Lecture 40 Topics Module 8 SEISMIC SLOPE STABILITY Lectures 37 to 40) 8.6.15 Analysis of Weakening Instability 8.6.16 Flow Failure Analysis 8.6.17 Analysis of Stability 8.6.18 Analysis of Deformation 8.6.19 Deformation Failure Analysis 8.6.20 Hamada et al. Approach 8.6.21 Youd and Perkins Liquefaction Severity Index)Approach 8.6.22 Byrne Approach 8.6.23 Bazaar et al. Approach 8.6.24 Bartlett and Youd Approach 8.6.15 Analysis of Weakening Instability Through a process of pore pressure generation and/or structural disturbance, earthquake induced stresses and strains can reduce the shear strength of a soil. Weakening instabilities can occur when the reduced strength drops below the static and dynamic shear stresses induced in the slope. Weakening instabilities are usually associated with liquefaction phenomena and can be divided into two main categories, flow failures and deformation failures. Flow failures occur when the available shear strength becomes smaller than the static shear stress required maintaining equilibrium of a slope, flowing failures, therefore are actually driven by static stresses. They can produce very large deformations that occur quickly and without warning. Deformation failures occur when the shear strength of a soil is reduced to the point where it temporarily exceeded by earthquake induced shear stresses. Much like inertial failures, deformation failures occurs as a series of pulse of permanent displacement that cease at the end of earthquake shaking. Different procedures are available for the analysis of flow failures and deformation failures. 8.6.16 Flow Failure Analysis Because they usually involve significant reduction in soil strength, flow failures usually produce large deformations and severe damage. The first step in their analysis is generally to determine whether or not one will occur. To estimate the extent of the damage produced by flow failures, procedures for estimation of flow failure deformations have also been developed. 8.6.17 Analysis of Stability Dept. of Civil Engg. Indian Institute of Technology, Kanpur 1
Potential flow slide instability is most commonly evaluated by conventional static slope stability analyses using soil strength based on end of earthquake conditions Marcuson et al. 1990). In a typical analysis, the factors of safety against liquefaction at all points on a potential failure surface are first computed. Residual strengths are then assigned to those portions of the failure surface on which the factor of safety against liquefaction is less than 1. At locations where the factor of safety against liquefaction is greater than 1, strength values are based on the effective stresses at the end of the earthquake i.e., considering pore pressures generated during the earthquake_. With these strengths, conventional limit equilibrium slope stability analyses are used to calculate as overall factor of safety against flow sliding. If the overall factor of safety is less than 1, flow sliding is expected. The possibility of progressive failure must be considered in stability evaluations of this type-the redistributions of stresses involved in progressive failure are not accounted for directly in limit equilibrium analyses. 8.6.18 Analysis of Deformation If stability analyses indicate that flow failure is likely, the extent of the zone influenced by the failure can be determined from an analysis of flow failure deformations. By neglecting the small deformations that precede the triggering of flow sliding rough estimate of flow sliding deformations can be obtained from procedures based on limit equilibrium, fluid mechanics, and stress-deformation analyses. Simple plane strain limit equilibrium procedures can be used to estimate the distance a liquefied soil would flow over a gentle slope Lucia et al., 1981). By assuming that the liquefied soil would eventually come to rest with a linear surface a post failure geometry that satisfies equilibrium and volumetric constraints can be identified. With reference to the rotation of figure 8.22), the procedure can be implemented in the following steps: Figure 8.22 Geometric notation for estimation of flow failure distance by procedure of Lucia et al., 1981) 1. Using figure 8.23.a), compute values of the height of the slope at the end of flow when the static factor of safety reaches 1.0) based on strength considerations using for various assumed values of the slope angle,. 8.17) Dept. of Civil Engg. Indian Institute of Technology, Kanpur 2
Figure 8.23 Charts for estimation of flow failure distance: a) stability number charts for computing strength curve; b) determination of values that simultaneously satisfy strength and volume constraints. After Lucia et al., 1981) Plot the data in the form of a strength curve as in figure 8.23.b). 2. For various assumed values of calculate the height of the slope after flow based on constant-volume conditions using and is the estimate volume of soil involved in the flow slide. 8.18) Where Plot the resulting data in the form of a volume curve as in figure 8.23.b). 3. The strength and volume curves intersect where. The resulting and values satisfy both strength and volume requirements with a factor of safety equal to 1. The horizontal distance covered by the flow slide can then be computed as 8.19) Dept. of Civil Engg. Indian Institute of Technology, Kanpur 3
