Selecting parameters to optimize in model calibration by inverse analysis
Introduction
In a finite element simulation of a geotechnical problem, calibrations of the models used to reproduce soil behavior often pose significant challenges. Real soil is a highly nonlinear material, with both strength and stiffness depending on stress and strain levels. Numerous constitutive models have been developed that can capture many of the important features of soil behavior. However, developing soil parameters for use in constitutive models is a procedure that involves much judgment and usually is best accomplished by experienced users of a particular model. An effective and more objective way to calibrate a soil model employs inverse analysis techniques to minimize the difference between experimental data (laboratory or field tests) and numerically computed results [1], [2].
For some large geotechnical engineering projects, for example, deep supported excavations in urban environments, it is usual to record ground movements developed during construction to evaluate the performance of the designed system. In some cases the data are used to control the construction process and update predictions of movements given the measured deformations at early stages of constructions. This procedure is referred to as the “observational method” [3], [4], [5]. This approach usually entails the use of pre-construction analysis and parametric studies coupled with much engineering judgment. Inverse analysis techniques conceptually can be used to enhance the conventional observational method practice by using the monitoring data to optimize automatically a numerical model of a geotechnical project. Recent work in related civil engineering fields (e.g. [6], [7], [8], [9]) demonstrate that inverse modeling provides capabilities that help modelers significantly, even when the simulated systems are very complex.
However, there are a number of issues that affect proper calibration, including the number of parameters to be optimized, which depends on both the site stratigraphy and number of parameters in the selected constitutive model, the interdependence of the model parameters within the framework of the constitutive model, the number of observations, and the type of system under consideration.
In this paper, these factors are discussed and illustrated by presenting results of inverse analyses used to optimize the calibration of the Hardening-Soil (H-S) model [10] for four layers of Chicago glacial clays. The models are initially calibrated using results from triaxial compression tests performed on specimens from the four clay layers and subsequently re-calibrated using inclinometer data that recorded the displacements of a supported excavation in these clays [11]. This paper describes the concepts of model calibration by inverse analysis, summarizes the soil model used to define the behavior of the clay considered, discusses the factors that affect proper calibration, presents the results of the model calibration from triaxial test data and from field monitoring data and draws conclusions.
Section snippets
Model calibration by inverse analysis
In inverse analysis, a given model is calibrated by iteratively changing input values until the simulated output values match the observed data (i.e., observations). Fig. 1 shows a schematic of an inverse analysis procedure. The input parameters are initially estimated by conventional means. Much literature exists on this subject, for example, a number of papers in the McGill conference (i.e. [12], [13], [14]) describe how this first step is done for a number of constitutive models for soils,
Chicago glacial clays
Much of the subsoil in the Chicago area consists of fairly distinct strata deposited during the advances and retreats of a glacier during the Wisconsin Stage. The advance and retreat process, marked by terminal moraines, created easily identifiable clay strata. In order of deposition they are the Valparaiso, Tinley, Park Ridge, Deerfield, Blodgett, and Highland Park tills [18]. Fig. 4 shows the soil profile at the site of the excavation considered herein, typical for the downtown area of
The H-S model
The soil model used to simulate the clay behavior is the H-S model as implemented in PLAXIS 7.11. The H-S model is an elasto-plastic, multi-yield surface, effective stress soil model. Failure is defined by the Mohr–Coulomb failure criterion. Two families of yield surfaces are incorporated in the model to account for both volumetric and shear plastic strains. Fig. 5 shows the yield surfaces of the model in p–q stress space. A yield cap surface controls the volumetric plastic strains. On this
Optimization of laboratory data
Triaxial compression tests were performed on samples from the four most compressible clay layers on the site of the Chicago Avenue and State Street subway renovation project. The triaxial testing program was part of an experimental laboratory program conducted to define the soil properties at the excavation site [19], [20]). The H-S model, used to simulate the behavior of the clay specimens, was calibrated for the four clay layers based on these triaxial results using the inverse analysis
Field application: deep excavation
Inverse analysis becomes more complicated when multiple soil layers and complicated loading paths are encountered in a problem, as is the case when computing ground movements associated with deep excavations. To illustrate the logic behind steps 2 and 3 in Fig. 2, the calibration of the finite element simulation of a supported excavation is presented herein. The excavation made to renovate a subway station in downtown Chicago [11] consisted of removing 12.2 m of soft to medium clay within 2 m
Results
Table 7 shows the parameters that were re-calibrated at every construction stage. Two parameters per layer, E50ref and Eoedref, were updated by inverse analysis at each stage. The value of parameter Eoedref, which cannot be independently estimated by the regression, is related to the value of parameter E50ref.
The simplest way to evaluate the difference between the results of the simulations based on the initial guess and the recalibrated parameters is to compare the inclinometer data with the
Conclusions
The inverse modeling procedure described in this paper combines a finite element analysis and a parameter optimization algorithm to efficiently calibrate a soil model by minimizing the errors between experimental observations and computed responses. Based on the results presented herein, the following conclusions can be drawn:
- 1.
Inverse analysis can be effectively used to calibrate a numerical soil model based on triaxial experimental results. When the relevant and uncorrelated H-S input
Acknowledgements
This work was supported by funds from Grant CMS-0115213 from the National Science Foundation. The support of Dr. Richard Fragaszy, the cognizant program manager, is greatly appreciated.
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