US Army Corps 

of Engineers 

Waterways Experiment 

Station 

Miscellaneous Paper HL-94-7 

October 1994 

Application of a Two ... Dimensional Model 

of Hydrodynamics to San Timoteo Creek 

Flood-Control Channel, California 

by Richard L. Stockstill 

Approved For Public Release; Distribution Is Unlimited 

Prepared for U.S. Army Engineer District, Los Angeles 
The contents of this report are not to be used for advertising, 

publication, or promotional purposes. Citation of trade names 

does not constitute an official endorsement or approval ofthe use 

of such commercial products. 

ft \.1 PRINTED ON RECYCLED PAPER 
Miscellaneous Paper HL-94-7 

October 1994 

Application of a Two-Dimensional Model 

of Hydrodynamics to San Timoteo Creek 

Flood-Control Channel, California 

by Richard L. Stockstill 

U.S. Army Corps of Engineers 

Waterways Experiment Station 

3909 Halls Ferry Road 

Vicksburg, MS 39180-6199 

Final report 

Approved for public release; distribution is unlimited 

Prepare,d for U.S. Army Engineer District, Los Angeles 

Los Angeles, CA 90053-2325 
US Army Corps 

of Engineers 

Waterways Experiment 

Station 

N 

HEADOUAIITERS 

BUILDING 

500 

FOR INFORMATION CONTACT: 

PUBLIC AFFAIRS OFFICE 

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WATERWAYS EXPERIMENT STATION 

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AREA OF RESERVATION _ 2.7sq km 

Waterways Experiment Station Cataloging-in-Publication Data 

Stockstill, Richard L. 

Application of a two-dimensional model of hydrodynamics to San Timoteo Creek 

flood-control channel, California / by Richard L. Stockstill; prepared for U.S. Army Engineer District, Los Angeles. 

49 p. : ill. ; 28 cm. - (Miscellaneous paper; HL-94-7) 

Includes bibliographic references. 

1. Flood control - California - San Bernardino County. 2. San Timoteo Creek 

(Calif.) - Channelization. 3. River engineering - California - San Timoteo Creek. 

4. Stream channelization - California - Riverside County. I. United States. Army. 

Corps of Engineers. Los Angeles District. II. U.S. Army Engineer Waterways Experiment Station. III. Hydraulics Laboratory (U.S.) IV. Title. V. Series: Miscellaneous 

paper (U.S. Army Engineer Waterways Experiment Station) ; HL-94-7. 

TA7 W34m no.HL~94-7 
Contents 

Preface 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 iv 

Conversion Factors, Non-SI to SI Units of Measurement 0 0 0 0 0 0 0 0 0 0 0 0 v 

1-lntroduction 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Background 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 

Purpose 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 

Approach 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 

2-Model Description 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 

Governing Equations 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 

Assumptions and Limitations 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 

3-Model Applications 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 

Geometry and Computational Mesh 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 

Boundary Conditions 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 

Model Parameters 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 

4-Results 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 

Design Discharge, 19,000 cfs 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 

Initial tests (n = 00014) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 

Decreased roughness (n = 00012) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 

12,000-cfs Discharge 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 

5-Summary and Conclusions 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 

References 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 

Tables 1-5 

Plates 1-12 

Appendix A: The Hydrodynamic Model: HIVEL2D 0 0 0 0 0 0 0 0 0 0 0 0 0 A1 

SF 298 

iii 
iv 

Preface 

The two-dimensional numerical modeling of the flow conditions in the 

proposed San Timoteo Channel was performed for the U. S. Army Engineer 

District, Los Angeles (SPL). The study was authorized by the U.S. Army 

Engineer Division, South Pacific, on 26 August 1993. SPL personnel 

involved in this study were Mr. Algis Bliudzius and Ms. Wendy Gist under 

the supervision of Mr. Brian Tracy, Chief of the Hydraulics Section. 

The study was conducted in the Hydraulics Laboratory of the U.S. Army 

Engineer Waterways Experiment Station (WES) during the period December 

1993 to April 1994 under the direction of Messrs. F. A. Herrmann, Jr., 

Director of the Hydraulics Laboratory; R. A. Sager, Assistant Director of the 

Hydraulics Laboratory; and G. A. Pickering, Chief of the Hydraulic Structures Division, Hydraulics Laboratory. 

This work was performed by Messrs. Richard L. Stockstill and Mikel W. 

Ott under the supervision of Mr. John F. George, Chief, Locks and Conduits 

Branch, Hydraulic Structures Division. Technical assistance in the form of 

consultation and peer review was provided by Dr. R. C. Berger, Estuaries 

Division, Hydraulics Laboratory. The report was prepared by Mr. Stockstill. 

At the time of publication of this report, Director of WES was 

Dr. Robert W. Whalin. Commander was COL Bruce K. Howard, EN. 

The contents of this repon are not to be used for advenising, pUblication, 

or promotional purposes. Citation of trade names does not constitute an 

official endorsement or approval of the use of such commercial products. 
Conversion Factors, Non-51 to 

51 Units of Measurement 

Non-SI units of measurement used in this report can be converted to SI units 

as follows: 

I Multiply I By I To Obtain 

cubic feet 0.02831685 cubic meters 

degrees (angle) 0.01745329 radians 

feet 0.3048 meters 

I 

v 
1 Introduction 

Background 

The San Timoteo Creek is a tributary of the Santa Ana River and drains 

portions of San Bernardino and Riverside Counties (Figure 1). The existing 

creek has the capacity to protect the surrounding community from approximately a 20-year-frequency flood (U.S. Army Engineer District, Los Angeles, 

1993). The recommended plan would provide a 100-year level of protection 

(19,000 CfS).l 

i I 

-N-

~ 

;;",_ "ARSH\AREA I " ' '\ 

Figure 1. Vicinity and location maps 

KS DAM 

The proposed design within the reach studied includes a sediment basin 

(the last of a series of basins for the project), a concrete weir followed by a 

chute having converging sidewalls, a compound horizontal curve consisting of 

spirals between a circular curve and the upstream and downstream tangents 

A table of factors for converting non-SI units of measurement to SI units is found on 

page v. 

Chapter 1 Introduction 

1 
2 

with a banked invert, and a bridge pier associated with the San Timoteo 

Canyon Road. The modeled reach extended from basin sta 5 +00 to channel 

sta 280+00, resulting in a total simulated channel length of 2,396.94 ft. 

Geometrical details of the proposed channel design are shown in the plan view 

provided in Plate 1. 

Purpose 

This investigation was initiated because there was concern as to the 

adequacy of a one-dimensional analysis of the flow conditions within the channel chute. There was a question as to whether computing cross-sectional averaged flow variables provided a sufficiently accurate estimate of flow depths 

within the geometrically complex chute. It was known that the supercritical 

flow in the chute would produce oblique standing waves. These waves do not 

present a problem as long as the channel walls are of sufficient height. However, the flow conditions in the upper end of the channel are further complicated by the fact that the chute is followed by a channel curve, followed by 

the San Timoteo Canyon Road bridge. A two-dimensional analysis was 

deemed necessary to evaluate the chute's influence on the flow conditions in 

the curve and the curve's impact on the flow conditions at the bridge. 

Approach 

The two-dimensional, depth-averaged flow model, HIVEL2D, was used to 

simulate the flows in the high-velocity channel. This model was chosen 

because of its ability to simulate supercritical flow and capture shocks such as 

oblique standing waves. 

Chapter 1 Introduction 
2 Model Description 

Governing Equations 

HIVEL2D (Stockstill and Berger 1994) solves the depth-averaged unsteady 

shallow-water equations implicitly using finite elements. The shallow-water 

equations are the tesult of vertical integration of the equations of mass and 

momentum conservation for incompressible flow assuming hydrostatic pressure distribution. The dependent variables of the two-dimensional fluid 

motion are defined by the flow depth and the x-direction and y-direction 

components of unit discharge. These variables are functions of the spatial 

Cartesian coordinates x and y and time. A brief description of the finite element model is provided in Appendix A. 

Assumptions and Limitations 

An important (and standard) assumption made in the derivation of the 

governing equations is that vertical accelerations are negligible when compared to the horizontal accelerations and the acceleration due to gravity. This 

assumes that the pressure distribution is hydrostatic. The hydrostatic pressure 

assumption is generally applicable to high-velocity channels; however, certain 

limited areas of the flow field are decidedly nonhydrostatic. One must resort 

to engineering judgment to assess the ramifications of this difference, noting 

that hydrostatic models overestimate the speed of short wavelengths. 

Another significant assumption is that the invert slope is geometrically mild 

(less than about 0.02), though it may be hydraulically steep, producing supercritical flow. This is a reasonable assumption for most high-velocity channels. 

However, the flow speed in long channel reaches with a favorable slope 

greater than about 0.05 will tend to be overestimated and the flow depth will 

tend to be underestimated, whereas adverse steep slopes will tend to overestimate the flow depth and underestimate the flow speed. A general discussion of the assumptions associated with the shallow-water equations is 

presented in Berger and Stockstill (1994). 

Chapter 2 Model Description 

3 
4 

3 Model Applications 

Application of the model to the proposed channel design requires the construction of a numerical model computational mesh to represent the design's 

geometry and the specification of boundary conditions and model parameters. 

Geometry and Computational Mesh 

The reach of the San Timoteo Creek channel modeled in this study was 

from basin sta 5+00 to 0+20 and from channel sta 299+ 16.94 to 280+00, a 

total length of 2,396.94 ft. The sub critical flow in the sediment basin at the 

upper end is controlled by the concrete weir, which begins the concrete-lined 

high-velocity channel. The upstream face of the weir is a IV on 2H slope. 

The weir crest, which is immediately followed by a 940-ft converging sidewall 

chute, is 20 ft long in the direction of flow. The chute was designed to transition from the 338-ft-wide sediment basin to the 86-ft-wide high-velocity channel. A channel bend is located 83.35 ft downstream of the chute end. The 

bend was designed with spiral curves and a banked invert. The San Timoteo 

Canyon Road crosses the channel downstream of the bend. One pier for this 

bridge is located within the channel, near the channel center line. Plate 1 

shows a plan view of the modeled reach. 

The width of the flow domain within the sediment basin is dependent on 

the water-surface elevation in this vicinity because the channel sidewalls are 

sloping. Therefore, the numerical model computational mesh of the sediment 

basin was different for the two discharges simulated. Initial numerical tests 

were conducted to determine an adequate top bank elevation to use for the 

domain limit. By trial, a top bank of elevation 1316.01 was found appropriate for modeling a discharge of 19,000 cfs. Representing the basin flow using 

a fixed grid was deemed adequate because the flow in this region is subcritical. Fixed grid boundary conditions are sufficient for simulation of steady 

subcritical flow in channels having sloping sidewall boundaries. 

All elevations (el) cited herein are in feet referenced to the National Geodetic Vertical 

Datum (NGVD). 

Chapter 3 Model Applications 
The San Timoteo Canyon Road bridge pier presently has a semicircular . 

nose and tail. The pier was modeled with a triangular nose and tail. Significantly more grid refinement would be needed to simulate a semicircular nose 

and tail and was not deemed necessary for this study. Proposed channel 

modifications include the addition of a debris nose on this pier. A sloping 

debris nose cannot be accurately modeled with a depth-averaged model; therefore, only the existing pier configuration was simulated in this study. 

