基于等效时间的双屈服面三维流变模型

胡亚元; 丁盼

doi:10.11779/CJGE202001006

基于等效时间的双屈服面三维流变模型 English Version

胡亚元,
丁盼

浙江大学滨海和城市岩土工程研究中心,浙江　杭州310058

详细信息

作者简介:
胡亚元（1968— ）,男,博士,副教授,主要从事环境土工和土体本构关系的研究工作。E-mail：huyayuan@zju.edu.cn

中图分类号: TU43
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出版历程
- 收稿日期: 2019-01-15
- 网络出版日期: 2022-12-07
- 刊出日期: 2019-12-31

Three-dimensional rheological model for double-yield surface based on equivalent time

Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China

摘要

摘要: 为了同时描述土体剪缩剪胀及流变特性,运用Yin-Graham等效时间法建立了双屈服面三维流变模型。首先,以Yin-Graham三维流变方程作为反映剪缩机制的第一屈服面流变方程；其次,以Matsuoka-Nakai屈服准则作为反映剪胀机制的第二屈服面,以黏塑性功为硬化参数,采用非相关联流动法则,借鉴Mesri建模思路构建应力-黏塑性功-时间关系,利用等效时间法得到应力-黏塑性功-黏塑性功速率关系式,借助Perzyna过应力理论建立第二屈服面三维流变方程；再次,按照双屈服面模型理论将以上两个流变方程结合起来,提出一个基于等效时间的双屈服面三维流变模型,并利用经典的四阶Rung-Kutta方法编制差分计算程序,获得流变模型的数值解答；最后,利用加拿大膨润土及香港重塑海相沉积土三轴固结不排水流变试验将预测值与实测值进行对比,以验证该模型在流变试验中的适用性。结果表明：建立的流变模型可以较好地模拟不排水流变试验多级加载和单级加载发展过程以及土体剪缩剪胀特性。
- 等效时间 /
- 剪缩剪胀特性 /
- 双屈服面 /
- 流变模型
Abstract: In order to describe shear contractibility, dilatancy and rheological properties of soils, Yin-Graham’s equivalent time method is used to derive a three-dimensional rheological model for double-yield surface. Firstly, Yin-Graham’s three-dimensional rheological equation is used as the first yield surface rheological equation reflecting the shear-contraction mechanism. Secondly, Matsuoka-Nakai yield criterion is used as the second yield surface reflecting the dilatancy mechanism, viscoplastic work is used as hardening parameter and the non-associated flow rule is adopted, the stress-viscoplastic work-time relationship is proposed using Mesri’s modeling idea, stress-viscoplastic work-viscoplastic work rate relationship is obtained according to the equivalent time method, and the second yield surface three-dimensional rheological equation is established under Perzyna’s over-stress theory. Again, according to the theory of double-yield surface model, a three-dimensional rheological model of double-yield surface is proposed by combining the two rheological equations. The classical fourth-order Rung-Kutta method is used to compile the difference calculation program, and the numerical solution of the rheological model is obtained. Finally, the predictions are compared with the measured values by using triaxial consolidation undrained rheological test data of Canadian bentonite and remoulded Hong Kong marine deposits to verify the applicability of the model in rheological tests. The results show that the model can simulate the development process of multi-stage and single-stage loading in undrained rheological tests, and can reflect dilatancy and shear contractibility of soils.
- equivalent time /
- dilatancy and shear contractibility /
- double-yield surface /
- rheological model

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图 1 双屈服面模型

Figure 1. Double-yield surface model

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图 2 $(k - k_{t})$ 与 $W^{p}$ 关系图

Figure 2. Relationship between $(k - k_{t})$ and $W^{p}$

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图 3 $\ln (W^{vp2})$ 与 $l n [(24 + t_{e}) / 24]$ 关系图

Figure 3. Relationship between $\ln (W^{vp2})$ and $l n [(24 + t_{e}) / 24]$

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图 4 等效时间线示意图

Figure 4. Schematic diagram of equivalent time line

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图 5 $\ln (W^{vp2})$ 与 $l n (t_{a} / t_{r})$ 关系图

Figure 5. Relationship between $\ln (W^{vp2})$ and $l n (t_{a} / t_{r})$

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图 6 Fortran程序框图

Figure 6. Flow chart of Fortran

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图 7 实测与预测结果对比

Figure 7. Comparison between measured and predicted results

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图 8 剪应变与时间关系图

Figure 8. Relationship between shear strain and time

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图 9 $p^{'}$ - $q$ 空间有效应力路径图

Figure 9. Effective stress paths in $p^{'}$ - $q$ space

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图 10 剪应变与时间关系图

Figure 10. Relationship between shear strain and time

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图 11 $p^{'}$ - $q$ 空间有效应力路径图

Figure 11. Effective stress paths in $p^{'}$ - $q$ space

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表 1 试样的物理特性指标^[23]

Table 1 Physical properties of sample

土样	重度/(kN·m^-3)	含水率/%	饱和度/%	土粒相对密度	比容V₀	泊松比 $ν$
CB	16.46	22.3	99.4	2.70	1.609	0.3

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表 2 部分模型参数^[23]

Table 2 Part of model parameters

$φ^{'}$ /(°)	$λ / V_{0}$	$κ / V_{0}$	$ψ / V_{0}$	${p^{'}}_{mo}$ /kPa	t₀/h	$ε_{vo}^{vp1}$
15	0.05	0.025	0.0025	1900.77	24	0

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表 3 模型参数

Table 3 Model parameters

m	(k-k_t)_ult	E_i	A	t_r/h
0.02018	0.7658	0.0317	0.42	24

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表 4 试样物理特性指标

Table 4 Physical properties of sample

土样	含水率/%	饱和度/%	土粒相对密度	比容V₀	泊松比 $ν$
RHKMD	48.3	98	2.66	2.216	0.3

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表 5 模型参数

Table 5 Model parameters

$λ / V_{0}$	$κ / V_{0}$	$ψ / V_{0}$	${p^{'}}_{mo}$ /kPa	t₀/h	$ε_{vo}^{vp1}$
0.0793	0.018	0.0025	15.2	24	0
$φ^{'}$	m	${(k - k_{t})}_{ult}$	E_i	A	t_r/h
31.5°	0.0328	4.003	0.2565	0.58	24

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