Sea to Sky Geotechnique 2006

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1 EFFECTS OF ROCK COLUMN GEOMETRY AND LAYOUT FOR STABILIZING NATURAL RIVERBANKS Wisam Abdulrazaq, Department of Civil Engineering, University of Manitoba, Winnipeg, MB, Canada. Marolo Alfaro, Department of Civil Engineering, University of Manitoba, Winnipeg, MB, Canada. James Blatz, Department of Civil Engineering, University of Manitoba, Winnipeg, MB, Canada. ABSTRACT The City of Winnipeg is located on glacial lake Agassiz clay and silt sediments. The clay is high plastic with a relatively weak with a low friction angle. As such, riverbank instabilities are a problem along much of the 240 km of waterfront property in the City of Winnipeg. Rockfill columns have become a recognized and commonly used technique for riverbank stabilization in Winnipeg. Two design constraints are examined through evaluating riverbank stabilization works. The first constraint examines the geometry such as spacing and configuration of columns along the riverbank. The second is the slope movements that are expected following installation of rockfill columns. The assessment of the stability of riverbanks in Winnipeg has been conducted using the conventional limit equilibrium methods (LEM) to calculate the factor of safety, which is a good indication of slope stability. LEM can also be used for evaluating the degree of improvement followed by implementing slope reinforcing element such as rockfill columns. However, Finite Element Method (FEM) is a powerful technique to analyze the stability of slopes. At the same time FEM provides valuable information about the magnitude of movements in the slopes. Results of the analysis showed that the location and distribution of rockfill columns can affect the safety factor & the associated deformation of the stabilized riverbank. RÉSUMÉ La ville de Winnipeg est située sur les sédiments d argile et de limon du lac glacial Agassiz. L argile est relativement maigre et possède un bas angle de frottement. Les instabilités la longue des 240 km de la rive de la ville de Winnipeg sont un problème. Les colonnes d enrochement sont une technique reconnue et utilisée pour stabiliser les rives à Winnipeg. Il y a deux préoccupations d après la stabilisation d une rive : la première est l écartement et la configuration des colonnes; le deuxième est le mouvement des pentes dès l installation des colonnes d enrochement. L évaluation de la stabilité des rives à Winnipeg a été exécutée en utilisant la méthode des limites d équilibre pour calculer le coefficient de sécurité, ceci est une bonne indication de la stabilité de la pente. De plus, cette méthode peut être utilisée dans l évaluation de la mise au point ainsi comme élément pour renforcer la pente, par exemple des colonnes d enrochement. Cependant, pour analyser la stabilité des pentes, la méthode des éléments finis (MEF) est très puissante. Cette dernière offre de l information très valable au sujet de la grandeur des mouvements des pentes. Les résultats ont démontré que le lieu et la distribution des colonnes d enrochement peuvent affecter le coefficient de sécurité et la déformation d une rive stable. 1. INTRODUCTION The City of Winnipeg is located on glacio-lacustrine Lake Agassiz clay rich soils and alluvial deposits of layered clays, silt and sands. The lacustrine high plastic clay soils are relatively weak resulting in considerable instability along many of the major rivers within the City of Winnipeg. These riverbank failures are deep seated extending to meters below ground service. Rockfill columns have been used for over a decade now to stabilize failing riverbanks in Winnipeg. Many authors report that rockfill columns can be used effectively for slope stabilization (Aboshi et al. 1979, Abramson et al. 2002). Goughnour et al. (1990) stated that rockfill columns, which are stronger than the surrounding native soil with higher shear stiffness, have been used successfully in stabilizing natural slopes. The traditional Limit Equilibrium Method (LEM) is the most popular method used for examining the impact of proposed stabilization works because of its simplicity. However, with the availability of more powerful and faster computers, the Finite Element Method (FEM) has become increasingly popular for slope stability analysis and remedial design. FEM enjoys many advantages including the ability to predict stresses and associated deformations with and without reinforcement (Matsui and San 1992, Duncan 1996, Griffiths and Lane 1999, Dawson et al. 2000, Hammah et al. 2004). Alternatively there are some difficulties that limit using FEM for stability analysis. The FEM method requires more soil parameters and boundary condition definitions. Nevertheless, many authors have concluded that FEM can be used to achieve an optimum design solution (Hammah et al. 2004, Baker 2003, Shukha and Baker 2003, Yamagami et al. 2000, Duncan 1996, Poulos 1995, Matsui and San 1992). One of the greater advantages of the FEM solution is that it is mathematically rigerous. Traditional assumptions required to obtain LE solutions include the failure surface location, the failure surface shape, the forces and directions between slices, and the critical failure surface shape (Griffiths and Lane, 1999). 415

