Total stress rapid drawdown analysis of the Pilarcitos Dam failure using the finite element method

Abstract

Rapid drawdown is a critical design condition for the upstream or riverside slope of earth dams and levees. A new total stress rapid drawdown method based on finite element analysis is used to analyze the rapid drawdown failure that occurred at Pilarcitos Dam in 1969. Effective consolidation stresses in the slope prior to drawdown are determined using linear elastic finite element analysis. Undrained strengths from isotropically consolidated undrained (ICU) triaxial compression tests are related directly to the calculated consolidation stresses and assigned to the elements in the model by interpolation. Two different interpretations of the undrained strength envelope are examined. Strength reduction finite element analyses are used to evaluate stability of the dam. Back analysis suggests that undrained strengths from ICU tests must be reduced by 30% for use with this rapid drawdown method. The failure mechanism predicted for Pilarcitos Dam is sensitive to the relationship between undrained strength and consolidation stress.

Keywords

rapid drawdown / finite element / total stress / slope stability

Introduction

The upstream slopes of dams and levees must be designed for stability during rapid drawdown, RDD. Rapid drawdown occurs when the water level adjacent to the slope drops quickly after a long period at the normal reservoir level, or after a prolonged flood in the case of levees.

The shear stresses in the slope increase during drawdown as the stabilizing effect of the water acting on the surface of the slope is removed. If the soil permeability is low relative to the rate of drawdown, excess pore pressures will develop, resulting in an undrained condition. While pore pressures will decrease due to unloading, the magnitude of this decrease will depend on the tendency of the soil to dilate or contract under the increased shear stress.

Procedures for rapid drawdown analysis have been proposed using both effective stress and total stress frameworks.

Effective stress approaches to rapid drawdown analysis attempt to predict pore pressures following drawdown. Limit equilibrium and finite element approaches have both been used to perform effective stress analyses. These methods make assumptions that almost always over-simplify pore pressures induced by changes in shear stress. As a result, both well-compacted and poorly-compacted fill are treated as having the same pore pressure response, usually making the analysis overly conservative.

Total stress methods, like the one used in this paper, have traditionally been used in geotechnical engineering for undrained problems because of the difficulty of correctly predicting pore pressures during undrained loading or unloading. The pore pressure response of the soil is implicitly considered through the use of undrained strengths.

The undrained strength, s_u, of soil is related to the effective consolidation stress that was present prior to application of the design loading condition. In the case of RDD, effective consolidation stresses are determined with the water level high and steady-state seepage conditions. Because the void ratio does not change during an undrained (constant volume) process, the consolidation stress determines a soil’s undrained strength. As a first order approximation, undrained strengths are often considered to be a function solely of the major effective consolidation stress, {\sigma }_{1\mathrm{c}}^{\prime } [1].

Current total stress RDD methods, such as Duncan et al. [2], use limit equilibrium analysis and isotropically consolidated undrained (ICU) triaxial compression tests to evaluate RDD stability. Normal and shear stresses along trial failure surfaces in drained analyses at steady-state seepage conditions are used to estimate effective consolidation stresses, which are then used to calculate undrained strengths. The undrained strengths are used to evaluate stability following drawdown.

The Pilarcitos Dam case study is used in this paper to illustrate a new method for analysis of rapid drawdown stability based on the finite element method, which was presented by VandenBerge et al. [3]. The method uses three basic steps:

1) Calculate effective consolidation stresses in the embankment using finite element analysis,

2) Relate undrained strengths from ICU tests to the effective consolidation stresses, and

3) Evaluate embankment stability following RDD using finite element strength reduction analysis.

Pilarcitos Dam history and geometry

Pilarcitos Dam was built from compacted sandy clay with a total unit weight of 21.2 kN/m³. The 23.8 m high homogenous earth dam has an upstream slope inclined at 2.5H:1V up to El. 206.7 m and inclined at 3H:1V above that point. The long-term water level was 1.8 m below the crest. A cross-section of the dam’s upstream slope is shown in Fig. 1.

