DISCUSSIONS Static and seismic passive earth pressure coefficients on rigid retaining structures: Discussion 1 Jyant Kumar Discussion 1150 The author needs to be commended for his computational efforts in determining the passive earth pressure coefficients for both the static case as well as in the presence of pseudo- static earthquake forces. The upper bound theorem of limit analysis with the use of a kinematically admissible translational failure mechanism was formed as the basis for solving the problem. In this discussion, the passive earth pressure coefficients given by the author have been com- pared with those obtained on the basis of the limit equilib- rium technique by employing the composite logarithmic spiral failure surface both for the static (Kumar and Subba Rao 1997) and the pseudo-static cases (Kumar 2001). The comparison of all of the results is given in Tables D1 and D2. The two approaches compare well with each other. The passive earth pressure coefficients generated on the basis of the upper bound limit analysis in most of the cases are found to be either almost the same or only marginally greater (for larger values of d ) than those computed with the limit equi- librium approach. However, compared to the limit equilib- rium technique, the limit analysis has an obvious advantage in that it can take into account the kinematics of the prob- lem. The upper bound theorem of limit analysis is based on the associated flow rule condition. However, it was recently demonstrated by Drescher and Detournay (1993) that for a statically determinate translational collapse mechanism, the upper bound theorem of limit analysis can also be extended to determine the solutions of stability problems even for ma- terial following the non-associated flow rule. In his paper the author has given an expression, as originally formulated by Drescher and Detournay (1993), for obtaining equivalent c* and f * values in place of c and f values (where c is the cohesion and f is the angle of internal friction) for non- associated flow rule material depending on the given value of the dilatancy angle, y. It should be noted that this expres- sion is applicable only for soil mass with coaxial flow rule, i.e., material having the same directions of principle stresses and plastic strain rates. However, for noncoaxial flow rule material, which is often the case, the passive earth pressure coefficients even in the case of non-associated flow rule ma- terial will remain unchanged irrespective of the value of y. Can. Geotech. J. 38: 1149–1150 (2001) © 2001 NRC Canada 1149 DOI: 10.1139/cgj-38-5-1149 Received January 8, 2001. Accepted March 12, 2001. Published on the NRC Research Press Web site at http://cgj.nrc.ca on October 15, 2001. J. Kumar. Civil Engineering Department, Indian Institute of Science, Bangalore-560012, India (e-mail: jkumar@civil.iisc.ernet.in). 1 Paper by A.H. Soubra. 2000. Canadian Geotechnical Journal, 37: 463–478. Static passive earth pressure coefficient, K pg d =0 d = f /3 d =2f /3 d = f f Kumar and Subba Rao (1997) Soubra (2000) Kumar and Subba Rao (1997) Soubra (2000) Kumar and Subba Rao (1997) Soubra (2000) Kumar and Subba Rao (1997) Soubra (2000) 10 1.42 1.42 1.51 1.51 1.59 1.60 1.66 1.67 15 1.70 1.70 1.89 1.89 2.06 2.08 2.22 2.25 20 2.04 2.04 2.38 2.39 2.73 2.77 3.07 3.12 25 2.46 2.46 3.06 3.08 3.72 3.79 4.42 4.51 30 3.00 3.00 4.02 4.05 5.26 5.40 6.68 6.86 35 3.69 3.69 5.42 5.48 7.78 8.06 10.76 11.13 40 4.60 4.60 7.58 7.70 12.24 12.83 18.86 19.62 45 5.83 5.83 11.10 11.36 20.88 22.22 36.95 38.61 Table D1. A comparison of static passive earth pressure coefficients for b/f = l/f = 0. d ; angle of wall friction.