﻿ 考虑非线性流变的一维修正UH模型
 哈尔滨工业大学学报  2020, Vol. 52 Issue (11): 107-112  DOI: 10.11918/201904113 0

### 引用本文

LIU Zhongyu, ZHANG Jiachao, XIA Yangyang, CUI Penglu. One-dimensional modified UH constitutive model considering nonlinear rheological behavior[J]. Journal of Harbin Institute of Technology, 2020, 52(11): 107-112. DOI: 10.11918/201904113.

### 文章历史

One-dimensional modified UH constitutive model considering nonlinear rheological behavior
LIU Zhongyu, ZHANG Jiachao, XIA Yangyang, CUI Penglu
School of Civil Engineering, Zhengzhou University, Zhengzhou 450001, China
Abstract: In view of the nonlinear rheological characteristics of saturated clayey soil, the secondary consolidation coefficient was assumed as a hyperbolic function of the logarithm of time, and a modified secondary consolidation equation was proposed. Based on this idea, the unified hardening (UH) constitutive model was modified. To verify the effectiveness of the modified UH constitutive model, by taking a kind of reconstituted clayey soil in Henan province as an example, a series of one-dimensional rheological oedometer tests with one-way drainage were carried out. Test results illustrate that there was still some pore water pressure to be dissipated in the soil sample, when the primary consolidation determined by the Cassagrande method was completed. Then, the modified UH constitutive model was applied to simulate the measured data obtained at different loading stages, and results show that the model could fit the data well. Finally, in order to further verify the applicability of the model, some oedometer test results reported in the literature were simulated.
Keywords: nonlinear rheology    secondary consolidation coefficient    time effect    constitutive model    oedometer test

 $\Delta e = {C_\alpha }{\rm{lg}}(t/{t_1}).$ (1)

 $\Delta e = \beta {\rm{lg}}[(t + {t_0})/{t_0}].$ (2)

1 UH模型修正及非线性流变参数求解 1.1 UH模型的修正

 ${\rm{d}}{\varepsilon _{\rm{v}}} = \left\{ {\begin{array}{*{20}{l}} {{\rm{d}}\varepsilon _{\rm{v}}^e + {\rm{d}}\varepsilon _{\rm{v}}^{{\rm{sp}}} + {\rm{d}}\varepsilon _{\rm{v}}^{{\rm{tp}}},{\rm{d}}{\sigma ^\prime } \ge 0,}\\ {{\rm{d}}\varepsilon _{\rm{v}}^e + {\rm{d}}\varepsilon _{\rm{v}}^{{\rm{tp}}},{\rm{d}}{\sigma ^\prime } < 0.} \end{array}} \right.$ (3)
 ${\rm{d}}\varepsilon _{\rm{v}}^{\rm{p}} = \left\{ {\begin{array}{*{20}{l}} {{\rm{d}}\varepsilon _{\rm{v}}^{{\rm{sp}}} + {\rm{d}}\varepsilon _{\rm{v}}^{{\rm{tp}}},{\rm{d}}{\sigma ^\prime } \ge 0,}\\ {{\rm{d}}\varepsilon _{\rm{v}}^{{\rm{tp}}},{\rm{d}}{\sigma ^\prime } < 0.} \end{array}} \right.$ (4)

 ${{\rm{d}}\varepsilon _{\rm{v}}^{\rm{e}} = \frac{{{C_{\rm{S}}}}}{{{\rm{ln}}10(1 + {e_0})}}\frac{{{\rm{d}}{\sigma ^\prime }}}{{{\sigma ^\prime }}},}$ (5)
 ${{\rm{d}}\varepsilon _{\rm{v}}^{{\rm{sp}}} = \frac{{{C_{\rm{C}}} - {C_{\rm{S}}}}}{{{\rm{ln}}10(1 + {e_0})}}\frac{{{M^4}}}{{M_{\rm{f}}^4}}\frac{{{\rm{d}}{\sigma ^\prime }}}{{{\sigma ^\prime }}},}$ (6)
 ${{\rm{d}}\varepsilon _{\rm{v}}^{{\rm{tp}}} = \frac{{{C_\alpha }}}{{{\rm{ln}}10(1 + {e_0})}}\frac{{{\rm{d}}t}}{{{t_a} + {t_0}}}.}$ (7)

