基于精细化数值模拟的EPS轻质土宏细观变形机理研究

申志福; 沈光明; 王志华; 高洪梅

doi:10.11779/CJGE20220136

基于精细化数值模拟的EPS轻质土宏细观变形机理研究 English Version

南京工业大学交通运输工程学院，江苏南京 210009

基金项目:

国家自然科学基金青年基金项目 51908284

国家自然科学基金面上项目 52178336

江苏省科技厅自然科学基金青年基金项目 BK20190667

江苏省高等学校自然科学研究面上项目 19KJB560015

江苏省高等学校自然科学研究重点项目 18KJA560002

江苏高校“青蓝工程”中青年学术带头人项目资助项目

详细信息

作者简介:
申志福(1988—)，男，四川绵阳人，博士，副教授，主要从事宏微观土力学方面研究。E-mail: zhifu.shen@njtech.edu.cn

通讯作者:
高洪梅（E-mail: hongmei54@163.com）

中图分类号: TU34
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出版历程
- 收稿日期: 2022-02-07
- 网络出版日期: 2023-05-18
- 刊出日期: 2023-04-30

Macro- and meso-scopic deformation mechanisms of EPS-mixed soils based on refined numerical simulation

School of Transportation Engineering, Nanjing Tech University, Nanjing 210009, China

摘要

摘要: EPS轻质土是双固相组分（水泥土与EPS颗粒）、具有特殊细观结构的混合土。当前对其宏观力学特性研究较多，而对细观力学响应规律研究甚少。为此，分别在Mohr-Coulomb模型和Drucker-Prager模型框架内，基于水泥土和EPS材料试验结果规律总结，发展了二者的简单实用本构模型；基于水泥土和EPS材料界面剪切试验，总结了界面剪切硬化/软化规律；对EPS轻质土三轴剪切试验进行精细化数值模拟，再现了EPS轻质土宏观应力-应变响应规律和试样变形模式。基于精细化模拟分析发现，EPS轻质土的整体剪切、局部鼓胀、整体均匀3种宏观变形模式是细观力学响应的结果，EPS颗粒与水泥土两种材料力学特性的差异引起试样内部应力、应变的非均匀分布，EPS颗粒的非均匀排列强化应力、应变非均匀分布程度，两种因素共同决定试样宏观变形的非均匀性。
- EPS轻质土 /
- 宏细观机理 /
- 三轴剪切试验 /
- 变形模式 /
- 精细化数值模拟
Abstract: The EPS-mixed soils are composed of two solid phases (cemented soils and EPS beads) with the unique mesoscopic structure. The macroscopic behaviour of the EPS-mixed soils has been widely investigated so far, but the focus has seldom been put on the mesoscopic behaviour. In this study, following the frameworks of Mohr-Coulomb model and Drucker-Prager model respectively, the constitutive descriptions of the cemented soils and the EPS materials are developed based on their mechanical test results. Besides, the strain hardening/softening laws of the cemented soil-EPS material interface are summarized based on the interface shear tests. The refined numerical simulations of triaxial shear tests on the EPS-mixed soils are carried out, with which the macroscopic stress-strain behavior and deformation modes of the EPS-mixed soil specimens are replicated. The refined numerical simulations reveal that the three types of deformation modes of the specimens (shear banding, local lateral expansion, overall uniform deformation) can be attributed to the non-uniform mesoscopic mechanical responses. The distinct mechanical behavior of the cemented soils and the EPS materials is the origin of non-uniform stress and strain distributions, and such non-uniformity is enhanced by the non-uniform spatial distribution of the EPS beads. The two factors collaboratively determine the non-uniformity of the macroscopic deformation observed for the EPS-mixed soil specimen.
- EPS mixed soil /
- macro- and meso-scopic mechanism /
- triaxial shear test /
- deformation mode /
- refined numerical simulation

HTML全文

宋二祥老师对敝人《稳定安全系数计算公式中荷载与抗力错位影响探讨》^[1]（以下简称原文）提出了宝贵的指导及讨论意见,非常感谢！

宋文提出“边坡稳定安全系数的定义......是边坡土体所具有的抗剪强度与保持边坡刚好稳定所需要的强度之比,所以没有抗力与荷载错位的问题”。正如宋老师在其文献[4]^[2]所指出的,边坡稳定安全系数目前主要有两种定义方法：①为抗滑力矩与下滑力矩之比（可简化为抗力荷载比）,相应的稳定安全系数计算方法一般采用单一安全系数法；②即为上述的抗剪强度比,毕肖普、简布等将之定义为滑动面上的抗剪强度与实际产生的剪应力之比,相应的稳定安全系数计算方法一般采用强度（抗剪强度）折减法。宋文认为自然边坡等土工结构的稳定更适合采用第二种定义形式而不是第一种。原文没有讨论哪种安全系数定义更合理,讨论的是业界按第一种定义编写的安全系数计算公式有时并不完全符合第一种定义这种现象,现在讨论边坡稳定工程中按第二种定义会不会有抗力与荷载错位现象及强度折减法适用性问题。