Although the procedure involves several simplifying assumptions and requires an estimate of the strength of the liquefied soil, it can provide at least a crude estimate of the deformation involved in certain flow slides. The fluidlike behavior of liquefied soils has motivated fluid mechanics approaches to the modeling of flow slide behavior. Most of this work has been directed toward debris flows e.g., Johnson, 1970; Iverson and Denligner, 1987) and tailings dam failures e.g., Jeyapalan et al., 1981). Rheological modeling of liquefied soils is quite difficult. The Bingham model strength, where are the Bingham yield strength and plastic viscosity, respectively, and is the shear strain rate) is most commonly used Johnson, 1970, Jeyapalan, 1980: O Brien and Julien, 1988; Phillips and Davies, 1991), although its ability to represent the fractional nature of liquefied soil is limited Iverson and LaHusen, 1993). The development of advanced nonlinear dynamic analyses has made an alternative approach possible. The finite element program TARA-3FL Finn and Yogendrakumar, 1989), for example, can reduce the strength of any element is initiated. The program periodically updates the finite element mesh at each time step to allow computation of large deformation figure 8.24). Finn 1990) described its application to Sardis Dam in Mississippi, where liquefaction of the core and a thin seam of clayey silt was expected figure 23). Analyses of this type not only indicate whether flow sliding will occur but also provide an estimate of the distribution and magnitude of any resulting deformations. Figure 8.24 Initial dashed) and postliquefaction solid) configurations of Sardis Dam in Mississippi from TARA-3FL analyses. Note the large strains due to liquefaction in core and thin seam below the upstream shell. After Fin, 1990). 8.6.19 Deformation Failure Analysis Although deformation failures generally involve smaller deformations than flow failures they are capable of causing considerable damage. Lateral spreading is the most common type of deformation failure. In recent years a number of investigators have developed methods to estimate permanent displacement produced by deformations failures. Because the mechanisms that produce deformation failures are so complicated, procedures for prediction of the resulting displacements are largely empirical in nature. Dept. of Civil Engg. Indian Institute of Technology, Kanpur 4
8.6.20 Hamada et al. Approach Hamada et al. 1986) considered the effects of geotechnical and topographic conditions on permanent ground displacements observed in uniform sands of medium grain size in the 1964 Niigata M=7.5), 1971 San Fernando M=7.1) and 1983 Nihonkai-Chubu M=7.7) earthquake. Permanent displacements were found to be most strongly influenced by the thickness of the liquefied layer and the slope of the ground surface and lower boundary of the liquefied zone. Permanent horizontal ground displacement, D, was found to vary according to the empirical relationship 8.20) Where H is the thickness of the liquefied layer in meters and is the larger of ground surface slope or the slope of the lower boundary of the liquefied zone in percent. For case histories from the three listed earthquakes, 80% of the observed displacements were within a factor of 2 of those predicted by equation 8.20). Note that equation 8.20) does not account for the strength of the liquefied soil; like all such empirical approaches, it must be applied cautiously when conditions vary from those on which it is based. 8.6.21 Youd and Perkins Liquefaction Severity Index)Approach Based on observed lateral displacements from a number of case histories in the western United States. Youd and Perkins 1987) defined the liquefaction severity index LSI) as the general maximum d-value in inches) for lateral spreads generated on wide active flood plains, deltas, or other areas of gently sloping Late Holocene fluvial deposits. As defined the LSI represents a conservative estimate of ground displacement in a given area; failure with smaller displacements would also be expected in the area. An analysis of the case history database indicated that LSI could be predicted by 8.21) Where R is the horizontal distance from the seismic energy source in kilometers. The variation of LSI with M and R is shown in figure 8.25). Qualitative descriptions of the nature of deformation failures for different LSI values are presented in table 5. The dependence of LSI on magnitude and distance lends itself to incorporation into a probabilities seismic hazard analysis. Youd and Perkins 1987) used this approach to produce probabilistic LSI maps for southern California. Dept. of Civil Engg. Indian Institute of Technology, Kanpur 5
