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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2024, Vol. 58 Issue (7): 1446-1456    DOI: 10.3785/j.issn.1008-973X.2024.07.014
    
Constitutive model of saturated fractured porous rock mass based on mixture theory
Yayuan HU(),Fei YE
Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China
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Abstract  

Considering the relationship between strain and pressure of solid in the saturated fractured porous rock mass, a new constitutive model was developed to enhance the theoretical foundation for determining the mechanical parameter values of the model. Within the framework of mixture theory, the solid volumetric strain was decomposed into the volumetric strain of fractured skeleton, porous skeleton, and rock material according to the deformation characteristics. Assuming the strain only depended on the conjugate stress in the energy equation, a constitutive model of saturated fractured porous rock mass was developed by the free-energy potential function, and a method for determining the values of mechanical parameters was derived according to the mechanical meaning of the model. The governing equations for fluid-solid coupling were deduced using Darcy’s law. The analysis of the one-dimensional consolidation case showed that, compared with previous parameter value methods, the initial fluid pressure calculated using the parameters determined in the derived method was lower, the initial settlement was larger, and the dissipation of pore excess pressure lagged behind the fracture excess pressure. The sensitivity analysis of the parameters showed that increasing the permeability coefficient ratio greatly improved the consolidation rate of the rock mass while increasing the shape factor had little impact on the dissipation of fracture excess pressure and rock mass settlement.

Key words： saturated fractured porous rock mass      mixture theory      rock material deformation      parameter determination method      one-dimensional consolidation     
Received: 29 June 2023      Published: 01 July 2024
CLC:  TU 452  
Fund:  国家自然科学基金资助项目（52178360）.
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Yayuan HU
Fei YE
Cite this article:

Yayuan HU,Fei YE. Constitutive model of saturated fractured porous rock mass based on mixture theory. Journal of ZheJiang University (Engineering Science), 2024, 58(7): 1446-1456.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2024.07.014     OR     https://www.zjujournals.com/eng/Y2024/V58/I7/1446


基于混合物理论的饱和孔隙-裂隙岩体本构模型

考虑饱和孔隙-裂隙岩体中固相材料应变与固相材料压力间的关系，完善模型力学参数的取值理论依据，建立新的本构模型. 在混合物理论框架内，依据变形特征将固相体应变分解为裂隙骨架体应变、孔隙骨架体应变、岩块材料体应变. 假定应变仅取决于能量方程中的共轭应力，基于自由能势函数构建饱和孔隙-裂隙岩体本构模型，根据模型力学含义推导模型力学参数取值方法. 结合达西定律建立流固耦合控制方程. 一维固结算例分析表明，相比其他方法确定的参数，所提方法确定参数计算的初始超孔压偏低、初始沉降偏大，孔隙超孔压消散滞后于裂隙超孔压. 参数敏感性分析表明，增大渗透系数比会显著提高岩体固结速率，增大形状系数对裂隙超孔压消散和岩体沉降影响较小.