In 1969, a rapid drawdown slide occurred after the reservoir level was lowered 10.7 m in 43 days. The observed failure surface was about 5 m deep (measured perpendicular to the slope) and 28 m long. The slide occurred at approximately mid-slope. Wahler and Associates [4] investigated the failure and performed ICU triaxial compression tests on samples obtained from the embankment. Subsequent studies, including Wong et al. [5] and Duncan et al. [1], have used the failure at Pilarcitos Dam to compare and validate various RDD analysis methods.

Consolidation Stress Analysis

The first step in a total stress rapid drawdown analysis is to determine the consolidation stresses within the embankment at steady-state seepage and the normal or elevated water level. The void ratio and undrained strength of the fill will be directly related to these consolidation stresses. The major effective consolidation stress, {\sigma }_{1\mathrm{c}}^{\prime }, will be used to predict undrained strength with this method.

The finite element model was created using the software Phase² v.8.011. The finite element model consisted of 1631 six-noded triangular elements with a total of 3432 nodes. Nodes along the base of the embankment were fixed.

The Pilarcitos Dam embankment was assumed to be symmetric about the centerline with a total crest width of 13.7 m. The figures in this paper only show the upstream half of the embankment; however the entire embankment was modeled in the finite element analyses to obtain the appropriate stress state. The reservoir load only applies to upstream face, causing a tendency for deflection in the downstream direction. If a rigid boundary is included at the centerline of the embankment, the calculated consolidation stress state will be significantly different.

The models used an effective stress formulation in which the steady-state pore pressures directly influence the finite element solution for the consolidation stresses. In other words, displacements and the corresponding strains in the embankment occur as a result of changes in effective stress. Because the pore pressures are included in the solution, the effective stress formulation helps to reduce the size of the tensile zones that tend to develop in linear elastic embankment stress analyses and a more realistic consolidation stress distribution is obtained. In Phase², this formulation is only partially coupled so that changes in stress do not directly cause pore pressure changes.

Two different constitutive theories were used to represent the embankment soil in this phase of the study. A simple linear elastic model was used first to calculate consolidation stresses. A nonlinear elastic model was also used to check the effects of simplifications due to linear elasticity.

Linear elastic model

The consolidation stress state for Pilarcitos Dam was first determined assuming linear elastic properties for the soil. The modulus of elasticity and the Poisson’s ratio were assumed to be 10.8 MPa and 0.42, respectively.

The consolidation stress analysis was performed in three stages. Gravity loads from the embankment fill were assigned to the elements in the first stage. Initial vertical stresses were assigned to each element based on the depth below the ground surface and the unit weight of the soil. Initial horizontal stresses were assumed to be equal to the vertical stress. The boundary load from the water in the reservoir was applied in the second stage. In the third stage, an array of pore pressures corresponding to steady-state seepage was assigned throughout the embankment and applied to the elements by interpolation.

The contours of σ’_1c are shown in Fig. 2 for the linear elastic model. The major effective stresses are greater than the vertical effective stress near the toe of the embankment. This occurs as the principal stresses rotate during consolidation, and stresses from higher in the slope concentrate at the embankment toe.

Nonlinear elastic model

A separate nonlinear elastic consolidation stress analysis was performed for Pilarcitos Dam with the Duncan-Chang constitutive model. Assuming that nonlinear constitutive theory will improve the accuracy of the calculated stresses, the nonlinear analysis can be used to check whether the simpler linear elastic model gives reasonable results.

Phase² uses dimensionless parameters for the Duncan-Chang model to calculate stress-dependent values of modulus, unloading modulus, and bulk modulus. The following values were assumed for each of these parameters based on the reported soil properties.

