setting up the constitutive model of rock and soil is essentially an inverse problem, which belongs to the model Identification in inverse problem theory. Since the artificial neural network (ANN) has powerful nonlinear mapping and self-learning abilities, it provides a new approach for solving this inverse problem, The authors have set up six nonlinear ANN models of constitutive relations for sand and clay. These researches have shown that many difficulties in setting up the constitutive models for rock and soil can be overcomed by using ANN, especially finding the mathematical expressions of models can be avoided and the process to determine the model parameters is greatly simplified. In addition, the ANN model can easily reflect the influence of stress path and also has strong fault-tolerance function.


Now many investigators proposed more than one hundred constitutive models for rock and soil. However, there are only a few models that are widely applied in engineering. There are two chief reasons for that: 1. Rock and soil are geological materials and situated in natural environment, which have suffered various actions. Therefore, it is difficult to describe the complex deformation of rock and soil by using a simple mathematical model that has only a few parameters; 2. There also exists a basic paradox in traditional modeling method. One aspect requires the models are able to describe the constitutive relation of rock and soil accurately; the other requires the model parameters are as less as possible and also an e easily determined in tests. The inverse problem theory (Tarantola, 1987) is a new field that studies the inverse processes of various physical phenomena. In fact, back inferring the constitutive law of rock and soil from their mechanical response measured in tests is an inverse problem. Based on the inverse problem theory, the first author has investigated various possible pathes for solving this inverse problem and proposed an ANN approach. ANN (Rumelhan et al. 1986) is an information processing system with a capability of massive parallel processing, which is set up by imitating the neural architecture of the human brain. The unique capability of ANN is to acquire the know ledges from real world, i.e. self-learning ability. The authors have set up six nonlinear ANN models of constitutive relations for sand and clay. The study results have shown that ANN is good at dealing with the inverse problems in modeling the constitutive law of rock and soil.


In the process of knowing world, people discover the general relations of cause and effect. Inferring the effect from cause is called the forward problem. However, back inferring the cause from effect is an inverse problem. The main task of the inverse problem theory is to set up a map from the observable parameters to model parameters. In fact, modeling the constitutive law of rock and soil is back inferring their inherent stress-strain relation from their mechanical behaviors.

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