Statistical analysis of scale effect on equivalent elastic modulus of jointed rock masses
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ORIGINAL PAPER
Statistical analysis of scale effect on equivalent elastic modulus of jointed rock masses Haijiang Ni 1,2 & Weiya Xu 2,3 & Wei Wang 2,3 & Bo Lu 4 & Anchi Shi 5 & Lifang Zou 6
Received: 15 February 2014 / Accepted: 15 October 2015 / Published online: 10 March 2016 # Saudi Society for Geosciences 2016
Abstract The study of scale effects plays an important role in the evaluation of mechanical properties of rock masses. There have been many studies on this topic; however, few have been able to effectively analyze relationships between size and deformation properties analytically. This paper presents an investigation of scale effects on deformation properties of jointed rock masses by using analytical and statistical methods. First, the analytical formula for Eeq (equivalent elastic modulus) of jointed rock with a parallel joint set was derived. This derivation is related to a geometrical parameter ρ’, defined as joint trace length per unit area. Second, model of a half-space rock with a parallel joint set was constructed and subsequently sampled to specimens with different locations and lengths. The expectation and standard deviation of the ρ’ of rock samples were derived to statistically describe scale effect of ρ’. Then, the scale effect of 1/Eeq (equivalent elastic compliance) was analyzed. The investigation shows that expectation of 1/ Eeq is a constant with varying size and standard deviation of 1/
* Haijiang Ni [email protected] * Wei Wang [email protected] 1
School of civil Engineering and Architecture, Zhejiang Industry Polytechnic College, Shaoxing 312000, Zhejiang, China
2
Geotechnical Research Institute of Hohai University, Nanjing 210098, Jiangsu, China
3
Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing 210098, Jiangsu, China
4
East China Architectural Design & Research Institute Co., Ltd. UD Architectural Design Institute, Shanghai 200041, China
5
PowerChina Huadong Engineering Corporation Limited, Hangzhou, Zhejiang 310014, China
6
College of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, Jiangsu, China
Eeq decreases and periodically fluctuates with increasing size. The applicability of the conclusions was discussed, and some extended studies on stochastic jointed rock masses were made. Finally, representative elementary volumes of the rock model were determined according to the analytical solutions. Keywords Jointed/fractured rock . Equivalent elastic modulus . Scale/size effect . Representative elementary volume (REV) . Statistics
Introduction Scale effects are important phenomena in rock mechanics. Rock mass properties obtained from laboratory and in situ tests are related to the size of the specimens used. These size effects are termed scale effects. According to Hudson and Harrison (2000), one way to quantify this scale dependency is by using the representative elementary volume (REV) of a rock mass, as illustrated in Fig. 1. REV is the volume at which the size of the tested sam
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