关键词： 饱和孔隙-裂隙岩体,  混合物理论,  岩块材料变形,  参数的取值方法,  一维固结 
Fig.1 Saturated fractured porous rock mass[6,9]
Fig.2 Test data and model calculation results
参数Anderson 01Gilson 02
裂隙体积分数${\varphi _{{\text{F0}}}}$0.0131[24]0.00804[24]
煤块弹性模量${E_{\text{r}}}$/$ {\text{MPa}} $1379[24]1379[24]
煤块泊松比$\mu $0.35[24]0.35[24]
$ {C_{{\text{CC}}}} $/$ {\text{MP}}{{\text{a}}^{ - 1}} $3×10?44×10?4
$ {C_{\text{b}}} $/$ {\text{MP}}{{\text{a}}^{ - 1}} $9.53×10?41.1×10?3
$ {\beta _{\text{F}}}+{\beta _{\text{P}}} $0.50.5
Tab.1 Parameters used in model fitting
参 数数值
孔隙体积分数${\varphi _{{\text{P0}}}}$，裂隙体积分数${\varphi _{{\text{F0}}}}$0.1，0.05
形状系数$\overline \alpha $15
岩块的弹性模量${E_{\text{r}}}$/$ {\text{GPa}} $14.4
岩块材料柔度系数${C_{{\text{RS}}}}$/$ {\text{GP}}{{\text{a}}^{ - 1}} $0.025
孔隙的渗透系数${k_{\text{P}}}$/(${\text{m}} \cdot {{\text{s}}^{ - 1}}$)1×10-10
裂隙渗透系数${k_{\text{F}}}$/(${\text{m}} \cdot {{\text{s}}^{ - 1}}$)1×10?7
岩块泊松比${\mu _{\text{r}}}$，节理泊松比${\mu _{\text{j}}}$0.2
节理法向刚度${k_{\text{n}}}$/($ {\text{GPa}} \cdot {{\text{m}}^{ - 1}} $)8
节理间距$d$/${\text{m}}$0.2
流体材料的柔度系数${C_{{\text{R}}f}}$/$ {\text{GP}}{{\text{a}}^{ - 1}} $0.303
Tab.2 Mechanical basic parameters of intact rock and joints
参数计算公式数值文献[6]计算公式文献[6]数值
${C_{{\text{HH}}}}$/$ {\text{GP}}{{\text{a}}^{ - 1}} $$ 3{\varphi _{{\text{SP0}}}}(1 - 2{\mu _{\text{r}}})/{E_{\text{r}}} - \varphi _{{\text{SP0}}}^2{C_{{\text{RS}}}}/{\varphi _{{\text{S0}}}} $0.092$ 3(1 - 2{\mu _{\text{r}}})/{E_{\text{r}}} $0.125
${C_{{\text{CC}}}}$/$ {\text{GP}}{{\text{a}}^{ - 1}} $$ 1/({{\text{k}}_{\text{n}}}d)+({\varphi _{{\text{F0}}}}{C_{{\text{HH}}}}/{\varphi _{{\text{SP0}}}}) $0.630$ 1/({{\text{k}}_{\text{n}}}d) $0.625
${C_{{\text{SS}}}}$/$ {\text{GP}}{{\text{a}}^{ - 1}} $$ {C_{{\text{RS}}}}/{\varphi _{{\text{S0}}}} $0.033——
$ {C_{\text{b}}} $/$ {\text{GP}}{{\text{a}}^{ - 1}} $$ {C_{{\text{CC}}}}+{C_{{\text{HH}}}}+{C_{{\text{SS}}}} $0.755$ {C_{{\text{CC}}}}+{C_{{\text{HH}}}} $0.75
$ {C_{\text{M}}} $/$ {\text{GP}}{{\text{a}}^{ - 1}} $$ {C_{{\text{HH}}}}+{\varphi _{{\text{SP0}}}}{C_{{\text{SS}}}} $0.123$ {C_{{\text{HH}}}} $0.125
$ G_{\text{b}}^{\text{M}} $/$ {\text{GPa}} $$ {E_{\text{r}}}/2(1+{\mu _{\text{r}}}) $6$ {E_{\text{r}}}/2(1+{\mu _{\text{r}}}) $6
$ {G_{{\text{CC}}}} $/$ {\text{GPa}} $$ 3(1 - 2{v_{\text{j}}})/[2(1+{v_{\text{j}}}){C_{{\text{CC}}}}] $1.19$ 3(1 - 2{v_{\text{j}}})/[2(1+{v_{\text{j}}}){C_{{\text{CC}}}}] $1.2
$ {G_{\text{b}}} $/$ {\text{GPa}} $$ {\varphi _{{\text{SP0}}}}G_{\text{b}}^{\text{M}}{G_{{\text{CC}}}}/({G_{{\text{CC}}}}+{\varphi _{{\text{SP0}}}}G_{\text{b}}^{\text{M}}) $0.98$ {\varphi _{{\text{SP0}}}}G_{\text{b}}^{\text{M}}{G_{{\text{CC}}}}/({G_{{\text{CC}}}}+{\varphi _{{\text{SP0}}}}G_{\text{b}}^{\text{M}}) $0.97
$ {E_{\text{S}}} $/$ {\text{GPa}} $$ (4{G_{\text{b}}}{C_{\text{b}}}+3)/3{C_{\text{b}}} $2.631$ (4{G_{\text{b}}}{C_{\text{b}}}+3)/3{C_{\text{b}}} $2.627
$ {\beta _{\text{F}}} $$ {\text{ }}1 - {C_{\text{M}}}/{C_{\text{b}}} $0.84$ 1 - {C_{\text{M}}}/{C_{\text{b}}} $0.83
$ {B_{{\text{FF}}}} $式(27)1.15×10?4式(27)1.19×10?4
$ {B_{{\text{FP}}}} $, $ {B_{{\text{PF}}}} $式(27)?7.74×10?5式(27)?1.04×10?4
$ {\beta _{\text{P}}} $$ ({C_{\text{M}}} - {\varphi _{{\text{S0}}}}{C_{{\text{SS}}}})/{C_{\text{b}}} $0.12$ ({C_{\text{M}}} - {\varphi _{{\text{S0}}}}{C_{{\text{SS}}}})/{C_{\text{b}}} $0.17
$ {B_{{\text{PP}}}} $式(27)1.08×10?4式(27)1.34×10?4
Tab.3 Parameters of saturated fractured porous rock mass
Fig.3 Fracture and pore excess pressure dissipation for different parameter determination methods
Fig.4 Consolidation settlement for different parameter determination methods
Fig.5 Diagram of fracture and pore excess pressure dissipation for different permeability coefficient ratios
Fig.6 Diagram of consolidation settlement for different permeability coefficient ratios
Fig.7 Diagram of fracture and pore excess pressure dissipation for different shape factors
Fig.8 Diagram of consolidation settlement for different shape factors
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