• Modulus number, K_e = 150

• Unloading modulus number, K_u = 225

• Bulk modulus number, K_b = 100

• Failure ratio, R_f = 0.7

• Modulus exponent, n = 0.45

• Bulk modulus exponent, m = 0.2

The stresses and displacements in a nonlinear finite element model are dependent on the loading sequence because the moduli vary with the stress level. In this FE model, the Pilarcitos Dam embankment was “built” in 78 lifts by adding elements to the model in 78 stages. The elements were assigned isotropic initial stresses based on the overburden stress. The boundary loads from the reservoir were gradually increased, modeling a gradual water rise. Finally, the pore pressures in the embankment were incrementally increased to the steady-state seepage values in five stages. The contours of {\sigma }_{1\mathrm{c}}^{\prime } corresponding to steady-state seepage are shown in Fig. 3.

Comparison of linear and nonlinear elastic consolidation stresses

Values of σ’_1c from the linear and nonlinear elastic analyses were compared at 2000 points evenly spread throughout the upstream slope. To examine the effect of the constitutive model, the percent difference between the linear elastic stresses, {\sigma }_{1\mathrm{c}-\mathrm{L}\mathrm{E}}^{\prime }, and nonlinear elastic stresses, {\sigma }_{1\mathrm{c}-\mathrm{N}\mathrm{L}\mathrm{E}}^{\prime }, at each point was defined as \mathrm{\delta }=\left({\sigma }_{1\mathrm{c}-\mathrm{L}\mathrm{E}}^{\prime }-{\sigma }_{1\mathrm{c}-\mathrm{N}\mathrm{L}\mathrm{E}}^{\prime }\right)/{\sigma }_{1\mathrm{c}-\mathrm{N}\mathrm{L}\mathrm{E}}^{\prime }\times 100\%. For the upstream half of the embankment, the average value of δ was 6%, meaning that the linear elastic stresses were slightly higher than those from the nonlinear analysis. At more than half of the comparison points, the absolute value of δ was less than 10%. The linear elastic analysis tends to predict higher {\sigma }_{1\mathrm{c}}^{\prime } near the slope surface at about one-quarter of the height and near the base of the embankment below the crest. The linear elastic values of {\sigma }_{1\mathrm{c}}^{\prime } were lower at the toe and along the slope surface from mid-height and higher. In general, the largest differences in {\sigma }_{1\mathrm{c}}^{\prime } occurred along the boundaries of the finite element models.

The calculated differences in {\sigma }_{1\mathrm{c}}^{\prime } were considered acceptable in light of the increased simplicity provided by linear elastic analysis. The undrained strengths used for rapid drawdown are directly related to the values of {\sigma }_{1\mathrm{c}}^{\prime } in the method used in this study. Under or over-prediction of {\sigma }_{1\mathrm{c}}^{\prime } will lead to lower or higher strengths, respectively. This source of potential error should be kept in mind when considering the results of the stability analyses.

Undrained strengths

In the second step of a total stress rapid drawdown analysis, undrained strengths are related to the consolidation stresses. Consolidated undrained laboratory tests must be performed on specimens representative of the field conditions. In the case of Pilarcitos Dam, Wahler and Associates [4] performed ten ICU tests on specimens from the dam. Wong et al. [5] presented total and effective Mohr circles at failure from these tests, from which the principal total and effective stresses at failure were determined for this study. The relationship between undrained strength and major effective consolidation stress was interpreted from the ICU data in two ways, as discussed in the following sections.

Strength envelope #1

The first undrained strength envelope was based on the variation in the drained strength of the clay and the undrained pore pressure response with isotropic consolidation stress. To this end, the effective secant friction angle, {\varphi }_{\mathrm{s}\mathrm{e}\mathrm{c}}^{\prime }, and the pore pressure parameter at failure, {\overline{A}}_{\mathrm{f}}, were calculated for each ICU test [6]. A relationship between these parameters and the isotropic consolidation stress, {\sigma }_{1\mathrm{c}}^{\prime }, was desired.

