Stability Analysis Of Slopes

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STABILITY ANALYSIS OF SLOPES USING NUMERICAL SIMULATION BASED ON FINITE ELEMENT METHOD AND LIMITING EQUILIBRIUM APPROACH Article  in  Asian Academic Research Journal of Multidisciplinary · August 2015 CITATIONS

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AARJMD

VOLUME 2

ISSUE 3

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ISSN : 2319 - 2801

A Peer Reviewed International Journal of Asian Academic Research Associates

AARJMD ASIAN ACADEMIC RESEARCH JOURNAL OF MULTIDISCIPLINARY

STABILITY ANALYSIS OF SLOPES USING NUMERICAL SIMULATION BASED ON FINITE ELEMENT METHOD AND LIMITING EQUILIBRIUM APPROACH JAMAL ALI 1 ; KHYZER AHMED 2 ; KAMRAN AKHTAR3 ; ABDUL QUDOOS KHAN 4 ; MANZOOR HUSSAIN 5 1

MS Student, National University of Sciences and Technology, Islamabad, Pakistan MS Student, National University of Sciences and Technology, Islamabad, Pakistan 3 Associate Professor, National University of Sciences and Technology, Islamabad, Pakistan 4 Associate Professor, National University of Sciences and Technology, Islamabad, Pakistan 5 Associate Professor, National University of Sciences and Technology, Islamabad, Pakistan 2

Abstract This paper presents the use of simplified numerical methods to determine the probabilities of failure for slopes. Numerical methods based on Finite element approach and Limit equilibrium methods can be effectively used to model slopes with complex geometries and provide a relatively simple and fast way of computing results. The use of numerical methods has been presented with the help of a case study of San Luis Dam that failed after 14 years of its operation due to rapid drawdown of water at the upstream slope of dam. Stark and Duncan (1992) concluded that the fundamental cause of failure is attributed to the generation of additional cyclic loads due to rapid drawdown, and the shear strength of clay reduced from peak to residual strength thus causing the failure of slope. Numerical simulations have been run in professional software i.e. Rocscience Phase2 and Rocscience Slide-6.0, where the effect of cyclic loading has been incorporated using the advanced features like drawdown etc. The factor of safety was computed using the residual shear strength parameters of clay taken from Stark and Duncan (1992) and analyzing the stability of slope for two cases i.e. full reservoir capacity and rapid drawdown case. The results suggest that the factor of safety is equal to unity for rapid drawdown case predicting a possible failure of upstream slope. It has been concluded that the numerical based methods provide a relatively easy and fast solution to complex geotechnical problems and must be used during design stage to avoid possibilities of failure. Keywords: Slope Stability Analysis; San Luis Dam; Numerical Analysis; Dam Failure; Limit equilibrium Method; FEM; Rapid drawdown, Case study. Asian Academic Research Journal of Multidisciplinary

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1. Introduction The use of computers and development of software has brought significant change in the computational aspects of slope stability analysis. Complex and lengthy analyses can now be done much rapidly and thoroughly, and, based on principles of mechanics of forces and equilibrium, also ensure the accuracy of solution if input parameters are correct. But to get the best possible results, the concepts of soil mechanics and soil strength, a thorough understanding of the computer program and the ability to interpret and comprehend the results is very much important to avoid mistakes that may lead to inaccurate design. Realistic deformation analyses of open excavations and slopes and embankments were not possible in the past but now it is very much possible due to the development of finite-element method and limit equilibrium methods. The principal requirement for attaining reasonably accurate results that are close to in-situ behavior of soil mass from these analyses methods using numerical simulation is suitable representation of the stress-strain behavior of soil and the use of soil constitutive model that is most appropriate [1]. Numerical simulations based on finite element method (FEM) and shear strength reduction (SSR) procedures provide a very quick and reasonable estimate of stability for natural and manmade slopes. One of the advantages of finite element over limiting equilibrium is that no assumption is needed about the shape and location of the critical failure surface [2]. Different ground conditions can be simulated by varying the properties of materials and boundary conditions of the model to reach a specific conclusion and hence provide a very important insight to the designer during early stage of planning and designing. These advanced methods were not available in the past which lead to the use of more rigorous and intensive methods of stability analysis that has certain limitations as well. The use of numerical methods for analysis of slopes is described using the case study of San Luis Dam. San Luis dam is located in San Francisco (about 170 km south east) in the central valley of California. After the draw-down of 180 feet in 120 days the reservoir experienced a major Slide in upstream side of the dam after 14 years of dam’s operation. Total height of the section where failure occurred was 200 feet. The cross section of dam is shown in Fig. 1. Different materials used in construction of Dam are also shown in Fig.1 differentiated by zones and material properties are shown in Table 1. The dashed line in the Fig.1 corresponds to the shape of upstream soil slope after failure. The Slide was deep seated that extended below the base of the foundation in the upstream side of the Dam [3]. Stark and Duncan Asian Academic Research Journal of Multidisciplinary

