Effect of parallel joint interaction on mechanical behavior of jointed rock mass models

International Journal of Rock Mechanics & Mining Sciences 92 (2017) 40–53

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International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms

Effect of parallel joint interaction on mechanical behavior of jointed rock mass models

MARK

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Xu-Xu Yanga,b, Hong-Wen Jinga, , Chun-An Tangc, Sheng-Qi Yanga a

State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, PR China Shandong Provincial Key Laboratory of Civil Engineering Disaster Prevention and Mitigation, Shandong University of Science and Technology, Qingdao 266590, PR China c State Key Laboratory of Coastal & Offshore Engineering, Dalian University of Technology, Dalian 116024, PR China b

A R T I C L E I N F O

A BS T RAC T

Keywords: Rock mass Joint interaction Joint spacing Joint overlap Mechanical behavior

To better understand the interaction of parallel joints and its effect on the mechanical behavior of jointed rock mass models, the results of a physical experiment program undertaken in the laboratory were present in this manuscript. The joint spacing and joint overlap are varied to alter the relative positions of parallel joints in geometry. Accordingly, four basic failure modes identified from the testing results are tensile failure across the joint plane, shear failure along the joint plane, tensile failure along the joint plane, and intact material failure. The wing cracks from tensile failure across the joint plane mode represent the interaction between parallel joints which depends on the joint dip angle, joint spacing and joint overlap. With the increment of parallel joint interaction, the corresponding normalized strength and maximum displacement at peak stress of jointed rock mass models reduced generally except at α=0°.

1. Introduction A common problem in rock engineering is the reliable estimation of mechanical properties of a rock mass consisting of intact rock and discontinuities such as joints, bedding planes, shear zones and faults. These discontinuities dominate the mechanical properties of rock mass not only because of their interaction with the intact rock, but also because of the interaction between themselves. On the other hand, a rock bridge along the joint orientation gives an effective cohesion to the joint plane and a block of rock cannot fall or slide until all the rock bridges fail.1 With respect to the size proportion of joints relative to an orientated plane comprising joints and rock bridges, the joint persistency parameter is proposed to geometrically quantify the rock mass. The degree of joint persistency determines how much intact rock material contributes to stability, and in the case of the persistency degree less than 1.0, the rock mass is considered non-persistent. The mechanical behavior of non-persistent jointed rock mass has been extensively investigated though physical and numerical modeling. Prudencio and Van Sint Jan 2 have performed biaxial compression tests on physical models of rock with non-persistent joints and indicated that the geometry of the joint systems, the orientation of the principal stresses and the intact material compressive strength have a significant effect on the failure modes and strengths of jointed rock masses. Tests

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showed three basic failure modes: failure through a planar surface, stepped failure, and failure by rotation of new blocks. Furthermore, Bahaaddini et al.3 carried out a sensitivity study through particle flow modeling 4 to look into the effect of joint configuration parameters on the failure mode, unconfined compressive strength and deformation modulus of the rock mass having non-persistent joints. It is found that the failure mode is determined principally by joint orientation and step angle, and the joint orientation with respect to principal stress direction is the parameter with the greatest influence on rock mass properties. Fan et al.,5 by using PFC3D software package 4, performed numerical simulations to study the influence of multi-non-persistent joints on jointed rock block mechanical behavior. They demonstrated the significant influence of joint orientation and joint persistency on the strength and deformation modulus values of jointed rock blocks. Moreover, Yang et al.6 numerically simulated the mechanical behavior of a jointed rock mass with non-persistent joints adjacent to a free surface on the wall of an excavation. The effect of joint orientation and support stress on the free surface on mechanical behavior was investigated, and three failure modes identified are intact rock failure, step-path failure, and planar failure. The aforesaid physical and numerical experiments shed light on the significance of joint configuration on the mechanical behavior of jointed rock masses. However, these researchers laid their emphasis

Corresponding author. E-mail address: [email protected] (H.-W. Jing).

http://dx.doi.org/10.1016/j.ijrmms.2016.12.010 Received 16 March 2016; Received in revised form 9 September 2016; Accepted 22 December 2016 1365-1609/ © 2016 Elsevier Ltd. All rights reserved.

