Comparison of Stress-Dilatancy Rules and Research on Stress-Dilatancy Rule for Rocks
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摘要:
为研究典型应力-剪胀关系对常见岩土材料力学响应的预测效果，构建适合岩石材料的应力-剪胀关系，提升本构模型的准确性，本文结合试验数据对典型应力-剪胀关系展开对比分析，并构建适用于岩石的应力剪胀关系模型. 首先，基于热动力学框架和能量守恒方程，梳理出3种典型的应力-剪胀关系模型，并将多种岩土材料的应力-剪胀数据与典型应力-剪胀关系进行对比；随后，以Rowe剪胀关系模型为基本框架，考虑多种因素影响，提出适用于岩石的改进Rowe应力-剪胀关系模型，分析了其对试验数据的拟合效果，并对比所提模型和变剪胀角模型对加载过程剪胀角演化的模拟效果；最后，将修正Rowe剪胀关系与修正剑桥模型耦合，与经典的修正剑桥模型的模拟结果和试验数据进行对比校验. 研究结果表明：由于黏聚力的影响，基于纯摩擦假设推导的经典应力-剪胀关系无法准确描述含黏聚力岩土材料的应力-剪胀响应；修正Rowe剪胀关系模型可以有效反映岩石的应力-剪胀响应，并能模拟数据中的“回旋勾”现象；本文提出的应力-剪胀关系模型不仅形式简洁，且参数数量较变剪胀角模型少；应用所提修正Rowe剪胀关系模型可以提升本构模型在变形预测方面的准确性.
Abstract:In order to evaluate the prediction accuracy of typical stress-dilatancy rules on the mechanical response of common geomaterials, propose a stress-dilatancy rule suitable for rocks, and improve the accuracy of constitutive models, typical stress-dilatancy rules were compared with experimental data to propose a stress-dilatancy model suitable for rocks. Firstly, based on the thermodynamic framework and the energy conservation equation, three typical stress-dilatancy models were sorted out, and the stress-dilatancy data of various geomaterials were compared with those typical stress-dilatancy rules. Then, by taking the Rowe dilatancy model as the basic framework and considering the influence of various factors, an improved Rowe stress-dilatancy model suitable for rocks was proposed, and its fintness on the experimental data was analyzed. The fitness of the proposed model and the variable dilatancy angle model on the evolution of dilatancy angle during loading was compared. Finally, the modified Rowe dilatancy rule was coupled with the modified Cam-clay model, and the simulation results and test data of the classical modified Cam-clay model were compared and verified. The results show that the classical stress-dilatancy rule based on the pure friction hypothesis cannot accurately describe the stress-dilatancy response of geomaterials with cohesion due to the influence of cohesive force. The modified Rowe dilatancy model can effectively reflect the stress-dilatancy response of rock and simulate the “turning hook” phenomenon in the data. Furthermore, the proposed stress-dilatancy model is not only simple in form but also has fewer parameters than the mobilizing dilatant angle models. The proposed modified Rowe dilatancy model can improve the accuracy of the constitutive model in deformation prediction.
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Key words:
- stress-dilatancy rule /
- rocks /
- cohesive force /
- dilatancy angle /
- models
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图 1 砂土和大坝堆填料的应力-剪胀关系对比
Figure 1. Comparison of stress-dilatancy rules for sand and dam fill
图 2 水泥和生物水泥加固砂土的应力-剪胀关系对比
Figure 2. Comparison of stress-dilatancy rules for cement-enhanced and biocement-enhanced sands
图 3 软岩/硬岩的应力-剪胀关系对比
Figure 3. Comparison of stress-dilatancy rules for a soft rock and a hard rock
图 4 含黏聚力材料的应力-剪胀特性
Figure 4. Stress-dilatancy characteristics of materials with cohesive force
图 5 改进Rowe应力-剪胀关系特征
Figure 5. Characteristics of modified Rowe’s stress-dilatancy rule
图 6 改进Rowe关系与数据对比
Figure 6. Comparison between modified Rowe rule and experimental data
图 7 不同模型预测剪胀角与试验数据对比
Figure 7. Comparison between dilatancy angle predicted by different models and experimental data
图 8 修正应力-剪胀关系校验及应用
Figure 8. Validation and application of modified stress-dilatancy rule
表 1 3种典型应力-剪胀关系
Table 1. Three classical stress-dilatancy rules
典型应力-剪胀关系 $ {{{W}}_{\mathrm{e}}} $ 形式 $ {{\varPhi }} $ 形式 $ {{\varPsi }} $ 形式 应力-剪胀关系形式 剑桥模型[8] $p{\mathrm{d}}\varepsilon _{{\rm{v}}}^{{\mathrm{p}}} + q{\mathrm{d}}\varepsilon _{{\text{γ} } }^{{\mathrm{p}}}$ $Mp{\mathrm{d}}\varepsilon _{{\text{γ} } }^{{\mathrm{p}}}$ 无 $d = M - \eta $ 修正剑桥模型[10] $\dfrac{1}{2}{p_{{\mathrm{c}}}}\sqrt {{{\left( {{\mathrm{d}}\varepsilon _{{\rm{v}}}^{{\mathrm{p}}}} \right)}^2} + {{\left( {M{\mathrm{d}}\varepsilon _{{\text{γ} } }^{{\mathrm{p}}}} \right)}^2}} $ $ \dfrac{1}{2}{p_{{\mathrm{c}}}}{\mathrm{d}}\varepsilon _{{\mathrm{v}}}^{{\mathrm{p}}} $ $d = \dfrac{{{M^2} - {\eta ^2}}}{{2\eta }}$ Rowe[6] $Mp{\mathrm{d}}\varepsilon _{{\text{γ} } }^{{\mathrm{p}}} + \dfrac{{2q - 3p}}{9}M{\mathrm{d}}\varepsilon _{{\rm{v}}}^{{\mathrm{p}}}$ 无 $d = \dfrac{{9\left( {M - \eta } \right)}}{{9 + 3M - 2M\eta }}$ 
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表 2 改进Rowe准则参数
Table 2. Parameters of modified Rowe rule
岩石 $E$ $b$ $ \xi $ $ \omega $ 中粒砂岩 30 0.30 6.00 0.10 Eibenstock Ⅱ花岗岩 50 0.10 4.80 0.20
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表 3 模拟所用参数
Table 3. Parameters for simulation
参数 取值 $\mu $ 0.23 $\kappa $ 0.015 $\lambda $ 0.15 $M$ 1.10 ${p_{{{\mathrm{c}}0}}}$/MPa 70 ${v_0}$ 1.258 $ \xi $ 4 $\omega $ 0.15 $E$ 0.05 $b$ 20
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