Slope instability due to pore water pressure increase

March 29, 2018 | Author: Dariusz Wanatowski | Category: Landslide, Strength Of Materials, Materials Science, Earth & Life Sciences, Earth Sciences


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Slope instability due to pore water pressure increaseS. Leroueil Laval University, Quebec City, Quebec, Canada J. Chu Nanyang Technological University, Singapore D. Wanatowski The University of Nottingham, Nottingham, United Kingdom ABSTRACT: Chu et al. (2003) developed a framework based on specific stress paths followed in slopes subjected to pore water pressure increase and concepts of soil instability and critical state. This framework applies to loose as well as dense sands. In this paper, these concepts are slightly extended and confirmed on the basis of physical model observations and case studies. Practical implications related to the evaluation of slope stability and the significance of calculated factor of safety are then discussed. 1 INTRODUCTION Flow slides associated with heavy rainfalls are often devastating, causing many casualties in many parts of the world. However, their development has not been well understood until recently, in particular because the stress paths followed in slopes subjected to pore pressure increase were not considered and the concepts of instability of cohesionless soils were not well understood. When a slope is subjected to pore pressure increase due to infiltration or rising water table, total stresses and shear stresses remain essentially constant but effective stresses, mean effective stress in particular, decrease. This corresponds to a specific stress path which, examined within the concepts of critical state and instability, provides a general framework for understanding slope behaviour in both loose and dense soil deposits (Chu et al. 2003). The first part of the paper focuses on the onset of slope instability (i.e. development of plastic strains), and post-failure as such is not considered. In the second part, evidences from physical models and case histories supporting the framework are presented. Finally, there is a discussion on the practical implications of the framework on the evaluation of slope stability. soil is consolidated, isotropically or anisotropically, in a triaxial cell and then subjected to an undrained compression test, the stress-strain curve shows a peak and then moves towards an ultimate state, often called steady state or critical state. Figure 1 presents such stress paths in a q/p’cs vs p’/p’cs diagram, in which p’cs is the mean effective stress at the critical state. Sladen et al. (1985b) called the line joining the peaks obtained in CIU tests to the critical state (CS) the Collapse surface. At a given void ratio and in a p’ vs q diagram, that would be a collapse line; at a different void ratio, the collapse line is different. Lade (1993) defines these lines as instability lines (IL). The zone bounded by the IL and the critical state line (CSL) is the zone of instability in which loose sand becomes unstable when an undrained condition is imposed (Chu et al., 2003; Wanatowski et al., 2009a). The IL also appears to be a state boundary surface that is followed by soil elements that reach it to move towards the critical state. This was evidenced by Sasitharan et al. (1993) who performed constant shear drained (CSD) tests, with constant deviatoric stress and decreasing mean effective stress from initial stress conditions at point I, on loose Ottawa sand (Fig. 2). The specimen collapsed at point Y, well below the (CSL), at a void ratio of 0.809. The collapse (or instability) line corresponding to the same void ratio is also shown on the figure. It can be seen that yielding in the CSD test has been obtained when the stress path reached the instability line, indicating that instability is associated with the same effective stresses and void ratio, regardless of drainage conditions. 2 MECHANISMS LEADING TO SLOPE INSTABILITY Before considering slopes, it is useful to examine some aspects of cohesionless soil behaviour. When a 3) with respect to the CSL. if stress conditions on the collapse surface are described by an angle of strength mobilization φ’mob (e. However. In the context of slopes subjected to pore water pressure increase. . Anderson & Riemer. (1985b)’s data (see Fig. these strains started developing at a faster rate. it turns out that. In fact. the instability point B is well below the critical state line. On the basis of the results. (2003) suggested calling this difference the modified state pa__ rameter Ψ (Fig. corresponding to M6. Ψ is defined in a e vs p’ diagram (Fig. In the laboratory.0.9 for the test consolidated at 6. Two specimens of loose sand (ec = 0. (2003) defined the term instability as behaviour in which large plastic strains are generated rapidly due to the inability of a soil element to sustain a given stress or load. at point B. at an angle of strength mobilization φ’mob lower than φ’cs. under the same mean effective stress. Positive values of Ψ are associated with contractant soil behaviour whereas negative values of Ψ are associated with dilatant soil behaviour. Figure 4 illustrates instability under CSD tests. 