仍以瑞典条分法为例,当滑弧中心点O位于边坡上方时,如图1所示,土条1～（m-1）的重力产生下滑力 $\sum_{i = 1}^{m - 1} G ti$ ,土条m～n的重力产生抗滑力 $\sum_{i = m}^{n} G_{ti}$ ,两者作用方向相反,稳定安全系数K计算公式按第一种定义、当抗力与荷载发生原文所示第1类错位现象时可写为

图 1 瑞典条分法边坡稳定分析简图

Figure 1. Sketch about slope stability analysis by Swedish Slicing Method

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$\sum_{i = 1}^{m - 1} G_{t i} - \sum_{i = m}^{n} G_{t i} = \frac{\sum_{i = 1}^{n} (G_{n i} \tan φ_{i} + c_{i} l_{i})}{K}$ 。

(1)

按笔者建议的抗力与荷载归位时可写为

$\sum_{i = 1}^{m - 1} G_{t i} = \sum_{i = 1}^{n} \frac{G_{n i} \tan φ_{i} + c_{i} l_{i}}{K} + \frac{\sum_{i = m}^{n} G_{t i}}{K}$ ,

(2)

按强度折减法可写为

$\sum_{i = 1}^{m - 1} G_{t i} = \sum_{i = 1}^{n} (G_{n i} \frac{\tan φ_{i}}{K} + \frac{c_{i}}{K} l_{i}) + \frac{\sum_{i = m}^{n} G_{t i}}{1}$ 。

(3)

将式（1）～（3）进行比较可知：

（1）式（3）与式（1）相同。式（3）在形式上用强度指标除以K,直观地表达了强度折减法,因为K只涉及到抗剪强度而没有涉及其它抗力或荷载,即 $\sum_{i = m}^{n} G_{ti}$ 等作为荷载还是抗力都不会影响到K计算结果,也就不存在错位与否,故从第二种定义角度来看,式（1）所表达的第1类错位问题不存在。

（2）原文中总结了抗力与荷载错位现象的3类基本形式及2类组合形式（原文中式（5）～（9））,其中第2类形式以图1为例可写为

$\sum_{i = 1}^{m - 1} G_{t i} = \sum_{i = m}^{n} G_{t i} = \sum_{i = 1}^{n} (G_{n i} \frac{\tan φ_{i}}{K} + \frac{c_{i}}{K} l_{i})$ 。

(4)

第2类错位现象把部分抗力 $\sum_{i = m}^{n} G_{t i}$ 作为荷载直接与荷载 $\sum_{i = 1}^{m - 1} G_{t i}$ 相加,可认为是对抗力与荷载概念的理解有误或故意为之（目的是在目标安全系数K维持不变时提高设计抗力、以使工程变得更安全）,这与采用第一种或第二种定义无关,故采用第二种定义亦不能解决；第3类错位现象对部分荷载也除以了安全系数,采用第二种定义时因为安全系数不涉及荷载,故也不存在这类错位现象；第4类错位现象是第1类与第3类的组合,从第二种定义角度来看也没有错位问题；第5种错位现象是第2类与第3类的组合,存在着与第2类同样的问题,具体不再赘述。总之,在对抗力与荷载的概念理解及应用无误时,采用第二种定义的安全系数计算公式,如宋文所言,确实不存在采用第一种定义时的抗力与荷载错位问题。

（3）和式（3）及式（1）相比,式（2）对 $\sum_{i = m}^{n} G_{t i}$ 项等所有抗力均除以了同一安全系数K,符合单一安全系数法规定的安全系数为抗力与荷载之比这个定义,故为单一安全系数法。从概率设计的角度,可认为式（3）中 $\sum_{i = m}^{n} G_{t i}$ 项的抗力分项系数为1,而抗剪强度的抗力分项系数为K,因两者不等且通常K>1,故式（3）表达的强度折减法具有了概率含义,并非传统意义上的单一安全系数法。

采用强度折减法时：

（1）因岩土重力的变异性小于抗剪强度的,式（3）中 $\sum_{i = m}^{n} G_{t i}$ 项对应的抗力分项系数取1,小于K看起来也合理,但仅取1,没有一点安全裕度是否合适?式（3）比式（2）计算得到的K值更高,对于工程而言更偏于不安全。