The numerical model computational mesh is shown in Plate 2. The mesh 

consisted of 945 nodes and 918 elements. Grid resolution was more refined 

in the vicinity of sidewall boundary alignment changes and at all grade breaks. 

Boundary Conditions 

This study included the simulation of two discharges, the design discharge 

of 19,000 cfs and a lesser discharge of 12,000 cfs. The inflow boundary 

located in the sediment basin was subcritical and therefore required two 

boundary conditions. The x- and y-direction components of unit discharge 

were specified for the inflow boundary conditions. These unit discharges 

were computed assuming a constant velocity over the inflow boundary cross 

section. A water-surface elevation at the inflow boundary was assumed, then 

the inflow velocity was computed as the discharge divided by the flow area. 

The unit discharges were calculated as the product of the flow depth at each 

inflow node times the computed velocity. These unit discharges were further 

resolved into x- and y-components normal to the inflow boundary. The outflow boundary was supercritical and therefore required no boundary 

conditions. 

Model Parameters 

Model and flow parameters used in the initial simulation are provided in 

the following tabulation, where ex is the temporal differencing weight (ex = 1 

is first-order and ex = 1.5 is second-order backward differencing); (3SM and (3SH 

are the Petrov-Galerkin parameters for smooth flow and for shocks, respectively; CSM and CSH are the coefficients used in determination of eddy 

viscosity; and g is acceleration due to gravity. Descriptions of these 

conditions are presented in Appendix A. 

I Model Condition Ivalue I 

a 1.0 

flSM' flSH 0.1,0.5 

CSM' CSH 0.1,0.5 

g 32.2 ft/sec 2 

Chapter 3 Model Applications 

5 
6 

Becaus.e a steady-state solution was sought, the temporal difference order was 

irrelevant. Therefore, a first-order temporal differencing was used in all 

simulation runs. 

Chapter 3 Model Applications 
4 Results 

As stated previously, this study included the simulation of two discharges, 

the design discharge of 19,000 cfs and a lesser discharge of 12,000 cfs. This 

12,000-cfs discharge was selected for testing because a one-dimensional analysis conducted by the U.S. Army Engineer District, Los Angeles, found that 

the 12,000-cfs discharge actually resulted in larger Froude numbers in the 

channel chute. It was felt that these larger Froude numbers might be accompanied by higher standing waves at a particular station than those produced by 

the design discharge (19,000 cfs). 

The prototype flow geometry and boundary roughness for the concrete 

channel reach will most likely result in a Manning's n value of approximately 

0.014. The concrete reach of channel extends from the toe of the upstream 

face of the weir (basin sta 0+44 at center line) downstream to the end of the 

modeled reach (sta 280+00). However, an envelope of possible hydraulic 

conditions was established by also performing simulations of the flow conditions resulting from a very smooth boundary by using an n value of 0.012. 

All simulations used an n of 0.030 for the sediment basin, which has riprapped side slopes and a natural bed. 

The sensitivity of simulation results to the choice of model parameters and 

mesh refinement was determined. This sensitivity was established by changing one condition per run and then comparing the results with previous runs to 

assess the condition's impact on simulation results. 

Design Discharge, 19,000 cfs 

Initial tests (n = 0.014) 

Water-surface profiles resulting from a discharge of 19,000 cfs and an n 

value of 0.014 are presented in Plate 3 and in tabular form in Table 1. The 

profiles illustrate the variation in the depth of flow at the sidewalls resulting 

from supercritical flow in the channel chute. A significant setup is noted in 

the channel bend. It is interesting to note the rise in the water-surface elevation in the basin as the flow approaching the structure decelerates. Of course 

the total energy grade line decreases in the direction of flow, but due to the 

Chapter 4 Results 

7 
8 

gradual expansion of the basin, the velocity head reduction is greater than the 

loss of total head. It is clearly shown in the profile that sufficient clearance is 

provided through the San Timoteo Canyon Road bridge. The significant 

runup on the upstream face of the pier is more of a model artifact than what 

would actually occur. Vertical accelerations immediately upstream of the pier 

nose are of such magnitude that the hydrostatic assumption is not valid. 

A hydrostatic model provides a poor estimate of this sudden runup. To 

illustrate this point, a first approximation of the magnitude of these accelerations results in the conclusion that this pier nose runup is a violation of the 

hydrostatic assumption and that the runup is overestimated. A first approximation of the magnitude of these accelerations is obtained by applying the 

kinematic boundary condition to the water surface: 

where 

dh 

dt 

ah + I VI ah 

at as 

Ws = vertical component of velocity at the water surface 

h = flow depth 

t = time 

s = stream direction 

and 

(1) 

where u and v are the x- and y-direction components of velocity, respectively. 

The vertical acceleration az is: 

dw aw 

dt at + IVI aw 

as 

aw + w_ 

az 

Neglecting the last term and applying to steady flow, 

and 

IVI ah 

as 

(2) 

(3) 

Chapter 4 Results 
a = I VI oW = I VI ~ [I VI Oh] z oS oS oS (4) 

Using difference approximations of the results of a simulation of 

19,000 cfs and an n value of 0.014, the ratio of a/g at the pier nose was 

calculated to be 9.7. This definitely violates the hydrostatic assumption, i.e., 

that the vertical accelerations are negligible when compared to gravity (Appendix A). Pressures at the pier nose in the actual system (prototype) will be 

greater than hydrostatic, which will act to suppress the water-surface rise. 

Determination of what the water-surface elevation will be in the prototype is 

difficult. However, it will be significantly less than that calculated assuming a 

hydrostatic pressure distribution. 

To illustrate that the hydrostatic assumption is appropriate elsewhere in the 

flow field, the vertical acceleration was approximated in the area of the 

oblique standing wave initiated at the pier nose (sta 282+ 10, 10 ft right of 

center line). The vertical acceleration in this vicinity, relative to gravity, was 

calculated to be 0.4. Although this is not insignificant, it shows that the 

hydrostatic assumption is reasonable even in areas where the flow is extremely 

rough. 

Depth contours for a discharge of 19,000 cfs and an n value of 0.014 are 

presented in Figure 2. Depth contours within the chute are shown in figure 3. The contours illustrate the oblique standing waves resulting from the 

converging sidewalls. Vertically exaggerated water-surface mesh plots 

(Plates 4 and 5) show the variation in depths and the supere1evation in the 

channel bend. Depth contours in the vicinity of the bridge are provided in 

Figure 4. 

At this point in the study, there was interest in the effect of the oscillations 

of the computed depths at the sidewalls in the vicinity of the crest on the 

results downstream, particularly if these oscillations were a numerical rather 

than a physical phenomenon. A second run using the discharge of 19,000 cfs 

and an n value of 0.014 was made using a different Petrov-Galerkin weighting 

parameter for smooth flow, {3SM' This simulation used a {3SM of 0.25 rather 

than a {3 SM of 0.1, which was used in the initial simulation. The {3SM is the 

minimum damping parameter used throughout the flow field. 

The results obtained from the two {3SM'S are compared in Plate 6. These 

profiles show that the variation of {3SM resulted in only minor changes in the 

computed depths. Moreover, the two runs converged to practically the same 

solution 150 ft downstream of the crest. Therefore, it is apparent that the 

solution of this particular flow field is not significantly influenced by the 

choice of the Petrov-Galerkin weighting parameter, {3SM' 

The model's simulation of the flow in the crest vicinity was further 

analyzed by grid refinement. The density of the original mesh was doubled in 

both directions on and adjacent to the crest. Details of the original and 

Chapter 4 Results 

9 
10 

OEPTH. FT 

Figure 2. Depth contours for the design discharge (n 0.014) 

refined grids in this area are provided in Plate 7. 

Water-surface profiles for the design discharge and an n value of 0.014 

computed using the refined grid are shown in Plate 8 and Table 2. The 

refined solution also oscillated at the crest. The results obtained from the 

original and fine grids «(3 SM = 0.1 for both tests) are compared in Plate 9. 

Again it is apparent that a node-to-node oscillation occurred upstream and 

downstream of the point at which the flow was accelerating from subcritical to 

supercritical regardless of grid refinement. The oscillations were pronounced 

only at the sidewalls where the flow passed around the wing walls and 

intercepted the converging sidewalls. Therefore, it is difficult to determine 

whether these results are a numerical artifact or physical. However, the 

solutions converged at a distance of 150 ft downstream of the crest. 

Therefore, using the original grid and a (3SM of 0.1 are adequate for design 

purposes and were used throughout the remainder of the study. 

Chapter 4 Results 
Figure 3. Depth contours within the chute (discharge 

n = 0.014) 

Decreased roughness (n = 0.012) 

19,000 cfs and 

Water-surface profiles produced by a discharge of 19,000 cfs and an n 

value of 0.012 are presented in Plate 10 and Table 3. The reduced n value 

resulted in the heights of the standing waves being about the same, but the 

wave crests were located further downstream compared to those from an n 

value of 0.014. The flow conditions within the reach are much more 

dependent on the channel form rather than channel friction; that is, the converging sidewalls in the chute, the horizontal curve, and the bridge pier had 

such an effect on the flow that the differences in an n value of 0.012 compared to an n value of 0.014 were insignificant. The maximum water-surface 

Chapter 4 Results 

11 
DEPTH. fT 

Figure 4. Depth contours in vicinity of San Timoteo Canyon Road bridge pier (discharge 

19,000 cfs and n = 0.014) 

12 

elevations computed using an n value of 0.012 were less than or equal to 

those computed using an n value of 0.014. 

12,OOO-cfs Discharge 

A new numerical model computational mesh was constructed for the simulation of a discharge of 12,000 cfs. This new mesh was needed because the 

domain width in the sediment basin was reduced from that resulting from a 

discharge of 19,000 cfs. The top bank elevation was selected by first determining the expected water-surface elevation in the basin for a discharge of 

12,000 cfs. Given the water-surface elevation simulated for a discharge of 

19,000 cfs, a discharge coefficient for the "broad-crested weir" was calculated. This discharge coefficient was then used to compute the basin watersurface elevation for a discharge of 12,000 cfs. It was then determined that a 

top bank elevation of 1314.0 was appropriate to use to construct the grid for 

the lesser discharge. The numerical model computational mesh for a discharge of 12,000 cfs differed from the original mesh only in the vicinity of 

the side boundaries within the basin. 

Simulation results with a discharge of 12,000 cfs for n values of 0.014 and 

0.012 are presented as water-surface profiles in Plates 11 and 12 and Tables 4 

and 5, respectively. As expected, the depths are less than those produced by 

the design discharge and no adverse standing waves were noted. The 

Chapter 4 Results 
maximum water-surface elevations resulting from a discharge of 12,000 cfs 

using either an n value of 0.014 or an n value of 0.012 were less than those 

computed for the design discharge with an n value of 0.014. 