Drained strength envelopes for most soils have some curvature, and the secant friction angle will vary with confining stress. Values of {\varphi }_{\mathrm{s}\mathrm{e}\mathrm{c}}^{’} were determined for each test from

(1)\varphi {\prime }_{\sec }={\sin }^{-\mathrm{1}}\left({\displaystyle \frac{\sigma {\prime }_{\mathrm{1}f}-\sigma {\prime }_{\mathrm{3}f}}{\sigma {\prime }_{\mathrm{1}f}+\sigma {\prime }_{\mathrm{3}f}}}\right)

where: {\sigma }_{1\mathrm{f}}^{\prime } = the major effective stress at failure, and {\sigma }_{3\mathrm{f}}^{\prime } = the minor effective stress at failure.

A log-linear trend was observed between {\varphi }_{\mathrm{s}\mathrm{e}\mathrm{c}}^{\prime } and {\sigma }_{1\mathrm{c}}^{\prime } as shown in Fig. 4. This trend can be represented using an equation of the form suggested by Wong and Duncan [7]

(2)\varphi {\prime }_{\sec }=\varphi {\prime }_{\mathrm{0}}+\mathrm{\Delta }\varphi \prime \cdot \log \left({\displaystyle \frac{\sigma {\prime }_{\mathrm{1}c}}{p_a}}\right),

where {\varphi }_0^{\prime } = {\varphi }_{\mathrm{s}\mathrm{e}\mathrm{c}}^{\prime } at {\sigma }_{1\mathrm{c}}^{\prime } equal to P_a, ∆ø′ = change in {\varphi }_{\mathrm{s}\mathrm{e}\mathrm{c}}^{\prime } per log cycle of {\sigma }_{1\mathrm{c}}^{\prime }/ P_a, and P_a = atmospheric pressure (101.3 kPa).

The pore pressure response of the clay from Pilarcitos Dam also varied with confining pressure as shown in Fig. 3. A parabolic trend line was fit to the values of {\overline{A}}_{\mathrm{f}}, excluding the two filled-in data points as outliers. For {\sigma }_{1\mathrm{c}}^{\prime } above 248 kPa, {\overline{A}}_{\mathrm{f}} was assigned a constant value of 1.

With the relationships shown by the trendlines in Fig. 3 and Fig. 4, the values of {\varphi }_{\mathrm{s}\mathrm{e}\mathrm{c}}^{\prime } and {\overline{A}}_{\mathrm{f}} can be determined for any value of {\sigma }_{1\mathrm{c}}^{\prime }. From these, the undrained strength can be calculated using the equation proposed by Skempton and Bishop [8] for isotropic consolidation

(3)s_{\mathrm{u}}={\displaystyle \frac{\sigma {\prime }_{\mathrm{1}\mathrm{c}}\sin \varphi {\prime }_{\sec }}{\mathrm{1}+\left(\mathrm{2}{\overline{A}}_{\mathrm{f}}-\mathrm{1}\right)\sin \varphi {\prime }_{\sec }}}.

This relationship between s_u and {\sigma }_{1\mathrm{c}}^{\prime } is indicated by the strength envelope #1 in Fig. 6. The strengths fit the laboratory data well and provide a conservative lower bound to the undrained behavior over the full range of stresses tested. Above 248 kPa, the relationship between s_u and {\sigma }_{1\mathrm{c}}^{\prime } is nearly linear as {\overline{A}}_{\mathrm{f}} becomes constant. Figure 2 shows that {\sigma }_{1\mathrm{c}}^{\prime } is below 200 kPa throughout most of the embankment. This lower stress range is shown in Fig. 6(b), where the model matches all of the ICU data points but one. The outlying test result had lower pore pressure at failure and is one of the points excluded from the {\overline{A}}_{\mathrm{f}} trend line in Fig. 5.

