Open Geosci. 2016; 8:523–537 Research Article Open Access Qitao Pei*, Xiuli Ding, Bo Lu, Yuting Zhang, Shuling Huang, and Zhihong Dong An improved method for estimating in situ stress in an elastic rock mass and its engineering application DOI 10.1515/geo-2016-0047 Received Jan 20, 2016; accepted Jun 30,2016 1 Introduction Abstract: The main contribution of this paper is to develop Knowledge of the in situ stress is a basic requirement a method to determine the in situ stress on an engineering for the design and construction of underground projects. scale by modifying the elasto-static thermal stress model Especially for those involving underground excavation (Sheorey’s model). The suggested method, firstly, intro- projects, an understanding of the initial state of stress, i.e., duces correction factors for the local tectonism to reflect that prior to any excavation or construction, is essential. the stress distribution difference caused by local tectonic Generally speaking, the in situ stress values in the movements. The correction factors can be determined by three mutually perpendicular directions of the Earth’s the least-squares approach based on laboratory tests and crust are unequal. Vertical stress can be obtained eas- local in situ stress measurements. Then, the rock elastic ily based on the overburden pressure without causing modulus is replaced by rock mass elastic modulus so as to much error in most instances [1]. However, the horizon- show the effect of rock discontinuities on the in situ stress. tal stresses can be affected significantly by plate tecton- Combining with elasticity theory, equations for estimating ics, major geological features, topography, etc., which are the major and minor horizontal stresses are obtained. It is difficult to estimate. Karl and Richart [2] performed many possible to reach satisfactory accuracy for stress estima- studies on the distribution characteristics of in situ stress tion. To show the feasibility of this method, it is applied to in sedimentary rocks. Li [3] proposed a method for estimat- two deep tunnels in China to determine the in situ stress. ing in situ stress in coal and soft rock masses. Brown and Field tests, including in situ stress measurements by con- Hoek [4] summarised the relationship between horizontal- ventional hydraulic fracturing (HF) and rock mass mod- to-vertical in situ stress ratio k with depth of cover by ulus measurements using a rigid borehole jack (RBJ), are analysing a large amount of measured data. Furthermore, carried out. It is shown that the stress field in the two deep González de Vallejo and Hijazo [5] plotted a large dataset tunnels is dominated by horizontal tectonic movements. of stress magnitudes versus depth on a global scale. She- The major and minor horizontal stresses are estimated, re- orey [6] presented an elasto-static thermal stress model of spectively. Finally, the results are compared with those de- the Earth to estimate crustal stress, but did not consider rived from the HF method. The calculated results in the two the main factors (e.g., local tectonic movements) affect- tunnels roughly coincide with the measured results with ing the state of stress. Other methods such as the geolog- an average of 15% allowable discrepancy. ical (tectonic structure analysis), or seismic (focal mech- anisms), can only determine the orientations of principal Keywords: in situ stress; field tests; Sheorey’s model; stress stresses rather than their magnitude. To reflect the influ- estimation; hydraulic fracturing ence of geological and geophysical factors affecting stress magnitude, González de Vallejo and Hijazo [5] proposed a new method for estimating the ratio k of the major horizon- tal stress to vertical stress based on the decision tree prob- *Corresponding Author: Qitao Pei: Key Lab. of Geotechnical Me- abilistic method and the empirical relationship between chanics and Engineering of Ministry of Water Resources, Yangtze River Scientific Research Institute, Wuhan 430010, P. R. China; the Tectonic Stress Index and k values. In addition, the in- Email: [email protected], Tel.: +86-27-82826540 crease of in situ stress due to local factors was expressed Xiuli Ding, Bo Lu, Yuting Zhang, Shuling Huang, Zhihong Dong: by the Stress Amplification Factor, which could provide an Key Lab. of Geotechnical Mechanics and Engineering of Ministry of estimate of structural stresses in rock masses for rock ex- Water Resources, Yangtze River Scientific Research Institute, Wuhan cavations [7, 8]. Although many scholars have undertaken 430010, P. R. China © 2016 Q. Pei et al., published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. 