基于统计损伤修正的冻结砂-黏混合土改进 Duncan-Chang 模型

Improved Duncan-Chang model for frozen sand-clay mixed soil based on statistical damage correction

摘要

为描述冻结砂-黏混合土的偏应力一应变关系，进行不同含砂量冻结砂-黏混合土的冻土三轴压缩试验。基于改进的 Duncan-Chang 模型（D-C 模型），引人统计损伤理论，拟合三轴压缩试验结果，分别建立以 Mises 强度准则和应变发展为微元强度变量的统计损伤修正模型，对比计算结果与试验数据。结果表明：冻结砂一黏混合土偏应力峰值随含砂量的增加而增加，偏应力一应变曲线由应变硬化型逐渐过渡到应变软化型的临界含砂量为 50% 。当含砂量介于 20 \mathrm{\%} \sim 60 \mathrm{\%} 时，基于统计损伤理论的修正改进 D-C 模型能有效拟合应变硬化型曲线和具有轻微应变软化现象的偏应力一应变曲线。当含砂量为 90% 时，基于应变发展的统计损伤修正模型的偏应力峰值与试验结果相差 3% ，具有较强适用性。该结果为不同微元强度变量的统计损伤修正模型提供参考。

Abstract

To describe the stress-strain relationship of frozen sand clay mixed soil, triaxial compression tests were conducted on frozen soil with different sand contents. Based on the improved Duncan-Chang model (D-C model), statistical damage theory is introduced to fit the results of triaxial compression tests. Statistical damage correction models with Mises strength criteria and strain development as micro element strength variables are established, and compared with experimental data. The results show that the peak value of deviatoric stress in frozen mixed soil increases with the increase of sand content, and the critical sand content of the deviatoric stress-strain curve gradually transitions from strain hardening type to strain softening type. When the sand content is between 20% and 60%, the improved D-C model based on statistical damage correction can effectively fit the strain hardening curve and the deviatoric stress-strain curve with slight strain softening phenomenon. When the sand content is 90%, the peak deviation stress of the statistical damage correction model based on strain development is 3% different from the experimental results, indicating strong applicability. This result provides a reference for statistical damage correction models with different micro element strength variables.

关键词

冻结砂-黏混合土 / 三轴压缩试验 / 改进 Duncan-Chang 模型 / 统计损伤理论 / 应变软化模型

Key words

frozen sand-clay mixed soil / triaxial compression test / improved Duncan-Chang model / statistical damage theory / strain softening model

参考文献

[1] 郝红永, 徐常晫, 郭晟豪, 等. 砂砾岩压缩破坏形态及影响因素分析[J]. 东北石油大学学报, 2022, 46(3):66-73.

[2] HAO Hongyong, XU Changzhuo, GUO Shenghao, et al. Analysis on compression failure characteristics and influencing factors of conglomerate[J]. Journal of Northeast Petroleum University, 2022, 46(3):66-73.

[3] 邓智, 程礼军, 潘林华, 等. 层理倾角对页岩三轴应力应变测试和纵横波速度的影响[J]. 东北石油大学学报, 2016, 40(1):33-39.

[4] DENG Zhi, CHENG Lijun, PAN Linhua, et al. Effect of bedding angle on shale triaxial stress,testing and velocity of P-wave and S- wave[J]. Journal of Northeast Petroleum University, 2016, 40(1):33-39.

[5] 姜自华, 姚兆明, 陈军浩. 含砂率和含水率对人工冻土单轴抗压强度的影响[J]. 矿业研究与开发, 2016, 36(12):47-50.

[6] JIANG Zihua, YAO Zhaoming, CHEN Junhao. Influence of sand ratio and water content on uniaxial compressive strength of artificial frozen soil[J]. Mining Research and Development, 2016, 36(12):47-50.

[7] 贾卫兵, 郭飞, 杨爱武. 考虑含砂量影响的砂一黏混合土应力一应变关系特性研究[J]. 工程地质学报, 2014, 22(6):1102-1108.

[8] JIA Weibing, GUO Fei, YANG Aiwu. Stress-strain relationships of sand-clay mixture with different sand contents[J]. Journal of Engineering Geology, 2014, 22(6):1102-1108.

[9] 张彬, 张晓雷, 田广宇. 含砂量对黏一砂混合土力学特性影响的试验研究及工程应用[J]. 水运工程, 2022(6):195-201.

[10] ZHANG Bin, ZHANG Xiaolei, TIAN Guangyu. Experimental study on effect of sand content on mechanical properties of clay sand mixed soil and engineering application[J]. Port & Waterway Engineering, 2022(6):195-201.

[11] 王壹敏, 陈志敏, 孙胜旗, 等. 基于邓肯一张模型的低液限粉质黏土一砂的强度规律[J]. 科学技术与工程, 2021, 21(8):3252-3257.

[12] WANG Yimin, CHEN Zhimin, SUN Shengqi, et al. The strength of the low-liquidlimit silty clay-sand in Duncan-Chang model[J]. Science Technology and Engineering, 2021, 21(8):3252-3257.

[13] 丁一, 冀卫东, 王旭东. 颗粒级配对混合土力学性质影响的试验研究[J]. 南京工业大学学报(自然科学版), 2018, 40(1):127-132.

[14] DING Yi, JI Weidong, WANG Xudong. Experimental study on effects of grain size distribution on mechanical properties of mixed soil[J]. Journal of Nanjing Tech University(Natural Science Edition), 2018, 40(1):127-132.

[15] 曹文贵, 方祖烈, 唐学军. 岩石损伤软化统计本构模型之研究[J]. 岩石力学与工程学报, 1998(6):628-633.