Strength envelope #2

The second interpretation of undrained strength used a simpler approach to represent the behavior of the compacted clay at Pilarcitos Dam. The following method was used to fit the s_uvs. {\sigma }_{1\mathrm{c}}^{\prime } data to a power curve of the form

(4)s_{\mathrm{u}}=a\cdot P_{\mathrm{a}}{\left({\displaystyle \frac{\sigma {\prime }_{\mathrm{1}\mathrm{c}}}{P_{\mathrm{a}}}}\right)}^b,

where a = curve fit parameter controlling the overall slope of the envelope, b = curve fit parameter controlling the curvature of the envelope, and P_a = atmospheric pressure in the same units as s_u and {\sigma }_{1\mathrm{c}}^{\prime }.

The values of s_u and {\sigma }_{1\mathrm{c}}^{\prime } from each test were first normalized by the atmospheric pressure. The logarithm of the normalized strength varies in a linear fashion with the logarithm of the normalized consolidation stress, such that

(5)\log \left({\displaystyle \frac{s_{\mathrm{u}}}{P_a}}\right)=b\cdot \log \left({\displaystyle \frac{\sigma {\prime }_{\mathrm{1}\mathrm{c}}}{P_a}}\right)+c,

where b is the slope of the transformed data and c is the y-intercept of the transformed data.

Linear regression was used to determine the slope and y-intercept. The slope of the regression line is equal to the power curve parameter b. The curve fit parameter a is equal to 10^c.

For the Pilarcitos Dam ICU tests, a and b were determined to be 0.57 and 0.77, respectively. Using these values, the undrained strength can be calculated at any consolidation stress using Eq. (4). The corresponding strength envelope #2 is plotted in Fig. 6. This second envelope represents an average relationship between undrained strength and consolidation stress for all the data.

In the region close the surface of the slope where the failure occurred, the effective consolidation stresses were generally below about 100 kPa. Within this low stress range, the strength envelopes are essentially equivalent with strength envelope #2 slightly lower than envelope #1 for {\sigma }_{1\mathrm{c}}^{\prime } less than 75 kPa. The consolidation stresses increase at greater depths within the embankment up to a maximum calculated {\sigma }_{1\mathrm{c}}^{\prime } of 367 kPa. At these higher stresses, the undrained strengths from envelope #2 are up to 23% higher than those from envelope #1.

Rapid drawdown strength reduction analysis

The third step in total stress RDD analysis is to evaluate stability using undrained strengths. The same finite element model used to calculate the consolidation stresses was used to evaluate stability following rapid drawdown with a few minor modifications to the material properties.

First the stress-strain properties for all of the elements were changed to elastic-plastic for the strength reduction analyses. The elastic modulus was not changed. A dilation angle of 0° was assigned as recommended by Griffiths and Lane [9].

Dissipation of excess pore pressure during drawdown should be considered, especially for cases where the drawdown occurs over a long period of time. Drained strength parameters should be used where drained conditions prevail near the surface of the embankment, and. This is especially important for cases where the undrained strength is greater than the drained strength at low consolidation stresses. In the case of Pilarcitos Dam, the water level was lowered over the course of 43 days and it is likely that some dissipation of excess pore pressure occurred in the soils near the surface of the dam.

A simple approach based on one-dimensional consolidation theory was used to determine the depth of this drained zone. Drained properties were assumed to be appropriate for regions exhibiting at least 90% dissipation of excess pore pressure, which corresponds to a time factor of 1.03. The coefficient of consolidation, c_v, was assumed to be 46 cm²/day based on the soil description and reported hydraulic conductivity of 4 × 10^-8 cm/s. The depth of the drained zone can then be approximated using

(6)z_{\mathrm{d}\mathrm{r}}=\sqrt{{\displaystyle \frac{c_{\mathrm{v}}{t}_{\mathrm{R}\mathrm{D}\mathrm{D}}}{T}}},

where z_dr = depth of drained zone measured perpendicular to the slope face, t_RDD = time of drawdown, and T = time factor based on one-dimensional consolidation theory.