2 Matsui and San (1992) presented a finite element slope stability analysis solution using the shear strength reduction (SSR) technique. They applied their method to a existing reinforced cutting using field test data. Results showed that the slip surface can be successfully traced for embankment and excavation slopes by the shear strength reduction technique. They stated that an agreement between the shear strength reduction technique and the modified Fellenius method was satisfactory. Chow (1996) and Hassiotis et al. (1997) concluded that FEM can be used for assessing slope stabilization designs. Numerical methods were used to analyze the stability of unrienforced and reinforced slopes including single and pile groups to achieve an optimum design solution; pile diameter, centre-to-centre distance, and location of the pile row. These parameters are significant to get the determined strength so that the slope stability and the pile integrity are assured under operating conditions. Hassiotis et al. (1997) developed relationships between factor of safety and spacing between piles in terms of pile diameter. They indicated that a spacing of equal to or less than 2.5 the pile diameter should be sufficient to allow the piles to act as a group. Furthermore, they recommended that piles must be placed in the upper middle portion of the slope to provide an optimum safety factor. Griffiths and Lane (1999) stated that the finite element method is a very effective method for slope stability analysis of natural slopes and dams. They concluded that using the FEM in conjunction with an elastic-perfectly plastic (Mohr-coulomb) stress-strain method has been shown to be a reliable and robust method for assessing the factor of safety for slopes. They have concluded that the Mohr-Coulomb criterion remains the one most widely used in geotechnical practice and has been used throughout their analysis. Dawson et al. (2000) stated that the factor of safety of a slope can be computed accurately with finite element or finite difference code using soil shear strength reduction (SSR) in stages until the slope fails. They mentioned that SSR method has a number of advantages over the method of slices for slope stability analysis. This technique is a general purpose tool that can be applied to almost any geotechnical stability problem. Duncan (1996) stated that the factor of safety for slopes can be calculated iteratively by dividing the shear strength of soil by a factor to bring the slope to the verge of failure. This scenario is defined as the shear strength reduction method. The factor used for the iteration is called the Shear Reduction Factor (SRF). Hammah et al. (2005) confirmed the above observations in that finite element analysis using shear reduction method has some advantages. This method can predict stresses and deformations of the reinforced element, such as piles, anchors, and geotextile in various stages and bring them to failure. Swan and Seo (1999) presented comparisons between the classical method (limit equilibrium analysis) and finite element method approaches for slope stability analysis. They applied both gravity increased method and strength reduction method for finite element analysis. They stated that in purely cohesive soils, both methods yield identical results. But strength reduction method appears well suited for analyzing the stability of existing slopes in which unconfined active seepage is occuring. The gravity increase method (GIM) is conducted by increasing the gravity load (g) until the slope becomes unstable, and an equilibrium solution no longer exists (Swan and Seo 1999, Pham and Fredlund 2003): Shear strength reduction method is conducted by decreasing the shear strength parameters of the slope soil until the slope becomes unstable and equilibrium solutions no longer exist (Swan and Seo 1999, Griffiths and Lane 1999): f(t) equilibrium solution exist t critical equilibrium solution does not exist Figure 1 Critical boundaries for shear reduction method (after Swan and Seo, 1999). [1] S(t) = Sa * f(t) [2] FS SSR = Where: S S a ( t critical ) Sa = the actual strength parameters, S(t) = the variable shear strength, it changes as the factor of reduction changes, Swan and Seo (1999) suggested that the SSR technique is suited for slope stability analysis of natural slopes because of the potential seepage in the slopes. On the other hand, the GIM approach is well suited for stability analysis of embankment and fill applications because the closely simulated staged construction of embankments and fills. Therefore SSR was used in this study to analyze the stability of the natural riverbanks. This study assumes a plane strain condition and uses the Mohr-Coulomb constitutive model. Phase 2 is the computer software used in this study, which is a two-dimensional finite element program developed by Rocscience Inc., (Rocscience 2005). The shear strength τ can be calculated through Mohr- Coulomb model by using soil parameters such as cohesion, friction angle, and the applied normal stress: [3] τ = c + σ N tan φ t 416