3).value and decreasing p’ value called constant shear drained (CSD) tests (Brand.9 p’cs). Such tests had been performed by Anderson & Riemer (1995) on colluvial soil and by Santos et al. were anisotropically consolidated at p’ = 200 kPa (point A for DR7. From Sladen et al. the value of Ψ in a slope varies with seasons whereas slope instability and __ possibly failure depends on Ψ . 3) as the difference between the current void ratio eo (at a point such as I) and the void ratio on the steady state line (or CSL). 3) and the corresponding Ψ value but rather by the relative position of the point at yielding Y (Fig. 4a) and then sheared at an essentially constant deviatoric stress at a rate not allowing the development of pore pressure during the test that was thus fully drained. indicating unstable behaviour. (2003) performed a series of triaxial tests. 1). 1995). Leroueil (2001) indicated that instability is not controlled by initial stress conditions at point I (Fig.35 mm and a uniformity coefficient of 2. Fig.g. From A to B. such stress paths can be simulated by drained tests with constant q Chu et al. In the interpretation of the tests. Chu et al. (1996) on residual soil. Chu et al. 4b). the stress paths followed are at an essentially constant shear stress with decreasing effective stresses.30-0.94). this angle is lower than the critical state friction angle φ’cs and increases towards its value when the consolidation stress p’/p’cs decreases towards one. DR7 and DR10. 1981. including CSD tests. As shown in Figure 4a. ess(I). there were little axial and volumetric strains (Fig. on Changi sand having a mean grain size of 0. Ψ = eo – ess. Been & Jefferies (1985) proposed the state parameter Ψ for characterising the behaviour of sands. ηIL = q/p’. from D to E. varies from about __ __ 0.060 for the loose specimens and about -0. As the deviatoric stress at C is smaller than that due to gravity forces in the slope (q at Ils).15. The relationships between the effective stress ratio at insta__ Two specimens of the same sand. The critical state line is also shown on the figure.16 for plane strain tests. at the intersection of the CSL and IL. ηIL. M values equal to 1.35 for triaxial tests and 1. (2009a) showed that. It can be seen that in these cases. However. From these results. Figure 4c shows the location of the instability points for the previously mentioned tests in an e vs log p’ diagram. As shown on Figure 4b. triaxial or plane strain.186 for the dense specimens.70 for Ψ > 0. 5a). the axial strain started increasing. Wanatowski et al.ever. 4a) and then sheared at an essentially constant deviatoric stress.10 to about 1. below the CSL. but dense (ec = 0. were anisotropically consolidated at about p’ = 260 kPa (point D for DR39. It can be seen that the modified state __ parameter Ψ is equal to about 0. It can be seen that ηIL. 5b). there will be static liquefaction of the soil and collapse of the slope. instability is reached at an angle of strength mobilization φ’mob larger than φ’cs. the soil will have a tendency to move towards its critical state C. both curves come on a unique one (Fig. At Yls. Fig. (2003) developed a general framework for understanding the instability of slopes in loose or dense sand subjected to pore water pressure increase.35 at critical state. initial conditions will be at a point such as Ils in Figure 6 and instability will be reached at a point such as Yls. Chu et al. equal to 1. 6). when normalised with respect to the M value obtained in the relevant type of test. However. and Ψ were also different. From these tests and other triaxial tests performed on the same sand. as shown in Figures 4b and 4c.50 for Ψ < . the critical state lines obtained in both tests were different with. (2009b) performed plane strain tests on the same Changi sand and observed a general behaviour similar to that obtained in triaxial conditions.65). Leroueil (2004) summarised it by using a q/p’cs vs p’/p’cs diagram in which the CSL and IL (linear for simplicity) were drawn (Fig. Wanatowski & Chu (2007) and Wanatowski et al. C is the normalised critical state. Chu et al. and Ψ (Fig. at point E. Major consequences of this phenomenon are that failure is triggered at an angle of strength mobilization smaller than the critical state friction angle and that instabil- . How- bility. indicating the onset of instability. this latter instability was associated with dilation of the dense soil specimens. in particular.0. (2003) defined the relationship between the effective stress ratio at instabil__ ity. DR39 and DR40. the axial and volumetric strains were small. For normalised q values larger than the one at C (generally relatively loose sands for slopes of precarious stability). If failure is reached. If at point Y. both axial strain and volumetric strain (dilative in that case) will start increasing at point Y. 7b). As the corresponding strength is smaller than the applied shear stress.e. In such a case.. C2 under undrained conditions. under drained condition).ity (at Yls) is followed by an increase in pore water pressure since p’ decreases. If the pore water pressure can dissipate freely (i. 2009a) and the stress state will move towards point C3 (Fig. at . and is subjected to pore water pressure increase. However. On the other hand. failure is delayed. 