Chapter 4 Results 

13 
14 

5 Summary and Conclusions 

Two-dimensional (depth-averaged) simulations of the flow conditions in the 

San Timoteo Channel were conducted to assess the adequacy of the proposed 

design. Particular attention was given to the variation in flow depths within 

the entrance chute. The flow at the crest accelerated from subcritical to 

supercritical flow and remained supercritical through the chute and channel 

thereafter. Oblique standing waves were produced when the supercritical flow 

intercepted the chute's laterally converging sidewalls. However, these standing waves were expected and given that the sidewalls will be designed of sufficient height, the flow conditions were deemed acceptable. 

The prototype flow geometry and boundary roughness will most likely 

result in a Manning's n value approximately equal to 0.014. However, flow 

conditions resulting from a Manning's n value of 0.012 were also simulated so 

that an envelope of possible hydraulic conditions could be established. Along 

this same line of reasoning, in addition to the design discharge (19,000 cfs), a 

smaller discharge (12,000 cfs) was simulated. For a given discharge, there 

was no significant difference in the water-surface elevations computed using 

an n value of 0.014 and an n value of 0.012. The smaller n value did, however, result in the wave crests being located further downstream due to the 

increase in velocity. No adverse flow conditions were noted for a discharge 

of 12,000 cfs. 

Simulation results indicate that the proposed San Timoteo Channel design 

and in particular, the San Timoteo Canyon Road bridge, will convey the 

design discharge of 19,000 cfs in an acceptable manner. The prototype will 

experience significantly less runup on the pier nose than the simulation results 

indicated. Sidewall heights should be designed based on the simulation results 

realizing the uncertainties associated with the analyses. 

Chapter 5 Summary and Conclusions 
References 

Abbott, M. B. (1979). Computational hydraulics, elements of the theory of 

free sUlface flows. Pitman Advanced Publishing Limited, London. 

Berger, R. C. (1993). "A finite element scheme for shock capturing," 

Technical Report HL-93-12, U.S. Army Engineer Waterways Experiment 

Station, Vicksburg, MS. 

Berger, R. c., and Stockstill, R. L. (1994). "Considerations in 2-D 

modeling of hydraulically steep flow." Hydraulic engineering, Proceedings, 

1994 National Conference, ASCE, Buffalo, New York, 1-5 August 1994. 

New York, 1285-1289. 

Rodi, W. (1980). "Turbulence models and their application in hydraulics - A 

state of the art review," State-of-the Art Paper, International Association 

for Hydraulic Research, Delft, The Netherlands. 

Stockstill, R. L., and Berger, R. C. (1994). "HIVEL2D: A two-dimensional 

flow model for high-velocity channels," Technical Report REMR-HY-12, 

U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS. 

U.S. Army Engineer District, Los Angeles. (1993). "Santa Ana River Mainstem Project including Santiago Creek; Basis for design - San Timoteo 

Creek, channel and sediment control structure," Design Memorandum 

No.7, Vols 1 and 2, Los Angeles, CA. 

References 

15 
Irable 1 

Water-Surface Elevations, Discharge 19,000 cfs, n = 0.014 

Elevation Elevation Elevation 

~tation Left Side Station Center IStation Right Side 

5 + 00.00 1317.45 5 + 00.00 1317.51 5 + 00.00 1317.74 

4 + 42.82 1317.56 4 + 40.00 1317.52 4 + 50.89 1317.16 

3 + 83.61 1317.54 3 + 80.00 1317.63 3 + 91.28 1317.61 

3 + 83.60 1317.51 3 + 20.00 1317.70 3 + 46.00 1317.67 

3 + 43.97 1317.68 2 + 72.00 1317.75 2 + 87.60 1317.74 

3 + 06.91 1317.80 2 + 24.00 1317.79 2 + 47.99 1317.75 

2 + 70.02 1317.82 1 + 88.00 1317.81 2 + 11.60 1317.79 

2 + 29.47 1317.88 1 + 64.00 1317.82 1 + 75.99 1317.78 

1 + 87.11 1317.78 1 + 40.00 1317.84 1 + 55.55 1317.81 

1 + 61.01 1317.77 1 + 16.00 1317.83 1 + 27.99 1317.79 

1 + 39.81 1317.85 o + 92.00 1317.89 1 + 03.99 1317.82 

1 + 18.76 1317.83 o + 68.00 1317.83 0+79.99 1317.77 

o + 97.88 1317.85 0+44.00 1317.97 o + 55.39 1317.82 

o + 81.31 1317.84 299 + 16.94 1317.35 o + 42.45 1317.55 

o + 68.04 1317.80 298 + 96.94 1314.69 0+31.32 1317.92 

o + 55.40 1317.87 298 + 76.94 1313.98 299 + 16.94 1317.85 

o + 43.51 1317.64 298 + 46.94 1313.38 299 + 16.94 1317.79 

o + 31.61 1318.02 298 + 22.94 1313.03 299 + 06.94 1314.79 

299 + 16.94 1317.92 297 + 90.94 1311.63 298 + 96.94 1317.44 

299 + 16.94 1317.77 297 + 58.94 1311.98 298 + 86.94 1315.51 

299 + 06.94 1315.51 297 + 26.94 1312.77 298 + 76.94 1315.91 

298 + 96.94 1317.38 296 + 96.94 1312.14 298 + 61.94 1315.07 

298 + 86.94 1315.93 296 + 66.94 1311.65 298 + 46.94 1314.76 

298 + 76.94 1316.00 296 + 36.94 1311.13 298 + 22.94 1314.16 

298 + 61.94 1315.32 296 + 06.94 1310.53 297 + 90.94 1313.57 

298 + 46.94 1314.95 295 + 74.94 1309.90 297 + 58.94 1312.91 

298 + 22.94 1314.34 295 + 45.61 1309.75 297 + 26.94 1312.39 

297 + 90.94 1313.68 295 + 16.28 1308.97 296 + 96.94 1311.60 

297 + 58.94 1313.03 294 + 86.94 1308.28 296 + 66.94 1311.27 

297 + 26.94 1312.47 294 + 46.94 1308.29 296 + 36.94 1310.47 

296 + 96.94 1311.75 294 + 06.94 1308.24 296 + 06.94 1309.45 

296 + 66.94 1311.31 293 + 64.94 1307.38 295 + 74.94 1310.02 

296 + 36.94 1310.51 293 + 22.94 1305.26 295 + 45.61 1310.23 

296 + 06.94 1309.70 292 + 80.94 1302.82 295 + 16.28 1310.01 

295 + 74.94 1309.99 292 + 38.94 1301.92 294 + 86.94 1309.64 

295 + 45.61 1310.13 291 + 96.94 1302.10 294 + 46.94 1308.50 

295 + 16.28 1309.92 291 + 54.94 1301.81 294 + 26.94 1308.13 

294 + 86.94 1309.52 291 + 12.94 1299.90 294 + 06.94 1306.86 

294 + 46.94 1308.40 290 + 70.94 1297.82 293 + 85.94 1304.79 

294 + 26.94 1308.08 290 + 28.94 1297.11 293 + 64.94 1305.07 

294 + 06.94 1306.76 290 + 07.94 1297.11 293 + 22.94 1305.32 

293 + 85.94 1304.68 289 + 86.94 1297.11 292 + 80.94 1304.65 

293 + 64.94 1305.01 289 + 66.29 1296.89 292 + 38.94 1303.35 

293 + 22.94 1305.38 289 + 45.64 1296.49 291 + 96.94 1301.28 

(Continuedll 

Note: Sides of channel are referenced to looking downstream. 
~able 1 (Concluded) I 