3 At failure the shear strength required can be defined as : [4] τf = cf + σ N tan φf SRF c {cf = ; tan φf = tan -1 tan φ ( )} SRF SRF The shear strength parameter c and tan φ are reduced by a Shear Reduction Factor (SRF) until the slope is no longer stable. One of the indications of slope instability in finite element analysis is through the non-convergence results of stress distribution in Mohr-Coulomb criterion. This criteria needs to be examined carefully since an actual solution is not achieved. 2. STATEMENT OF THE PROBLEM The typical riverbank failure mechanism in Winnipeg is dominated by soft high plastic fissured clay that represents a large component of the riverbank mass. Rockfill column lengths required vary depending on the column location in the slope. The columns penetrate a stiff till layer to completely cut off failures in the soft clay mass. Riverbank failure mechanisms are expected to differ from those in engineered embankments. The primary difference between embankments and natural slopes such as those commonly encountered in riverbanks is the way shear resistance is mobilized in the columns. In the case of embankment applications, the applied vertical stress from the weight of the embankments themselves can enhance the normal effective stress in the column. In the case of riverbank stabilization, the normal stress at any point in the column relies generally on the weight of the column materials above that point. Field evidence exists that show potential failure surfaces similar to those shown in Figure 2. An attempt was made to simulate this type of failure mechanism in the laboratory using large-scale rockfill materials, and to measure volume change during shearing. 3. LABORATORY RESULTS The natural riverbanks along the Red River predominantly consist of glacio-lacustrine high plastic clays. The clays are relatively weak with undrained shear strengths ranging from 35 to 85 kpa depending on location and depth in the riverbank profile. The strength of the clay typically decreases towards the bottom of the clay deposit at the top of the dense basal till layer (Graham et al. 1983). Many authors have reported that failure of riverbanks inside Winnipeg incorporate large sections of the slope that are deep seated up to 15 meters depth below ground surface, and extend horizontally as far as 60 m from the river s edge (see Mishtak 1964). Therefore undisturbed clay samples were collected from depths m below ground surface to provide representative materials for laboratory testing (Abdulrazaq et al. 2005). Large-scale and conventional direct shear tests have been performed on the undisturbed lacustrine clays. The reason behind conducting these tests is that the measured strength parameters can be used in numerical analysis. The conventional direct shear test is useful to determine the effective shear strength parameters under drained conditions. The test results for peak, post-peak, and residual strength have been obtained for this soil at normal stresses 50, 75, and 100 kpa. The measured clay cohesion and angle of internal friction for the post-peak shear strength were 4 kpa and 15 respectively. The authors found it is appropriate to use the post-peak strength parameters to represent the riverbank soil strength to be used as input data for the FEM. Graham (1986) reported that post-peak strengths have been used with success in first-time slides in high plastic clays where no previous failures existed. Using peak strengths for brittle soils can lead to inaccurate and overestimated stability analysis. TOP OF BANK Potential Failure Surface Direct Shear Failure Mechanism Shear strength of rockfill materials have been obtained after large scale direct shear tests of the actual rockfill sizes. The effective friction angle φ is 50 for densely compacted rockfill. LACUSTRINE CLAY GLACIAL TILL 2m - 3m dia. ROCKFILL COLUMN RIP RAP BLANKET Figure 2 Typical riverbank cross-section stabilized with rockfill columns (after City of Winnipeg 2000). direct shear testing, particularly in the clay-rockfill composite material. Large-scale direct shear tests were carried out using composite undisturbed-clay-rockfill samples to simulate and evaluate the performance of rockfill columns to stabilize Winnipeg riverbanks. The large-scale apparatus is required to test the actual size of 4. NUMERICAL ANALYSIS AND DESIGN In this section the behavior of riverbank in Winnipeg with and without rockfill columns is presented. Numerical analysis of a typical riverbank in Winnipeg has been performed. FEM has many advantages. One of the significant advantages of FEM is its ability to compute the stresses, strains, and the associated shear stresses in the riverbank. A number of researchers (Griffiths and Lane 1999, Dawson et al. 2000, Hammah et al. 2005, Shukha and Baker 2003, Duncan 1996) reported several advantages of SSR technique including the ability to predict stresses and deformations of support elements, such as piles, anchors and geosynthetic reinforcement, even at the verge of failure. Figure 3 shows typical riverbank geometry in Winnipeg area. 417