7a). If the pore water pressure can dissipate freely (i. 7b). dilation cannot be accommodated. If failure is reached at C1. which takes time. on the critical state line that is also the failure line for loose sands. The soil will then remain stable. If soil in a slope is at Ids. negative pore water pressure will develop (see Wanatowski et al. During this process. there may be development of flow at the post-failure stage. post-failure could be essentially undrained. the stress path will move towards Yds where there is development of plastic strains and then have a tendency to go towards its critical state C.e. at a normalised q value smaller than the one at C (generally relatively dense sands). and the stress state will move towards the failure line at a point such as F1. on the IL at __ the corresponding Ψ value. For dense sand. When a loose sand is sheared along a q = cst path starting from point I (Fig. i. large axial and volumetric strains will develop and the void ratio of the soil will decrease (Fig. with a stress path moving towards point C4 in Figure 7b. under drained conditions). 1996). 7b). instability is reached above the CSL but below the failure line. the stress path will move towards the critical state associated with its current water content. where the soil becomes unstable (Fig. as there is then equilibrium between the applied shear stress and the critical state strength. For dense sand. this can only be achieved if the soil dilates and q/p’cs increases. it could however become unstable and the slope could possibly fail when pore water pressure will dissipate. such as for undrained conditions. the stress path will eventually reach the failure state at point C1. This framework can be described in more details by referring to Figure 7. if the pore-water pressure cannot dissipate freely. There will thus be runaway failure and development of flow.. the stress path moves from point I to point Y. instability occurs at point Y. Figure 7c shows a particular case in which instability is reached at the same time as the CSL. the kinetic energy available at yielding will be large. the available kinetic energy will be small and the rate of movement should be small (Leroueil et al. As the corresponding strength may be smaller than the shear stress applied by gravity forces in the slope.e. instability is then associated with a tendency of the soil to dilate before failure can be reached. with smaller runout distance. 1984)). The Nerlerk berm was constructed over two seasons in the Beaufort Sea. then post-failure may not evolve into a flow slide but rather into a slide or debris avalanche. These latter possibilities are not examined here. and as indicated by several reported case histories. In that case. the onset of failure can be obtained at an angle of strength mobilization. instability is associated with failure. it is tried to avoid in this paper cases where failure could be associated with erosion or excavation at the toe of slopes. Also. 3 EVIDENCE FROM PHYSICAL MODEL TESTS AND FIELD OBSERVATIONS The framework previously described has important implications for slopes: In loose sand. however. the onset of instability is reached at a mobilized friction angle.point C5. However. Nerlerk berm. (p – uw) decreases and the strength envelope is lowered. where the depth of water was approximately 45 m. However. That framework has been established for saturated conditions. matric suction (ua – uw) decreases. with infiltration. 1999) and failure of the Mississippi riverbanks (Torrey & Weaver. Bangladesh. These authors also mention that if the soil is not saturated at the onset of failure. there does not seem to have detailed information on what happens to instability lines with changing suction. φ’mob. The berm consisted of Ukaler sand core overlaid by Nerlerk sand. the concepts previously described apply. At the turn of July and August 1983. It is more complex for unsaturated soils since. in such case. failure may also result from redistribution of void ratio within a globally undrained sand layer or spreading of excess pore water pressure in a slope. As suggested by the US National Research Council (NRC 1985). failure at the Jamuna Bridge. In addition. The slope angle of the berm was approximately 13°. φ’mob. Several cases from the literature are examined hereunder in comparison with the implications of this framework. as there is then equilibrium between the applied shear stress and the critical state strength. several slides occurred.g. smaller than φ’cs. This sand was assumed to have a relative density of . Such cases involve different stress paths and possibly a quasi-undrained or partly drained behaviour (e. In dense sand. larger than φ’cs.. post-failure will evolve into a flow slide as for saturated soils. involving only Nerlerk sand. Olivares & Damiano (2007) specify that when the soil is susceptible to static liquefaction and is essentially saturated at the onset of slope failure. the available kinetic