For Pilarcitos Dam, Eq. (6) results in a drained zone 0.46 m thick. A separate zone of elements was defined along the upstream face of the embankment in the finite element model to represent this drained zone. The drained friction angle and Poisson’s Ratio were applied to the elements in this region. The elements above the steady-state phreatic surface were also assumed to behave in a drained manner.

The remaining elements were assigned a Poisson’s ratio of 0.49 and undrained strengths based on the consolidation stress analysis and the strength envelopes. The values of {\sigma }_{1\mathrm{c}}^{\prime } at each node were exported from the consolidation stress analysis to a spreadsheet. The corresponding values of s_u were calculated using the strength envelopes shown in Fig. 6. The particular values of s_u were next assigned at the nodal locations in the undrained portion of the finite element model. The undrained strength for each element was determined automatically from the array of s_u values using the TIN interpolation scheme. The resulting contours of undrained strength based on strength envelope #2 are shown in Fig. 7.

Stability following RDD was evaluated using strength reduction analysis with two-stage finite element models. In the first stage, the gravity loads due to element weight and the boundary load due to the full reservoir level were applied. In the second stage, the reservoir level was lowered 10.7 m by removing the appropriate boundary loads. The critical strength reduction factor, SRF_crit, was then determined by the software, using non-convergence as the failure criterion as suggested by Griffiths and Lane [9]. SRF_crit is commonly assumed to be equivalent to the factor of safety.

The values of SRF_crit for Pilarcitos Dam using each of the strength envelopes are provided in Table 1. These SRF are the result of using undrained strengths directly from the ICU triaxial test (Fig. 6). The critical strength reduction factor for Pilarcitos Dam should be about 1.0 since the embankment failed. The results in Table 1 indicate that the undrained strengths from ICU triaxial compression tests are too high to be used directly for RDD analysis. A similar conclusion was reached by Wong et al. [5] based on limit equilibrium analysis. A method of adjusting the ICU strengths is discussed in the next section.

Undrained strength adjustment

ICU triaxial compression tests are commonly used for slope stability analysis and are relatively easy to perform. However, ICU tests do not represent the conditions at consolidation or failure for most soil elements within an embankment. The field conditions that cause these differences include the effects of unequal major and minor consolidation stresses, principal stress rotation from consolidation to failure, compaction prestress, and anisotropic strength and deformation characteristics. Most of these factors tend to reduce undrained strength. In addition, failure occurs in embankments under conditions much closer to plane strain, which tends to increase strength compared to the triaxial test. Most of these influences are difficult and/or expensive to evaluate using conventional laboratory tests.

The factors noted above suggest that it is reasonable to expect field strengths to be lower on average than those measured by ICU triaxial compression. The reduction in undrained strength caused by these factors can be made by applying a constant adjustment factor to the ICU strengths such that

(7)s_{\mathrm{u}-\mathrm{A}\mathrm{D}\mathrm{J}}=R\cdot s_{\mathrm{u}-\mathrm{I}\mathrm{C}\mathrm{U}}

where: s_u-ADJ = undrained strength adjusted for the influence of the factors noted above, R = empirical adjustment factor, and s_u-ICU = undrained strength measured in ICU laboratory tests.

Equation (7) was applied to strength envelope #1, varying the value of R. In each case, the strength reduction analysis was repeated with the adjusted undrained strengths corresponding to the value of R. The critical strength reduction factors for a range of R values are listed for strength envelope #1 in Table 2. An adjustment factor, R, of 0.7 results in SRF_crit of 1.01. For comparison, Ref. [1]’s limit equilibrium method gives a factor of safety of 1.04 for Pilarcitos Dam. The strength reduction analysis was repeated for strength envelope #2 using R = 0.7, resulting in SRF_crit of 0.98.