524 Ë Q. Pei et al. much valuable research into stress estimation, the major 35 km and minor horizontal stresses on an engineering-scale re- Crust(solid) main hard to determine. Upper mantle 700 km (solid,plastic) Field testing is a direct method used to obtain the 2900 km Moho discontinuity orientations and magnitude of in situ stresses. In recent Lower mantle decades, in situ stress testing equipment and relative (solid,plastic) 5150 km methods have made significant progress. In 2003, the In- Gutenberg 6371 km ternational Society for Rock Mechanics (ISRM) published discontinuity some suggested methods for determining rock stress [9– Outer core(liquid) 12]. These methods cover the basic principles of over- coring and hydraulic fracturing/hydraulic testing of pre- existing fracture methods. However, conventional meth- Inner core(solid) ods of measurement are only available for hard rock (e.g. granite, marble, and similar rocks with high strength), which could not be applied to soft or broken rock (e.g. such as is found in fault fracture zones). Besides, for some high Figure 1: Cross-section of the Earth (modified from Sheorey’s model in situ stress regions, or at great depth, core disking ren- (1994)). ders the over-coring method inapplicable, and reduces the success rate of the hydraulic fracturing method [13]. horizontal free surface [14]: Here, a method for estimating the major and minor horizontal stresses in an elastic rock mass at engineering- σzz = 훾H (1) scale, is presented. Unlike the general Sheorey’s model, the improved method takes into account not only the vari- ν σ = σ = 훾H (2) ation of elastic constants, density, and thermal expansion xx yy 1 − ν coefficient of the crust and mantle, but also the stress dis- Where, 훾 is the bulk unit weight of the material, ν is Pois- tribution difference caused by local tectonic movements. son’s ratio, and H is the depth from the free surface. The In addition, the rock mass elastic modulus, which can re- terms σxx and σyy are two horizontal stresses, and σzz sym- flect the effect of rock discontinuities onthe in situ stress, bolises the vertical stress at depth H. especially at shallow crustal depths, is adopted to replace However, a large number of field measurements show the rock elastic modulus. The improved method can be that the horizontal stresses commonly do not follow Equa- much better applied to local, shallow rock masses rather tion (2), and in many places are several times larger than than at a global, or regional, scale. Finally, the results of the vertical stress. So, assumption (2) is likely to be inap- the application of this method to the determination of in plicable in many cases. situ stress around two deep tunnels in China are presented. The Earth can be treated as a concentric geoid struc- ture: from the surface to the centre, the Earth is divided into crust, mantle, and core. The widely accepted cross- section of the Earth is shown in Figure 1. Displacements 2 Estimation method of in situ should be zero at the mantle-core interface (Gutenberg dis- continuity) rather than at the crust-mantle interface (Mo- stress based on Sheorey’s model horovičić discontinuity). Supposing that the Earth’s crust is taken as a solid 2.1 Overview of methods spherical shell filled with an incompressible liquid, the equilibrium equation is [15]: So far, the formation mechanism of crustal stress is not yet dσ 2(σ − σ ) clear. As a result, the methods for its estimation always in- r − θ r − 훾 = 0 (3) volve some simplifying assumptions. The most common dr r practice is to assume lateral confinement (i.e., no horizon- Here σr denotes the radial (vertical) stress, and σθ is the tal displacement anywhere due to gravitational loading). tangential (horizontal) stress in polar coordinates (r, θ). Based on the mentioned assumption, the following equa- The relationship between σr (σθ) with the radial displace- tions are often used to determine the initial state of in situ stress in a relatively uniform soil or rock mass beneath a Estimating in situ stress in an elastic rock mass and its application Ë 525 Table 1: Values of different parameters for isotropic rocks [6]. Location Slice No. R (103 km) E (GPa) 훾 (MPa/m) β (10−5/∘C) mantle 1 3.47 760 0.052 2.4 2 3.87 700 0.048 1.9 3 4.37 610 0.045 1.6 4 4.87 520 0.043 1.35 5 5.37 360 0.040 1.25 6 5.958 200 0.037 1.2 crust 7 6.335 20 0.027 0.77 8 6.34 30 0.027 0 9 6.346 40 0.027 2.2 10 6.352 45 0.027 1.5 11 6.358 50 0.027 0.9 12 6.364 50 0.027 0.6 Boundaries between adjacent slices in crust R12 R7 R6 R5 Boundaries R4 between adjacent R3 slices in mantle R2 R1 Liquid core Figure 2: Simplified spherical shell model of the Earth (modified from Sheorey’s model (1994)).