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Elastic modulus of a rock mass based on the two parameter negative-exponential (TPNE) distribution of discontinuity spacing and trace length

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Abstract

The frequency, spacing and trace length of rock mass discontinuities appear to follow a negative exponential distribution. However, in some cases this distribution has limitations. To overcome this, it is necessary to choose a target distribution which is flexible enough to simulate the spacing and trace length of the discontinuities. The paper shows how the two parameter negative exponential (TPNE) distributions can meet the requirements. An improved constitutive equation of rock mass based on this new distribution has been determined from which a new method to calculate rock mass elastic modulus (Em) is proposed, taking into account the rock mass anisotropy. It was found that the geo-stresses influence Em in two ways: it varies with changes in the orientation of the geo-stress and with the size of geo-stress. The work is illustrated by a case study on the abutment slope of the 295 m high arched dam of the Xiao wan hydroelectric power station in Yunnan province, Southwest of China.

Résumé

La fréquence, l’espacement et la longueur de trace de discontinuités de masses rocheuses apparaissent suivre une distribution exponentielle négative. Cependant, dans certains cas, cette distribution ne convient pas. Afin de surmonter cette difficulté, il est nécessaire de choisir une distribution cible suffisamment souple pour représenter l’espacement et la longueur de trace de discontinuités. L’article montre comment les distributions exponentielles négatives à deux paramètres peuvent répondre au problème. Une loi de comportement améliorée de la masse rocheuse, basée sur cette nouvelle distribution, a été déterminée, à partir de laquelle une nouvelle méthode de calcul du module d’élasticité d’un massif rocheux est proposée, prenant en compte l’anisotropie du massif rocheux. Il a été montré que les contraintes géostatiques influencent le module d’élasticité de deux façons : il varie avec les changements d’orientation du champ de contrainte géostatique et avec son intensité. Ce résultat est illustré par une étude de cas concernant l’appui rocheux d’un barrage voûte de 295 m de hauteur de la centrale électrique de Xiao Wan dans la province du Yunnan, dans le sud-ouest de la Chine.

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Acknowledgments

The authors would like to thank to Senior Engineer Zhuang Huaze, Dr. Liu Tong, Dr. Yan Changgen, Dr. Chai Jianfeng and Dr. Yang Xiaoyong; most of the field work was undertaken by them. Dr. Qi Shengwen, Dr. Tao Bo and Dr. Liu Haiyan also took part in the field investigations, and their work is appreciated. Dr. Qi Shengwen kindly read and revised the manuscript. The Work was supported by The Key Laboratory of Engineering Geomechanics, Institute of Geology and Geophysics, Chinese Academy of Sciences.

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Authors and Affiliations

  1. Key Laboratory of Engineering Geomechanics, Institute of Geology and Geophysics, Chinese Academy of Sciences, P.O. Box 9825, Beijing, 100029, P. R. China

    Xiuhong Hu & Faquan Wu

  2. School of Resources and Geoscience, China University of Ming and Technology, Xuzhou, 221116, China

    Qiang Sun

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  1. Xiuhong Hu
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  2. Faquan Wu
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  3. Qiang Sun
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Correspondence to Xiuhong Hu.

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Hu, X., Wu, F. & Sun, Q. Elastic modulus of a rock mass based on the two parameter negative-exponential (TPNE) distribution of discontinuity spacing and trace length. Bull Eng Geol Environ 70, 255–263 (2011). https://doi.org/10.1007/s10064-010-0321-z

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  • DOI: https://doi.org/10.1007/s10064-010-0321-z

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