energy will be small and the rate of movement should also be small. (Hight et al. and if essentially undrained the onset of failure is followed by an increase in pore pressure. Figures 9a and b show typical results obtained on these materials in loose conditions. At 60 g. similarly to Eckersley (1990) observation (Fig. Eckersley (1990) concluded: “Excess pore pressures are a consequence of failure initiation rather than a cause. the coal was placed for the bottom 400 mm at 9% water content with no compaction (dry density of 0. Unfortunately. Centrifuge tests. The construction of the dam was completed in 1907 and failure occurred in the upstream slope during the first reservoir filling. Failure occurred in drained conditions as filling of the reservoir was very slow . Wachusett Dam. Stage 1 comprised two shallow slides over a 2 s period.4° and built with the soil at a relative compaction of 68%. For the experiment considered here (Experiment 7). He also back calculated a mobilized angle of strength at the onset of failure of 24-27°. 8a). According to Olson et al. The two materials tested were silica sandy silt and pyroclastic sand respectively.0 Mg/m3. the remaining 600 mm was placed dry at a dry density of 1. Back analysing the failures. when the model was subjected to an acceleration of 60 g. Eckersley (1990) examined flow slides in coking coal stockpiles. Failure occurred in three stages as indicated in Figure 8a. Sladen et al. indicating instability considerably below the CSL at a friction angle of 31°. It was followed by Stages 2 and 3 that occurred in the 4 following seconds along the shear zones shown in Figure 8a. It can be seen in both cases that pore water pressures slowly increased before the onset of failure and rapidly increased after. Flume tests. 2008) have performed centrifuge tests for examining the failure mechanisms of sandy slopes subjected to rainfall and rising water table.30% (Lade. The material used was Leighton Buzzard fine sand that shows pronounced strain-softening in undrained triaxial shear tests performed on loose specimens. (2000). What can be seen is that pore water pressures mostly increased after the onset of failure defined on the basis of video camera pictures (arrows in Fig. the slope was de-stabilised by rising water level and the soil liquefied statically and flowed. (1985b) found a mobilized angle of strength of 1316°. 1993) and a friction angle at critical state of 31°. much less than the critical friction angle of 40° obtained from laboratory tests. These pore water pressures became positive during raising of the water table and were slowly increasing at the time of failure. The coal particles ranged from fine sand and silt sizes to gravel with a critical state friction angle of 40°. However. and static liquefaction is therefore a post-failure phenomenon”. Wang & Sassa (2001) and Damiano (2003) examined rainfall-induced flow slides in laboratory flume tests. the slope was densified to 80% of the maximum relative compaction and flattened to 24°.7 Mg/m3). Instability was induced in 1 m high stockpiles by raising the water level within the slope (Fig. Failure was induced by sprinkling water on the surface of the soil models. 8b). Zhang & Ng (2003. also reported by Ng. the pore water pressures reported by Ng (2008) are not very detailed. the upstream fill consisted primarily of fine sands that were placed without compaction. Pore water pressures observed during experiment 7 at locations indicated in Figure 8a are shown in Figure 8b. The model was 305 mm high with a slope of 29. 8b). Coking coal stockpile physical model. other laboratory tests indicated a critical state friction angle of 36. (c) the material is highly susceptible to liquefaction when saturated (see Fig.9 kPa. and the debris slid down at high velocity. Also. The volcanic soils include layers of pumice and volcanic ash classified as sand. Sau Mau Ping landslides. it is thought by Olivares & Picarelli (2003) that on 16 December 1999 slope failed because suction vanished. Laboratory direct shear box tests carried out under a vertical consolidation stress of 25 kPa showed a contractant behaviour for dry densities lower than 1. The Cervinara landslide occurred on 16 December 1999 along a steep slope of about 40° covered by about 2. Suction measurements made on the same site give values of 20 to 50 kPa during the dry season and 4 to 8 kPa during the wet season. Two landslides involving man-made fill slopes occurred after heavy rainfall on 18 June 1972 and 25 August 1976 at Sau Mau Ping in Hong Kong (Ho & Sun. Investigation of the 1976 landslide showed that the fill was extremely loose (ρd = 1. The mobilized angle of strength was then probably very close to the critical state friction angle of the soil. 10). Olivares & Picarelli (2001. between 1. killing 18 persons. to a depth of 7 m and about 1. slightly less than half of the strength at failure. (2000) is that sandy fills that subsequently will be saturated should not be placed without compaction.8°. stroke several houses and killed 5 persons. beyond the crest. In addition. It was estimated that the fill could have been saturated to depths between 2 m and 