Elevation Elevation Elevation 

~tation Left Side Station Center ~tation Right Side 

292 + 38.94 1303.42 288 + 70.26 1293.77 291 + 12.94 1299.80 

291 + 96.94 1301.38 288 + 36.92 1293.27 290 + 70.94 1299.18 

291 + 54.94 1299.80 288 + 03.59 1293.76 290 + 28.94 1297.77 

291 + 12.94 1299.66 287 + 61.97 1293.71 290 + 07.94 1297.35 

290 + 70.94 1299.11 287 + 20.35 1292.78 289 + 86.94 1296.37 

290 + 28.94 1297.78 286 + 78.74 1291.78 289 + 66.29 1294.72 

290 + 07.94 1297.39 286 + 37.12 1291.29 289 + 45.64 1294.44 

289 + 86.94 1296.20 285 + 95.50 1291.04 289 + 03.59 1295.31 

289 + 66.29 1294.78 285 + 53.88 1290.68 288 + 70.26 1296.03 

289 + 45.64 1294.46 285 + 12.26 1290.07 288 + 36.92 1295.63 

289 + 03.59 1295.34 284 + 70.64 1289.44 288 + 03.59 1295.48 

288 + 70.26 1294.11 284 + 29.03 1288.87 287 + 61.97 1294.68 

288 + 36.92 1292.63 283 + 87.41 1288.43 287 + 20.35 1294.26 

288 + 03.59 1291.11 283 + 45.79 1287.89 286 + 78.74 1293.96 

287 + 61.97 1290.65 283 + 12.46 1287.49 286 + 37.12 1293.57 

287 + 20.35 1290.68 282 + 79.12 1286.99 285 + 95.50 1293.17 

286 + 78.74 1290.26 282 + 62.46 1286.65 285 + 53.88 1292.68 

286 + 37.12 1289.32 282 + 45.79 1286.44 285 + 12.26 1292.32 

285 + 95.50 1288.37 282 + 38.08 1286.43 284 + 70.64 1291.80 

285 + 53.88 1287.70 282 + 30.38 1286.15 284 + 29.03 1291.04 

285 + 12.26 1287.28 282 + 25.25 1285.51 283 + 87.41 1290.37 

284 + 70.64 1286.94 282 + 20.12 1295.03 283 + 45.79 1289.82 

284 + 29.03 1286.56 281 + 76.12 1282.46 283 + 12.46 1288.67 

283 + 87.41 1286.14 281 + 75.50 1281.66 282 + 79.12 1287.03 

283 + 45.79 1285.63 281 + 71.89 1283.52 282 + 62.46 1287.00 

283 + 12.46 1286.01 281 + 65.46 1284.70 282 + 45.79 1286.79 

282 + 79.12 1286.52 281 + 59.22 1285.35 282 + 32.98 1286.64 

282 + 62.46 1286.77 281 + 50.18 1285.78 282 + 20.12 1286.52 

282 + 45.79 1286.81 281 + 39.32 1286.22 282 + 09.11 1286.37 

282 + 32.98 1286.39 281 + 23.85 1285.84 281 + 98.11 1286.62 

282 + 20.12 1286.22 280 + 95.40 1285.89 281 + 87.10 1286.17 

282 + 09.11 1286.12 280 + 63.60 1286.07 281 + 76.09 1286.30 

281 + 98.11 1285.97 280 + 31.80 1285.75 281 + 59.61 1287.43 

281 + 87.10 1286.01 280 + 00.00 1285.20 281 + 43.10 1287.38 

281 + 76.09 1285.38 281 + 27.20 1286.27 

281 + 59.61 1285.86 280 + 95.40 1285.06 

281 + 43.10 1287.03 280 + 63.60 1284.93 

281 + 27.20 1286.71 280 + 31.80 1285.13 

280 + 95.40 1285.25 280 + 00.00 1285.36 

280 + 63.60 1285.03 

280 + 31.80 1285.38 

280 + 00.00 1285.92 
lTable 2 

lWater~Surface Elevations, Discharge 19,000 cfs, n = 0.014, Fine 

Grid 

Elevation Elevation 

Ei'~ Station Left Side Station Center ~tation Right 

5 + 00.00 1317.34 5 + 00.00 1317.40 5 + 00.00 1317.66 

4 + 42.82 1317.45 4 + 40.00 1317.42 4 + 50.89 1317.03 

3 + 83.61 1317.43 3 + 80.00 1317.52 3 + 91.28 1317.50 

3 + 83.60 1317.39 3 + 20.00 .59 3 + 46.00 1317.57 

3 + 43.97 1317.57 2 + 72.00 1317.65 2 + 87.60 1317.62 

3 + 06.91 1317.69 == 2 + 24.00 1317.69 • 2 + 47.99 1317.65 

2 + 70.02 1317.71 1 + 88.00 1317.70 2 + 11.60 1317.67 

2 + 29.47 1317.78 1 + 64.00 1317.72 1 + 75.99 1317.69 

1 +87.11 1317.67 1 + 40.00 1317.73 1 + 55.55 1317.70 

1 + 61.01 1317.67 1 + 16.00 1317.74 1 + 27.99 1317.70 

1 + 39.81 1317.74 o + 92.00 1317.76 1 + 03.99 1317.71 

1 + 18.76 1317.74 o + 68.00 1317.77 0+79.99 1317.68 

0+97.88 1317.73 0+44.00 1317.78 0+ 55.39 1317.70 

o + 81.31 1317.74 o + 32.00 1317.71 0+42.45 1317.47 

0+68.04 1317.69 299 + 16.94 1316.98 0+31.32 1317.80 

o + 55.40 1317.76 299 + 06.94 1314.92 299 + 16.94 1317.68 

o + 43.51 1317.55 298 + 96.94 1314.87 299 + 16.94 1317.77 

0+31.61 1317.91 298 + 76.94 1314.11 299 + 11.94 1314.02 

299 + 16.94 1317.65 298 + 46.94 1313.47 299 + 06.94 1317.14 

299 + 16.94 1317.88 298 + 22.94 1312.83 299 + 01.94 ~.68 

1~9 + 11.94 1315.11 297 + 90.94 1311.91 298 + 96.94 16.77 

9 + 06.94 1317.18 297 + 58.94 1312.44 298 + 91.94 1316.08 

299 + 01.94 1316.10 297 + 26.94 1312.67 298 + 86.94 1316.00 

298 + 96.94 1316.91 296 + 96.94 1312.09 298 + 81.94 1315.72 

298 + 91.94 1316.36 296 + 66.94 1311.64 298 + 76'9~15'55 

= 298 + 86.94 1316.19 296 + 36.94 1311.05 298 + 66.94 15.30 

298 + 81.94 1315.96 296 + 06.94 1310.52 298 + 46.94 14.73 

298 + 76.94 1315.78 295 + 74.94 1309.96 298 + 22.94 1314.21 

298 + 66.94 1315.51 295 + 45.61 1309.74 297 + 90.94 1313.55 

I~ + 46.94 1314.93 295 + 16.28 1308.87 297 + 58.94 1312.94 

+ 22.94 1314.38 294 + 86.94 1308.44 297 + 26.94 312.3~-i1 297 + 90.94 1313.69 294 + 46.94 1308.54 296 + 96.94 311.68 

297 + 58.94 1313.05 294 + 06.94 1308.15 296 + 66.94 311.23 

:297 + 26.94 1312.47 293 + 64.94 1307.28 296 + 36.94 1310.29 

'296 + 96.94 1311.81 1293 + 22.94 1305.23 296 + 06.94 1309.67 

296 + 66.94 1311.27 292 + 80.94 1302.88 295 + 74.94 1310.33 

296 + 36.94 1310.43 292 + 38.94 1302.03 295 + 45.61 1310.19 

296 + 06.94 1309.89 291 + 96.94 1302.10 295 + 16.28 1310.00 

295 + 74.94 1310.23 291 + 54.94 1301.71 294 + 86.94 1309.63 

.295 + 45.61 1310.11 291 + 12.94 1299.83 294 + 46.94 1308.39 

1295 + 16.28 1309.88 290 + 70.94 1297.87 294 + 26.94 1308.08 

294 + 86.94 1309.50 290 + 28.94 1297.20 294 + 06.94 1306.88 

294 + 46.94 1308.30 290 + 07.94 1297.13 293 + 85.94 1304.85 

(Continued) 

I~ Sides of channel are referenced to looking downstream. 
Table 2 (Concluded) 

