70 Basic Geotechnical Earthquake Engineering Fig. 6.10 Plot used to determine cyclic resistance ratio for clean and silty sands for M = 7.5 earthquake (Courtesy: Day, 2002) Table 6.1 Magnitude scaling factors (Courtesy: Day, 2002) Anticipated earthquake magnitude Magnitude scaling factor 8.5 0.89 7.5 1.00 6.75 1.13 6 1.32 5.25 1.50 Factor of safety against Liquefaction: Factor of safety (FS) against liquefaction is defined as: FS = CRR/CSR. If the cyclic stress ratio caused by anticipated earthquake is greater than cyclic resistance ratio of in-situ soil, liquefaction could occur during earthquake. Liquefaction will not take place otherwise. Higher the factor of safety, more is the resistance of soil against liquefaction during earthquake. Soil having factor of safety slightly greater than one can also liquefy. For example if lower layer liquefies, then upward water flow could induce liquefaction of upper layer as well. This layer has factor of safety against liquefaction slightly greater than one. However, in the above analysis, there are lot of corrections. These corrections are applied both to cyclic stress ratio as well as to cyclic resistance ratio. This is done for more accurate analysis. Otherwise the entire analysis is only gross approximation. Consequently, [...]...80 Basic Geotechnical Earthquake Engineering q′ = q″ = where, q′ = q″ = Q = e = B = Q(B + 6e) (7.9) B2 Q(B − 6e) (7.10) B2 largest bearing pressure under footing smallest bearing pressure under footing load per unit length of footing This includes dead, live... During the earthquake, the inclined footing could translate laterally along the sloping soil or rock contact If a sloping contact of underlying hard material will be encountered during excavation of footing, the hard material should be excavated in order to construct a level footing that is entirely founded within hard strata 82 Basic Geotechnical Earthquake Engineering 7.3 GRANULAR SOIL WITH EARTHQUAKE. .. the undrained shear strength is 60 kPa Calculate the factor of safety of the footing using punching shear analysis for: (a) 1m wide strip footing under total load of 60 kN/m (b) 2m wide square spread footing under total load of 60 0 kN Solution: (a) For strip footing, using Eq (7.1), T = 1.8 + 1.2 – 0.5 = 2.5 m, τf = undrained shear strength of cohesive soil = 60 kPa P = 60 kN/m Substituting the values... cohesive soil = 60 kPa, P = 60 0 kN and B = L = 2 m Substituting the values in Eq (7.2): FS = 2.0 Example 7.2 Perform total stress analysis using Terzaghi equations for general and local shear failure to find out factor of safety for 1m wide strip footing Use data from Example 7.1 Solution: From Example 7.1, P = 60 kN/m for 1 m wide strip footing, T = 1.8 + 1.2 – 0.5 = 2.5 m c1 = su = 60 kPa = 60 kN/m2 &... follows: qult = 5.5su 1 + 0.3 qult FS = q all .(7.18) qult in Eq (7.18) is determined using Eq (7. 16) or (7.17) qall in Eq (7.18) is allowable bearing capacity There are standard guidelines in terms of undrained shear strength that should be utilized for earthquake engineering analysis (Triandafilidis, 1 965 ) These guidelines for selection of undrained shear strength is given in subsections below 7.4.1... groundwater table These soils above groundwater table have negative pore pressures This is due to capillary tension This tends to hold soil particles together It also provides additional strength 84 Basic Geotechnical Earthquake Engineering Undrained shear strength should be determined by performing unconfined compression or vane shear tests under these conditions Due to negative pore pressure, a future increase... (sensitivity > 8), earthquake- induced ground shaking could lead to significant shear strength loss during earthquake shaking The stress-strain curve from an unconfined compression test on such soils exhibits peak shear strength developed at low vertical strain This is followed by dramatic drop-off in strength with continued straining Estimated reduction in undrained shear strength due to earthquake shaking... stress and seismic induced shear stress during earthquake shaking exceeds undrained shear strength, there is significant reduction in shear strength (Cunny and Sloan, 1 961 ) Cohesive soils having sensitivity in between 4 and 8 tend to be intermediate case There are other factors also which may be considered in bearing capacity analysis Peak ground acceleration and earthquake magnitude is such factor Higher... determined by multiplying qult with reduced footing dimensions is determined using Eq (7 .6) and Eq (7.7) with reduced footing dimensions FS = qult Special design techniques are available for sloping ground conditions under earthquake loading conditions Special design techniques are also for inclined base of footing under earthquake loading conditions Methods have also been developed to determine allowable... allowable bearing capacity FS = 7.4 BEARING CAPACITY ANALYSIS FOR COHESIVE SOIL WEAKENED BY EARTHQUAKE Cohesive soils as well as organic soils can also be susceptible to a loss of shear strength during the earthquake In dealing with such soils, it is often desirable to limit the stress exerted by the footing during the earthquake The stress exerted should be less than the maximum past pressure of the cohesive . ratio induced by the design earthquake. Solution: Using results of Example 6. 1, σ v0 = 58 + 20 = 78 kPa. σ v0 ′ = 43 + 20 = 63 kPa. Using Eq. (6. 4), CSR = 0 .65 (0. 96) (78 /63 )(0.45) = 0.347 Home Work. 70 Basic Geotechnical Earthquake Engineering Fig. 6. 10 Plot used to determine cyclic resistance ratio for clean and silty sands for M = 7.5 earthquake (Courtesy: Day, 2002) Table 6. 1 Magnitude. liquefaction in field? 6. Develop cyclic stress ratio equation. 7. How is cyclic resistance ratio determined from shear wave velocity method? 76 Basic Geotechnical Earthquake Engineering EARTHQUAKE RESISTANT