Drucker Prager Strength Criterion Research Articles

A dynamic material model for rock materials under conditions of high confining pressures and high strain rates

A dynamic material model is presented to characterize the mechanical behavior of rock materials under high confining pressures and high strain rates. The yield surface is defined based on the extended Drucker–Prager strength criterion and the Johnson–Cook material model. Two internal damage variables are introduced to represent, respectively, the tensile and compressive damage of rock materials. The proposed dynamic material model of rocks is incorporated into the nonlinear dynamic analysis code LS-DYNA through a user-defined material interface. Its reliability and accuracy are verified by the simulation of various basic experiments with different loading conditions. The present rock model is also applied to simulate the penetration of granite target plate by hard projectile. The typical damage and failure on the granite targets predicated by the proposed dynamic material model of rocks agree well with the experimental results. It demonstrates that the proposed model is capable of capturing the failure of rock materials.

Effect of Radial Inertia Confinement on Dynamic Compressive Strength of Concrete in SHPB Tests

This paper extends the study of Dharan on the stress state in an elastic solid specimen subjected to axial strain acceleration to compressible materials. And an improved Dharan model is presented. Based on the Drucker-Prager strength criterion, analytical equations of the radial inertia confinement effect on dynamic compressive strength of concrete in split Hopkinson pressure bar tests is derived. Comparison and discussion on the analytical, experimental and numerical results are performed. It is proved that the strain rate effect of compressive strength of concrete materials is a pseudo material property partly caused by the radial inertia confinement. Special attentions should be paid to dynamic tests of low-strength concrete to get the real mechanical properties.

Analysis of Äspö Pillar Stability Experiment: Continuous thermo-mechanical model development and calibration

The paper describes an analysis of thermo-mechanical (TM) processes appearing during the Äspö Pillar Stability Experiment (APSE). This analysis is based on finite elements with elasticity, plasticity and damage mechanics models of rock behaviour and some least squares calibration techniques. The main aim is to examine the capability of continuous mechanics models to predict brittle damage behaviour of granite rocks. The performed simulations use an in-house finite element software GEM and self-developed experimental continuum damage MATLAB code. The main contributions are twofold. First, it is an inverse analysis, which is used for (1) verification of an initial stress measurement by back analysis of convergence measurement during construction of the access tunnel and (2) identification of heat transfer rock mass properties by an inverse method based on the known heat sources and temperature measurements. Second, three different hierarchically built models are used to estimate the pillar damage zones, i.e. elastic model with Drucker–Prager strength criterion, elasto-plastic model with the same yield limit and a combination of elasto-plasticity with continuum damage mechanics. The damage mechanics model is also used to simulate uniaxial and triaxial compressive strength tests on the Äspö granite.

A note on the Mohr–Coulomb and Drucker–Prager strength criteria

This paper presents different expressions of the Mohr–Coulomb (M–C) criterion as well as the interrelationships between them, which lays a foundation for the definition of the equivalent M–C friction angle φ mc . The characteristics of four types of Drucker–Prager cones matched with the M–C surface are compared as the friction angle φ varies from 0° to 90°. The minimum and maximum value of φ for them is given and the influence of the intermediate principal stress σ 2 to the major principal stress σ 1 is demonstrated using their φ mc .

The effect of the intermediate principal stress on the ultimate bearing capacity of a foundation on rock masses

In this paper, the strength envelope of rock masses is considered to follow a non-linear unified strength criterion that considers the effect of the intermediate principal stress. A unified slip line method for resolving the differential equation system that governs the stress field is established to research the ultimate bearing capacity, which can be adapted for a wide variety of rock masses. Through this new theory, a suitable characteristic method for rock masses of interest can be obtained, and the relationships between different types of characteristic methods are revealed. The characteristic methods are based on different strength criteria, such as the Hoek–Brown criterion, modified Hoek–Brown criterion, or non-linear twin-shear strength criterion; each of these criteria is a special case of the proposed theory. Moreover, a series of new characteristic methods can be easily derived from it. In terms of the proposed theory, the ultimate bearing capacity with the Hoek–Brown criterion forms the lower bound; the ultimate bearing capacity with a non-linear twin-shear strength criterion forms the upper bound; and a series of the ultimate bearing capacities ranging between these two bounds may be derived from a non-linear unified strength criterion. A comparison is made between existing numerical analyses and non-linear finite element analysis solutions with the Drucker–Prager strength criterion. It is shown that the present results are in good agreement with existing numerical analyses and non-linear finite element analysis solutions with the Drucker–Prager strength criterion.

Numerical prediction of blast‐induced stress wave from large‐scale underground explosion

AbstractThis paper presents a numerical model for predicting the dynamic response of rock mass subjected to large‐scale underground explosion. The model is calibrated against data obtained from large‐scale field tests. The Hugoniot equation of state for rock mass is adopted to calculate the pressure as a function of mass density. A piecewise linear Drucker–Prager strength criterion including the strain rate effect is employed to model the rock mass behaviour subjected to blast loading. A double scalar damage model accounting for both the compression and tension damage is introduced to simulate the damage zone around the charge chamber caused by blast loading. The model is incorporated into Autodyn3D through its user subroutines. The numerical model is then used to predict the dynamic response of rock mass, in terms of the peak particle velocity (PPV) and peak particle acceleration (PPA) attenuation laws, the damage zone, the particle velocity time histories and their frequency contents for large‐scale underground explosion tests. The computed results are found in good agreement with the field measured data; hence, the proposed model is proven to be adequate for simulating the dynamic response of rock mass subjected to large‐scale underground explosion. Extended numerical analyses indicate that, apart from the charge loading density, the stress wave intensity is also affected, but to a lesser extent, by the charge weight and the charge chamber geometry for large‐scale underground explosions. Copyright © 2004 John Wiley & Sons, Ltd.

Modeling of wave propagation induced by underground explosion

Abstract A piecewise linear Drucker–Prager strength criterion and an isotropic continuum damage model with the damage scalar depending on an equivalent tensile strain are suggested to model rock mass behavior under blast loading. A rate-dependent constitutive relation is employed to model the energy dissipation caused by two sources, namely irreversible degradation of damage and permanent deformation caused by plasticity. The suggested model is incorporated with a commercially available software AUTODYN through its user’s subroutine function. Coupling of Euler and Lagrange processors are used to include all the materials under consideration such as explosive, air and rock mass, in the calculation. Using AUTODYN and the suggested model, shock wave propagation in rock mass induced by an underground explosion is simulated. Numerical results obtained agree favorably well with those obtained from an independently conducted field test. It demonstrates that the suggested model can be used to predict the damage area, plastic zone and ground motions generated by underground explosions.