Cyclic bounding surface model for carbonate sand incorporating particle breakage
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摘要: 钙质砂作为一种海洋生物成因的易破碎材料,由其构成的地基在海洋环境下长期受到动荷载的作用,故模拟钙质砂在循环荷载作用下的颗粒破碎及其对应力应变行为的影响具有重要意义。将引起塑性应变和颗粒破碎的机制分解为两种：有效球应力增加引起的压缩机制和剪应力比变化引起的剪切机制。压缩机制引起的颗粒破碎可由Hardin公式模拟,为适应复杂应力路径,在Hardin公式的基础上建立了增量型的压缩破碎模型。剪切机制引起的颗粒破碎满足两个“递减率”：①在每一个单向剪切过程中,颗粒破碎的累积速率总是在单向剪切起始处最大,并随着单向剪应变的增加而减小；②在总的剪切过程中,颗粒破碎的累积速率随颗粒破碎量的增大而逐渐减小。在边界面本构模型框架中引入所建立的压缩和剪切破碎模型,通过随颗粒破碎量移动的临界状态线反映颗粒破碎对模量、强度和剪胀等应力应变行为的影响,建立了一个考虑颗粒破碎的循环本构模型。通过对钙质砂的单调和循环三轴试验结果的模拟初步验证了所提出本构模型的合理性。Abstract: The carbonate sand is a crushable granular material formed by the marine organisms, and its foundation is subjected to long-term dynamic loading under the ocean environment. Hence, it is of great significance to simulate the particle breakage of the carbonate sand under cyclic loading and its influences on the stress-strain behavior. The mechanism of particle breakage is decomposed of two parts: the compression mechanism with the increase in the mean effective stress, and the shear mechanism with the change of shear stress ratio. The particle breakage caused by the compression mechanism can be simulated by the Hardin’s formula. In order to adapt to the complex stress path, an incremental compression breakage model is established on the basis of the Hardin’s formula. The shear-induced breakage model includes two "declining rules" under the cyclic loading: (1) The accumulate rate of the particle breakage has a maximum value at the initial phase of the monotonic shear process, but decreases with the increasing shear strain. (2) It continuously descends during the whole shear process with the increasing amount of the particle breakage. The compression and shear breakage models are introduced to the framework of the bounding surface constitutive model, and a novel constitutive model considering the particle breakage is established by reflecting the effects of the particle breakage on the stress-strain behaviors such as modulus, strength and dilatancy through the critical state line moving with the amount of the particle breakage. The simulation capability of the proposed constitutive model is verified by comparing with the experimental results of the carbonate sand which is under the monotonic and cyclic drained triaxial compression tests.
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Keywords:
- carbonate sand /
- particle breakage /
- cyclic loading /
- bounding surface /
- constitutive model
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图 5 临界状态应力比随颗粒破碎的变化
Figure 5. Variation of critical stress ratio with particle breakage
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图 6 单调三轴排水试验的模拟结果
Figure 6. Simulated results of monotonic drained triaxial compression tests
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图 7 循环三轴排水试验的模拟结果
Figure 7. Simulated results of cyclic drained triaxial compression tests
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图 8 相对破碎随循环周次演化过程的模拟结果
Figure 8. Simulated results of development of relative breakage with cyclic number
表 1 本构模型参数
Table 1 Parameters of constitutive model
颗粒破碎 临界状态 剪胀 弹性 塑性 c1=0.07 eΓ0=1.302 d0=0.9 G0=225 np=1.0 c2=1.2 λb=0.1 β=1000 κ=0.007 nd=2.2 A=55.0 λp=0.128 h=0.3 α=400 Mcs0=1.838 λ=0.012 k0=2.5×106 nb=1.393 
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