4 Rocscience Slide 5 provides a simple graphical user interface. It allows the user to choose from several LEM methods. Figure 3. Geometry of riverbank in Winnipeg. For our study, a traditional limit equilibrium method; Morgenstern and Price s (Duncan and Wright 2005) method was applied to analyse the stability of the riverbank. This method is the most popular in the industry and it takes into account both the forces and moments. The in-situ factor of safety for the natural riverbank (before using rock columns) was determined to be 0.99 using the Morgenstern and Price s method. The strength and material properties that were specified directly in the analysis were taken from the laboratory measurements. The less than unity indicates that the section examined is unstable and some errors exist in the inputs as a factor of safety lower than one is not physically meaningful. The SSR was used to analyze the stability of the riverbank. Phase 2 software (Rocscience 2005) was chosen to run the numerical analysis. The model used 6 noded triangles, and was set for maximum number of iterations equal to 500 and a tolerance value of These settings are recommended values given in Rocscience (2005). The values of soil modulus for both high plastic clay and rockfill material are required for the soil constitutive model used to analyze the performance of the riverbank. Values of equivalent Young s modulus, Ε, and Poisson s ratio, υ, in combination with shear strength parameters are required to compute the stresses and deformations in the riverbank. The principal function of stabilizing the riverbank using rockfill columns is to provide stiffer and stronger material compared to the surrounding soil, and to act as a drain to relieve pore water pressure at the interface layer between the clay soil and the underlying till. Through these rockfill columns the average shear strength along the potential slip surface will increase significantly, to stabilize and reinforce riverbanks. The rockfill column depth extends into the stiff till layer. This insertion will enable reinforced columns to act as a key (pin) inside the stiff layer in order to force the failure mode to go through the rockfill columns (instead of mass failure that fail underneath the columns). Many factors may contribute to the effective function of stabilized columns in riverbanks. Engineering properties of rockfill materials, durability of rockfill materials, column s shear resistance, column s shear stiffness, relative density, column diameter, and position of column insertion inside the stiff till layer are key aspects of the rock column layout (Abdulrazaq et al. 2005). One of the significant factors to be investigated in this study is the amount of shear strain (and thus displacement) required to mobilize shear resistance of rockfill columns without exceeding the allowable maximum deformation in the stabilized riverbanks. Graham (1986) reported maximum shear strains in the unstabilized riverbanks in the range of 1.8% to 4.0% in brittle high plastic clays are susceptible to strain softening. Therefore in the numerical analysis it is vital to deduce the amount of shear strain required to mobilize shear resistance of rockfill columns in these soils. This will then help us evaluate if the associated shear deformation is acceptable in terms of the serviceability requirements of the riverbanks or of the structures near riverbanks. Table 1 Soil properties for both lacustrine clay and the weak soil. Type of Soil E kn/m 3 ν γ kn/m 3 φ Degree c kn/m2 Clay Weak Clay Rockfill Column Till Layer 10e Duncan (1996) stated that values of c and φ determined from direct shear tests have been found to be essentially the same as values determined from drained triaxial or consolidated undrained (CU) tests with pore water pressure measurements. The soil properties used in this study (for analysis and design) are shown in Table 1 which has been determined from our laboratory direct shear tests (both large-scale and conventional direct shear tests). 5. EVALUATION OF RIVERBANK STABILITY The stability of natural riverbanks can be investigated by two methods, the first is limit equilibrium method, and the second is the finite element method. FEM is useful to estimate the mode of failure and slope displacement in addition to the factor of safety. However FEM requires more parameters and more time to perform analysis. Therefore in this study the LEM will be used for stability investigation of stabilized riverbanks, while the FEM is used for the optimum case only. Mohr-coulomb failure criterion is the one used for LEM analysis for the factor of safety calculation. While the constitutive model used for FEM is elastic-perfectly plastic. The analyses, performed on a typical riverbank geometry with various lengths of rockfill columns are relevant to the column location in the slope. According to installation specifications, columns should be inserted at minimum one meter inside the till layer. Many parameters have been investigated; number of stabilized rows, columns diameter, columns optimum locations, and spacing between columns. Every time a new parameter is selected, the failure surfaces changes and, consequently the value of factor of safety changes. Location of the column was considered with respect to 418

