head (feet), and white arrows show 

flow directions and relative magnitude.
54 Geophysical investigations at Hidden Dam—Flow simulations

Figure 38. Flow model results for the profile A baseline model with an additional deep sediment channel and reservoir elevation of 510 ft (flow scenario 

5). Background colors represent the effective saturation, contours indicate hydraulic head (feet), and white arrows show flow directions and relative 

magnitude.
Geophysical investigations at Hidden Dam—Flow simulations 55

Figure 39. Flow model results for the profile A baseline model with an additional deep sediment channel layer and reservoir elevation of 540 ft (flow 

scenario 5). Background colors represent the effective saturation, contours indicate hydraulic head (feet), and white arrows show flow directions 

and relative magnitude.
56 Geophysical investigations at Hidden Dam—Flow simulations

Figure 40. Seepage (feet per second) through the downstream embankment and ground surface as a function of 

distance for the three different reservoir elevations illustrated in figure 37–39 (flow scenario 5).
Geophysical investigations at Hidden Dam—Flow simulations 57

Figure 41. Volumetric flow (gallons per minute) through the downstream embankment (blue) and ground surface (red) 

per foot along the length of the dam as a function of reservoir elevation for flow scenario 5.
58 Geophysical investigations at Hidden Dam—Flow simulations

Figure 42. Predicted water levels in observation wells 15 feet (left) and 90 feet (right) from the downstream toe for 

flow scenario 5. The predicted water level relative to ground surface (positive upwards) is shown for different 

reservoir elevations and any well depth between 0 and 50 feet.
Geophysical investigations at Hidden Dam—Flow simulations 59

Figure 43. Self-potential (millivolts) values predicted along the downstream embankment and ground surface for the 

three different reservoir elevations illustrated in figure 37–39 for flow scenario 5.
60 Geophysical investigations at Hidden Dam—Flow simulations

Figure 44. Historical record of reservoir elevation (top) and water levels relative to ground surface (negative values 

are below ground) for observation wells OW-22 and OW-7.
Geophysical investigations at Hidden Dam—Flow simulations 61

Figure 45. Detailed view of reservoir elevation and observation-well data for OW-22 and OW-7 from 2001–2004.
62 Geophysical investigations at Hidden Dam—Flow simulations

Figure 46. Crossplots of reservoir elevation and observation-well water level data for OW-22 (A) and OW-7 (B), along 

with model-predicted results from the various flow scenarios in this study. The large number of zero-values and 

absence of positive water levels in the OW-22 data indicate the inability to record water levels that are higher than 

the ground surface. In OW-7, above-ground water levels are measured with pressure transducers.
Geophysical investigations at Hidden Dam—Flow simulations 63

Figure 47. Gradation curves for primary Hidden Dam model units.
64 Geophysical investigations at Hidden Dam—Flow simulations

Figure 48. Soil-water retention curves for primary Hidden Dam model units.