Application of unconstrained optimization and sensitivity analysis to calibration of a soil constitutive model

Abstract

SUMMARYLarge sets of soil experimental data (field and laboratory) are becoming increasingly available for calibration of soil constitutive models. A challenging task is to calibrate a potentially large number of model parameters to satisfactorily match many data sets simultaneously. This calibration effort can be facilitated by optimization techniques. The current study aims to explore systematic approaches for exercising optimization and sensitivity analysis in the area of soil constitutive modelling. Analytical, semianalytical and numerical optimization techniques are employed to calibrate a multi-surface-plasticity sand model. Calibration is based on results from a number of drained triaxial sample tests and a dynamic centrifuge liquefaction test. The analytical and semi-analytical approaches and associated sensitivity analysis are applied to calibrate the model non-linear shear stress-strain response. Thereafter, model parameters controlling shear-volume coupling effects (dilatancy) are calibrated using a solid-fluid fully coupled finite element program in conjunction with an advanced numerical optimization code. A related sensitivity study reveals the challenges often encountered in optimizing highly non-linear functions. Overall, this study demonstrates applicability and limitations of optimization techniques for constitutive model calibration.

Oracle-based optimization applied to climate model calibration

“…In this implementation the number of function evaluations is of the order of several thousands. In (Yang and Elgamal, 2003) a second-order method based on the Broyden-Fletcher-Goldfarb-Shano (BFGS) method is used to calibrate three parameters of a soil constitutive model. In this application only three parameters had to be estimated and the number of calls to the function evaluation was of the order of fifty to several hundreds.…”

Calibration of an elasto-plastic constitutive model by a constrained optimisation procedure

“…However, the goal of the research is to find a point where F(p) assumes its least value, or the global minimum, inside the considered domain. According to [6] there is no general way to determine whether a minimum point is global or not. To achieve the global minimum, a possible strategy could be to run the search algorithm as many times as possible, each time from a different point.…”

“…When both g(p) and H(p) can be evaluated directly, the Newton method is typically the most efficient for optimisation. In cases where the explicit expression of g(p) and/or H(p) are not available, the quasi-Newton algorithm using approximations for g(p) and/or H(p) can be employed [6]. The method adopted here is based on a subspace limited memory quasi-Newton algorithm proposed by Ni and Yuan [4].…”

“…(9). It is emphasised that optimisation is meaningful only if the model predictions (q n j ; e n vj and u n j ) adequately describe the essential physical mechanism of the experimental tests [6]. According to the definition of the objective function, the minimisation can be achieved by means of a wide range of optimisation algorithms [7].…”

A survey of geotechnical system identification techniques

“…16) of 2-D quay wall-soil systems [110]. The concept of employing experimental data sets and local in-situ measurements to calibrate complex constitutive laws with large number of parameters have been systematically investigated by Yang and Elgamal [100], Levasseur et al [56,57], Hashash et al [46,35], and Calvello and Finno: [15].…”