Elevation Elevation Elevation 

Station Left Side ~tation Center Station Right Side 

294 + 26.94 1308.01 289 + 86.94 1297.09 293 + 64.94 1305.26 

294 + 06.94 1306.76 289 + 66.29 1296.88 293 + 22.94 1305.32 

293 + 85.94 1304.71 289 + 45.64 1296.38 292 + 80.94 1304.58 

293 + 64.94 1305.23 289 + 03.59 1294.99 292 + 38.94 1303.28 

293 + 22.94 1305.40 288 + 70.26 1293.92 291 + 96.94 1301.27 

292 + 80.94 1304.67 288 + 36.92 1293.39 291 + 54.94 1299.90 

292 + 38.94 1303.36 288 + 03.59 1293.74 291 + 12.94 1299.83 

291 + 96.94 1301.38 287 + 61.97 1293.67 290 + 70.94 1299.13 

291 + 54.94 1299.88 287 + 20.35 1292.76 290 + 28.94 1297.73 

291 + 12.94 1299.67 286 + 78.74 1291.81 290 + 07.94 1297.52 

290 + 70.94 1299.05 286 + 37.12 1291.32 289 + 86.94 1296.11 

290 + 28.94 1297.80 285 + 95.50 1291.06 289 + 66.29 1294.81 

290 + 07.94 1297.24 285 + 53.88 1290.67 289 + 45.64 1294.55 

289 + 86.94 1296.15 285 + 12.26 1290.06 289 + 03.59 1295.26 

289 + 66.29 1294.92 284 + 70.64 1289.44 288 + 70.26 1296.03 

289 + 45.64 1294.74 284 + 29.03 1288.89 288 + 36.92 1295.63 

289 + 03.59 1295.14 283 + 87.41 1288.43 288 + 03.59 1295.48 

288 + 70.26 1294.07 283 + 45.79 1287.89 287 + 61.97 1294.72 

288 + 36.92 1292.74 283 + 12.46 1287.49 287 + 20.35 1294.29 

288 + 03.59 1291.14 282 + 79.12 1286.98 286 + 78.74 1293.94 

287 + 61.97 1290.64 282 + 62.46 1286.64 286 + 37.12 1293.58 

287 + 20.35 1290.67 282 + 45.79 1286.47 285 + 95.50 1293.14 

286 + 78.74 1290.25 282 + 38.08 1286.44 285 + 53.88 1292.74 

286 + 37.12 1289.32 282 + 30.38 1286.17 285 + 12.26 1292.31 

285 + 95.50 1288.38 282 + 25.25 1285.47 284 + 70.64 1291.74 

285 + 53.88 1287.73 282 + 20.12 1295.00 284 + 29.03 1291.05 

285 + 12.26 1287.30 281 + 76.12 1282.46 283 + 87.41 1290.38 

284 + 70.64 1286.94 281 + 75.50 1281.62 283 + 45.79 1289.83 

284 + 29.03 1286.55 281 + 71.89 1283.48 283 + 12.46 1288.70 

283 + 87.41 1286.14 281 + 65.46 1284.66 282 + 79.12 1287.05 

283 + 45.79 1285.63 281 + 59.22 1285.33 282 + 62.46 1286.95 

283 + 12.46 1286.01 281 + 50.18 1285.84 282 + 45.79 1286.76 

282 + 79.12 1286.51 281 + 39.32 1286.07 282 + 32.98 1286.67 

282 + 62.46 1286.72 281 + 23.85 1285.85 282 + 20.12 1286.53 

282 + 45.79 1286.84 280 + 95.40 1285.85 282 + 09.11 1286.37 

282 + 32.98 1286.43 280 + 63.60 1286.11 281 + 98.11 1286.59 

282 + 20.12 1286.23 280 + 31.80 1285.78 281 + 87.10 1286.18 

282 + 09.11 1286.13 280 + 00.00 1285.18 281 + 76.09 1286.33 

281 + 98.11 1285.95 281 + 59.61 1287.48 

281 + 87.10 1286.03 281 + 43.10 1287.34 

281 + 76.09 1285.35 281 + 27.20 1286.35 

281 + 59.61 1285.92 280 + 95.40 1284.96 

281 + 43.10 1286.97 280 + 63.60 1284.9 

281 + 27.20 1286.75 280 + 31.80 1285.31 

280 + 95.40 1285.23 280 + 00.00 1285.32 

280 + 63.60 1285.10 

280 + 31.80 1285.90 

280 + 00.00 1285.36 
lTable 3 

iWater-Surface Elevations, Discharge 19,000 cfs, n = 0.012 

Elevation Elevation Elevation 

~tation Left Side Station Center Station Right Side 

5 + 00.00 1317.44 5 + 00.00 1317.50 5 + 00.00 1317.74 

4 + 42.82 1317.55 4 + 40.00 1317.52 4 + 50.89 1317.15 

3 + 83.61 1317.54 3 + 80.00 1317.62 3 + 91.28 1317.60 

3 + 83.60 1317.50 3 + 20.00 1317.69 3 + 46.00 1317.66 

3 + 43.97 1317.67 2 + 72.00 1317.75 2 + 87.60 1317.73 

3 + 06.91 1317.79 2 + 24.00 1317.78 2 + 47.99 1317.74 

2 + 70.02 1317.81 1 + 88.00 1317.80 2 + 11.60 1317.78 

2 + 29.47 1317.87 1 + 64.00 1317.81 1 + 75.99 1317.77 

1 + 87.11 1317.77 1 + 40.00 1317.83 1 + 55.55 1317.80 

1 + 61.01 1317.76 1 + 16.00 1317.83 1 + 27.99 1317.78 

1 + 39.81 1317.84 o + 92.00 1317.88 1 + 03.99 1317.82 

1 + 18.76 1317.82 o + 68.00 1317.82 o + 79.99 1317.76 

o + 97.88 1317.84 0+44.00 1317.96 0+55.39 1317.82 

o + 81.31 1317.83 299 + 16.94 1317.34 o + 42.45 1317.54 

o + 68.04 1317.79 298 + 96.94 1314.68 0+31.32 1317.92 

o + 55.40 1317.86 298 + 76.94 1313.97 299 + 16.94 1317.85 

o + 43.51 1317.63 298 + 46.94 1313.30 299 + 16.94 1317.77 

o + 31.61 1318.02 298 + 22.94 1313.01 299 + 06.94 1314.74 

299 + 16.94 1317.77 297 + 90.94 1311.71 298 + 96.94 1317.46 

299 + 16.94 1317.91 297 + 58.94 1311.52 298 + 86.94 1315.45 

299 + 06.94 1315.48 297 + 26.94 1312.64 298 + 76.94 1315.91 

298 + 96.94 1317.39 296 + 96.94 1312.12 298 + 61.94 1315.03 

298 + 86.94 1315.89 296 + 66.94 1311.50 298 + 46.94 1314.75 

298 + 76.94 1316.00 296 + 36.94 1311.11 298 + 22.94 1314.11 

298 + 61.94 1315.29 296 + 06.94 1310.55 297 + 90.94 1313.53 

298 + 46.94 1314.94 295 + 74.94 1309.81 297 + 58.94 1312.84 

298 + 22.94 1314.29 295 + 45.61 1309.43 297 + 26.94 1312.35 

297 + 90.94 1313.64 295 + 16.28 1309.02 296 + 96.94 1311.55 

297 + 58.94 1312.98 294 + 86.94 1308.26 296 + 66.94 1311.04 

297 + 26.94 1312.42 294 + 46.94 1307.40 296 + 36.94 1310.62 

296 + 96.94 1311.69 294 + 06.94 1307.87 296 + 06.94 1309.40 

296 + 66.94 1311.15 293 + 64.94 1307.68 295 + 74.94 1309.26 

296 + 36.94 1310.61 293 + 22.94 1305.41 295 + 45.61 1309.97 

296 + 06.94 1309.61 292 + 80.94 1302.89 295 + 16.28 1309.86 

295 + 74.94 1309.38 292 + 38.94 1301.21 294 + 86.94 1309.46 

295 + 45.61 1309.85 291 + 96.94 1301.12 294 + 46.94 1308.53 

295 + 16.28 1309.78 291 + 54.94 1301.79 294 + 26.94 1308.23 

294 + 86.94 1309.37 291 + 12.94 1300.68 294 + 06.94 1306.84 

294 + 46.94 1308.39 290 + 70.94 1298.05 293 + 85.94 1304.79 

294 + 26.94 1308.13 290 + 28.94 1296.36 293 + 64.94 1304.28 

294 + 06.94 1306.73 290 + 07.94 1295.99 293 + 22.94 1304.77 

293 + 85.94 1304.73 289 + 86.94 1296.19 292 + 80.94 1304.49 

293 + 64.94 1304.18 289 + 66.29 1296.26 292 + 38.94 1303.63 

293 + 22.94 1304.70 289 + 45.64 1296.82 291 + 96.94 1301.63 

I (ContinUed)1 

Note: Sides of channel are referenced to looking downstream. 
~able 3 (Concluded) I 

Elevation Elevation Elevation 

Station Left Side Station Center Station Right Side 

292 + 80.94 1304.62 289 + 03.59 1295.65 291 + 54.94 1299.34 

292 + 38.94 1303.72 288 + 70.26 1293.85 291 + 12.94 1298.91 

291 + 96.94 1301.68 288 + 36.92 1292.55 290 + 70.94 1299.06 

291 + 54.94 1299.45 288 + 03.59 1292.74 290 + 28.94 1298.00 

291 + 12.94 1298.81 287 + 61.97 1293.40 290 + 07.94 1297.35 

290 + 70.94 1298.93 287 + 20.35 1292.98 289 + 86.94 1296.28 

290 + 28.94 1298.00 286 + 78.74 1291.83 289 + 66.29 1294.50 

290 + 07.94 1297.39 286 + 37.12 1290.83 289 + 45.64 1293.76 

289 + 86.94 1296.35 285 + 95.50 1290.44 289 + 03.59 1295.04 

289 + 66.29 1294.28 285 + 53.88 1290.33 288 + 70.26 1295.79 

289 + 45.64 1293.95 285 + 12.26 1289.96 288 + 36.92 1295.60 

289 + 03.59 1294.81 284 + 70.64 1289.28 288 + 03.59 1295.55 

288 + 70.26 1293.77 284 + 29.03 1288.52 287 + 61.97 1294.57 

288 + 36.92 1292.81 283 + 87.41 1287.97 287 + 20.35 1293.96 

288 + 03.59 1291.05 283 + 45.79 1287.51 286 + 78.74 1293.86 

287 + 61.97 1290.06 283 + 12.46 1287.20 286 + 37.12 1293.70 

287 + 20.35 1289.79 282 + 79.12 1286.73 285 + 95.50 1293.18 

286 + 78.74 1289.65 282 + 62.46 1286.39 285 + 53.88 1292.57 

286 + 37.12 1289.01 282 + 45.79 1286.17 285 + 12.26 1292.06 

285 + 95.50 1288.02 282 + 38.08 1286.12 284 + 70.64 1291.60 

285 + 53.88 1287.13 282 + 30.38 1285.85 284 + 29.03 1291.08 

285 + 12.26 1286.59 282 + 25.25 1285.15 283 + 87.41 1290.44 

284 + 70.64 1286.33 282 + 20.12 1294.72 283 + 45.79 1289.81 

284 + 29.03 1286.02 281 + 76.12 1282.46, 283 + 12.46 1288.59 

283 + 87.41 1285.55 281 + 75.50 1281.35 282 + 79.12 1286.83 

283 + 45.79 1284.94 281 + 71.89 1282.94 282 + 62.46 1286.67 

283 + 12.46 1285.31 281 + 65.46 1284.10 282 + 45.79 1286.46 

282 + 79.12 1285.88 281 + 59.22 1284.84 282 + 32.98 1286.34 

282 + 62.46 1286.17 281 + 50.18 1285.30 282 + 20.12 1286.19 

282 + 45.79 1286.46 281 + 39.32 1285.78 282 + 09.11 1286.02 

282 + 32.98 1286.06 281 + 23.85 1285.72 281 + 98.11 1286.08 

282 + 20.12 1285.83 280 + 95.40 1285.43 281 + 87.10 1286.10 

282 + 09.11 1285.84 280 + 63.60 1285.57 281 + 76.09 1285.47 

281 + 98.11 1285.72 280 + 31.80 1285.51 281 + 59.61 1286.47 

281 + 87.10 1285.84 280 + 00.00 1285.03 281 + 43.10 1287.08 

281 + 76.09 1285.37 281 + 27.20 1286.41 

281 + 59.61 1285.37 280 + 95.40 1284.80 

281 + 43.10 1286.37 280 + 63.60 1284.37 

281 + 27.20 1286.53 280 + 31.80 1284.59 

280 + 95.40 1284.99 280 + 00.00 1284.71 

280 + 63.60 1284.49 

280 + 31.80 1284.62 

280 + 00.00 1284.86 
Table 4 

Water-Surface Elevations, Discharge 12,000 cfs, n = 0.014 

Elevation Elevation Elevation 

Station Left Side Station Center Station Right Side 

'5 + 00.00 1315.82 5 + 00.00 1315.89 5 + 00.00 1315.99 

4 + 42.82 1315.94 4 + 40.00 1315.90 4 + 50.89 1315.72 

3 + 83.61 1315.93 3 + 80.00 1315.95 3 + 91.28 1315.95 

3 + 83.60 1315.91 3 + 20.00 1315.99 3 + 46.00 1315.97 

3 + 43.97 1315.96 2 + 72.00 1316.02 2 + 87.60 1316.01 

3 + 06.91 1316.05 2 + 24.00 1316.04 2 + 47.99 1316.01 

2 + 70.02 1316.05 1 + 88.00 1316.05 2 + 11.60 1316.04 

2 + 29.47 1316.08 1 + 64.00 1316.05 1 + 75.99 1316.03 

1 + 87.11 1316.04 1 + 40.00 1316.06 1 + 55.55 1316.05 

1 + 61.01 1316.03 1 + 16.00 1316.06 1 + 27.99 1316.03 

1 + 39.81 1316.07 o + 92.00 1316.09 1 + 03.99 1316.06 

1 + 18.76 1316.05 o + 68.00 1316.05 0+79.99 1316.02 

o + 97.88 1316.07 0+44.00 1316.15 o + 55.39 1316.03 

0+81.31 1316.05 299 + 16.94 1315.74 o + 42.45 1315.94 

o + 68.04 1316.03 298 + 96.94 1313.61 0+31.32 1315.98 

o + 55.40 1316.07 298 + 76.94 1313.04 299 + 16.94 1315.72 

o + 43.51 1315.94 298 + 46.94 1312.35 299 + 16.94 1315.78 

o + 31.61 1316.09 298 + 22.94 1312.00 299 + 06.94 1314.50 

299 + 16.94 1316.01 297 + 90.94 1311.32 298 + 96.94 1315.44 

299 + 16.94 1315.80 297 + 58.94 1310.41 298 + 86.94 1314.50 

299 + 06.94 1314.54 297 + 26.94 1310.81 298 + 76.94 1314.25 

298 + 96.94 1315.54 296 + 96.94 1310.91 298 + 61.94 1313.81 

298 + 86.94 1314.58 296 + 66.94 1310.21 298 + 46.94 1313.45 

298 + 76.94 1314.40 296 + 36.94 1309.69 298 + 22.94 1312.95 

298 + 61.94 1313.91 296 + 06.94 1309.32 297 + 90.94 1312.31 

298 + 46.94 1313.57 295 + 74.94 1308.76 297 + 58.94 1311.81 

298 + 22.94 1313.03 295 + 45.61 1308.22 297 + 26.94 1311.19 

297 + 90.94 1312.40 295 + 16.28 1307.87 296 + 96.94 1310.71 

297 + 58.94 1311.85 294 + 86.94 1307.34 296 + 66.94 1309.90 

297 + 26.94 1311.27 294 + 46.94 1306.11 296 + 36.94 1309.60 

296 + 96.94 1310.72 294 + 06.94 1305.15 296 + 06.94 1308.89 

296 + 66.94 1310.01 293 + 64.94 1305.51 295 + 74.94 1308.05 

296 + 36.94 1309.61 293 + 22.94 1303.99 295 + 45.61 1307.92 

296 + 06.94 1308.91 292 + 80.94 1301.95 295 + 16.28 1308.12 

295 + 74.94 1308.16 292 + 38.94 1300.15 294 + 86.94 1307.87 

295 + 45.61 1308.01 291 + 96.94 1298.64 294 + 46.94 1306.76 

295 + 16.28 1308.06 291 + 54.94 1298.45 294 + 26.94 1306.58 

294 + 86.94 1307.83 291 + 12.94 1298.29 294 + 06.94 1305.65 

294 + 46.94 1306.74 290 + 70.94 1297.19 293 + 85.94 1303.88 

294 + 26.94 1306.52 290 + 28.94 1295.70 293 + 64.94 1303.43 

294 + 06.94 1305.58 290 + 07.94 1294.70 293 + 22.94 1302.57 

293 + 85.94 1303.78 289 + 86.94 1293.91 292 + 80.94 1302.00 

293 + 64.94 1303.47 289 + 66.29 1293.44 292 + 38.94 1301.65 

293 + 22.94 1302.49 289 + 45.64 1293.36 291 + 96.94 1300.41 

I (Continuedll 

Note: Sides of channel are referenced to looking downstream. 
~able 4 (Concluded) I 