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geneous and isotropic behaviors due to the uniform and refined particle size distribution. The pre-existing joints were created by inserting 0.3 mm-thick greased thin nickel alloy strips into the precut slots and removing them after the setting of the mixture slurry had started. Tilt test was used to determine joint friction angle of the pre-existing plane, and the joint friction angle is 37°. In present paper, the aforementioned rock-like material as well as the specimen preparation procedure was adopted to further investigate the effect of parallel joint (in different joint planes) interaction on mechanical behavior of jointed rock mass models. Fig. 1 displays the specimen preparation procedure. Note that before pouring the mixture (plaster and water) into the mould, the nickel alloy strips were already fixed on the bottom plate of the mould through the prefabricated slots (Fig. 1c). The geometry of these slots are carefully designed according to Section 2.2. After curing for several hours when the mixture start to solidify, the nickel alloy strips would be pulled out slowly to leave joints in the specimens. The specimens were then removed from the mould by dismantling it, as shown in Fig. 1d.

on the pre-existing joints inducing anisotropy of rock mass with comparison to intact rock block or on the rock bridges enhancing resistance capability of rock mass with comparison to that having persistent joints. The knowledge about the interaction of joint and rock bridge has been advanced a lot,7–10 whereas the interaction between joints has not been comprehensively studied. Tang et al.11 have observed the crack coalescence to occur along the weakest coalescence path among all possible paths between any two flaws. Zhang and Wong 12 have numerically studied the cracking and coalescence behavior in a rectangular rock-like specimen containing two parallel pre-existing open flaws under uniaxial compression load. They claimed that the spacing between two flaws and the inclination of a line linking up the inner flaw tips have different effects on the coalescence patterns, coalescence stresses as well as peak strength of specimens. The interaction of two or three pre-existing flaws and its effect on the mechanical behavior of rock or rock-like specimens have been investigated by other researchers.13–16 Nevertheless, the interaction between joint planes in a non-persistent jointed rock mass has rarely been investigated. Response of the rock mass with non-persistent joints varies depending on joint configuration and loading conditions. The behavior of each joint is affected by the presence of other joints. 3 Laboratory experiments are an attractive procedure because, with systematic design, they can expose failure mechanisms that may not become evident by other means, such as field observation. Moreover, laboratory testing results are also useful to calibrate analytical solutions and numerical studies. In this manuscript, the results of a laboratory experimental program designed to look at the interaction of parallel joints and its effect on the failure mode, strength and deformation behavior of jointed rock masses are presented. The joint spacing and joint overlap are varied to alter the relative positions of parallel joints in geometry.

2.2. Joint geometry design Geometric characterization of rock joints is the basis for most of the work of engineering geologists, civil and mining engineers when dealing with rock masses. An ideal characterization of jointing would involve the specific description of each joint in the rock mass.19 This is not possible due to the fact that the joint system is significantly complicated, and the complete description of joints is difficult because of their three-dimensional nature. Therefore, joints in a rock mass are usually described as an assemblage rather than individually. The assemblage has stochastic character in that joint characteristics vary in space. Such variations may be negligible as in the case of the orientation of a set of approximately parallel joints or they may be great if a particular property has substantial variability. One major approach to describe the assemblage of geometric joint characteristics in a rock mass is disaggregate characterization, in which each joint characteristic is described separately. Chen et al.17,18 established a conceptual jointed rock model by considering different joint characteristic separately, as shown in Fig. 2. In the jointed rock model, the existence of rock bridge intermits the joints going through the rock model to make them nonpersistent. The non-persistent joints dramatically enrich the rock mass geometric configurations, and the rock bridge strength plays an important role on global behavior of rock mass.1,6 Furthermore, the interaction of adjacent parallel joints in one column also has significant influence on mechanical behavior of jointed rock mass. Chen et al.17,18 investigated the influence of joint orientation and joint persistence on mechanical behavior of jointed rock mass by varying α and k while keeping other geometric parameters constant (e.g., d=30 mm, h=30 mm). Herein, we focus on the interaction of adjacent parallel joints in one column, thus the joint spacing, d, was varied to be 75 mm, 50 mm, 37.5 mm and 30 mm, as shown in Fig. 3. Correspondingly, the jointed rock mass models have 2, 3, 4 and 5 parallel joint planes respectively. In addition, the joint overlap, Lo, was introduced to describe the relative distance along the joint dip direction between joints (or joint and rock bridge) in adjacent parallel joint planes. Note that a similar joint geometric parameter such as joint step angle was investigated by other researches.20 However, the joint step angle is dependent of joint overlap, joint spacing and joint length. Thus, the joint overlap seems more independent and suitable to geometrically describe the parallel joint position. The joint overlap, Lo, was varied to be 3 mm, 10.5 mm and 18 mm, as shown in Fig. 4. Moreover, as one of the most important geometric parameters that influence the anisotropic behavior of jointed rock mass,21,22 the joint dip angle is prior considered when dealing with the effect of other joint geometrical parameters, i.e. joint spacing, d, and joint overlap, Lo. That is to say, the effect of other joint geometrical parameters is investigated under different joint orientation. A range of joint dip angle is selected from 0° to 90° at an interval of 15°. On the other hand, the joint length,

