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Volume 13, Number 3, September 2017

Physical and mechanical properties of rocks are of interest in many fields, including materials science, petrophysics, geophysics and geotechnical engineering. Uniaxial compressive strength UCS is one of the key mechanical properties, while density and porosity are important physical parameters for the characterization of rocks. The economic interest of carbonate rocks is very important in chemical or biological procedures and in the field of construction. Carbonate rocks exploitation depends on their quality and their physical, chemical and geotechnical characteristics. A fast, economic and reliable technique would be an evolutionary advance in the exploration of carbonate rocks. This paper discusses the ability of ultrasonic wave velocity to evaluate some mechanical and physical parameters within carbonate rocks (collected from different regions within Tunisia). The ultrasonic technique was used to establish empirical correlations allowing the estimation of UCS values, the density and the porosity of carbonate rocks. The results illustrated the behavior of ultrasonic pulse velocity as a function of the applied stress. The main output of the work is the confirmation that ultrasonic velocity can be effectively used as a simple and economical non-destructive method for a preliminary prediction of mechanical behavior and physical properties of rocks.

Key Words
ultrasonic velocity; non-destructive testing; carbonate rocks; compressive strength; UCS; porosity; density

(1) Mohamed Abdelhedi, Monia Aloui, Thameur Mnif, Chedly Abbes:
Universite de Sfax Faculté des Sciences de Sfax, Route de Soukra, Département des Sciences de la Terre, BP 802, 3018 Sfax, Tunisie;
(2) Mohamed Abdelhedi, Monia Aloui, Chedly Abbes:
Laboratoire de Modélisation des Systèmes Géologiques et Hydrologiques (LR16ES17), Faculté des Sciences de Sfax, BP 802, 3018 Sfax, Tunisie;
(3) Thameur Mnif:
Laboratoire de Géoressources, Matériaux, Environnement et Changements Globaux (LR/13/ES-23), Faculte des Sciences de Sfax, BP 802, 3018 Sfax, Tunisie.

This work presents a simple and refined nth-order shear deformation theory for mechanical and thermal buckling behaviors of functionally graded (FG) plates resting on elastic foundation. The proposed refined nth-order shear deformation theory has a new displacement field which includes undetermined integral terms and contains only four unknowns. Governing equations are obtained from the principle of minimum total potential energy. A Navier type analytical solution methodology is also presented for simply supported FG plates resting on elastic foundation which predicts accurate solution. The accuracy of the present model is checked by comparing the computed results with those obtained by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed theory can achieve the same accuracy of the existing HSDTs which have more number of variables.

Key Words
buckling; functionally graded plate; elastic foundation; plate theory

(1) Asmaa Fahsi, Abdelouahed Tounsi, Habib Hebali, Abdelbaki Chikh, E.A. Adda Bedia:
Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria;
(2) Abdelouahed Tounsi:
Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria;
(3) Habib Hebali, Abdelbaki Chikh:
Université Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algérie;
(4) S.R. Mahmoud:
Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia;
(5) S.R. Mahmoud:
Mathematics Department, Faculty of Science, University of Sohag, Egypt.

A Spectral Element Method for 3D seismic wave propagation simulation is derived based on the threedimensional fluctuating elastic dynamic equation. Considering the 3D real terrain and the attenuation characteristics of the medium, the topographic effect of Wenchuan earthquake is simulated by using the Spectral Element Method (SEM) algorithm and the ASTER DEM model. Results show that the high PGA (peak ground acceleration) region was distributed along the peak and the slope side away from the epicenter in the epicenter area. The overall distribution direction of high PGA and high PGV (peak ground velocity) region is parallel to the direction of the seismogenic fault. In the epicenter of the earthquake, the ground motion is to some extent amplified under the influence of the terrain. The amplification effect of the terrain on PGA is complicated. It does not exactly lead to amplification of PGA at the ridge and the summit or attenuation of PGA in the valley.

Key Words
topographic effect; Spectral Element Method; seismogenic; peak ground acceleration; peak ground velocity; peak ground displacement

(1) School of Civil Engineering, Chongqing University, Chongqing 400045, China;
(2) Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing.

Rock bridges in rock masses would increase the bearing capacity of Non-persistent discontinuities. In this paper the effect of ratio of rock bridge surface to joint surface, rock bridge shape and normal load on failure behaviour of intermittent rock joint were investigated. A total of 42 various models with dimensions of 15 cm × 15 cm × 15 cm of plaster specimens were fabricated simulating the open joints possessing rock bridge. The introduced rock bridges have various continuities in shear surface. The area of the rock bridge was 45 cm2 and 90 cm2 out of the total fixed area of 225 cm2 respectively. The fabricated specimens were subjected to shear tests under normal loads of 0.5 MPa, 2 MPa and 4 MPa in order to investigate the shear mechanism of rock bridge. The results indicated that the failure pattern and the failure mechanism were affected by two parameters; i.e., the ratio of joint surface to rock bridge surface and normal load. So that increasing in joint area in front of the rock bridge changes the shear failure mode to tensile failure mode. Also the tensile failure change to shear failure by increasing the normal load.

