能量耗散弹性损伤本构方程及其在围岩稳定分析中的应用

在内变量不可逆热力学的理论框架下，应用能量耗散的基本原理，求解弹性损伤的等效应变和损伤演化方程，建立损伤屈服准则。应用考虑能量耗散的本构方程，求解大型地下洞室围岩稳定问题，从分析结果能够给出洞室围岩损伤演化区的范围和损伤值的大小，进而判断洞室围岩何处发生损伤和断裂。认为损伤值等于1．0时，材料发生完全断裂，此时材料的破坏分析应借助宏观断裂力学的手段来进行。因此，该法为工程分析提供了细观上的理论依据，同时也为宏观分析提供了手段。

DAMAGE CONSTITUTIVE EQUATIONS FOR ENERGY DISSIPATION AND ITS APPLICATIONS TO STABILITY ANALYSIS OF SURROUNDING ROCK MASS OF CAVERNS

The constitutive model is formulated within the irreversible thermodynamics framework,appling the basic principle of energy dissipation;the effective strain of the elastic-damage,the evolution equations of the damage and the yielding criterion of the damage are derived. The constitutive equations for the damaged rock mass are written according to the principle of strain energy equivalence between the raw rock mass and damaged rock. The damaged rock mass is modeled by using the constitutive laws of the effective undamaged rock mass in which the nominal stresses are replaced by the effective stresses. An additive decomposition of the total strain into elastic and inelastic parts is adopted. The elastic part is further decomposed into two portions,one is recoverable elastic distortion and the other is unrecoverable elastic distortion,namely elastic damaged distortion. The inelastic part is also decomposed into two portions,one is plastic distortion and the other is crack closure distortion. The proposed models are applied to analyze the stability of caverns of which the result gives the damage values and zones of the surrounding rock mass of caverns. These values and zones show where damage and fracture occur. The paper supposes that when the damage value is equal to 1.0,the rock mass is defined as fully fractured. And then the method changes to macro-fracture mechanics. So the method provides some theoretical foundations for the micro-mechanics and some ways of the macro analysis in the fields of rock mass engineerings.