西安建筑科技大学学报(自然科学版)

基于表观弹性模量变化规律的类岩石材料滞回环形态分类及预测研究

刘杰^1,2,谢晓康^1,2,高素芳³,杨渝南^1,2,兰俊^1,2,王飞^1,2

(1.三峡大学湖北省地质灾害防治工程技术中心,湖北宜昌443002; 2.三峡大学三峡库区地质灾害教育部重点实验室,湖北宜昌 443002; 3.北京市勘察设计研究院有限公司,北京 100038)

Study on classifications and prediction of rock hysteresis loop based on apparent elastic modulus change law

LIU Jie^1,2, XIE Xiaokang ^1,2,GAO Sufang³, YANG Yunan^1,2,LAN Jun^1,2, WANG Fei^1,2

(1. Engineering Technology Center for Geological Disaster Prevention of Hubei Province, China Three Gorges University,Hubei Yichang 443002,China; 2.Key Laboratory of Geological azards on Three Gorges Reservoir Area, Ministry of Education, China Three Gorges University, Hubei Yichang 443002,China; 3.BGI Engineering Consultants Ltd., Beijing 100038,China)

Keywords： cyclic loading and unloading; apparent elastic modulus; classification of hysteresis loops; prediction of hysteresis loops

DOI: 10.15986-j.1006-7930.2020.04.004

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基于RMT-150C岩石力学试验系统,研究循环载荷下砂岩的力学响应,基于提出的E(t)=af(t)+b关系式,根据加载段表观弹性模量的变化规律,将非瞬时加载的滞回环形态分为持续增大、持续减小和先增后减三种形态.指出表观弹性模量的变化是由试样内部微裂隙、微孔洞的压密系数a1和滑移展开数a2两种因素共同作用的结果,并结合公式中a=a1+a2值的正负变化分析三种形态滞回环产生机理.根据公式中a值和b值随峰值、加载频率和围压变化存在的规律,可由两个及以上已知滞回环完成对其它任意滞回环的预测,并给出了详细的计算公式及流程,同时对每种不同滞回环的实例进行机理分析.试验证明,本预测方法适用于不同峰值(64～112 kN)、不同加载速率(0.2～20 kN/s)与围压(0～20 MPa)条件下三种不同形态滞回环.

Based on the RMT-150C rock mechanics test system, the mechanical response of sandstone samples under cyclic loading was studied. Based on the proposed E(t)=af(t)+b relation, and according to the change law of apparent elastic modulus of the loading section, the hysteretic loop forms under non-instantaneous loading were divided into three forms: continuous increased, continuously decreased, and first increase and then decrease. It is pointed out that the change of the apparent modulus of elasticity is the result of the joint action of the micro-crack inside the sample, the compression density coefficient a1 of the micro-hole and the slip expansion number a2. In combination with the positive and negative change of a=a1+a2 value in the formula, the mechanism of the three forms of hysteresis loop is analyzed. According to the change law of A value and B value in the formula with the change of peak value, loading frequency and confining pressure, two or more known hysteresis loops can be used to predict any other hysteresis loops, and the detailed calculation formula and process are given. Meanwhile, the mechanism analysis of each different hysteresis loop is carried out. The test results show that the prediction method is applicable to three types of hysteresis loops with different peak values(64～112 kN), loading rates(0.2～20 kN/s)and confining pressures(0～20 MPa).

引言
1 循环加卸载下表观弹性模量分析
2 三种滞回环形态曲线预测研究
3 结论

图1 RMT-150C岩石力学试验系统<br/>Fig.1 RMT-150C Rock mechanics test system

图1 RMT-150C岩石力学试验系统
Fig.1 RMT-150C Rock mechanics test system

图2 砂岩加载0.1 Hz频率不同波形下E(t)随时间变化关系<br/>Fig.2 Relationship betweenE(t)and time variation of loads 0.1 Hz frequency

图2 砂岩加载0.1 Hz频率不同波形下E(t)随时间变化关系
Fig.2 Relationship betweenE(t)and time variation of loads 0.1 Hz frequency

图3 强风化砂岩22 kN峰值循环载荷下滞回环图<br/>Fig.3 Hysteresis loop diagram of strongly weathered sandstone under 22 kN peak cyclic load

图3 强风化砂岩22 kN峰值循环载荷下滞回环图
Fig.3 Hysteresis loop diagram of strongly weathered sandstone under 22 kN peak cyclic load

图4 三种滞回环形态<br/>Fig.4 Three hysteresis loops

图4 三种滞回环形态
Fig.4 Three hysteresis loops

图5 Ⅰ型:花岗岩试件循环加卸载下试件的应力 - 应变图[18]<br/>Fig.5 Type I:Stress-strain diagram of specimen under cyclic loading and unloading of granite specimen[18]