（2）如图1所示,按式（3）计算第二种定义的安全系数, $\sum_{i = 1}^{m - 1} G_{t i}$ = $\sum_{i = m}^{n} G_{t i}$ 时K值无穷大, $\sum_{i = 1}^{m - 1} G_{t i}$ < $\sum_{i = m}^{n} G_{t i}$ 时K值为负,但显然安全系数不能无穷大甚至为负。这种情况而非完全虚拟,例如土石坝拦挡淤泥工程, $\sum_{i = m}^{n} G_{t i}$ 项抗力由土石坝产生,土石坝足够稳定时就有可能发生类似计算结果；再如原文所示的锚固结构,锚杆提供的抗力足够大时也可能发生类似计算结果,也就是说当岩土体抗剪强度以外的因素产生了抗滑力且较大时,式（3）所示的强度折减法也可能会产生安全系数计算结果不合理问题,如同发生抗力与荷载错位现象一样；但如果按原文所建议的抗力与荷载归位后的计算公式则没有类似问题。故强度折减法可能更适用于仅由岩土体抗剪强度提供抗滑力时的自然边坡稳定计算,这也许就是现有技术标准中不太采用第二种定义形式对有支挡结构的人工边坡进行稳定验算的主要原因。

总结：①原文边坡稳定安全系数计算公式中的抗力与荷载错位现象是按第一种定义总结的,部分错位现象是对抗力与荷载概念的理解及应用不当造成的,采用第二种定义并不能解决因此而导致的安全系数不准确问题；②在对抗力与荷载概念的理解及应用无误时,采用第二种定义则不存在第一种定义时抗力与荷载错位问题,宋文观点是正确的；③有岩土体抗剪强度以外的因素提供抗滑力且较大时,强度折减法计算结果与发生了错位现象的抗力荷载比法一样,都存在着稳定安全系数计算结果不合理现象,对有支挡的人工边坡有时可能不太适用。

以上观点不妥之处,敬请宋老师及读者们继续批评指正。

图 1 水泥土的三轴剪切力学特性（m_c/m_s = 8%）

Figure 1. Mechanical behaviors of cemented soils under triaxial loading (m_c/m_s = 8%)

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图 2 水泥土发挥强度指标随等效塑性剪应变的变化

Figure 2. Variation of mobilized strength indices with equivalent plastic shear strain for cemented soils

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图 3 EPS材料的典型三轴剪切力学响应（ρ=20 kg/m³）^[30]

Figure 3. Typical mechanical behaviors of EPS materials under triaxial shear loading

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图 4 EPS材料的剪切硬化拟合参数b₁，b₂的变化（ρ=30 kg/m³，数据源自文献[27]）

Figure 4. Variation of b₁ and b₂ in shear hardening law of EPS materials (ρ=30kg/m³, data adapted from Reference [27])

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剪切塑性势参数 ${q_\psi }$ 随围压的变化

Variation of parameter ${q_\psi }$ in shear plastic potential function with confining pressure

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图 6 EPS轻质土的三轴剪切数值模型

Figure 6. Numerical model for EPS-mixed soils under triaxial shear loading

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图 7 各因素对EPS轻质土力学特性的影响

Figure 7. Effects of various factors on mechanical behavior of EPS-mixed soils

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图 8 EPS轻质土模拟与试验剪切变形

Figure 8. Simulated and tested deformations of EPS-mixed soils

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图 9 EPS轻质土内部的剪应力分布(m_c/m_s=6%, V_E/V_S=25%, σ₃=50 kPa)

Figure 9. Distribution of deviator stress in EPS-mixed soils (m_c/m_s= 6%, V_E/V_S=25%, σ₃=50 kPa)

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图 10 EPS轻质土内部的剪应变分布(m_c/m_s=6%, V_E/V_S=25%, σ₃=50 kPa)

Figure 10. Distribution of deviator strain in EPS-mixed soils (m_c/m_s= 6%, V_E/V_S=25%, σ₃=50 kPa)

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表 1 不同水泥掺入比下水泥土发挥剪胀角公式的拟合参数

Table 1 Fitting parameters for mobilized dilation angle of cemented soils under different cement contents

水泥掺入
比/% a₁ a₂ a₃ a₄ a₅

6 398 7.0 0.40 -0.020 -56

8 177 3.2 0.72 -0.030 -53

10 70.0 1.3 0.75 -0.008 -57

下载: 导出CSV

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