The Earthquake Engineering Online Archive

Nonlinear seismic response of earth structures

Dibaj, Mostafa; Penzien, Joseph

UCB/EERC-69/02, Earthquake Engineering Research Center, University of California, Berkeley, 1969-01, 149 pages (480/D52/1969)

The finite element method, a step-by-step integration method, and several other numerical techniques are employed to develop an incremental procedure for nonlinear earthquake analysis of earth structures. By this procedure, the total nonlinear problem is reduced to a number of successive linear problems. Each time interval is selected sufficiently small so that the resulting incremental stresses and deformations may be related by a linear constitutive law containing parameters that are changed after each time interval. A brief discussion of the fundamental concepts of plasticity theory and its general constitutive laws are given, and suitable yield criteria for soils are selected. An extension of the Drucker-Prager yield criterion to include work-hardening effects is developed, and the stress-strain relations for materials obeying this yield criterion are derived. A finite element formulation of the nonlinear dynamic response of earth structures of a general type subjected to either uniform or non-uniform base motion is given. Results of several nonlinear analyses are presented and compared with those obtained from linear analyses. Relative differences between the two types of solutions, i.e. linear versus nonlinear, are illustrated, and it is shown that realistic response predictions of deformation can be achieved only by nonlinear analysis procedures.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-69-02.pdf (10 MB)