2. Experimental program 2.1. Specimen preparation As a common kind of model material used in physical model studies, plaster has the characteristics of being easily accessible, inexpensive and reproducible and has been selected as rock-like material to simulate jointed rock masses having different joint configurations. The chemical component of the plaster is hemihydrate (CaSO4 • 1/2H2 O ). On mixing with water, hemihydrate is hydrated to form dihydrate(CaSO4 • 2H2 O ), which will precipitate to become hardened plaster. Recently, Chen et al.17,18 has utilized plaster specimens with non-persistent open flaws to investigate the combined influence of joint orientation and joint persistence on strength and deformation behavior of jointed rock mass. They demonstrated the significant influence of joint orientation and joint persistence on global responses of jointed rock mass under uniaxial compression. Their rock-like specimens were carefully prepared through a mixture of plaster and water in a proportion of 1: 0.6 by weight. The specimens were cured at room temperature for 21 days before being subjected to uniaxial compression testing. The mechanical properties of the plaster specimens are listed in Table 1. The dimensions of the test synthetic rock specimens were 150×150×50 mm3 (high × wide× thick). In preference to natural rock, this rock-like material presents much more homoTable 1 Mechanical properties of the plaster specimens.17,18. Density (kg/m3)

UCS (MPa)

Tensile strength (MPa)

Intact material cohesion (MPa)

Intact material friction angle

Poisson's ratio

Young's modulus (GPa)

1158

8.51

1.44

2.2

38°

0.11

2.56

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Fig. 1. Specimen preparation procedure.

Fig. 2. Joint arrangement and geometrical parameters.

and compared in a computer, and quadrangle isoparametric transforming approach is applied to achieve coordinate transformation from photo global coordinate system to specimen global coordinate system to fulfill calibration and calculation of displacements. A number of mechanical responses of the specimen under different experimental conditions can then be recorded, and the displacement, strain and other variables can then be obtained vividly in a post script software package.

rock bridge length and joint persistence are kept unchanged, i.e. Lj=18 mm, Lr=12 mm, k=0.6. 2.3. Testing procedure Uniaxial compression tests were carried out for identifying the effect of the two parameters aforesaid that describing the geometric relationship between adjacent parallel joints (Figs. 3 and 4). All experiments were performed at the State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology. Axial displacement was controlled to keep the rock-like specimens in a quasi-static state under compression at a rate of 0.0025 mm/s. The axial force and displacements were recorded automatically by the loading equipment. A photogrammetric system called PhotoInfor developed by Li et al.23 was utilized for all tests. The PhotoInfor system provides information on deformation at the surface of the specimen during testing, by tracking fine movements of particles on the outside of the specimen. During the test, a digital camera is set up to take photographs of the specimen at different stages. After the test, changes of the coordinates of each point in the surface of the specimen are identified