5 the crest of the riverbank. The influence of rockfill column locations has been studied along the riverbank. Slope stability analysis using limit equilibrium methods can be near the crest col. diameter: 2 m col. spacing: 4 m near the toe Distance from the crest, meter Figure 4. Effect of columns location (refer to Figure 3) col. diameter: 2 m col. spacing: 4 m riverbank in Winnipeg as shown in Figure 5. The number of rows of columns will be considered for the number that provide factor of safety equal or above 1.5 (using LEM). Therefore 5 rows of rockfill columns at the vicinity of the centre of the riverbank slope (position of the maximum factor of safety) have been chosen for further analysis. Again when spacing between rows of columns is altered, the location of the potential slip failure changes as illustrated in Figure 6. This is significant since for the same number of columns but with a closer spacing provides the configuration provides a higher shear strength and therefore factor of safety. This finding matches similar results from laboratory large scale direct shear tests of a group of columns. Another factor has influence on the measured factor of safety. The ratio of S2/S1 value which represents the clear distance between columns to the centre to centre distance (see Figure 7) has been investigated. It is obvious that the lower the stress ratio (S2/S1) value the higher the factor of safety as shown in Figure 8. The optimum rockfill column location has been investigated through the Finite Element Method as shown in Figure 9. The results from FEM using shear reduction method indicated a factor of safety of a stabilized riverbank in Winnipeg is equal to This means that LEM provides overestimated values compared to SSR for the stabilized riverbanks. The results of the comparison of factors of safety between LEM and FEM are consistent with those observed by Hammah et al. (2005). It is observed that the potential shear failure plane has moved from the interface between the till layer and the weak clay col. diameter: 2 m Number of rows Figure 5. Number of rows versus factor of safety. used to calculate factor of safety of riverbanks with and without rockfill columns as discussed earlier. The calculated factor of safety of a natural riverbank indicates unstable analysis as the factor of safety is 0.99 by using Morgenstern and Price s method. While the calculated factor of safety using the shear strength reduction method for natural riverbank is approximately 1.0. The analysis also shows that the potential shear failure plane is along the clay till interface which represents the weakest clay zone. This finding agrees with field observations because the undrained shear strengths frequently decrease towards the bottom of the deposit (Graham et al. 1983). It is clear that the centre of the potential shear failure is the best position for rock columns to maximize the factor of safety as shown in Figure 4 provided all other variables are constant. Other factors have been studied including the number of columns rows on the stability of the typical Spacing between columns c/c, meters Figure 6. Spacing between rows versus factor of safety for a rockfill column diameter of 2 meters. upward at the locations of rockfill columns. This change of failure plane location is due to the high shear strength generated with the reinforced riverbank. The mobilized shear resistance of rockfill columns is highly influenced by the effective normal stress applied at the location of the shear plane (Abdulrazaq et al. 2005). 419

6 The increase in depth does not increase the relative shear resistance in the clay as much as it increases in the rockfill columns. This phenomenon forces the shear failure plane to move upward where the applied normal stress is less, as shown in Figure 9. Figure 9 also indicates the maximum shear strain at the critical strength reduction factor (SRF critical value is equivalent to the value of ). This maximum shear strain is a good indication of the potential slip plane. The estimated shear strain can be used to predict the mobilized shear strength of the composite soil. The riverbank displacement is important in assessing the performance of the riverbank even if the factor of safety is acceptable col. spacing: 4 m d S1 S Figure 8 safety Diameter of rockfill columns, meter Rockfill column s diameter versus factor of 2m - 3m dia. ROCKFILL COLUMN LACUSTRINE CLAY GLACIAL TILL Figure 7 Rockfill columns pattern along riverbank. Figure 10 shows the total displacements in the riverbank was equal to 8 cm. The maximum displacement occurs at the upslope of the riverbank. The FEM performed to study the mode of failure for 0.6 S2/S1 value compared to 0.5 cases. It is obvious that at the lower value of S2/S1 the columns work as a group while in the second case the mode of failure shows individual behaviour as shown in Figure 11. There is another finding has been observed from FEM analysis is the maximum shear strain measured is reduced with the closer spacing of rows. This is notably significant, that the slope displacement required to mobilize shear resistance of rockfill columns is less than the conventional case. Figure 9 Maximum shear strain of the optimum columns location (2 meter diameter and 4 meter spacing). 