Key Words
rock bridges; joint; normal loads; shear and tensile failure mode

(1) Vahab Sarfarazi:
Department of Mining Engineering, Hamedan University of Technology, Hamedan, Iran;
(2) Hadi Haeri:
Young Researchers and Elite Club, Bafgh Branch, Islamic Azad University, Bafgh, Iran;
(3) Alireza Bagher Shemirani:
Department of Civil Engineering, Sadra Institute of Higher Education, Tehran, Iran;
(4) Alireza Bagher Shemirani:
Department of Civil Engineering, Sharif University of Technology, Tehran, Iran.

This study proposes a sensitivity analysis method for slope stability based on the least squares support vector machine (LS-SVM) to examine the influencing factors of slope stability. The method uses LS-SVM as an algorithm for machine learning. An appropriate training dataset is established according to the slope characteristics, and a testing dataset is designed orthogonally. Results of the testing data in the experiment design are calculated after training using the LS-SVM model. The sensitivity of the slope stability of each factor is examined via gray correlation analysis. The results are consistent with those of the traditional Bishop analysis and can be used as a reference for optimizing slope design.

Key Words
slope stability; sensitivity analysis; orthogonal design; least squares support vector machine; gray correlation

(1) Juncai Xu, Qingwen Ren, Zhenzhong Shen:
College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China;
(2) Juncai Xu:
State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China.

To investigate the mechanical properties of Expanded Polystyrene (EPS) Beads Stabilized Lightweight Soil (EBSLS), Laboratory studies were conducted. Totally 20 sets of specimens according to the complete test design were prepared and tested with unconfined compressive test and consolidated drained triaxial test. Results showed that dry density of EBSLS (0.67-1.62 g/cm3) decreases dramatically with the increase of EPS beads volumetric content, while increase slightly with the increase of cement content. Unconfined compressive strength (10-2580 kPa) increases dramatically in parabolic relationship with the increase of cement content, while decreases with the increase of EPS beads volumetric content in hyperbolic relationship. Cohesion (31.1-257.5 kPa) increases with the increase of cement content because it is mainly caused by the bonding function of hydration products of cement. The more EPS beads volumetric content is, the less dramatically the increase is, which is a result of the cohesion between hydration products of cement and EPS beads is less than that between hydration products of cement and sand particles. Friction angle (14.92-47.42°) decreases with the increase of EPS beads volumetric content, which is caused by the smoother surfaces of EPS beads than sand grains. The stress strain curves of EBSLS tend to be more softening with the increase of EPS beads content or the decrease of cement content. The shear contraction of EBSLS increases with the increase of ce or the decrease of cc. The results provided quantitative relationships between physico-mechanical properties of EBSLS and material proportion, and design process for engineering application of EBSLS.

Key Words
lightweight soil; density; strength; cohesion; friction angle; deformation behavior

(1) Mingdong Li:
HoHai University, Nanjing, Jiangsu 210098, ChinaHoHai University, Nanjing, Jiangsu 210098, China;
(2) Mingdong Li, Anguo Tian:
School of Civil Engineering, Huaihai Institute of Technology, 59 Cangwu Road, Lianyungang, Jiangsu 222005, China;
(3) Kejun Wen, Lin Li:
Department of Civil and Environmental Engineering, Jackson State University, 1400 J.R. Lynch Street, Jackson, MS, 39217, USA.

Geotechnical data contributes substantially to the cost of engineering projects due to increasing cost of site investigations. Existing information in the form of soil maps can save considerable time and expenses while deciding the scope and extent of site exploration for a proposed project site. This paper presents spatial interpolation of data obtained from soil investigation reports of different construction sites and development of soil maps for geotechnical characterization of Multan area using ArcGIS. The subsurface conditions of the study area have been examined in terms of soil type and standard penetration resistance. The Inverse Distance Weighting method in the Spatial Analyst extension of ArcMap10 has been employed to develop zonation maps at different depths of the study area. Each depth level has been interpolated as a surface to create zonation maps for soil type and standard penetration resistance. Correlations have been presented based on linear regression of standard penetration resistance values with depth for quick estimation of strength and stiffness of soil during preliminary planning and design stage of a proposed project in the study area. Such information helps engineers to use data derived from nearby sites or sites of similar subsoils subjected to similar geological process to build a preliminary ground model for a new site. Moreover, reliable information on geometry and engineering properties of underground layers would make projects safer and economical.

Key Words
site investigation; standard penetration resistance; spatial interpolation; geographic information systems; soil mapping

(1) Mubashir Aziz, Tauqir Ahmed:
College of Engineering, Al Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia;
(2) Tanveer A. Khan:
Department of Civil Engineering, Bahauddin Zakariya University, Multan, Pakistan.

The localized shear and the slip lines are easily observed in elastic-brittle-plastic rock. After yielding, the strength of the brittle rock suddenly drops from the peak value to the residual value, and there are slip lines which divide the macro rock into numbers of elements. There are slippages of elements along the slip lines and the displacement field in the plastic region is discontinuous. With some restraints, the discontinuities can be described by the combination of two smooth functions, one is for the meaning of averaging the original function, and the other is for characterizing the breaks of the original function. The slip lines around the circular opening in the plastic region of an isotropic H-B rock which subjected to a hydrostatic in situ stress can be described by the logarithmic spirals. After failure, the deformation mechanism of the plastic region is mainly attributed to the slippage, and a slippage parameter is introduced. A new analytical solution is presented for the plane strain analysis of displacements around circular openings. The displacements obtained by using the new solution are found to be well coincide with the exact solutions from the published sources.

Key Words
brittle plastic rock; H-B strength criterion; slip lines; slippage parameter

(1) Houxu Huang, Jie Li, Xiaoli Rong, Yiqing Hao, Xin Dong:
State Key Laboratory of Disaster Prevention and Mitigation of Explosion and Impact, PLA University of Science and Technology, Nanjing, China;
(2) Jie Li:
School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China;
(3) Yiqing Hao:
High-Tech Institute, Fan Gong-ting South Street on the 12th, Qingzhou, Shandong, China.

Based on the collapse characteristics of a shallow rectangular cavity, a three-dimensional failure mechanism which can be used to study the collapsing region of the rock mass above a shallow cavity roof is constructed. Considering the effects of surcharge pressure and surface bolt on the collapsing block, the external rate of works produced by surcharge pressure and surface bolt are included in the energy dissipation calculation. Using variational approach, an analytic expression of surface equation for the collapsing block, which can be used to study the collapsing region of the rock mass above a shallow cavity roof, is derived in the framework of upper bound theorem. Based on the analytic expression of surface equation, the shape of the collapsing block for shallow cavity is drawn. Moreover, the changing law of the collapsing region for different parameters indicates that the collapsing region of rock mass decreases with the increase of the density of surface bolt. This conclusion can provide reference for practicing geotechnical engineers to achieve an optimal design of supporting structure for a shallow cavity.

Key Words
shallow rectangular cavity; collapsing block; upper bound theorem; surface bolt

(1) Fu Huang:
School of Civil Engineering, Changsha University of Science and Technology, 960, 2nd Section, Wanjiali South RD, Changsha, China;
(2) Lian-heng Zhao:
School of Civil Engineering, Central South University, 22, Shaoshan South RD, Changsha, China;
(3) Sheng Zhang:
School of Civil Engineering, Hunan City University, 518, Yingbin East RD, Yiyang, China.

In this paper, with a graphical approach, a series of stability charts for homogeneous slopes with benches are presented based on the upper bound limit analysis theory and strength reduction technique. The objective function of the slope safety factor Fs is optimized by the nonlinear sequential quadratic programming, and a substantial number of examples are illustrated to use the stability charts for homogeneous slopes with benches driven by only the action of the soil weight. These charts can be applied to quick and accurate estimations of the stability status of homogeneous slopes with benches. Moreover, the failure modes and the formula for safety factor Fs of homogeneous slopes with benches are provided to illustrate the stability analysis of slopes with benches, which is validated by samples.

Key Words
slope stability analysis; safety factor; shear strength reduction technique; limit analysis

(1) Lianheng Zhao, Peng Xia, Liang Li, Xiao Cheng:
School of Civil Engineering, Central South University, Changsha, Hunan 410075, China;
(2) Lianheng Zhao:
Key Laboratory of Heavy-Haul Railway Engineering Structure, Ministry of Education, Central South University, Changsha, Hunan 410075, China;
(3) Rongfu Xie:
Xiamen Municipal Engineering Design Institute Co., Ltd., Xiamen, Fujian 361004, China;
(4) Yingbin Zhang:
Key Laboratory of Transportation Tunnel Engineering, Ministry of Education, Southwest Jiaotong University, Chengdu 610031, China;
(5) Yingbin Zhang:
Department of Geotechnical Engineering, School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China.

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