A STUDY ON NONLINEAR CONSTITUTIVE MODEL OF FROZEN SAND CONSIDERING PARTICLE BREAKAGE
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摘要: 颗粒破碎是粒状材料在高应力状态下的一种基本现象。为了研究冻结砂土中颗粒破碎对应力应变关系的影响，将冻结砂土视为复合颗粒材料，忽略冰的压融，考虑内摩擦角随应力状态的变化，构建一个适用于冻结砂土的考虑颗粒破碎的非线性本构模型。构建过程分为三步，首先是基于三轴剪切前后颗粒分析对冻结砂土颗粒破碎模式和产生机理进行探讨；其次是基于考虑颗粒破碎的能量平衡方程，对冻土在三轴剪切试验过程中的颗粒破碎耗能进行分析，结果表明颗粒破碎耗能随轴向应变呈双曲线变化趋势；最后应用考虑颗粒破碎的剪胀方程修正沈珠江三参数非线性模型中的体积切线模量νt，得到一个考虑颗粒破碎的非线性本构模型，模型参数可以通过单轴压缩试验和常规三轴试验确定。将原模型和修正后模型的计算结果与控制温度为-6℃，围压为1 MPa、4 MPa、6 MPa、8 MPa和10 MPa时冻结砂土的试验结果进行对比，结果表明该模型能够较好的模拟冻结砂土从低围压到高围压的应变软化特征与剪胀特征。Abstract: Particle breakage is a basic phenomenon of granular materials under high stress. In order to study the effect of particle breakage on the stress-strain relationship of frozen sand, the frozen sand is regarded as composite particle material, ignoring the melting of ice, considering the change of internal friction angle with stress state, a nonlinear constitutive model considering particle breakage for frozen sand is proposed. Firstly, based on particle analysis before and after the triaxial shearing, the fracture mode and mechanism of frozen sand particles were discussed. Secondly, based on the energy balance equation considering particle breakage, the energy consumption of particle breakage during the triaxial shear test of frozen soil was analyzed. The results show that the energy consumption of particle breakage shows a hyperbolic trend with axial strain. Finally, the volumetric tangent modulus νt in the three-parameter nonlinear model proposed by Shen Zhujiang is modified by the dilatancy equation considering particle breakage, a nonlinear constitutive model considering particle breakage suitable for frozen sand is obtained and the model parameters can be determined by uniaxial compression test and conventional triaxial test. The calculation results of the original model and the modified model are compared with the test results of frozen sand with the test temperature controlled at -6℃ and the confining pressure setting at 1 MPa, 4 MPa, 6 MPa, 8 MPa and 10 MPa, respectively. The comparison results show that the proposed model can better simulate the strain softening characteristics and dilatancy characteristics of frozen sand from low confining pressure to high confining pressure.
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Key words:
- frozen sand /
- particle breakage /
- energy principle /
- nonlinear constitutive model
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图 1 三轴剪切前后冻结砂土颗粒级配曲线图
Figure 1. Particle-size distribution curves before and after triaxial shear tests
图 3 点面接触型颗粒破碎物理模型
Figure 3. Physical model of particle breakage with point and surface contact
图 4 颗粒破碎耗能EB与总输入能ET比值曲线
Figure 4. The ratio curves between particle crushing energy of EB and total input energy of ET
图 6 颗粒破碎耗能与轴向应变关系曲线
Figure 6. Relationship between energy consumption of particle breakage and axial strain
表 1 与单轴压缩模量Mt与切线模量Et相关参数表
Table 1. Parameters related to the uniaxial compression modulus Mt and tangent modulus Et
σ3/MPa k km h i j 1.0 0.1700 0.1358 0.0017 4.0 0.1400 0.1219 0.0017 6.0 0.47 0.71 0.1200 0.1185 0.0017 8.0 0.1000 0.1121 0.0018 10.0 0.0980 0.0966 0.0025 
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表 2 与切线泊松比νt相关参数表
Table 2. Parameters related to the tangent poisson ratio νt
σ3/MPa a e f 其他参数 1.0 1.9006 0.0006 0.0227 4.0 1.0356 0.0005 0.0193 b=1.0200 6.0 0.7825 0.0004 0.0164 s=0.0009 8.0 0.603 0.0003 0.0144 t=0.0012 10.0 0.4638 0.0002 0.0125
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