Elevation Elevation Elevation 

Station Left Side Station Center !station Right Side 

292 + 80.94 1301.88 289 + 03.59 1293.15 291 + 54.94 1298.48 

292 + 38.94 1301.73 288 + 70.26 1292.56 291 + 12.94 1297.06 

291 + 96.94 1300.45 288 + 36.92 1291.70 290 + 70.94 1296.21 

291 + 54.94 1298.46 288 + 03.59 1291.28 290 + 28.94 1295.72 

291 + 12.94 1297.18 287 + 61.97 1291.14 290 + 07.94 1295.72 

290 + 70.94 1296.24 287 + 20.35 1290.76 289 + 86.94 1294.41 

290 + 28.94 1295.63 286 + 78.74 1290.12 289 + 66.29 1293.29 

290 + 07.94 1295.70 286 + 37.12 1289.48 289 + 45.64 1292.65 

289 + 86.94 1294.42 285 + 95.50 1288.95 289 + 03.59 1292.43 

289 + 66.29 1293.30 285 + 53.88 1288.52 288 + 70.26 1293.67 

289 + 45.64 1292.70 285 + 12.26 1288.09 288 + 36.92 1293.63 

289 + 03.59 1292.47 284 + 70.64 1287.63 288 + 03.59 1293.39 

288 + 70.26 1291.57 284 + 29.03 1287.11 287 + 61.97 1292.70 

288 + 36.92 1290.75 283 + 87.41 1286.59 287 + 20.35 1291.94 

288 + 03.59 1289.58 283 + 45.79 1286.02 286 + 78.74 1291.22 

287 + 61.97 1288.97 283 + 12.46 1285.64 286 + 37.12 1290.90 

287 + 20.35 1288.79 282 + 79.12 1285.18 285 + 95.50 1290.62 

286 + 78.74 1288.63 282 + 62.46 1284.86 285 + 53.88 1290.29 

286 + 37.12 1288.09 282 + 45.79 1284.72 285 + 12.26 1289.96 

285 + 95.50 1287.31 282 + 38.08 1284.68 284 + 70.64 1289.54 

285 + 53.88 1286.50 282 + 30.38 1284.48 284 + 29.03 1288.98 

285 + 12.26 1285.79 282 + 25.25 1283.94 283 + 87.41 1288.33 

284 + 70.64 1285.22 282 + 20.12 1291.17 283 + 45.79 1287.68 

284 + 29.03 1284.81 281 + 76.12 1281.01 283 + 12.46 1286.43 

283 + 87.41 1284.53 281 + 75.50 1280.98 282 + 79.12 1284.79 

283 + 45.79 1284.21 281 + 71.89 1282.37 282 + 62.46 1284.66 

283 + 12.46 1284.72 281 + 65.46 1283.48 282 + 45.79 1284.50 

282 + 79.12 1285.22 281 + 59.22 1284.00 282 + 32.98 1284.37 

282 + 62.46 1285.41 281 + 50.18 1284.04 282 + 20.12 1284.29 

282 + 45.79 1285.43 281 + 39.32 1284.36 282 + 09.11 1284.16 

282 + 32.98 1285.06 281 + 23.85 1283.99 281 + 98.11 1284.52 

282 + 20.12 1284.80 280 + 95.40 1283.92 281 + 87.10 1284.19 

282 + 09.11 1284.72 280 + 63.60 1284.11 281 + 76.09 1284.30 

281+98.11 1284.43 280 + 31.80 1283.91 281 + 59.61 1285.41 

281 + 87.10 1284.50 280 + 00.00 1283.47 281 + 43.10 1285.40 

281 + 76.09 1283.90 281 + 27.20 1284.24 

281 + 59.61 1284.06 280 + 95.40 1283.29 

281 + 43.10 1284.64 280 + 63.60 1283.71 

281 + 27.20 1284.88 280 + 31.80 1283.91 

280 + 95.40 1283.96 280 + 00.00 1283.64 

280 + 63.60 1283.16 

280 + 31.80 1283.37 

280 + 00.00 1283.20 
Table 5 

Water-Surface Elevations, Discharge 12,000 cfs, n = 0.012 

Elevation Elevation Elevation 

Station Left Side Station Center Station Right Side 

5 + 00.00 1315.81 5 + 00.00 1315.89 5 + 00.00 1315.99 

4 + 42.82 1315.93 4 + 40.00 1315.89 4 + 50.89 1315.71 

3 + 83.61 1315.92 3 + 80.00 1315.95 3 + 91.28 1315.94 

3 + 83.60 1315.90 3 + 20.00 1315.98 3 + 46.00 1315.96 

3 + 43.97 1315.96 2 + 72.00 1316.01 2 + 87.60 1316.00 

3 + 06.91 1316.05 2 + 24.00 1316.03 2 + 47.99 1316.01 

2 + 70.02 1316.04 1 + 88.00 1316.04 2 + 11.60 1316.03 

2 + 29.47 1316.08 1 + 64.00 1316.05 1 + 75.99 1316.02 

1 + 87.11 1316.03 1 + 40.00 1316.06 1 + 55.55 1316.05 

1 + 61.01 1316.02 1 + 16.00 1316.05 1 + 27.99 1316.02 

1 + 39.81 1316.06 o + 92.00 1316.09 1 + 03.99 1316.05 

1 + 18.76 1316.05 o + 68.00 1316.04 0+79.99 1316.01 

o + 97.88 1316.06 0+44.00 1316.14 o + 55.39 1316.02 

o + 81.31 1316.05 299 + 16.94 1315.74 o + 42.45 1315.93 

o + 68.04 1316.03 298 + 96.94 1313.59 0+31.32 1315.97 

o + 55.40 1316.07 298 + 76.94 1313.03 299 + 16.94 1315.71 

o + 43.51 1315.94 298 + 46.94 1312.32 299 + 16.94 1315.77 

o + 31.61 1316.08 298 + 22.94 1311.90 299 + 06.94 1314.49 

299 + 16.94 1316.00 297 + 90.94 1311.34 298 + 96.94 1315.45 

299 + 16.94 1315.79 297 + 58.94 1310.38 298 + 86.94 1314.48 

299 + 06.94 1314.53 297 + 26.94 1310.32 298 + 76.94 1314.24 

298 + 96.94 1315.54 296 + 96.94 1310.80 298 + 61.94 1313.78 

298 + 86.94 1314.55 296 + 66.94 1310.29 298 + 46.94 1313.41 

298 + 76.94 1314.39 296 + 36.94 1309.55 298 + 22.94 1312.92 

298 + 61.94 1313.88 296 + 06.94 1309.15 297 + 90.94 1312.26 

298 + 46.94 1313.53 295 + 74.94 1308.71 297 + 58.94 1311.76 

298 + 22.94 1313.00 295 + 45.61 1308.25 297 + 26.94 1311.13 

297 + 90.94 1312.35 295 + 16.28 1307.86 296 + 96.94 1310.64 

297 + 58.94 1311.80 294 + 86.94 1307.28 296 + 66.94 1309.90 

297 + 26.94 1311.21 294 + 46.94 1306.21 296 + 36.94 1309.41 

296 + 96.94 1310.66 294 + 06.94 1304.66 296 + 06.94 1308.88 

296 + 66.94 1309.97 293 + 64.94 1304.99 295 + 74.94 1308.16 

296 + 36.94 1309.47 293 + 22.94 1304.17 295 + 45.61 1307.38 

296 + 06.94 1308.91 292 + 80.94 1302.07 295 + 16.28 1307.55 

295 + 74.94 1308.18 292 + 38.94 1300.22 294 + 86.94 1307.81 

295 + 45.61 1307.55 291 + 96.94 1298.56 294 + 46.94 1306.68 

295 + 16.28 1307.60 291 + 54.94 1297.52 294 + 26.94 1306.31 

294 + 86.94 1307.72 291 + 12.94 1297.45 294 + 06.94 1305.55 

294 + 46.94 1306.66 290 + 70.94 1297.23 293 + 85.94 1303.75 

294 + 26.94 1306.32 290 + 28.94 1295.95 293 + 64.94 1303.60 

294 + 06.94 1305.50 290 + 07.94 1295.17 293 + 22.94 1302.51 

293 + 85.94 1303.65 289 + 86.94 1294.16 292 + 80.94 1301.26 

I (Continuedll 

Note: Sides of channel are referenced to looking downstream. 
/Table 5 (Concluded) 

Elevation Elevation Elevation 

Station Left Side Station Center Station Right Side 

293 + 64.94 1303.52 289 + 66.29 1293.28 292 + 38.94 1301.34 

293 + 22.94 1302.51 289 + 45.64 1292.82 291 + 96.94 1300.44 

292 + 80.94 1301.12 289 + 03.59 1292.54 291 + 54.94 1298.62 

292 + 38.94 1301.30 288 + 70.26 1292.16 291 + 12.94 1297.11 

291 + 96.94 1300.46 288 + 36.92 1291.66 290 + 70.94 1295.97 

291 + 54.94 1298.66 288 + 03.59 1291.27 290 + 28.94 1295.10 

291 + 12.94 1297.17 287 + 61.97 1290.92 290 + 07.94 1294.92 

290 + 70.94 1295.99 287 + 20.35 1290.45 289 + 86.94 1294.38 

290 + 28.94 1295.10 286 + 78.74 1289.85 289 + 66.29 1293.06 

290 + 07.94 1294.94 286 + 37.12 1289.25 289 + 45.64 1292.56 

289 + 86.94 1294.44 285 + 95.50 1288.73 289 + 03.59 1292.49 

289 + 66.29 1293.10 285 + 53.88 1288.29 288 + 70.26 1293.16 

289 + 45.64 1292.63 285 + 12.26 1287.84 288 + 36.92 1293.40 

289 + 03.59 1292.45 284 + 70.64 1287.36 288 + 03.59 1293.32 

288 + 70.26 1291.31 284 + 29.03 1286.81 287 + 61.97 1292.55 

288 + 36.92 1290.36 283 + 87.41 1286.29 287 + 20.35 1292.01 

288 + 03.59 1289.13 283 + 45.79 1285.76 286 + 78.74 1291.47 

287 + 61.97 1288.48 283 + 12.46 1285.37 286 + 37.12 1290.99 

287 + 20.35 1288.15 282 + 79.12 1284.90 285 + 95.50 1290.57 

286 + 78.74 1287.91 282 + 62.46 1284.56 285 + 53.88 1290.16 

286 + 37.12 1287.45 282 + 45.79 1284.41 285 + 12.26 1289.75 

285 + 95.50 1286.78 282 + 38.08 1284.31 284 + 70.64 1289.34 

285 + 53.88 1286.06 282 + 30.38 1284.15 284 + 29.03 1288.90 

285 + 12.26 1285.40 282 + 25.25 1283.44 283 + 87.41 1288.37 

284 + 70.64 1284.82 282 + 20.12 1290.73 283 + 45.79 1287.77 

284 + 29.03 1284.31 281 + 76.12 1281.01 283 + 12.46 1286.56 

283 + 87.41 1283.86 281 + 75.50 1280.80 282 + 79.12 1284.87 

283 + 45.79 1283.41 281 + 71.89 1281.95 282 + 62.46 1284.64 

283 + 12.46 1283.87 281 + 65.46 1282.78 282 + 45.79 1284.41 

282 + 79.12 1284.44 281 + 59.22 1283.34 282 + 32.98 1284.31 

282 + 62.46 1284.71 281 + 50.18 1283.53 282 + 20.12 1284.12 

282 + 45.79 1284.91 281 + 39.32 1283.96 282 + 09.11 1284.03 

282 + 32.98 1284.58 281 + 23.85 1283.99 281 + 98.11 1283.92 

282 + 20.12 1284.33 280 + 95.40 1283.56 281 + 87.10 1284.18 

282 + 09.11 1284.34 280 + 63.60 1283.58 281 + 76.09 1283.55 

281 + 98.11 1284.19 280 + 31.80 1283.63 281 + 59.61 1284.01 

281 + 87.10 1284.22 280 + 00.00 1283.32 281 + 43.10 1284.88 

281 + 76.09 1283.97 281 + 27.20 1284.43 

281 + 59.61 1283.72 280 + 95.40 1283.31 

281 + 43.10 1284.09 280 + 63.60 1282.80 

281 + 27.20 1284.63 280 + 31.80 1283.33 

280 + 915.40 1283.57 280 + 00.00 1283.28 

280 + 63.60 1282.93 

280 + 31.80 1282.61 

280 + 00.00 1282.63 
P.I. #31 

SAN TIMOTEO 

CANYON ROAD 

-N-

~ 

~ 

P.I. #32 - <t CURVE DATA 

CIRCULAR CURVE SPIRAL CURVE 

I', = 45' 39' 23.63" 1',5 = 4' 05' 33.20" 