The empirical adjustment factor, R = 0.7, is the result of back calculation for the Pilarcitos Dam case study. In this respect, the adjustment factor is specific to this particular dam. However, VandenBerge et al. [3] have shown that R = 0.7 is also appropriate for Walter Bouldin Dam, which the other case study typically used to validate rapid drawdown procedures. VandenBerge [10] also that a Louisiana levee rapid drawdown failure can be explained using R = 0.65. Using R = 0.7 produces SRF_crit similar to the factor of safety obtained by Ref. [1]’s limit equilibrium method.

Failure mechanism

The failure mechanism predicted by the strength reduction analyses can be examined by plotting contours of maximum shear strain within the embankment. Figures 8 9 show the shear strain contours for strength envelopes #1 and #2, respectively. The lighter zones indicate regions of high shear strain, showing the location of the predicted failure.

Strength envelope #1 results in a deep failure mechanism that intersects the base of the embankment as shown in Fig. 8. This failure surface matches neither the observed failure nor the critical surface predicted by limit equilibrium [1]. In this case, the deep failure is the result of the relatively low undrained strengths predicted by envelope #1 for {\sigma }_{1\mathrm{c}}^{\prime } in the range of 200 to 400 kPa.

Figure 9 shows the maximum shear strain contours for strength envelope #2. In this case, the failure surface predicted by strength reduction is almost identical to the critical surface from limit equilibrium. The failure occurs at a shallower depth for strength envelope #2 because the elements at the base of the embankments are significantly stronger compared to envelope #1 while those at shallow depth have essentially the same strength.

The observed failure occurred at a similar depth to the critical surfaces in Fig. 9 but slightly further downslope. Figure 10 shows the distribution of strength factor, which is defined as the shear strength divided by the shear stress, for the critical SRF with strength envelope #2. The darkest regions are elements that have a strength factor less than one, indicating that the elements have failed in shear. Figure 10 indicates that the soil’s undrained shear strength was fully mobilized throughout much of the upstream face of the embankment. For this reason, the location of the actual failure would have been quite sensitive to local variations in shear strength. The difference between the observed and predicted failure surface is likely due to a local variations in shear strength that were not captured by the laboratory test data or the numerical models.

Conclusions

Total stress rapid drawdown analysis can be performed using the finite element method by first calculating the effective consolidation stresses for the steady-state seepage condition. Undrained strengths can be related directly to the major effective consolidation stress. Slope stability during rapid drawdown can then be determined by strength reduction analysis using spatially varying undrained strengths.

The method used in this paper characterizes the undrained strength of the embankment soil as a function solely of the major effective consolidation stress based on the results of ICU triaxial compression tests. Other factors, such as unequal consolidation stresses, principal stress rotation from consolidation to failure, plane strain conditions, and laboratory recompression, also affect undrained strength. These effects are combined into a constant empirical adjustment factor, R, by which the undrained strengths from ICU tests are multiplied.

The rapid drawdown failure of Pilarcitos Dam provides one of the best documented case studies for this type of failure. Back analysis of the Pilarcitos failure suggests that strengths from ICU triaxial tests must be reduced by 30% for use with this method of RDD analysis.

In the Pilarcitos case study, the location of the predicted critical failure surface was sensitive to changes in interpretation of the undrained strength for the data. The embankment was analyzed using both lower bound and average strength envelopes. Analyses that used the average strength envelope predicted a failure mechanism that matched more closely with limit equilibrium results and the observed failure surface. The back calculated R value was the same for both strength envelopes.

References

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[7] WongK S. And DuncanJ. M. Hyperbolic Stress-Strain Parameters for Nonlinear Finite Element Analyses of Stresses and Movements in Soil Masses. Report No. TE-74–3. University of California, Berkeley, CA, 1974, 90

[8] SkemptonA W, BishopA W. Chapter X – Soils, Building Materials, Their Elasticity and Inelasticity. ReinerM, WardA G, eds. Amsterdam: North-Holland Publishing Co. 1954, 417-482

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[10] VandenBergeD R. Total stress rapid drawdown analysis using the finite element method. Dissertation for the Doctoral Degree. Blacksburg: Virginia Tech, 2014 (in Press)

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