6. CONCLUSIONS The first observation was that the Finite Element Method can successfully be used to predict the mode of failure of the stabilized riverbanks. The optimum rockfill column location should be placed in the vicinity of the centre of the critical shear failure surface as noted in the discussion. The most significant finding is that for the same number of columns rows, the closer spacing leads to a higher factor of safety and less slope displacement due to the mobilization of the column rows. The other finding that the closer spacing has the less maximum shear strain. Figure 10 location. Riverbank displacements at the optimum Figure 11 Maximum shear strain at the larger spacing (5 meter spacing). 420

7 7. ACKNOWLEDGEMENT The authors are grateful for the funding from the City of Winnipeg, KGS Group, Amec International, UMA- AECOM, Subterranean Ltd., and NSERC. The authors acknowledge Mr. Peter Mignacca of Subterranean Ltd. for providing the rockfill materials and for designing and fabricating sampling and trimming devices for large undisturbed clay samples. REFERENCES Abdulrazaq, W., Kim, G-S., Alfaro, M., and Blatz, J Shear Mobilization of rockfill columns for riverbank stabilization, Proceedings of the 58 th Canadian Geotechnical Conference, Winnipeg,MB, Canada. Aboshi, H. Ishimoto, Enoki, E. M., and Harada, K The composer-a method to improve characteristics of soft clays by inclusion of large diameter sand columns. Volume I, Paris: Abramson, L.W., Thomas S. Lee, Sunil Sharma, and Glenn M. Boyce Slope Stability and Stabilization Methods, John Wiley & Sons, New York, NY, USA. Baker, R Inter-relations between Experimental and Computational Aspects of Slope Stability Analysis, International Journal for Numerical and Analytical Methods in Geomechanics, 27: City of Winnipeg Riverbank Stability Characterization Study for City Owned Riverbanks, Planning, Property and Development Department, City of Winnipeg, Winnipeg, MB, Canada. Chow, Y.K Analysis of Piles used for Slope Stabilization, International Journal for Numerical and Analytical Methods in Geomechanics, vol. 20: Dawson, E., Motamed, F., Nesarajah, S., and Roth, M Geotechnical Stability Analysis by Strength Reduction, Slope Stability2000, ASCE Geotechnical Special Publication No Duncan, J.M State of the Art: Limit Equilibrium and Finite-Element Analysis of Slopes. Journal of Geotechnical Engineering, vol. 122, No. 7: Duncan, J.M. and Wright S.G Soil Strength and Slope Stability, John Wiley & Sons, New York, NY, USA. Graham, J., Noonan, M.L., and Lew, K.V Yield states and stress-strain relationships in a natural plastic clay, Canad.Geotech. Jour., 20, Graham, J Slope Stability Analysis: Applications in Plastic Clays, 34th Annual Soil Mechanics and Foundation Engineering Conference, Minneapolis, MN. Griffiths, D.V., and Lane, P.A Slope Stability Analysis by Finite Elements, Geotechnique, 49, n 3: Goughnour, R. R., Sung, J.T. and Ramsey, J.S Slide Correction by stone column, Deep Foundation Improvements: Design, Construction and Testing. Hammah, R., Curran, J., Yacoub, T., and Corkum, B. 2004a. Stability Analysis of Rock Slopes using the Finite Element Method, In Proceedings of the ISRM Regional Symposium EUROCK 2004 and the 53 rd Geomechanics Colloquy, Salzburg, Austria. Hammah, R., Yacoub, T., Corkum, B., Curran, J A Comparison of Finite Element Slope Stability Analysis with Conventional Limit-Equilibrium Investigation, Proceeding of the 58th Canadian Geotechnical Conference, Saskatoon, Saskatchewan, September Hassiotis, S., Chameau, J.L., and Gunaratne, M Design Method for Stabilization of Slopes with Piles, Journal of Geotechnical and Geoenvironmental Engineering, vol. 123, No. 4: Matsui, T., and Ka-Ching, San Finite Element Slope Stability Analysis by Shear Strength Reduction Technique, Soils and Foundations, vol. 32, No.1: Mishtak, J Soil Mechanics Aspects of the Red River Floodway, Canadian Geotechnical Journal, vol. 1, No. 3: Pham, Ha and Fredland, D.G The application of dynamic programming to slope stability analysis, Canadian Geotechnical Journal, 40, n Poulos, H.G Design of Reinforcing Piles to Increase Slope Stability, Canadian Geotechnical Journal, vol. 32: Shukha, R., and Baker, R Mesh Geometry Effects on Slope Stability Calculation by FLAC Strength Reduction Method-Linear and Non-Linear Failure Criteria, Proceeding of the 3rd International FLAC Symposium, Sudbury, Ontario, Canada: Swan, Colby C. and Seo, Young-Seo Slope Stability Analysis Using Finite Techniques, 13th Iowa ASCE Geotechnical Conference, Williamsburg, Iowa. Yamagami, T., Jinang, J-C. and Ueno, K A Limit Equilibrium Stability Analysis of Slope with Stabilizing Piles. Slope Stability 2000: