粗粒土在三向卸载时的强度特性试验研究

2020-05-19 15:06:35 《土木建筑与环境工程》 2020年2期

施维成 朱俊高 胡锡鹏 代国忠 李雄威 李书进

摘 要: 卸載是引起岩土材料破坏的常见工况,为了研究粗粒土在不同中主应力系数b情况下三向卸载时的强度特性,使用真三轴仪对粗粒土进行偏应力q保持300 kPa不变,球应力p不断减小的等q、等b三向等量卸载试验,分析三向卸载条件下粗粒土的强度特性,研究常用强度准则对卸载条件粗粒土的适用性。试验结果表明:在三向等量卸载条件下,粗粒土的强度参数与中主应力系数b有关;对于不同的b值,b=0时的内摩擦角φb最小,破坏应力比Mb最大;破坏应力比Mb随着b的增大而减小,且随着b的增大,减小的梯度在逐渐减小;内摩擦角φb在b值较小时随着b的增大而增大,在b值较大时随着b的增大而减小,3个方向剪切的共同影响可以解释这一变化规律;Matsuoka-Nakai强度准则、粗粒土应力不变量强度准则和Lade-Duncan强度准则这3个强度准则都能反映内摩擦角φb与b之间的这一规律,其中,Matsuoka-Nakai强度准则在b值较小时与试验结果较为接近,粗粒土应力不变量强度准则在b值较大时与试验结果较为接近;粗粒土角隅函数强度准则与等q、等b试验结果较为吻合。

关键词: 强度准则;粗粒土;强度参数;卸载;加载

中图分类号:TU447    文献标志码:A   文章编号:2096-6717(2020)02-0010-07

Experimental study on the strength characteristics of coarse-grained soil under three-dimensional unloading

Shi Weicheng1, Zhu Jungao2, Hu Xipeng3, Dai Guozhong1, Li Xiongwei1, Li Shujin1

(1.School of Civil Engineering & Architecture, Changzhou Institute of Technology, Changzhou 213032, Jiangsu, P.R.China;2.Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering,Hohai University,Nanjing 210098, P.R.China;3.CCCC Third Highway Engineering CO., LTD, Beijing 101300, P.R.China)

Abstract:  Unloading is a common condition that causes damage to geotechnical materials.In order to investigate the strength characteristics of the coarse-grained soil under three-dimensional unloading in different cases of the coefficient of intermediate principal stress b, several three-dimensional equal unloading tests in which the spherical stress p decreases with constant b and constant deviatoric stress q (300 kPa) were performed on coarse-grained soil by using true triaxial apparatus.The strength characteristics of coarse-grained soil were analyzed and the applicability of the commonly used strength criterions was studied.The test result shows that under the condition of three dimensional equal unloading, the strength parameter of coarse-grained soil is related to the coefficient of intermediate principal stress b.When b equals to 0, the internal friction angle φb is the minimum and the failure stress ratio Mb is the maximum.The stress ratio at failure decreases with the increase of b and, as b increases the gradient decreases gradually.The internal friction angle increases with b for small b values while decreases with the increase of b for large values.This can be explained by the co-impact of the shearing in three directions.All of the three strength criterions, including the Matsuoka-Nakai criterion, the criterion expressed by stress invariants of coarse-grained soil and Lade-Duncan criterion, can response the law between φb and b.It is found that the Matsuoka-Nakai criterion is the closest to the test results for small b values while the strength criterion expressed by stress invariants of coarse-grained soil is the closest to the test results for large b values.It is also found that the corner function strength criterion of coarse-grained soil is consistent with the experimental results.

当b继续增大,σ2-σ3继续增大,“因素2”使剪切强度参数减小的影响也繼续增大;而σ1-σ2继续减小,在σ3侧向约束下,σ1、σ2间的剪切作用继续减小,“因素3”继续使剪切强度参数增大;“因素1”中的σ2侧向约束继续增大,也是使剪切强度参数增大的因素。当b增大到某一值时(如试验中b=0.5时),“因素2”使剪切强度参数减小的影响与“因素3”、“因素1”使剪切强度参数增大的影响相同时,内摩擦角达到最大值。

当b增大到较大值时(如试验中b=0.75时),σ2-σ3增大到较大值,而σ1-σ2则减小到较小值,此时“因素2”使剪切强度参数减小的影响超过“因素3”、“因素1”使剪切强度参数增大的影响,内摩擦角较b=0.5时开始减小。

当b=1时,σ1=σ2,σ1-σ2=0,σ2-σ3=σ1-σ3,“因素3”不会对剪切强度参数产生影响;“因素1”和“因素2”都是在σ1侧向约束下的剪切作用σ1-σ3。和b=0时相比,σ1的侧向约束要强于σ3的侧向约束,故b=1时的剪切强度参数比b=0时的大。

4 强度准则适用性研究

笔者曾根据粗粒土的三向加载试验得到粗粒土应力不变量强度准则和角隅函数强度准则,将这些强度准则与等q、等b试验得到的试验结果进行比较,以验证其对粗粒土三向卸载情况的适用性。

4.1 应力不变量强度准则

笔者曾提出应力不变量表示的粗粒土强度准则[17],如式(1)所示。

I31+4I1I2 I3 =kf (1)

式中:I1、I2、I3分别为第一、第二、第三应力不变量,kf为常量,与材料性质有关。

对于粗粒土,假设凝聚力c=0,有[17]

kf= 63-63sin φ0+5sin2φ0+3sin3φ0 1-sin φ0-sin2φ0+sin3φ0

(2)

式中:φ0为b=0时的内摩擦角。

Lade和Duncan根据蒙特里砂试验结果,提出Lade-Duncan强度准则[18],表达式为

I31 I3 =kf (3)

式中

kf= (3-sin φ0)3 1-sin φ0-sin2φ+sin3φ0  (4)

Matsuoka-Nakai强度准则[19]表达式为

I1I2 I3 =kf (5)

式中kf= 9-sin2φ0 1-sin2φ0  (6)

将上述3个强度准则表示成φb与b的形式,并将π平面上的形状画出,与粗粒土三向卸载的试验结果进行比较,如图3所示。粗粒土三向卸载试验结果显示,b值较小时,内摩擦角φb随着b的增大而增大;b值较大时,内摩擦角φb随着b的增大而减小。显然,3个强度准则都能反映这一规律,Matsuoka-Nakai强度准则在b值较小时与试验结果较为接近,粗粒土应力不变量强度准则在b值较大时与试验结果较为接近。

4.2 角隅函数强度准则

土的三维强度准则通常可用角隅函数表示为

q p  f=Mc·g(b) (7)

式中:Mc为b=0时的破坏应力比。

笔者曾根据粗粒土的加载试验结果得到一个粗粒土角隅函数强度准则[20]

g(b)= 1 (1+k)-k·(b-1)2  (8)

式中:k是与土的性质有关的参数,可表示为[21-22]

k=1.462sin φ0-0.523 2 (9)

图4为粗粒土角隅函数强度准则和等q、等b试验结果,由图4可以看出,粗粒土角隅函数强度准则与等q、等b试验结果较为吻合。

5 结论

使用真三轴仪对粗粒土进行了等q、等b三向等量卸载试验,分析了三向卸载条件下粗粒土的强度特性,研究了常用强度准则对卸载条件粗粒土的适用性,得出以下结论:

1)不同b的粗粒土等q、等b三向等量卸载条件下,粗粒土的强度参数与中主应力系数b有关;b=0时的内摩擦角φb最小,破坏应力比Mb最大;破坏应力比Mb随着b的增大而减小,且随着b的增大,减小的梯度在逐渐减小;内摩擦角φb在b值较小时随着b的增大而增大,在b值较大时随着b的增大而减小。

2)三向主应力σ1、σ2、σ3共同作用下的剪切强度参数可以认为是受3个方向剪切的共同影响,进而可以解释上述内摩擦角φb随b的变化规律。

3)Matsuoka-Nakai强度准则、粗粒土应力不变量强度准则和Lade-Duncan强度准则这3个强度准则都能反映内摩擦角φb随b的变化规律,Matsuoka-Nakai强度准则在b值较小时与试验结果较为接近,粗粒土应力不变量强度准则在b值较大时与试验结果较为接近。

4)粗粒土角隅函数强度准则与等q、等b试验结果较为吻合。

致谢:

感谢江苏省高校“青蓝工程”、江苏省高校优秀中青年教师和校长境外研修计划项目资助。

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(編辑 王秀玲)

收稿日期:2019-07-18

基金项目:  国家自然科学基金 (51678083);常州市科技支撑计划(CE20195034)

作者简介:  施维成(1982- ),男,博士,教授,主要从事土的基本性质研究,E-mail: [email protected]

Received: 2019-07-18

Foundation items:  National Natural Science Foundation of China (No. 51678083); Changzhou Science and Technology Support Program (No. CE20195034)

Author brief:  Shi Weicheng (1982- ), PhD, professor, main research interest: basic properties of soil, E-mail: [email protected]