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Q. 20.1

A series of exploratory borings have been drilled at a site near Memphis, Tennessee where liquefaction might be a problem. The results of standard penetration and sieve analysis tests were as follows:

 Depth (ft) $(N_{1})_{60}$ Soil Classification Percent Fines 5 14 Silty sand (SM) 30 8 12 Fine to medium sand (SW) 5 11 10 Fine to medium sand (SW) 3 13 12 Fine to medium sand (SW) 6 17 11 Fine to medium sand (SW) 3 22 19 Silty sand (SM) 20 26 24 Silty sand (SM) 22

The design earthquake will occur in the New Madrid Fault Zone (the same zone that generated the 1811-1812 earthquakes). The causative fault is 75 km from the site and the design earthquake has a moment magnitude of 8.0. The site is underlain by deep cohesionless soils.

Using a unit weight of $110 lb/ft^{3}$ and a groundwater table 3 ft below the ground surface, evaluate the liquefaction potential at this site using the simplified method.

Verified Solution

Per Equation 20.3,   $\ln \left(a_{max/g}\right) _{rock}=2.20 + 0.81\left(M_{w} – 6\right) – 1.27\ln R + 0.11 \max \left\lgroup\ln \frac{R}{100},0 \right\rgroup = 0.0021R$    $a_{\max}= 0.16g$ in bedrock

Per Figure 20.4, $a_{\max}= 0.14g$ in deep cohesionless soil

Per Figure 20.14, Ψ = 0.65 (Arango)

 Depth (ft) Cyclic Stress Ratio to Cause Liquefaction $\sigma _{z0} (lb/ft^{2})$ $\sigma ^{\prime }_{z0} (lb/ft^{2})$ $r_{d}$ Cyclic Stress Ratio Produced by Earthquake F M = 7.5 M = 8.0 5 0.23 0.15 550 425 0.99 0.12 1.2 8 0.13 0.085 880 568 0.98 0.14 0.6 11 0.11 0.072 1210 711 0.97 0.15 0.5 13 0.14 0.091 1430 806 0.97 0.16 0.6 17 0.12 0.078 1870 996 0.96 0.16 0.5 22 0.29 0.189 2420 1234 0.95 0.17 1.1 26 – – – – – – High

Conclusion

The zone between depths of about 6 and 20 ft is clearly liquefiable. Below that depth, the increased density (as demonstrated by the higher N ) and the presence of fines makes liquefaction less likely.