ONDA: Computer Code for Nonlinear Seismic Response Analyses of Soil Deposits

This paper describes a newly developed computer code for performing one-dimensional nonlinear dynamic analysis (ONDA) of soil deposits. The code has been developed by revisiting the 1982 work by Ohsaki with the purpose of simulating the ground response to an earthquake of moderate intensity (i.e., values of peak ground acceleration on stiff soil on the order of 0.15 to $0.25g$ , which are typical of many sites in Italy). In the Ohsaki model a horizontally stratified soil deposit is idealized as a discrete mechanical system composed of a finite number of lumped masses connected with a series of springs and dashpots. Nonlinearity is modeled by assuming (1) a “backbone” curve that describes the initial monotonic loading of the stress-strain curve, and (2) a “rule” that simulates the unloading-reloading paths and stiffness degradation undergone by soil as seismic excitation progresses. Typically, the backbone curve is obtained from conventional cyclic undrained loading laboratory tests. The rule generally used is the so-called Masing criterion, which assumes that the unload-reload branches of the stress-strain curve have the same shape as the initial loading curve but are affected by a scale factor $\left(n\right)$ equal to 2. In this work, the Masing criterion has been modified by assuming a scale factor $\left(n\right)$ not necessarily equal to 2. It turns out that a factor $n$ greater than 2 allows the simulation of cyclic hardening, while cyclic softening can be modeled by assuming decreasing values of $n$ even smaller than 2. Pyke proposed in 1979 to use a scale factor $\left(n\right)$ lower than 2 to simulate cyclic degradation. According to Pyke, the $n$ parameter is a function of the mobilization factor. The generalization of the Masing criterion allows ONDA to properly simulate the phenomena of soil hardening and soil degradation, giving it the capability to compute the permanent strains developed during a seismic event. The procedure required to evaluate the model parameters is also described in the paper. Note that the laboratory tests examined gave values of $n$ between 2 and 6 for a strain level not greater than 0.3%. In ONDA the numerical solution of the nonlinear equations of motion is obtained using the unconditionally stable Wilson $\theta$ algorithm (with $\theta ⩾1.37$ ). The new method has been used to predict the seismic response at two sites in Italy. For these case studies, the maximum input acceleration was not greater than $0.3g$ and the computed shear strains were less than 0.2%. The ONDA results have been compared with those computed with SHAKE, EERA (equivalent-linear analysis), and NERA (nonlinear analysis).