R = 700.0' Ls = 100.00' 

L = 457.80' 

T = 237.42' 

CONCRETE 

\(0/_ 

~ 

P.1. C - tLCURVE DATA 

I', = 13' 57' 45.72" 

R = 1200.0' 

L = 292.43' 

T = 146.94' 

PLAN VIEW 

Plate 1 
-N-

~ 

~ 

Plate 2 

DETAILS OF MESH IN 

VICINITY OF BRIDGE PIER 

NUMERICAL MODEL 

COMPUTATIONAL MESH 

DISCHARGE 19,000 CFS 
~ 

a 

~ 

0 

> '-' z 

Iu.. 

:i 

0 

i= 

« 

> 

w 

....J 

w 

0 

> 

'-' z 

Iu.. 

:i 

0 

i= 

« 

> 

w 

....J 

w 

1330 

1320 

1310 

1300 

1290 

1280 

1270 

1320 

1310 

1300 

1290 

1280 

1270 

1260 

r-~ '\ S 0015 ~ :=::: ---~ = , "'" '" "'" , 1 VO! EL 1310.80 /11 S"'0.018 '/-

S;"0.069324 05 ~;:;; EL 130825 EL 1303.93 ' o~ w. w 

«+ '-' >-", 

(f)", 

z'" 

0« 

~t1 

,·Z, 

;;j- .. ~ "Ei 1301'.68 O>W .0:: <Dm . .. 0. 

+ ....J 

~----~--~----~--~-- § ~II--------------~~~--------~------~~~--~~~~----------~~ 

;;j- « 0> I 

<D U 

.co.L&.!. 

+ 0 ;;j- « 0>0:0 N,-, 

;;j- ....J 

0> « NS: 

5+00 

292+00 

3+00 

'" It) 

...; 

o 

'+ 

0> 

IX) 

N 

f-

(f) 

1+00 298+00 

STATIONS 

296+00 

'" ,.... 

ui 

'<t. 

+ 

n 

IX) 

'" () 

(f) 

0> 

,.... 

ui 

294+00 292+00 

"tlSAN llMOTEOCANYON . ROAD N 

IX) 

N 

(f) 

I-

.--~-=-:::::~.;;:-;.;:,~:~.:~~;.;:.:=-..:::::-~-.---.-

-----------~=~-=-~=~=~=:-:-~=:-=-~=: ----~-= I ""I .;..-~---= I 

J..E.G.E.i':!Q. 

EL 1288.71 :x: ;;j-« .... 

OO£D.q.W0 ~ i>! ~I W 

+-'" + ~ z 

C'\I 

~ 3:: ~ N"""'U ~ %~ 

290+00 

----- LEFT WALL 

-- RIGHT WALL 

--- CENTER LINE 

(]) 

It) 

"'tr} 

o 

+ ro 

·ro 

N 

(f) 

() 

LEFT INVERT 

S;:;0:oj207 

RIGHT iNVERT 

288+00 286+00 284+00 

STATIONS 

NOTE: THE LARGE RUNUP ON THE PIER NOSE IS 

MAINLY A MOOEL ARTIFACT. 

SEE CHAPTER 4. 

EL 1279.95 N 

·N·t.l~·(5 01 + OZ W 

N «« 

~ ~G 

282+00 

El 1278.62 

280+00 

WATER-SURFACE PROFILES 

DISCHARGE 19,000 CFS 

n = 0.014 

~~I--------------------------------------------------------------------------------------------------____________________ ~ 
NOTE: THE LARGE RUNUP ON THE PIER 

IS MAINLY A MODEL ARTIFACT. 

SEE CHAPTlER 4. 

EXAGGERATED PERSPECTIVE OF 

WATER-SURFACE MESH 

LOOKING DOWNSTREAM 

FROM BASIN 
'"C 

el-

(1) 

NOTE: THE LARGE RUNUP ON THE PIER 

IS MAINLY A MODEL ARTIFACT. 

SEE CHAPTER 4. 

"----------

EXAGGERATED PERSPECTIVE OF 

WATER-SURFACE MESH 

LOOKING DOWNSTREAM 

FROM STA 289+86.94 ~L-________________________________________________________________________________ ~ 
'"'0 

a 

(f) 1320 m 

1318 ~. 

-::::::::::: 

1316 

0 1314 > (;) 

Z 

fI.l.. 

Z. 1312 

0 

i= 

...: 

> w 

-.J 

w 1310 

1308 

1306 

0+50 

. ·0 '" ..,. o + '" <.d 

;': + (J) ~ 

Z N 

o « 1= f- « (/) ::> 

o II w 

"' .............. . ~. 

. CREST 

299+00 

STATlONS 

299+50 

Psm 0.1, f3sh 0.5 

LEFT WALL 

CENTER LINE 

RIGHT WAll 

(ism = 0.25 , PSh = 0.5 

- LEFT WALL 

CENTER LINE 

RIGHT WALL 

SENSITIVITY OF WATER SURFACE 

IN VICINITY OF CREST 

RELATIVE TO THE WEIGHTING 

COEFFICIENT, {Jim 

DISCHARGE 19,000 CFS 

n 0.014 
CREST 

CREST 

ORIGINAL GRID 

FINE GRID 

ORIGINAL AND FINE MESHES 

IN VICINITY OF CREST 

Plate 7 
-0 

e 1330 

<D 

(» 1320 

0 

> '-' Z 1310 

lt... 

Z 1300 0 

i= 

« 

> 

w 1290 -' w 

1280 

1270 

1320 

1310 

0 

> 1300 '-' z 

lt... 

Z 1290 

0 

i= 

;; 1280 w 

-' w 

1270 

1260 

2 --------'--_ 

i::::=======~~~5~::::::=========~1~~ .'. N .... ELJ31Q.!}Q 

+'" ow w 

<+ ~ 1-0') '¢« rn 0> 0'> :r: ZN t.D U 

04: N,W' 

~Iii e+: ~ 

5 II R\ 6 ~ __________________________________ ~ _____ w ________ ~ ______ ~ __________________ ~ ________________ ~ ______ ~ 

5+00 

292+00 

3+00 

290+00 

~ 

----- LEFT WALL 

-- RIGHT WALL 

--- CENTER LINE 

1+00 298+00 296+00 

STATIONS 

288+00 286+00 284+00 

STATIONS 

NOTE: THE LARGE RUNUP ON THE PIER NOSE IS 

MAINLY A MODEL ARTIFACT_ 

SEE CHAPTER 4: 

294+00 292+00 

SANTIMOiEO' CANYON·· ROAD 

282+00 280+00 

WATER-SURFACE PROFILES 

DISCHARGE 19,000 CFS 

n 0.014 

FINE GRID 
"U 

e 

(1) 

1320 

1318 _ ""'" 

1316 

§2 1314 

(5 

z 

Ju.. 

Z· 1312 

o 

i= 

« 

> 

w 

;:;:j 1310 

1308 

1306 

0+50 

o 

N '<t 

+ 0> 

o <0 

S=0.015 

299+00 

STATIONS 

299+50 

COARSE GRID 

LEFT WALL 

CENTER LINE 

RIGHT WALL 

FINE GRID 

LEFT WALL 

CENTER LINE 

RIGHT WALL 

SENSITIVITY OF WATER SURFACE 

IN VICINITY OF CREST 

RELATIVE TO GRID RESOLUTION 

DISCHARGE 19,000 CFS 

n = 0.014 

WL-______________________________________________________________________________________ ~ 
-0 

a 

(I) 

..... 

0 

§: 

<:> 

z 

II.e. 

:i 

0 

F 

:;; 

w 

...l 

w 

§: 

<:> 

z 

II.e. 

:i 

0 

F 

~ w 

...J 

w 

1330 

1320 

1310 

1300 

1290 

1280 

1270 

1320 

1310 

1300 

1290 

1280 

1270 

1260 

5+00 

292+00 

3+00 

290+00 

lliilliQ. 

----- LEFT WALL 

-- RIGHT WALL 

CENTER LINE 

1+00 298+00 296+00 

STATIONS 

288+00 286+00 284+00 

STATIONS 

NOTE: THE LARGE RUNUP ON THE PIER NOSE IS 

MAINLY A MODEL ARTIFACT. 

SEE CHAPTER 4. 

294+00 

'" d w 'N'W<;;:I' 

+ oz '" «l<{ 

~ ~i5 

282+00 

EL 1301'.68 

292+00 

a 1278.62 

280+00 

WATER-SURFACE PROFILES 

DISCHARGE 19.000 CFS 

n = 0.012 
""0 

a 

CD 

...... 

5: 

(!I 

z 

.... 

t... 

Z 

0 

F 

;; 

w 

....l 

w 

5: 

L> 

z 

llL 

Z 

0 

F 

« 

> 

w 

....l 

w 

1330 

1320 

1310 

1300 

1290 

1280 

1270 

1320 

1310 

1300 

1290 

1280 

1270 

1260 

5+00 

292+00 

3+00 

290+00 

~ 

----- LEFT WALL 

-- RIGHT WALL 

--- CENTER LINE 

1+00 298+00 296+00 

STATIONS 

----.. ---~ 

"-'" ui 

294+00 292+00 

.. "l .... SA~f TIMOtEOCANYON-RO;4.D N 

co 

N 

~ 

~ 

:3 

+, 

ro LEFT EL 1279.95 N S=0.006~42 

.0:> 

N 

({) 

U 

288+00 286+00 284+00 

STATIONS 

NOTE: THE LARGE RUNUP ON THE PIER NOSE IS 

MAINLY A MODEL ARTIFACL 

SEE CHAPTER 4. 

o .W "'·ttl·"'''· + OZ N «« co ~:r: N ~() 

282+00 

E1. 1278.62 

280+00 

WATER-SURFACE PROFILES 

DISCHARGE 12,000 CFS 

n=0.014 

...... L-________________________________________________________________________________________________________ --------~ 
"'lJ 

ell CD 1330 

...... 

