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EVALUATION OF LIQUEFACTION BY CYCLIC STRESS APPROACH A number of approaches to evaluate the potential for initiation of liquefaction have developed over the years. The most common of these are the cyclic stress approach and the cyclic strain approach. Each has its own advantages and limitations. and each is preferred by different groups of engineers. For particularly important projects, it is not unusual to use more than one approach in a liquefaction hazard evaluation.

CYCLIC STRESS APPROACH In the 1960s and 1970s, many advances in the state of knowledge of liquefaction phenomena resulted from the pioneering work of H. B. Seed and his colleagues at the University of California at Berkeley. This research was directed for evaluation of loading conditions required to trigger liquefaction. Loading was described in terms of cyclic shear stresses, and liquefaction potential was evaluated on the basis of amplitude & number of cycles of earthquake-induced shear stress. The general approach has come to be known as the cyclic stress approach. Seed and Lee defined initial liquefaction as the point at which the increase in pore pressure is equal to the initial effective confining pressure. The concept of cyclic stress approach is that the earthquake induced loading in terms of cyclic shear stresses is compared with the liquefaction resistance of the soil which is also expressed in terms of cyclic shear stresses. At locations where loading exceeds resistance, liquefaction is expected to occur.

Characterization of earthquake loading: The level of excess pore pressure required to initiate liquefaction is related to the amplitude & duration of earthquake induced cyclic loading. Excess pore pressure generation is related to the cyclic shear stresses, hence seismic loading expressed in terms of cyclic shear stresses. The loading can be predicted by: Ground response analysis or by the use of a simplified approach.

Ground response analyses can be used to predict time histories of shear stress at various depths within a soil deposit. Such analyses produce time histories with transient, irregular characteristics of actual earthquake motion. The laboratory data from which liquefaction resistance can be estimated are obtained from tests in which the cyclic shear stresses have uniform amplitudes. Comparison of earthquake induced loading with laboratory determined resistance requires conversion of irregular time history of shear stress to an equivalent series of uniform stress cycles. Seed et al. applied a weighting procedure to a set of shear stress time histories from recorded strong ground motions to determine number of uniform stress cycles,N_eq, that would produce increase in pore pressure equivalent to that of irregular time history. The equivalent number of uniform stress cycles increases with increasing earthquake magnitude. Fig.1: Number of equivalent uniform stress cycles for earthquakes of different magnitudes Simplified procedure: The uniform cyclic shear stress amplitude for level(or gently sloping ) sites can be estimated from a simplified procedure as:

τ_cyc₌ 0.65 a_max/g σ_v ϒ_d Where a_max is the peak ground surface acceleration, g the acceleration due to gravity, σ_v the total vertical stress, and ϒ_d the value of a stress reduction factor. In both these analyses, earthquake induced loading is characterized by a level of uniform cyclic shear stress that is applied for an equivalent number of cycles. Characterization of liquefaction resistance: The liquefaction resistance of an element of soil depends on how close the initial state of the soil & failure state are and the nature of the loading to move it from initial state to the failure state. Failure for flow liquefaction is easily defined using FLS and its initiation is easily recognized in the field. In Cyclic mobility, definition of failure is imprecise. When pore pressure become large enough to produce ground oscillation, lateral spreading or other damages at the ground surface, cyclic mobility failure is considered to occur. Presence of sandboils is frequently taken as the evidence of cyclic mobility. Characterization of liquefaction resistance developed along two lines: methods based on the results of laboratory tests, and methods based on in situ tests and observations of liquefaction behavior in past earthquakes. 1)Characterization based on laboratory tests: Laboratory tests were performed on isotropically consolidated triaxial specimens or Ko consolidated simple shear specimens. Liquefaction failure was defined as the point at which initial liquefaction was reached or some limiting cyclic strain amplitude was reached. Tests show that number of loading cycles required to produce liquefaction failure decrease with increasing shear stress amplitude & decreasing density.

