﻿ 基于中主应力强度准则岩石损伤本构模型研究 Study on the Constitutive Model of Rock Damage Based on Intermediate Principal Stress Criterion

Hans Journal of Civil Engineering
Vol.05 No.05(2016), Article ID:18355,10 pages
10.12677/HJCE.2016.55023

Study on the Constitutive Model of Rock Damage Based on Intermediate Principal Stress Criterion

Siqi Liu, Yonglai Zheng, Shuxin Deng

College of Civil Engineering, Tongji University, Shanghai

Received: Aug. 1st, 2016; accepted: Aug. 19th, 2016; published: Aug. 22nd, 2016

ABSTRACT

By discussing the form of new rock micro-unit strength based on intermediate principal stress criterion, which satisfies Weibull random distribution, and introducing a damage correction factor q, a statistical constitutive model of rock damage was developed based on the stress-strain curve of tri-axial tests for rocks. Moreover, the effect of the parameters of Weibull distribution and the damage correction factor on the model was studied. The model was rectified according to the properties of tri-axial stress-strain test curve of rock. Compared with the existing research results, this model can better simulate the rock strain softening under low confining pressure. Therefore, this model has broad prospects for application.

Keywords:Rock Failure, Damage, Intermediate Principal Stress, Constitutive Model

1. 引言

2. 岩石损伤本构模型的建立

2.1. 基本假设

1) 在宏观上，微元体及其损伤均表现为各向同性；

2) 在微元破坏前服从虎克定律，即微元体具有线弹性性质，破坏后不具备承载能力；

3) 各微元弹性体的强度服从概率统计规律。本文选用Weibull分布来描述各微元体强度的分布规律，其概率密度函数为：

(1)

2.2. 岩石损伤本构关系

(2)

(3)

2.3. 统计损伤演化方程

(4)

(5)

(6)

(7)

2.4. 岩石微元强度的表征

Mohr-Coulomb准则没有考虑强度的中主应力效应，而Drucker-Prager准则则高估了强度的中主应力效应，因此本文引用ZHENG Y等 [18] 提出的能更准确反映中主应力效应的强度准则，采用该强度准则来表征微元体的强度。岩石微元强度表示为：

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

2.5. 本构关系的确立

(17)

3. 模型参数的确定

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

(26)

Figure 1. Stress strain curve of typical rock in three axis

(27)

4. 模型参数分析

Figure 2. The curve of stress and damage variable change with strain

Figure 3. The influence of parameter m on the damage constitutive model of rock

Figure 4. The influence of parameter F0 on the damage constitutive model of rock

Figure 5. The influence of parameter q on the damage constitutive model of rock

5. 模型的验证

6. 结语

1) 所建立的模型的主要特点是能够反映三维应力状态下岩石的变形全过程，反映了岩石的破裂不仅受岩石微元强度的变化，而且受岩石应力状态的影响。采用基于破坏准则的岩石微元强度度量方法，引入反映中主应力影响的强度准则来表征岩石微元的强度，使得计算结果更加接近实际。

2) 引入损伤修正系数，使得Lemaitre应变等价性假说与损伤统计分布很好地衔接，通过调整损伤修正系数也使得本构模型的精度大为提高。

3) 与基于微裂纹变形和扩展的岩石细观损伤模型相比，本文建立的模型忽略了细观物理过程，避免了细观力学繁琐的计算，因此更容易在工程实际问题中得到应用。

(a) 围压3.5 MPa () (b) 围压7.0 MPa ()(c) 围压14.0 MPa () (d) 围压21.0 MPa ()

Figure 6.The comparison between the model calculation results in this paper and the experimental results

Figure 7. Rock damage evolution curve

4) 本文建立的模型参数较少，而且物理意义明确，应用方便。弹性模量参数可以通过应力应变曲线的初始段上升斜率来获得，强度准则参数可以通过拟合强度包络线来获得，Weibull分布参数可以通过多元函数极值理论来求解。

Study on the Constitutive Model of Rock Damage Based on Intermediate Principal Stress Criterion[J]. 土木工程, 2016, 05(05): 171-180. http://dx.doi.org/10.12677/HJCE.2016.55023

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