NI 1320 

5? 

0 

z 1310 

f-

"-

Z 1300 0 

f= 

;;; 

w 1290 ...J 

w 

1280 

1270 

1320 

1310 

5? 

0 1300 z 

f-

"-

Z 1290 

0 

f= 

<{ 

> 1280 w 

...J 

w 

1270 

1260 

2 ------::=::: --'~""7--~--"J:::::: I~ \ S 0015 7! S-0.018 

1 ILl EL 1310.80 /1 5 ~ + . ;;; EL 1308.25 . '. Om ' ~<~ ,~"'". <, EL 1303.93 

5+00 

292+00 

3+00 

,.~ ... <{ ..... 

0> 

ll'l 

..-; 

a 

+ 

OJ 

<Xl 

N 

........ 

'" 

O>w'" 

~ ~ ~ w~ +",,+ Sl z ~ :i ~ ... ~.~. 

N;:N~(.) 

290+00 

~ 

----- LEFT WALL 

-- RIGHT WALL 

--- CENTER LINE 

f-OJ 

"'OJ EL 130t68 

N ___________ :-~[l[[ ____ ~;;~~----~~'---;;~~---------- " 

Z 

o<{ 

~t;; 

:::> II [3 

1+00 298+00 296+00 294+00 292+00 

STATIONS 

:::~;':;::::;:::':'~--::-:-'7.~::::,:-:,~=--~-,-__ ... ::.,;.;.:.. _____ ~ 

----------

OJ 

ll'l 

j.i) 

a 

+ 

<Xl 

OCJ 

N 

'" (.) 

S;o;;b.6f2oj .. 

RIGHT iNVERT 

288+00 286+00 284+00 

STATIONS 

NOTE: THE LARGE RUNUP ON THE PIER NOSE IS 

MAINLY A MODEL ARTIFACT. 

SEE CHAPTER 4. 

OJ 

I'-

SAN'TIMOTEOCANVONROAD 

EL 1279 . .95 S=0.006042 

NW'0 01 + az w l N <{<{ 

<Xl (lj:r 

N 0(.) 

282+00 

EL 1278.62 

280+0Q 

WATER-SURFACE PROFILES 

DISCHARGE 12,000 CFS 

n=O.012 
Appendix A 

The Hydrodynamic Model: 

HIVEL2D 

HIVEL2D is designed to simulate flow typical in high-velocity channels. 

The model is a finite element description of the two-dimensional shallowwater equations in conservative form. The model does not include Coriolis, 

boundary, or wind effects as these are typically not important in high-velocity 

channels. 

Vertical integration of the equations of mass and momentum conservation 

for incompressible flow with the assumption that vertical accelerations are 

negligible compared to horizontal motions and the acceleration of gravity 

results in the governing equations commonly referred to as the shallow-water 

equations. The dependent variables of the two-dimensional fluid motion are 

defined by the flow depth h, the x-direction component of unit discharge p, 

and the y-direction component of unit discharge q. These variables are functions of the independent variables x and y, the two space directions, and time 

t. Neglecting free-surface stresses and the effects of Coriolis force as these 

are not considered important in high-velocity channels, the shallow-water 

equations in conservative form are given as (Abbott 1979)': 

oQ + 

oFx 

+ 

oFy + H = 0 at ox oy 

(A1) 

where 

Q 

[~ (A2) 

References cited in this Appendix are included in the References at the end of the main 

text. 

Appendix A The Hydrodynamic Model: HIVEL2D 

A1 
A2 

where 

P 

p2 + !..gh 2 huxx 

Fx h 2 p 

pq huyX 

h p 

q 

pq huxy 

Fy h p 

q2 + :"gh2 - huyy 

h 2 P 

0 

OZO n2pJp 2+q2 gh- - g 

H= AX C;h 7/3 

OZo n2qJp 2+q2 gh_ - g 

oy C;h7/3 

p = uh, u being the depth-averaged x-direction component of 

velocity 

q = vh, v being the depth-averaged y-direction component of 

velocity 

g = acceleration due to gravity 

(A3) 

(A4) 

(A5) 

uwuxy,uyx,Uyy = Reynolds stresses per unit mass where the first subscript 

indicates the direction and the second indicates the face on 

which the stress acts 

p = fluid density 

Zo = channel invert elevation 

n = Manning's roughness coefficient 

Co = dimensional constant (Co = 1 for SI units and Co = 1.486 for 

non-SI units) 

Appendix A The Hydrodynamic Model: HIVEL2D 
The individual terms in the conservation equations are as follows: 

a. Acceleration force per unit width: 

pp2 , Ppq , pqh2 

h h 

b. Pressure force per unit width: 

c. Body forces per unit area: 

OZo oZo pgh- ,p gh - ax oy 

d. Bed shear stresses: 

The Reynolds stresses are determined using the Boussinesq approach of 

gradient-diffusion: 

(A6) 

where Pc is the eddy viscosity, which varies spatially and is solved empirically 

as a function of local flow variables (Rodi 1980). 

Appendix A The Hydrodynamic Model: HIVEL2D 

A3 
A4 

(A7) 

where Cb is a coefficient that varies between 0.1 and 1.0. 

This system of partial differential equations is solved using the finite element method. The finite element approach taken is a Petrov-Galerkin formulation that incorporates a combination of the Galerkin test function and a 

non-Galerkin component to control oscillations due to convection. An integration by parts procedure is used to develop the weak form of the equations. 

The weak form facilitates the specification of boundary conditions. The weak 

form is given as: 

~ [ f [1/;. aQ - ac/JiF - ac/JiF + I{J.A aQ ~ 6 'at ax x ay Y ax 

+II'tB aQ +.I.H] dO + fc/J. (Fn + Fn)] = 0 T, ay 'Y, e I x x Y y 

r, 

(A8) 

where the variables are understood to be discrete values and 

e = subscript indicating a particular dement 

o = domain 

1/;i = c/Jl + l{Ji = test function 

¢i = Galerkin part of the test function 

I = identity matrix 

l{Ji = non-Galerkin part of the test function 

(nX' ny) = ;, = unit vector outward normal to the boundary re 

and 

A 

aFx - aQ (A9) 

B aFy - aQ 

Appendix A The Hydrodynamic Model: HIVEL2D 
Natural boundary conditions are applied to the sidewall boundaries through the 

weak statement. The sidewall boundaries are "no-flux" boundaries; that is, 

there is no net flux of mass or momentum through these boundaries. These 

boundary conditions are enforced through the line integral in the weak 

statement. 

Petrov-Galerkin Test Function 

The Petrov-Galerkin test function 1/;;, is defined (Berger 1993) as: 

(A 10) 

where 

[

act>. A act>. A] (/). = {3 Ax_IA + ~y_IB 

I ax oy 

(All) 

where {3 is a dissipation coefficient varying in value from 0 to 0.5, ct> is the 

linear basis function, and Ax and ~y are the grid intervals. A detailed A A 

explanation of this particular test function, in particular A and B, is given in 

Berger (1993). 

Shock Capturing 

Because a lower value of {3 ({3 = (3SM) is more precise, a large value of {3 

({3 = {3SH = 0.5 where {3SM and (3SH are the Petrov-Galerkin parameters for 

smooth flow and for shocks) is applied only in regions in which it is needed. 

HIVEL2D employs a mechanism that detects shocks and increases {3 automatically. Therefore, {3SH is implemented only when needed as determined by 

evaluation of the element energy deviation. In a similar manner, the eddy 

viscosity coefficient C varies from CSM to CSH' the effect being that eddy 

viscosity is increased only in areas of greatest element energy deviation. 

Temporal Derivatives 

A finite difference expression is used for the temporal derivatives. The 

general expression for the temporal derivative of a variable, Qj' is: 

[ ] 

m+1 

aQj 

ot [ 

flIl+1 Qm] [ Qm flIl-1 ] ~j - j (1 ) j - ~j :::::: a + - a 

tm+1 - t m t m - [In-I 

(A12) 

Appendix A The Hydrodynamic Model: HIVEL2D 

A5 
A6 

where j is the nodal location and m is the time-step. An Ol equal to 1 results 

in a first-order backward difference approximation, and an Ol equal to 1.5 

results in a second-order backward difference approximation of the temporal 

derivative. 

Solution of the Nonlinear Equations 

The system of nonlinear equations is solved using the Newton-Raphson 

iterative method. Let Ri be a vector of the nonlinear equations computed 

using a particular test function I/;i and using an assumed value of~. Ri is the 

residual error for a particular test function i. Subsequently, Ri is forced 

toward zero as: 

(A 13) 

where the derivatives composing the Jacobian are determined analytically. 

This system of equations is solved for Ilqj and then an improved estimate for Qr 1 is obtained from: 

n/<+I Qk A k 

5ttj = j + Uoqj (A14) 

where k is the iteration number. This procedure is continued until convergence to an acceptable residual error is obtained. 

Appendix A The Hydrodynamic Model: HIVEL2D 
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Application of a Two-Dimensional Model of Hydrodynamics to San Timoteo 

Creek Flood-Control Channel, California 

6. AUTHOR(S) 

Richard L. Stockstill 

7. PERfORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION 

REPORT NUMBER 

U.S. Army Engineer Waterways Experiment Station Miscellaneous Paper 

3909 Halls Ferry Road, Vicksburg, MS 39180-6199 HL-94-7 

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AGENCY REPORT NUMBER 

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Los Angeles, CA 90053-2325 

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13. ABSTRACT (Maximum 100 words) 

The San Timoteo Creek, located in southern California, is a tributary of the Santa Ana River and 

drains portions of the San Bernardino and Riverside Counties. The existing creek has the capacity to protect 

the surrounding community from approximately a 20-year-frequency flood. The proposed channel 

improvements will provide a 100-year level of protection. The proposed channel design within the reach 

studied includes a sediment basin, a concrete weir followed by a converging sidewall chute, a compound 

horizontal curve, and a bridge pier. This study was initiated because there was concern as to the adequacy of 

a one-dimensional analysis of the flow conditions within the channel chute. A two-dimensional analysis was 

deemed necessary to evaluate the chute's influence on the flow conditions in the curve and the curve's impact 

on the flow conditions at the bridge. 

The two-dimensional,.depth-averaged flow model, HIVEL2D, was used to simulate the flows in the 

high-velocity channel. This model was chosen because of its ability to simulate supercritical flow and capture 

shocks such as oblique standing waves. Simulation results indicated that the proposed San Timoteo Channel 

design and in particular, the San Timoteo Canyon Road bridge, will convey the design discharge (lOO-yearfrequency event, 19,000 cfs) in an acceptable manner. 

14. SUBJECT TERMS 

Finite element San Timoteo Creek, California 

Flood-control channels Shallow-water equations 

Numerical models Two-dimensional 

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