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Application of Genetic Algorithms with Hill Climbing Procedure to a Constitutive
Model for Hard Soils and Soft Rocks
Application des algorithmes génétiques avec la méthode de gradient à un modèle constitutif
pour sols durs et roches tendres
Pereira C., Caldeira L.
National Laboratory for Civil Engineering, Lisbon
Maranha das Neves E., Cardoso R.
ICIST, Instituto Superior Técnico, Lisbon Technical University
ABSTRACT: For engineering applications, the complex behaviour of hard soils / soft rocks can be modelled using advanced
constitutive models, although they require a great number of parameters. The application of Genetic Algorithms with a local search
technique has proven to be a useful tool to be used in their determination. A constitutive model for hard soil / soft rocks was used to
fit the experimental results measured in tests performed in marl specimen. This model was implemented in the explicit finite
difference code FLAC and its calibration was done using a Genetic Algorithm with Hill Climbing procedure implemented in
MATLAB. The use of the two programs with complete distinct objectives (MATLAB to the fitting process and FLAC to the
numerical calculations) provides great flexibility to the implementation of any constitutive model to reproduce the results from
experimental tests.
RÉSUMÉ : Pour les applications en ingénierie, le comportement complexe des sols durs / roches tendres peut être modélisé à l'aide de
modèles constitutifs avancés même s’ils nécessitent un grand nombre de paramètres. L’emploi des algorithmes génétiques avec une
technique de recherche locale, s’est avéré un outil utile pour la détermination de ces paramètres. Un modèle de comportement pour les
sols durs/ roches tendres a été utilisé pour ajuster les résultats expérimentaux mesurés lors de tests sur des échantillons de marne. Ce
modèle a été mis en œuvre dans le code aux différences finies explicite FLAC et son calibrage a été fait en utilisant un algorithme
génétique avec la procédure “Hill Climbing” installé dans MATLAB. L’utilisation conjointe de ces deux programmes avec des
objectifs complètement différents (MATLAB pour l’ajustage des paramètres et FLAC pour les calculs numériques) donne une grande
flexibilité à cette technique pour la mise en œuvre de modèles constitutifs pour reproduire les résultats d’essais.
KEYWORDS: Genetic Algorithm, Hill Climbing procedure, constitutive model, hard soils / soft rocks, marls.
1 INTRODUCTION
In general, marls are classified as hard soils / soft rocks, HSSR,
and exhibit evolutive behaviour, since their mechanical and
hydraulic properties are strongly affected by suction and stress
changes, related with plastic strain, wetting / drying cycles and
others weathering processes (Cardoso 2009). Evident physical
degradation results from these changes.
HSSR are often treated as bonded materials in which links
(cements or other physical connections) provide additional
strength and stiffness to the soil structure. Progressive rupture of
these bonds, caused by stress and suction changes, affects
irreversibly the hydro-mechanical behaviour of these materials.
Several constitutive models for HSSR can be found in the
literature (Nova 2005, Gens and Nova 1993, Kavvadas and
Belokas 2001, Hashiguchi 2009). Most of the existing models use
bond degradation as a function of the accumulated plastic strains
and damage laws to represent the behaviour of these materials.
An extensive experimental programme was developed in
order to characterise the physical, mechanical and hydraulic
properties of Abadia marls, dated from the Upper Jurassic. These
geomaterials occurred and were used in the A10 motorway
(Arruda dos Vinhos, Portugal). For the numerical modelling of
structures formed with these marls, a nine parameter
constitutive model based on the two yield surfaces concept
presented by Gens and Nova (1993) was developed and applied.
For the evaluation of these parameters a genetic algorithm (GA)
was implemented.
Previous GA application for parameter determination
purposes allowed demonstrating the efficiency and flexibility of
this procedure (Pal et al. 1996). Also the association of a local
search technique, like Hill Climbing (HC), improved the
convergence of GA (Taborda et al. 2011).
In this paper, a GA with an embedded HC procedure was
implemented in MATLAB to fit a HSSR constitutive model to
the marls experimental results. The constitutive model
formulation is herein presented and was implemented in the
explicit finite difference code FLAC (through the programming
language C++).
2 CONSTITUTIVE MODEL FOR HSSR
In the constitutive model presented in this section all the
stresses considered are effective stresses. This model has two
yield surfaces,
and
, based on modified Cam Clay yield
surface (see Figure 1), defined as:
= ∶
+ −
(1)
= ∶
+ +
−
(2)
where
represents the bonded material yield surface (current
yield surface),
the idealised yield surface of the unbounded
material corresponding to the limiting case of destructured soil,
= tr 3⁄
and
= dev
are the mean and deviatoric parts
of the effective stress tensor
, respectively,
is a material
parameter,
and
are the yield mean stress of the
unbonded and bonded materials, respectively, and
is the yield
mean stress in tension of the bonded material.
