Issue 30

L. Bing et alii, Frattura ed Integrità Strutturale, 30 (2014) 526-536; DOI: 10.3221/IGF-ESIS.30.63 529 Stress update The numerical algorithm of integral rate constitutive equation is called as stress update algorithm. Stress    ij σ t dt of  t dt can be obtained by   ij as follows:          ij ij ij σ t dt σ t dt (10a) The Cauchy stress rate can be expressed as:    ij       ij ik jk jk ik Ω Ω (10b) In the equation,   ij is the Jaumann rate,   ij  ijkl kl C D , ijkl C is the elastic constitutive tensor. Stress integral    ij σ t dt obtained through Eq. (10a) is performed to the unit nodes, and then node’s internal force vector int f is obtained. T HE DYNAMIC ELASTOPLASTIC DAMAGE CONSTITUTIVE OF THE SURROUNDING ROCK The Dynamic Elastoplastic Damage Constitutive Model of Civil Construction Foundation Surrounding Rock he dynamic elastoplastic damage constitutive model of civil construction foundation surrounding rock is the basis of simulation of the Children’s Palace earthquake disaster process. On the basis of theoretical study, we need to combine with a large number of indoor and outdoor tests, and establish a scientific and practical dynamic damage constitutive model of rock. Civil construction foundation surrounding rock shows the dynamic strengthening characteristics and fatigue damage properties of the surrounding rock. The research results [5] showed that: Under dynamic loading, the surrounding rock strain rate increases. And elastic modulus of surrounding rock materials and damage resistance are improved. While under cyclic loading conditions, there appears fatigue damage of surrounding rock and elastic modulus of surrounding rock materials and destruction resistant properties are reduced. The two factors are in opposition to each other and coexist at the same time. It should be considered in the constitutive model as follows: (1) The study on rock dynamic strengthening characteristics is mainly divided into high strain rate      2 1 10  s and middle strain rate          4 1 1 1 10 10  s s study. Among which, high strain rate is mainly to solve the problem of shock blasting. Because the loading ways are simple, there are relatively more tests. While Children’s Palace earthquake effect strain rate is generally at the range of        6 1 1 1 10 10  s s , belonging to medium strain rate and there are less tests. From the existing research results [5, 14 ~ 17] we can get the following conclusions:  Rock dynamic strength and modulus of elasticity increase with the increase of strain rate.  Rock dynamic strength increases with strain rate. This is because that cohesion increases with strain rate while internal friction angle is not affected by strain rate.  The dynamic characteristics of medium strain rate of the rock are affected by the way of loading, loading rate, rock type and test equipment. All kinds of test results are with large discreteness, so consistent rules are difficult to conclude based on experiments. (2) There are many rock damage constitutive researches. Damage description is usually with tensor description form of first, second and fourth order. In view of the aeoplotropism of seismic wave propagation, this paper adopts second order damage tensor to describe the damage of surrounding rock in the earthquake. Considering the above two kinds of characteristics of surrounding rock in the earthquake, the dynamic elastic modulus of surrounding rock of dynamic constitutive model can by expressed as:     0  E P E (11) In the equation, E is the static elastic modulus of surrounding rock; T