图5 Ⅰ型:花岗岩试件循环加卸载下试件的应力 - 应变图[18]
Fig.5 Type I:Stress-strain diagram of specimen under cyclic loading and unloading of granite specimen[18]

图6 Ⅱ型:三峡库区重庆段砂岩[19]<br/>Fig.6 Type Ⅱ:Chongqing section sandstone of the three gorges reservoir area[19]

图6 Ⅱ型:三峡库区重庆段砂岩[19]
Fig.6 Type Ⅱ:Chongqing section sandstone of the three gorges reservoir area[19]

图7 Ⅲ型:C30混凝土循环加卸载应力应变曲线 <br/>Fig.7 Type Ⅲ:Stress-strain curve of C30 concrete cyclic loading and unloading

图7 Ⅲ型:C30混凝土循环加卸载应力应变曲线
Fig.7 Type Ⅲ:Stress-strain curve of C30 concrete cyclic loading and unloading

图8 预测流程图
Fig.8 Forecast flow chart

图9 混凝土材料循环加卸载曲线分段图<br/>Fig.9 Segmented graphs of cyclic loading and unloading curve of concrete

图9 混凝土材料循环加卸载曲线分段图
Fig.9 Segmented graphs of cyclic loading and unloading curve of concrete

表1 部分计算结果表<br/>Tab.1 Part of the calculation results table

表1 部分计算结果表
Tab.1 Part of the calculation results table

图10 试件300-1加载段与卸载段a,b值拟合曲线<br/>Fig.10 Specimen 300-1 loading section and unloading section a,b value fitting curve

图10 试件300-1加载段与卸载段a,b值拟合曲线
Fig.10 Specimen 300-1 loading section and unloading section a,b value fitting curve

表2 试样300-1各循环加卸载段内的a、b值统计<br/>Tab.2 Samples 300-1 of each cycle loading and unloading section of the a, b value statistics

表2 试样300-1各循环加卸载段内的a、b值统计
Tab.2 Samples 300-1 of each cycle loading and unloading section of the a, b value statistics

图11 试样300-1预测与实际应力应变曲线对比图<br/>Fig.11 Specimen 300-1 loading section and unloading section a value fitting curve

图11 试样300-1预测与实际应力应变曲线对比图
Fig.11 Specimen 300-1 loading section and unloading section a value fitting curve

表3 预测不同峰值下加载段与卸载段a、b值<br/>Tab.3 Predict the load and unloading segments a and b at different peaks

表3 预测不同峰值下加载段与卸载段a、b值
Tab.3 Predict the load and unloading segments a and b at different peaks

图12 不同峰值下加载段与卸载段a、b拟合规律图<br/>Fig.12 The fitting pattern of loading and unloading section a and b under different peaks

图12 不同峰值下加载段与卸载段a、b拟合规律图
Fig.12 The fitting pattern of loading and unloading section a and b under different peaks

图13 预测曲线与原始曲线对比图<br/>Fig.13 Comparison of prediction curve and original curve

图13 预测曲线与原始曲线对比图
Fig.13 Comparison of prediction curve and original curve

图14 模拟泵油饱和南京砂岩<br/>Fig.14 Simulated pump oil saturated Nanjing sandstone

图14 模拟泵油饱和南京砂岩
Fig.14 Simulated pump oil saturated Nanjing sandstone

表4 预测不同峰值下加载段与卸载段a、b值<br/>Tab.4 Predict the load and unloading segments a and b at different peaks

表4 预测不同峰值下加载段与卸载段a、b值
Tab.4 Predict the load and unloading segments a and b at different peaks

图15 饱和南京砂岩加载段荷载 - 弹性模量线性关系图<br/>Fig.15 Linear correlation diagram of load-elastic modulus of saturated nanjing sandstone loading section

图15 饱和南京砂岩加载段荷载 - 弹性模量线性关系图
Fig.15 Linear correlation diagram of load-elastic modulus of saturated nanjing sandstone loading section

图16 预测曲线与实际曲线对比图<br/>Fig.16 Comparison of predictive curveand actual curve

图16 预测曲线与实际曲线对比图
Fig.16 Comparison of predictive curveand actual curve

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期刊信息

西安建筑科技大学学报(自然科学版)
（1957年创刊双月刊）

主管单位：陕西省教育厅

主办单位：西安建筑科技大学

主　　编：刘加平（院士）

副主编：史庆轩（常务）张引科张小龙

国内刊号：CN61-1295/TU

I S S N：1006-7930

地　　址：西安市雁塔路中段13号

国内发行：西安建筑科技大学学报编辑部

国外发行：中国出版对外贸易总公司

编辑出版：西安建筑科技大学学报编辑部

备注

引言

1 循环加卸载下表观弹性模量分析

2 三种滞回环形态曲线预测研究

3 结论

期刊信息