3. Effect of parallel joint interaction on mechanical behavior of jointed rock mass models 3.1. Mechanical behavior of jointed rock mass models having one joint plane For better understanding the effect of joint interaction from adjacent parallel joint planes, the mechanical behavior of jointed rock mass models just having one joint plane is firstly investigated. The joint dip angle, α, is varied from 0° to 90° with an interval of 15°, while the other joint geometrical parameters are kept constant (i.e. Lj=18 mm, Lr=12 mm, k=0.6). Fig. 5 displays the failure mode of jointed rock 42

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Fig. 3. Jointed rock mass models having different joint spacing (α=15°, Lo=18 mm).

Fig. 4. Jointed rock mass models having different joint overlap (α=0°, d=50 mm).

mass models having one joint plane. As shown in this figure, preexisting joints play a very significant role on failure behavior of jointed rock mass models. Specifically, as a specimen containing non-persistent joints is loaded under compression, new cracks are initiated at the tips of the joints subjected to high stress concentration. This phenomena is in agreement with Griffith's criterion.24 Also, the final failure mode is in great dependence of the joint dip angle. Accordingly, four failure modes can be defined in terms of the way in which newly generated cracks develop and coalesce, together with the pre-existing joints, to fail the jointed rock mass models having one joint plane. The four failure modes are, respectively, tensile failure across the joint plane (Ⅰ failure mode), shear failure along the joint plane (Ⅱ failure mode), tensile failure along the joint plane (Ⅲ failure mode), and intact material failure (Ⅳ failure mode). Note that the technical terminology used for failure modes in this manuscript is supposed to describe the geometric relationship between the pre-existing joint plane and the newly generated cracks. The tensile failure across the joint plane (Ⅰfailure mode) is in accordance with the stepped failure proposed by Prudencio and Van Sint Jan 2 or step-path failure proposed by Jamil 25 and Bahaaddini et al..3 Because theⅠfailure mode herein is defined according to the failure pattern of jointed rock model having just one joint plane, a step-path macro failure cannot be found. However, when the jointed rock models have three or four joint planes the step-path failures can be discovered. Moreover, the shear failure along the joint plane (Ⅱ failure mode) and tensile failure along the joint plane (Ⅲ failure mode) are consistent with the failure through a plane 2 or planar failure.3,25 According to Prudencio and Van Sint Jan,2 failure through a plane occurs when the failure surface propagates along a joint plane and the intervening rock bridges, developing a single plane with the same dip as the joints. But the failure through a plane or planar failure cannot describe the type of newly generated cracks (shear cracks or tensile cracks) found in the intervening rock bridges. Therefore, to indicate the difference occurring in the intervening bridges the planar failure is divided into the shear failure along the joint plane (Ⅱ failure mode) and tensile failure along the joint

plane (Ⅲ failure mode). When the pre-existing joints have negligible effect on the failure of the jointed rock models, the failure mode is defined as intact failure. When the joint dip angle is low (e.g., α=0° and 15°), with the axial compression stress increasing there are wing cracks developing from the pre-existing joint tips. As shown in Fig. 6, the wing cracks are tensile cracks that initiate at an angle from the joint tips and propagate in a stable manner towards the direction of maximum compression.26 With the development of wing cracks, macro failure planes going through the whole model fail the jointed rock mass models. At the same time, the joint interfaces come close to interact with each other. The open joints become closed joints. In present paper, the aforementioned failure phenomenon is defined as tensile failure across the joint plane (Ⅰ failure mode). This failure mode takes place to the jointed rock mass models with joint dip angle of 0° and 15° (Fig. 5). At α=45°, under compression loading the quasi-coplanar secondary cracks (Fig. 6) occur to these pre-existing joint tips. Secondary cracks are shear cracks that also initiate from the tips of joints and initially propagate in a stable manner. The new cracks propagate along a joint plane and the intervening rock bridges, finally together with preexisting joints developing a macro failure plane having the same dip angle as the joint plane. This failure phenomenon is defined to be shear failure along the joint plane (Ⅱ failure mode). Note that when the joint dip angle is 30° the jointed rock mass model fails in a mixed mode of Ⅰfailure mode and Ⅱ failure mode. When the joint dip angles are 60° and 75°, with increasing compression loading both the wing cracks and the oblique secondary cracks initiate from the joint tips, as shown in Fig. 7. Even though the wing cracks develop towards the direction of compression loading, they coalesce with the oblique secondary cracks (see Fig. 6) initiated from adjacent joint tips, or directly with the adjacent joint tips, in a short path rather than come to the jointed rock model boundary to create a through-going failure plane. The oblique secondary crack initiates at an angle with the pre-existing joint similar to the wing crack but in the opposite way. Thus, the intervening rock bridges between joints are 43