Figure 8.25 Variation of LSI with distance and earthquake magnitude. After Youd and Perkins 1986). 8.6.22 Byrne Approach Modeling a slope as a crust of intact soil resting on a layer of liquefied soil figure 8.26), Byrne 1991) used work energy principles with an elastic perfectly plastic model of liquefied soil to develop expressions for estimation of permanent slope displacement. In this approach, the permanent displacement, D, is obtained from Figure 8.26 Stress strain and geometric notation for deformation estimation model of Byrne 1991). 8.22.a) 8.22.b) Where is the residual strength of the liquefied soil, the limiting shear strain, the thickness of the liquefied layer, the average shear stress required for static equilibrium on a failure surface passing through the middepth of the liquefied layer), m the mass of the soil above the failure surface, and the velocity of the mss at the instant of liquefaction. Typical values of are presented I table 8.6). Displacements predicted by equations 8.22) agree well with those of equation 8.20) for slopes after flatter about 3% and. For higher Dept. of Civil Engg. Indian Institute of Technology, Kanpur 6
Table 8.5 Abundance and General Character of Liquefaction Effects for Different LSI Values in Areas with Widespread Liquefaction Deposits LSI Description 5 Very sparsely distributed minor ground effects include sand boils with sand aprons up to0.5 m 1.5 ft) in diameter, minor ground fissures with openings up to 0.1 m 0.3 ft) wide, ground settlement of up to 25 mm 1 in.). effects lie primarily in areas of recent deposition and shallow groundwater table such as exposed streambeds, a active floodplaints, mudflats, shotlines, etc. 10 Sparsely distributed ground effects include sand boils with aprons up to 1 m 3 ft) in diameter, ground fissures with openings up to 0.3 m 1 ft) wide, and ground settlements of a few inches over loose deposits such as trenches or channels filled with loose sand. Slumps with up to a few tenth of a meter displacement along steep banks. Effects lie primarily in areas of recent deposition with a groundwater table less than 3 m 10 ft) deep. 30 Generally sparse but locally abundant sand boils with aprons up to 2 m 6 ft) diameters ground fissures up to several tenths of ammeter wide, some fences and roadways noticeably offset, sporadic ground settlements of as much as 0.3 m 1 ft) of displacements common along steep stream banks. Lager effects lie primarily in areas of recent deposition with a groundwater table less than 3 m 10 ft) deep. 50 Abundant effects include sand boils with aprons up to 3 m 10 ft) in diameter that commonly coalesce into bands along fissures, fissures with width up to 1.5 m 4.5 ft), fissures generally parallel or curve toward streams or depressions and commonly break in multiple strands, fences and roadways are offset or pulled apart as much as 1.5 m 4.5 ft) in some places, ground settlements of more than 1 ft 0.3 m) occur locally, slumps with a meter of displacement are common in steep stream banks. 70 Abundant effects include many large sand boils [some with aprons exceeding 6 m 20 ft) in diameter that commonly coalesce along fissures]. Long fissures parallel to rivers or shorelines, usually in multiple strands with many openings as wide as 2 m 6 ft) down gentle slopes, frequent ground settlement of more than 0.3 m 1 ft) 90 Very abundant ground effects include numerous sand boils with large aprons, 30% or more of some areas covered with freshly deposited sand many long fissures with multiple parallel streams and shorelines with openings as wide as 2 m or more, some intact masses of ground between fissures are horizontally displaced as couple of meters down gentle slopes large slumps are common in stream and other steep banks ground settlement of more than 0.3 m 1 ft) are common. Table 8.6 Average Values of Limiting Shear Strain for Clean Sand 4 1.00 6 0.80 8 0.63 10 0.50 12 0.40 16 0.25 Dept. of Civil Engg. Indian Institute of Technology, Kanpur 7
20 0.16 30 0.05 40 0.015 50 0 Byrne et al. 1992) extended this approach to determine factors by which the initial stiffness of a soil should be reduced for finite-element analysis of deformation failures. Deformations predicted by this approach were in good agreement with those observed in the 1971 failure of Upper San Fernando Dam figure 8.27). Figure 8.27 a) Finite-element mesh for analysis of Upper San Fernando Dam with element determined to have liquefied by Serff et al., 1976) shaded; b) positions of original and final meshes displacement exaggerated by factor of 2) by procedure of Byrne et al. 1992). Example 6 The gently sloping site shown below consists of a 2 m thick layer of silty clay overlying a 4 m thick layer of loose, saturated sand. The sand has an average fines content of about 3% and an average mm. subsurface investigations indicate that the corrected SPT resistance of the sand in quite consistent with an average values of 11. Estimate the permanent displacement of the slop when subjected to earthquake shaking sufficient to cause liquefaction of the sand. Solution The static shear stress at the center of the liquefied layer is * ) ) ) )+ From table 8.6), and,. Assuming that the slope has no initial velocity, the direct solution of equation 22b gives Because this displacement is less than, the permanent displacement must be Dept. of Civil Engg. Indian Institute of Technology, Kanpur 8