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(1992) explained that the failure was due to rapid loss of strength from peak to residual value. The concept of residual strength was non-existent during the design and failure of the Dam, therefore, the stability analysis that were carried out based on fully softened shear strength resulted in factor of safety greater than unity.

Figure 1: Cross section of San Luis dam (Stark and Duncan 1992).

2. Problem Statement The application of numerical methods has been illustrated using the case study of San Luis Dam, that is located in San Francisco and upstream slope failure occurred after 14 years of Dam’s operation as a result of rapid draw down. Stark and Duncan (1992) suggested the probable cause of failure as the reduction in strength of stiff clay to its residual value (a concept that was not well understood at that time) and the effect of cyclic loading due to rapid drawdown of water. These conditions can be effectively modeled and analyzed in numerical software that can depict the behavior of slopes under different set of conditions with results that are close to practical.

3. Research Methodology The research mainly focuses on the use of numerical simulation procedures based on FEM and Limit equilibrium methods to model and analyze the causes of failure of San Luis Dam Asian Academic Research Journal of Multidisciplinary

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case study to determine the factor of safety of upstream slope. The research is carried out using commercially available software i.e. Rocscience Phase2 and Rocscience Slide-6.0. Analysis is carried out using the peak and residual shear strength parameters determined by Stark and Duncan (1992) and the effect of cyclic loading is incorporated in the analysis using the rapid drawdown case. The stress analysis was carried out to determine the factor of safety based on FEM and limit equilibrium method to determine the critical factor of safety. The analysis stages considered are; 

Stage 1: Normal operation (Full water level in Dam)



Stage 2: Rapid drawdown (180 feet head drop)

4. Numerical Modeling and Analysis 4.1.

Slope Geometry and Material Properties

The geometry of the model is drawn according to cross section of Dam as shown in Fig. 1. The upstream slope angle is equal to 18 degree while the downstream slope angle is equal to 23 degree. The properties of different materials used in the analysis were taken from Stark and Duncan (1992). Different material zones have been separated using material boundary option in the software. Mohr-Coulomb failure criterion was used to model stress-strain behavior of soil. Stark and Duncan (1992) stated that block samples were taken from site which was subjected to consolidation and direct shear test. Specimens were tested in soaked and un-soaked conditions. Compressibility characteristics showed that the soaking had no effect on compressibility of soil. Similarly, the soaking of specimens had also no effect on shear strength characteristics of material [3]. The test results are shown in Figure 2.

Figure 2: Shear strength characteristics for upstream slope from Direct Shear Test (Stark and Duncan 1992). Asian Academic Research Journal of Multidisciplinary

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The material properties used in analysis are summarized in Table 1. Shear strength parameters based on residual strength are used in this research. These values were used to calculate factor of safety for the upstream slope for reservoir’s full capacity and drawdown condition. Table 1: Shear strength parameters used in numerical analysis Peak Strength

Material

c' (psf)

ɸ' (degree)

c' (psf)

ɸ' (degree)

0

25

0

15

Zone 1

220

25

0

20

Zone 3

110

25

0

15

Zone 4 and 5

0

40

---

---

Slope wash upstream

4.2.

Residual Strength

Rocscience Phase2 Stability Analysis

Modeling and analysis was carried out on Rocscience Phase2 using material properties as shown in Table 1. Rocscience Phase2 is a powerful 2D elasto-plastic finite element stress analysis program for underground and surface excavations in rock or soil. It can be used for a wide range of engineering projects and includes support design, finite element slope stability, groundwater seepage and probabilistic analysis. One of the major features of this software is finite element slope stability analysis using the shear strength reduction method [4]. Plain strain conditions were taken with maximum number of iterations as 500. A three nodded triangular graded mesh was used with 60 nodes on external boundary. The reservoir level is kept at 530 feet. The downstream slope of the dam was modeled with fixed end boundary condition. The cause of failure was the cyclic loading due to rapid drawdown therefore following two cases were analyzed. Analysis results for both cases are shown in Fig. 4 and Fig. 5. 