 ${M = 6{\rm{sin}}\varphi /(3 - {\rm{sin}}\varphi ),}$ (8)
 ${{M_{\rm{f}}} = 6[\sqrt {\chi /R(1 + \chi /R)} - \chi /R],}$ (9)
 ${\chi = {M^2}/[12(3 - M)],}$ (10)
 $R = {\sigma ^\prime }/\sigma _0^\prime {\rm{exp}}[ - {\rm{ln}}10\varepsilon _{\rm{v}}^{\rm{p}}(1 + {e_0})/({C_{\rm{C}}} - {C_{\rm{S}}})].$ (11)

 $({t_{\rm{a}}} + {t_0})/{t_0} = {R^{ - \alpha }}.$ (12)

 ${C_\alpha }(t) = \frac{{{C_{\alpha 0}}}}{{1 + {C_{\alpha 0}}/A{\rm{lg}}(t + {t_0})}}.$ (13)

 $\Delta e = \frac{{{C_{\alpha 0}}{\rm{lg}}({t_a} + {t_0})}}{{1 + ({C_{a0}}/A){\rm{lg}}(t + {t_0})}}.$ (14)

t→∞，则ΔeA，即A就是由流变引起的孔隙比减小值的极限，为可通过试验确定的有限值.这样就不会出现因流变因素而导致的土体被无限压缩的问题.

 ${\rm{d}}\varepsilon _{\rm{v}}^{{\rm{tp}}} = - L\frac{{{\rm{d}}t}}{{t + {t_0}}} + N\frac{{{\rm{d}}{t_a}}}{{{t_a} + {t_0}}}.$ (15)

 ${\rm{d}}\varepsilon _{\rm{v}}^{{\rm{tp}}} = \frac{1}{{{\rm{ln}}10(1 + {e_0})}}\frac{{{C_{\alpha 0}}}}{{[1 + ({C_{\alpha 0}}/A){\rm{lg}}(t + {t_0})]}}\frac{{{\rm{d}}{t_{\rm{a}}}}}{{{t_{\rm{a}}} + {t_0}}}.$ (16)

1.2 非线性流变参数求解

 $\frac{{{\rm{lg}}(t + {t_0})}}{{\Delta e}} = \frac{1}{A}{\rm{lg}}(t + {t_0}) + \frac{1}{{{C_{\alpha 0}}}}.$ (17)

2 试验

 图 1 孔隙比与时间的变化曲线 Fig. 1 Relation between void ratio and time
 图 2 试样孔压随时间变化关系 Fig. 2 Relation between pore pressure and time

3 修正UH模型的验证 3.1 河南某地黏土

 图 3 孔隙比与时间的变化曲线 Fig. 3 Relation between void ratio and time
3.2 香港黏土

Yin[29]曾对香港地区的黏土进行过固结试验，部分实验数据见图 4.据此，Yin给出了一个非线性流变的计算公式及相应EVP模型参数的确定方法.Le等[37]认为Yin[29]的方法在确定模型参数时有一定的局限性，因此，建议了TRRLS方法，其模拟结果见图 4.本文按上述修正UH本构模型也对Yin[29]的试验数据进行模拟，所用参数见表 2.其中，不同荷载等级下的试样高度H0、压缩指数CC=0.525、回弹指数CS=0.036 1、初始孔隙比e0均参考Le等[37]模拟所用参数取值，非线性流变参数Cα0A根据Yin[29]试验数据按照1.2节计算方法获得，初始超固结参数R0和渗透系数k则根据试算选用，黏土的有效内摩擦角取为15°.模拟结果也示于图 4.不难发现，本文修正UH本构模型也能够较好地描述香港黏土的流变固结特性.

 图 4 竖向应变与时间的变化关系 Fig. 4 Relation between vertical strain and time

3.3 萧山黏土

 图 5 竖向变形与时间的关系 Fig. 5 Relation between vertical deformation and time

4 结论

1) 次固结系数的时间效应是影响流变非线性过程的重要因素，考虑次固结系数的时间效应，对完善非线性流变本构关系具有重要意义.

2) 次固结系数与时间对数的双曲线表达式(13)可以较好地描述黏性土的非线性流变特性.

3) 基于次固结系数时间效应修正的UH本构模型可以较好地描述多地黏性土的一维流变固结过程，因而具有较广的适用性.

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