双线性强化隧道和桩孔三剪弹塑性解

赵均海; 张磊; 张常光; 曹雪叶

doi:10.19818/j.cnki.1671-1637.2018.01.005

双线性强化隧道和桩孔三剪弹塑性解

doi: 10.19818/j.cnki.1671-1637.2018.01.005

长安大学建筑工程学院, 陕西西安 710061

基金项目:

国家自然科学基金项目 51508028

国家自然科学基金项目 41202191

陕西省社会发展科技攻关项目 2015SF272

中国博士后科学基金项目 2016T90879

中国博士后科学基金项目 2014M562357

中央高校基本科研业务费专项资金项目 310828173402

详细信息

作者简介:
赵均海(1960-), 男, 陕西蓝田人, 长安大学教授, 工学博士, 从事结构工程和岩土力学研究

中图分类号: U452
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出版历程
- 收稿日期: 2017-08-05
- 刊出日期: 2018-02-25

Elastic-plastic solutions of bilinear strain-hardening tunnel and pile cavity based on tri-shear failure criterion

School of Civil Engineering, Chang'an University, Xi'an 710061, Shaanxi, China

More Information

Author Bio:
ZHAO Jun-hai(1960-), male, professor, PhD, zhaojh@chd.edu.cn

摘要

摘要: 将隧道和桩孔简化为厚壁圆筒, 基于三剪强度准则和双线性强化模型, 考虑材料的应变强化和中间主应力效应, 推导了厚壁圆筒在均匀内外压作用下的弹塑性极限解, 并给出恒定外压条件下塑性区半径与内压的关系式, 分析了强化模量系数、半径比、中间主应力与材料强度拉压异性对厚壁圆筒弹塑性极限解的影响规律。研究结果表明: 所得弹塑性极限解克服了Tresca屈服准则与Mises屈服准则未考虑拉压异性, Tresca屈服准则与Mohr-Coulomb屈服准则未考虑中间主应力与双剪强度理论极限解存在滑移面突变现象的不足; 弹塑性极限解均随半径比与中间主应力影响系数的增大而增大, 随拉压强度比的增大而减小, 外压对极限内压的影响程度随着拉压强度比的增大而减小; 当强化模量系数为0.1、半径比为2时, 考虑强化效应的塑性极限内压比不考虑时相对增大10%以上, 随着半径比增大到4, 塑性极限内压比不考虑强化效应时相对增大38%以上, 强化效应影响更加明显, 故对于存在应变强化效应的材料, 采用双线性强化模型的分析结果更接近工程实际; 当不考虑中间主应力与应变强化时, 土体的极限扩孔压力弹塑性极限解与Vesic解相差在0.02%以内, 当考虑了土体的中间主应力和应变强化效应后, 塑性区半径与内半径比为10时, 弹塑性极限解分别是Vesic解的1.06、1.81倍, 因此, 基于Vesic解的极限扩孔压力过于保守。
- 隧道工程 /
- 厚壁圆筒 /
- 三剪强度准则 /
- 极限内压 /
- 双线性强化模型 /
- 中间主应力
Abstract: Tunnel and pile cavity were simplified as thick-walled cylinders, the effects of strain hardening and intermediate principal stress were considered, the elastic-plastic limit solution of thick-walled cylinder under uniform internal and external pressures was deduced based on the trishear failure criterion and the bilinear strain-hardening model, the relationship of internal pressure and elastic-plastic radius under constant external pressure was given, and the effects of many parameters on the limit solution of thick-walled cylinder were discussed, including strengthening modulus, radius ratio, intermediate principal stress and material strength heterogeneity of tension and compression.Research result shows that the proposed solution can overcome the deficiencies of material strength heterogeneity of tension and compression ignored by Tresca and Mises yield criteria, the intermediate principal stress ignored by Tresca and MohrCoulomb yield criteria, as well as the abrupt changing phenomenon of slip plane in twin shearstrength theory.The limit solution increases with the radius ratio and the intermediate principal stress coefficient, but decreases with the tension-compression strength ratio.The effect of external pressure on the limit internal pressure decreases with the tension-compression strength ratio.Compared with no considering strengthening modulus, when the strengthening modulus is0.1 and the radius ratio is 2, the plastic limit internal pressure increases by more than 10%.When the radius ratio increases to 4, the plastic limit internal pressure increases by more than38%, so the strengthening effect is more obvious.Obviously, for the material with strain hardening effect, the result analyzed by the bilinear strain-hardening model is closer to the engineering practices.When the intermediate principal stress and the strain hardening are not considered, the differences of limit expansion soil pressures calculated by the proposed solution are within 0.02% compared with the values calculated by the Vesic theory.However, when the intermediate principal stress and the strain hardening are considered and the ratio of the plastic zone radius to the inner radius is 10, the limit solutions are respectively 1.06 times and1.81 times the values calculated by the Vesic theory.As a result, the limit expansion pressure based on the Vesic theory is too conservative.
- tunnel engineering /
- thick-walled cylinder /
- tri-shear failure criterion /
- limit internal pressure /
- bilinear strain-hardening model /
- intermediate principal stress

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图 1 双线性强化模型

Figure 1. Bilinear strain-hardening model

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图 2 厚壁圆筒受力模型

Figure 2. Mechanical model of thick-walled cylinder

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图 3 p_s/σ_t0随r_b/r_a与m的变化规律(α=1.0, b=0)

Figure 3. Variation rules of p_s/σ_t0 with r_b/r_aand m (α=1.0, b=0)

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图 4 p_s/σ_t0随b与m的变化规律(α=1.0, r_b/r_a=2)

Figure 4. Variation rules of p_s/σ_t0 with band m (α=1.0, r_b/r_a=2)

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图 5 p_s/σ_t0随α与m的变化规律(b=0, r_b/r_a=2)

Figure 5. Variation rules of p_s/σ_t0 withαand m (b=0, r_b/r_a=2)

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图 6 p_e/σ_t0随r_b/r_a与b的变化规律(α=1.0)

Figure 6. Variation rules of p_e/σ_t0 with r_b/r_aand b (α=1.0)

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图 7 p_e/σ_t0随r_b/r_a与α的变化规律(b=0)

Figure 7. Variation rules of p_e/σ_t0 with r_b/r_aandα (b=0)

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图 8 p_s/σ_t0随r_b/r_a与α的变化规律(b=0)

Figure 8. Variation rules of p_s/σ_t0 with r_b/r_aandα (b=0)

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图 9 p_e/σ_t0随b与α的变化规律(r_b/r_a=2)

Figure 9. Variation rules of p_e/σ_t0 with b andα (r_b/r_a=2)

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图 10 p_s/σ_t0随b与α的变化规律(r_b/r_a=2)

Figure 10. Variation rules of p_s/σ_t0 with b andα (r_b/r_a=2)

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图 11 p_e/σ_t0随α与p₂/σ_t0的变化规律(r_b/r_a=2)

Figure 11. Variation rules of p_e/σ_t0 withαand p₂/σ_t0 (r_b/r_a=2)

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图 12 p_s/σ_t0随α与p₂/σ_t0的变化规律(r_b/r_a=2)

Figure 12. Variation rules of p_s/σ_t0 withαand p₂/σ_t0 (r_b/r_a=2)

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图 13 柱孔扩张模型

Figure 13. Cylindrical cavity expansion model

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图 14 三剪理论解和Vesic理论解的比较

Figure 14. Comparison of solutions gained by tri-shear failure criterion and Vesic theory

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