Most of the available constitutional equations indicating strain softening effect are based on stress space, but it is found that the elastic-plastic theory based on strain space is superior to stress space on solving the problem associate with large strain and softening. In this paper, a diatomaceous soft rock and its constitutive model are studied. A series of triaxial tests have been carried out on this soft rock. The constitutive equation of consolidated undrained triaxial stress state expressed in strain space is derived to simulate the stress-strain relationship of the results. It indicates that the elastic-plastic model based on strain space is applicable to express the strain softening effect of soft rock.


The existing constitutive models that can indicate the strain softening effect are mostly based on stress space. Elastic-plastic theories based on strain space, which are solving the problems about large strain and softening, are superior to the elastic-plastic theories based on stress space. In this paper, according to elastic-plastic constitutive equation based on strain space, a softening model of soft rock is analyzed and investigated. Using the Mises criterion and its associated flow rule, the stressstrain constitutive relationship of a diatomaceous soft rock is derived for the condition of consolidated undrained triaxial tests. The hardening functions are used to simulate the stress-strain curves for different confining pressures in consolidated undrained triaxial tests.

2.1 Elastic-plastic constitutive equation based on strain Space

  • (Equation in full paper)

2.2 Hardening function

The selection of parameter К in the hardening function is very important. К determines the expansion mode of load surface during loading.

Considering the material softening effect, the hardening function is established now. The yield function that satisfies isotropic hardening in the stress space can be expressed as

  • (Equation in full paper)

Considering the stress-strain relationship curve of some direct shear tests shown in Fig. 1, the hardening parameter К increases from point A to B, and then decreases and approaches constant after it reaches its maximum at point B if the material yield function satisfies equation (14).

  • (Equation in full paper)

3.1 Test condition

Test specimens were taken from a diatomaceous mud rock stratum in a late tertiary period Miocene epoch in the Noto Peninsula which lies on the edge of Ishikawa county in Japan. Traxial tests were conducted under different consolidation pressures and different rates of loading. The basic properties of the soft rock are presented in Table 1. The conditions and methods of the tests are in Table 2.

(Table in full paper)

3.2 Analysis of test results

Fig. 2 shows the stress-strain curves for the diatomaceous soft rock samples under different confining pressures in consolidated untrained triaxial tests. From Fig. 2, the peak strength always appears where the axial strain is from 2% to 3%, no matter what the consolidation pressure is. The curves are divided into two categories by the preconsolidated pressure of 1.5 MPa: normally consolidated and overconsolidated state.

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