[16] CAO Wengui, FANG Zulie, TANG Xuejun. A study of statistical constitutive model for soft and damage rocks[J]. Chinese Journal of Rock Mechanics and Engineering, 1998(6):628-633.

[17] 伍文龙, 袁林娟, 张锐, 等. 基于统计损伤理论的邓肯一张修正模型研究[J]. 水利水电技术, 2017, 48(4):131-135.

[18] WU Wenlong, YUAN Linjuan, ZHANG Rui, et al. Study on statistical damage theory based modified Duncan-Chang model[J]. Water Resources and Hydropower Engineering, 2017, 48(4):131-135.

[19] 王松鹤, 刘奉银, 齐吉琳. 考虑冻融的粉质黏土统计损伤本构关系研究[J]. 西北农林科技大学学报(自然科学版), 2016, 44(12): 226-234.

[20] WANG Songhe, LIU Fengyin, QI Jilin. Statistical damage constitutive model for silty clay after freeze-thaw cycling[J]. Journal of Northwest A & F University(Natural Science Edition), 2016, 44(12):226-234.

[21] 秦庆词, 李克钢, 李明亮, 等. 非均质性岩石材料损伤失效准则及其失效行为研究[J]. 岩石力学与工程学报, 2021, 40(9):1812-1825.

[22] QIN Qingci, LI Kegang, LI Mingliang, et al. Study on damage failure criterion and failure behavior of non-homogeneous rock materials[J]. Chinese Journal of Rock Mechanics and Engineering, 2021, 40(9):1812-1825.

[23] 黄安邦, 魏良帅, 贾逸, 等. 基于邓肯一张模型的饱和土统计损伤模拟方法研究[J]. 水力发电, 2019, 45(4):28-32.

[24] HUANG Anbang, WEl Liangshuai, JIA Yi, et al. Statistical damage simulation method for saturated soil based on Duncan-Chang model[J]. Water Power, 2019, 45(4):28-32.

[25] 谭维佳, 魏云杰, 王俊豪, 等. 考虑基质吸力的非饱和土邓肯一张统计损伤修正模型[J]. 水文地质工程地质, 2022, 49(1):84-91.

[26] TAN Weijia, WEI Yunjie, WANG Junhao, et al. The Duncan-Chang statistical damage correction model of unsaturated soil considering matric suction[J]. Hydrogeology & Engineering Geology, 2022, 49(1):84-91.

[27] LI Z, CHEN J, MAO C. Experimental and theoretical investigations of the constitutive relations of artificial frozen silty clay[J]. Materials, 2019, 12(19):1-16.

[28] 赖远明, 程红彬, 高志华, 等. 冻结砂土的应力一应变关系及非线性莫尔强度准则[J]. 岩石力学与工程学报, 2007, 26(8):1612-1617.

[29] LAI Yuanming,CHENG Hongbin,GAO Zhihua,et al. Stress-strain relationships and nonlinear mohr strength criterion of frozen sand clay[J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(8):1612-1617.

[30] 李怀鑫, 晏长根, 林斌, 等. 黏土一混凝土组合体强度及全过程统计损伤模型[J/OL]. 吉林大学学报(工学版):1-10[2024-04-10]. https://doi.org/10.13229/j.cnki.jdxbgxb.20230253.

[31] LI Huaixin, YAN Changgen, LIN Bin, et al. Strength and statistical damage model in whole process of clay-concrete combined[J/ OL]. Journal of Jilin University(Engineering and Technology Edition):1-10[2024-04-10].https://doi.org/10.13229/j.cnki.jdxbgxb.20230253.

[32] 张二锋, 刘慧, 康跃明, 等. 冻融受荷砂岩力学性能劣化与统计损伤模型研究[J/OL]. 煤炭科学技术:1-9[2024-04-10]. http://kns.cnki.net/kcms/detail/11.2402.TD.20231102.0951.001.html.

[33] ZHANG Erfeng, LIU Hui, KANG Yueming, et al. Study on deterioration of mechanical properties and statistical damage model of freeze-thaw loaded sandstone[J/OL]. Coal Science and Technology:1-9[2024-04-10]. http://kns.cnki.net/kcms/detail/11.2402.TD.20231102.0951.001.html.

[34] 陈榕, 孙鹤, 郝冬雪, 等. 单粒组冻结砂土三轴压缩颗粒破碎规律研究[J]. 岩土工程学报, 2022,44 (Supp.1):92-97.

[35] CHEN Rong, SUN He, HAO Dongxue, et al. Particle breakage characteristics of frozen Cideal uniform sands under triaxial compression[J]. Chinese Journal of Geotechnical Engineering, 2022,44 (Supp.1):92-97.

[36] 张德, 刘恩龙, 刘星炎, 等. 基于修正 Mohr-Coulomb 屈服准则的冻结砂土损伤本构模型[J]. 岩石力学与工程学报, 2018, 37(4): 978-986.

[37] ZHANG De, LIU Enlong, LIU Xingyan, et al. A damage constitutive model for frozen sandy soils based on modified Mohr-Coulomb yield criterion[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(4):978-986.

[38] 张同刚, 王昆仑, 金国清. 基于高斯牛顿法的 DEM 匹配算法[J]. 西南交通大学学报, 2017, 52(3):584-592.

[39] ZHANG Tonggang, WANG Kunlun, JIN Guoqing. DEM co-registration algorithm based on Gauss-Newton method[J]. Journal of Southwest Jiaotong University, 2017, 52(3):584-592.

基金资助

黑龙江省自然科学基金联合引导项目(LH2020E018)

东北石油大学创新引导项目(2023YDL-14)