determined using the cubic equation of equations 8.22.a.) From which Thus, the estimated permanent displacement would be about 1.9m. note that this estimate is based on an average value of the residual strength of the liquefied soil; considering the range of uncertainty of that strength the actual permanent displacement could be considerably smaller or larger. Figure 8.28 8.6.23 Bazaar et al. Approach Using a sliding block analysis to describe fundamental aspects of seismic slope stability, Baziar et al. 1992) developed a general expression for permanent lateral displacement where N is the equivalent number of cycles of harmonic loading,, is the peak horizontal velocity,, is the peak horizontal acceleration, and, is the yield acceleration. ) 8.23) The function ) was obtained by assuming harmonic accelerations figure 27). Calibration against case histories from the western United States suggested the use of for. By assuming a yield acceleration representative of those associated with the case history database of Youd and Perkins 1987). Bazaar et al. 1992) were able to compare displacements predicted by equation 8.23) with the corresponding LSI values. As shown in figure 8.29) the two approaches are quite consistent at longer site distances, but less so at shorter distances. Until additional near-source data becomes available, the physical basis of equation 8.23) appears to provide a stronger basis than LSI for estimation of displacements. Dept. of Civil Engg. Indian Institute of Technology, Kanpur 9
Figure 8.29 Variation of with After Baziar et al., 1992) 8.6.21Bartlett and Youd Approach Barlett and Youd 1992) used a large data base of lateral spreading case histories to develop empirical expressions relating lateral ground displacement to a number of source and site parameters. The database included sites from the western United States and Japan at source-site distances up to 90 km subjected to earthquakes ranging from. Regression analyses were used to identify the factors that most strongly influenced lateral ground displacements, so that the empirical model could be based on those factors. Two empirical models were developed: a free-face model for sites near steep banks and a ground slope model for gently along sites. For free-face sites, displacements can be obtained from 8.24) where is the estimated lateral ground displacement in meters, the moment magnitude, R the horizontal distance from the seismic energy source in kilometers, W the ratio of the height of the free face to the horizontal distance between the base of the free face and the point of interest figure 8.30), the cumulative thickness of saturated granular layers with in meters, the average fines content for the granular layers comprising in percent, and the average mean grain size for the granular layers comprising in millimeters. For gently sloping sites, the ground-slope model predicts 8.25) Where S is the ground slope in percent figure 29). Application of these equations to the case history database showed that 90% of the observed displacements were within a factor of 2 of the values predicted. The ranges of input parameters for which predicted results are verified by case history observations are shown in table 8.7). Dept. of Civil Engg. Indian Institute of Technology, Kanpur 10
Figure 8.30 Parameters describing slope geometry for free face and ground slope deformation models L, distance from toe of free face to site under consideration; H height of free face crest elev, -toe elev); W free face ratio = H/L)100), n, percent; S, slope of natural ground toward channel 1 = 1/X 100, in percent. After Barlett and Youd, 1992) Tale 8.7 Range of Parameters Values for Which Equations 8.24) and 8.25) Can Be Applied Input Parameter Range of Values Magnitude Free-face ratio Thickness of the loose layer Fines content Mean grain size Ground slope Depth to bottom of section Depth to bottom of liquefied zone < 15 m Example 7 Estimate the permanent displacement of the slope described in example 6 due to and earthquakes occurring at a horizontal source-site) distance of 30 km. Solution From the description in example 6, the ground slope model of Barlett and Youd is most appropriate. The relevant parameters are Then, the permanent displacement due to the from equation 8.25 )as earthquake can be estimated Dept. of Civil Engg. Indian Institute of Technology, Kanpur 11
So From the earthquake, So Dept. of Civil Engg. Indian Institute of Technology, Kanpur 12