6 m under the 25 August 1976 rainstorm. Kinetics analysis also indicated a post-failure strength of approximately 16 kPa.65 and 1. corresponding to a mobilized angle of strength that was close to the critical state friction angle of the sand (30°). as volcanic ash is very susceptible to liquefaction (Fig. However. numerical analyses showed that failure could have been triggered if 3 m . Detailed studies of the mechanical behaviour of volcanic ash have been performed at the Seconda Università di Napoli. (2000) indicate that failure occurred at average shear strength between 37.5 m of pyroclastic soils and developed into a flow slide that travelled over several kilometres.6 and 41. Back analysis of the failure performed by Olson et al.and was followed by a flow of the upstream fill soils over a distance of about 100 m into the reservoir. the 1976 landslide took place in a 35 m high and 33° steep slope. 2009). corresponding to about 75% standard compaction) to a depth of at least 2 m below the slope. the slope was 40 m high and inclined at 34° with the horizontal.5 Mg/m3.35 Mg/m3. Cernivara landslide. the landslide turned into a flow slide. For the 1972 landslide. (b) critical friction angle is of 38°. 2003) showed that: (a) strength significantly increases with matric suction. killing 71 persons.2 Mg/m3 (90% and 70% relative compaction). The slopes were made up of decomposed granite. A practical conclusion from Olson et al. The stability of the slope was thus insured by matric suction. ρd was also low and variable. 10).5 Mg/m3 down to 20 m. and turned into mud flow. there is not enough data available to be able to correlate ηIL/M with some physical characteristics of the soils. development of flow slide is very rapid. the two main practical questions are as follows: ηIL/M at large Ψ values is about 0. A major practical question concerns the location of the instability line relative to the critical state line or. what are the mobilizable strength parameters that should be considered in stability analyses of a slope subjected to pore water pressure increase? What is the representativeness of the factor of safety calculated by effective stress analyses? Even if extremely important. (2003) and described here. 5b). about 0. the mode of preparation of the specimens may significantly influence the test results (e. (b) natural soil variability may also be a difficulty. A simplified approach of the problem does not seem to be accessible for the time being.. probably Sau Mau Ping slope) or close to the critical state friction angle (Wachusett dam.of loose fill became saturated.83 tan φ’cs.5 for Changi sand (Fig. There are several reasons for that: (a) the number of tests that is necessary for determining the CSL and the ILs at different void ratios is important.2 Representativeness of a calculated factor of safety Another practical aspect is the representativeness of a calculated factor of safety for a given slope.55 for Leighton Buzzard sand (Fig. (b) Fleming et al. It is thought that the test results are the best indicators of the behaviour of a slope under increasing pore water pressure and can be directly used. where measured (and if the soil is not too pervious). in all cases. It seems how__ ever that the ηIL/M vs Ψ relationship is soil specific. As . Considering instability. The answer is given by a diagram such as Figure 5a and the ratio between ηIL __ at relatively large Ψ values and M. Coking coal stockpile. what is the angle of strength mobilization to be considered. (2004) concluded that instability was reached at mobilized friction angle φ’mob such that tan φ’mob = 0. reconsolidate them under stresses close to in situ stresses and then shear them at constant deviatoric stress and decreasing mean effective stress. 1) and about 0. Cervinara slope). __ 4 DISCUSSION The cases presented in the previous section confirm the soil model and its implications for slopes. they observed abrupt decreases in pore pressure 5 to 50 minutes before failure. In loose sandy soils. it is also suggested to define φ’cs for the considered soil. in other words. there was strain-softening of the soil and development of post-failure flow slide. to take undisturbed samples. ηIL/M thus appears to be variable __ from soil to soil and also with Ψ . but for strength conditions below the critical state strength envelope. (c) if reconstituted soil is used. (1990) triggered by artificial subsurface irrigation. instability is followed by pore water pressure increase (coking coal stockpile. in CSD tests. (1989) report observations of time lags between the beginning of landslide movements and the initiation of debris flows. On the other hand.73 to 0.9 for Cervinara volcanic ash (Fig. 4. post-failure behaviour is not considered here. Evidences of dilatant behaviours. Also. 4. there is evidence of dilatant behaviour and delay between the onset of instability (development of plastic strains) and failure as such. For comparison.g see Vaid et al. Olivares & Damiano (2007) indicate however that in these conditions. it seems that failure was initiated when the matric suction was close to zero.1 Practical application of the framework The framework and its implications being accepted. The possibility of dilatant behaviour of soil masses prior to some post failure movements is also supported by observations: (a) Casagrande (1975) indicates that prior to liquefaction and flow of large masses of rather dense granular talus in the alps. the onset of failure can be reached at an angle of strength mobilization lower than the critical state friction angle (Nerlerk berm. for the time being. In the cases of dense soils. 