Case 1: Full capacity reservoir



Case 2: Rapid Drawdown (180 feet head drop)

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Case 1 Figure 3: Stress analysis for case 1 (i.e. Full capacity reservoir) in Phase2

Case 2

Figure 4: Stress analysis for case 2 (i.e. Rapid Drawdown ) in Phase2

4.3.

Rocscience Slide-6.0 Stability Analysis

Similarly stability analysis was also carried out on Rocscience Slide-6.0, based on limit equilibrium method, to calculate the factor of safety and compare results with FEM. The limit equilibrium method has significant importance in geotechnical engineering problems, related to seepage and stability of slopes, for many years and uses the perfectly plastic Mohr– Coulomb criterion to model soil stress-strain behavior. This method is numerical static Asian Academic Research Journal of Multidisciplinary

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analysis technique, for maintaining the mass in equilibrium, depending on the three basic equations of equilibrium [5]. Circular slip surface was defined and slope limits were so adjusted that the critical slip surface passes through the points as shown in Fig. 1. Autorefine slope search option was used to determine the minimum factor of safety for most critical slip surface. Analysis in Rocscience Slide-6.0 focus only on rapid drawdown case as this is the more critical scenario when sudden removal of water can reduce the stability on the upstream slope of reservoir and hence the cyclic loading condition can be simulated in this manner as there is insufficient time for the pore water pressures to stabilize and maintain equilibrium state. The analysis results are shown in Figure 5.

Figure 5: Rocscience Slide-6.0 stability analysis results for drawdown case 4.4.

Discussion on results

This section includes the results of stability analysis from FEM and Limit equilibrium approach. The critical strength reduction factor for case 1 i.e. full capacity reservoir is 2.7 suggesting a stable slope. However, for case 2 i.e. drawdown case, the critical strength reduction factor is equal to unity indicating a possible chance of slope failure as was the case in actual. Similarly the results from Rocscience Slide-6.0 are conforming to FEM analysis

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and factor of safety equal to unity is observed for rapid drawdown case. The critical slip surface of both analyses are shown from Fig. 3-5.

5. Conclusion This study illustrates the use of simplified numerical methods to predict the behavior of slopes under various loading conditions that can serve as a very important guideline during early stages of design and hence failure can be controlled. The use of Finite element method and Limit equilibrium method in stability analysis of slopes has been demonstrated using a case study of San Luis dam that failed after 14 years of its operation during an event of rapid drawdown. The strength of material was high in dry state which reduced from peak to fully softened and ultimately to residual value and slope failed. The loading conditions were simulated in software in form of full capacity reservoir and drawdown case. It has been concluded that the factor of safety in Rocscience Phase2 and Rocscience Slide-6.0 is equal to unity for rapid drawdown case indicating failure. Hence the use of numerical methods is simple and provides a very good estimate of strength characteristics for dams and excavation support systems etc. It is concluded that effect of cyclic loading in stiff clays that is generated due to subsequent wetting and drying of stiff clays can be effectively modeled using the advanced features in software. Also in such cases it is advisable to perform laboratory tests on the clays to determine if cycling loading will result in continual deformation and loss of strength and substituting the modified shear strength parameters in numerical simulation to obtain results that are more close to the actual behavior of materials on site. Hence based on software results the loading condition on clays can be altered or loads can be reduced to avoid failure of soil mass.

6.

Acknowledgement

The authors acknowledge the financial assistance provided by National University of Sciences and Technology, Pakistan in carrying out this research study.

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7.

References

[1]

Duncan, J. (1996) State of the art: limit equilibrium and finite element analysis of slopes. J Geotech Geoenviron Eng ASCE 122(7):578–584

[2]

Hammouri, N.A., Husein Malkawi, A.I. and Yamin, M.M.A. (2008). “Stability analysis of slopes using the finite element method and limiting equilibrium approach”, Bulletin of Engineering Geology and the Environment, 67 (4), 471-478.

[3]

Stark, T.D. and J.M. Duncan, “Mechanisms of Strength Loss in Stiff Clays,” Journal of Geotechnical Engineering, ASCE, Vol. 117, No. 1, January, 1991, pp. 139-154.

[4]

Rocscience Inc. Phase2 – Two-dimensional finite element slope stability analysis.

[5]

Rocscience Inc. Slide-6.0 – Two-dimensional slope stability analysis for soil and rock slopes.

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