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Fig .2: Results of torsional shear tests on a)loose sand b)dense sand Cyclic strength curves: Relationship between density, cyclic stress amplitude & number of cycles to liquefaction failure can be expressed graphically by laboratory cyclic strength curves Cyclic Stress Ratio: Cyclic strength curves normalized by initial effective overburden pressure CSR of cyclic simple shear test: ratio of cyclic shear stress to initial vertical effective stress CSR of cyclic triaxial test: ratio of maximum cyclic shear stress to initial effective confining pressure Fig.3: cyclic stresses required to produce initial liquefaction and 20% axial strain Liquefaction resistance is influenced by differences in the structure of soil by different methods of specimen preparation. The history of prior seismic straining also increases liquefaction resistance. Also liquefaction resistance increases with increasing over consolidation ratio & lateral earth pressure coefficient. Also it increases with the length of time under sustained pressure. Thus characterization of liquefaction resistance by laboratory testing is extremely difficult. 2)Characterization based on In situ tests: An alternative approach, first described by Whitman, is to use liquefaction case histories to characterize liquefaction resistance in terms of measured in situ parameters.Case histories can be characterized by the combination of a loading parameter ℒ & liquefaction resistance parameter ℛ. In this approach, loading parameter- used is usually cyclic stress ratio and in situ parameters that reflect density & pore pressure generation characteristics of the soil are used as liquefaction resistance parameters. The boundary is drawn conservatively such that all the cases in which liquefaction has been observed lie above it. Fig.4: Plot showing combinations loading parameter and liquefaction resistance parameter

1)Standard penetration resistance: SPT has been the most commonly used in situ test for the characterization of liquefaction resistance. Factors that tend to increase liquefaction resistance also tend to increase SPT resistance.Presence of fines can affect SPT resistance & must be accounted for the evaluation of liquefaction resistance. Liquefaction resistance of sands not influenced by fines unless fines comprise more than 5% of soil. At higher fine contents, fines tend to inhibit liquefaction. Laboratory tests indicate little influence at plasticity indices below 10, and a gradual increase in liquefaction resistance at plasticity indices greater than 10. 2)Cone penetration resistance: The tip resistance from the cone penetration test can also be used as a measure of liquefaction resistance. It has a pronounced advantage over SPT to detect thin seams of loose soil. The database of sites at which CPT resistance has been measured & where occurrence or non occurance of liquefaction has been documented & supplementing the data with correlations between CPT & SPT resistances, minimum cyclic stress ratio at which liquefaction can be expected can be determined. Fig.5: CPT based liquefaction curves a)based on correlations with SPT data b)based on theoretical/experimental results In CPT based liquefaction evaluations, tip resistance is normalized to standard effective overburden pressure of 1 ton/sq feet by: q_c1₌q_c(√(P_a/〖σ^'〗_v0 )) Use of In Situ test results: SPT resistance is the most common test parameter for characterization of liquefaction resistance. SPT allows a sample to be retrieved & has the largest case history database of any in situ test. The CPT provides a continuous record of penetration resistance & much faster & less expensive than the SPT. Regardless of which is used, the insitu test parameters allow estimation of 〖CSR〗_L-the CSR required to initiate liquefaction. Evaluation of initiation of liquefaction: Evaluation of liquefaction potential is the comparison of loading & resistance throughout the soil deposit of interest. The evaluation is easily performed graphically.Firstly the variation of equivalent cyclic shear stress with depth is plotted.The variation of cyclic shear stress required to cause liquefaction with depth is plotted on the same graph. Fig.6: Process by which zone of liquefaction is identified 〖FS〗_L₌ (cyclic shear stress required to cause liquefaction)/(equivalent cyclic shear stress induced by earthquake )₌  τ_(cyc,L)/τ_cyc  ₌〖CSR〗_L/CSR Liquefaction can be expected at depths where loading exceeds resistance or when factor of safety against liquefaction is less than 1.