2009). Testing 3 different Japanese sands. brooks emerging from the toe of the talus stopped flowing. Orense et al. flume tests). 10). (c) in three slides that Harp et al. it appears difficult to develop a rational and practical methodology for the approach proposed by Chu et al. the possibility to have a flow slide is smaller. in all cases also. when possible. It can be thought however that some slopes failure can be reached when they are still unsaturated (in loess in particular). For the two slope cases reported here that were generally unsaturated (Cervinara and Sau Mau Ping). The recommendation following this investigation was that the soil has to be compacted to not less than 95% of standard maximum dry density for manmade fills (Ho & Sun. It is thus recommended. 1995). J. Harp. Transformation of dilative and contractive landslide debris into debris flows – An example from Marin County. This phenomenon is amplified by conventional limit equilibrium stability analyses.G. A state parameter for sands. 121(2): 216-219. soil instability is followed by pore water pressure increase. Weels. Proc. Martin. P. Brand. of Geotech. & Leong. Engng. reconsolidate them under in situ stresses and then shear them in CSD tests in order to evaluate their behaviour.. a solution for decreasing the possibility of soil instability and liquefaction is to increase the angle of strength mobilization by compaction.e. A. 35(2): 99-112. 3: 373-376. failure and post-failure mechanisms of loose and dense sandy slopes. Italy. Fleming. 4. & Algus. Leroueil. 5th Panamerican Conf.D. K.. 1990.A. It is also shown that calculated factor of safety of slopes in loose sand can strongly overestimate real stability. E.N. Proc. Mech. Meccanismi d’innesco di colate di fango in terreni piroclastici. S.. S. R. For loose cohesionless . If perfectly drained. M. E. negative pore pressures develop and the slope will not fail. Buenos Aires.3 Solutions to decrease the possibility of instability and flow slides As suggested by Olson et al. 2: 945-958. which implicitly assumes an effective stress path such as IG in Figure 11 (see Tavenas et al. IS Tohoku. Pore pressure response during failure in soils...previously indicated and as illustrated by the stress paths IY in Figs.G. & Jefferies. If not perfectly drained.W.. Geol. Damiano. Géotechnique. II & Sarmiento. for the case schematised in Figure 11. Bull. Collapse of saturated soil due to reduction in confinement.W.. Flow slides in micaceous sands.. soils. i.l. Observations made in physical model tests and interpretations of case histories confirm this framework. Sendai. instability (development of plastic strains) is reached at an angle of strength mobilization slightly larger than the critical state friction angle. The practical application of these concepts is however difficult to apply and it is suggested. The calculated factor of safety for a slope in loose sandy soil may thus significantly overestimate the real stability. In these analyses. 2. Liquefaction and cyclic deformation of sands. the factor of safety is calculated by comparing the applied shear stress to the shear stress at failure under the same normal effective stress. J.D. 1981. J. W. when possible. and Found. 1995. V. Hight. M. 40: 873-885. and Found. IY. Instrumented laboratory flowslides. Engng. Ng (2008) and other authors suggest reinforcement of the slope by methods such as nailing. Geol.. If perfectly drained and dilation allowed. S. to take undisturbed soil samples. flow and runaway failure. Chu. the initiation of failure may be obtained for an angle of strength mobilization smaller than φ’cs in loose sandy soil.K. Engng.D. & Riemer. 40(3): 489-502. ASCE. Eckersley. Am. Second Univ. failure is reached at the critical state with a rate of movement that should be small. 5 CONCLUSION The framework established by Chu et al. of Naples. 1980). 1975. D. 1999. J. Ph. Thesis. 2003. M. California. Symp.W. instability is reached at an angle of strength mobilization that is smaller than the critical state friction angle. Vol. J. Vol. Engng.A..F. that would mean a calculated factor of safety of about 2 (from I to G) whereas the slope is in fact close to collapse (from I to Y). 1990. For dense soils. A. thus very different from the stress path leading to failure. Some thoughts on rain-induced slope failures. 102(4): 428-438. Been. 4 and 7a. Casagrande. Ellen.K. Conf. (2003) and re-examined here provides a unified way to study the instability. on Soil. 1989. Int. a critical review.. 1985. E.W.G.. 5: 79133. Stockholm. Géotechnique. 27: 201-223. Canadian Geotech. 10th Int. Soc. Georgiannou. Proc. (2000) and Ho & Sun (2009). W. 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