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Fig. 5. Failure modes of jointed rock mass models with different joint angle.

separated to be independent small rock blocks (Fig. 5). As the wing cracks are generally linked with the oblique secondary cracks from adjacent joint tips, there is a macro failure plane generated along the joint plane which is similar to the shear failure along the joint plane (Ⅱ failure mode). Due to the involvement of wing cracks, this failure phenomenon is defined as tensile failure along the joint plane (Ⅲ failure mode) to differentiate it from Ⅱ failure mode. At α=90°, although cracks occur to the rock bridges between pre-existing joints along the joint plane, the jointed rock mass models finally fails through the intact material failure near the top and bottom ends. The joint plane has negligible effect on the failure behavior of the jointed rock mass. This failure phenomenon can be defined to be intact material failure mode. The aforesaid failure modes induce variation of resistance capability of jointed rock mass models having one joint plane. Fig. 8 displays the strength variation of jointed rock mass models with different joint orientation. Note that the strength value of jointed rock mass models was normalized by the strength value of intact rock model, i.e. 8.51 MPa. As shown in Fig. 8, the joint dip angle has significant effect

Fig. 6. Crack pattern observed in pre-jointed rock specimen (Adapted from Ref. 25).

Fig. 7. The tensile failure along the joint plane mode (α=75°).

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As the joint dip angle increases to 60° and 75°, the jointed rock mass models fail in tensile failure along the joint plane mode (Ⅲ failure mode), as shown in Fig. 5. With comparison to shear failure along the joint plane mode (Ⅱfailure mode), Ⅲ failure mode produces longer and more curved failure plane. Griffith theory states that the amount of energy that must be applied to cause fracture is (at least in part) governed by the length of intact material that must be ruptured in the failure process.24 In addition, even after the generation of macro failure plane the broken rock blocks can still resist the compression loading because of their contact with top and bottom loading plates. Therefore, the jointed rock mass models having dip angles of 60° and 75° produce higher strength values, which are 0.57 and 0.84 respectively. At α=90°, the normalized strength value the highest, 0.92 times of the intact rock model strength, due to the fact that the jointed rock model fails in intact material failure mode. Fig. 9 demonstrates the displacement distribution in the surface of jointed rock mass models at the peak stress stage. These displacement distribution images were analyzed and post scripted through PhotoInfor system based on a series of photos captured during the compression tests. As shown in Fig. 9, the displacement distribution in the surface of the jointed rock mass models is significantly influenced by the differently orientated pre-existing joint plane. In particular, when the joint dip angle is low (i.e. α=0° and 15°) the maximum displacement occurs near the right and left boundaries of the jointed rock mass models. Moreover, along the joint plane there is an obvious difference line of displacement which implies the closing of open joints as well as the crushing of rock bridges between joints. The maximum displacement values for α=0° and 15° are 4.91 mm and 4.56 mm, respectively. As the joint dip angle increases to 30°, the difference line of displacement is more obvious. This phenomenon is the result of the slipping responses along the pre-existing joint plane. In addition, at α=45° although the difference line of displacement seems to disappear, the shear failure along the joint plane mode leads to the opposite movements of the left and right jointed rock mass parts. The gap between joint interfaces changes to be larger rather than to be closed. At α=60° and 75°, the jointed rock mass models fail in a mode of tensile failure along the joint plane. Compared to α=45° case, the detachment

on strength behavior of jointed rock mass models having one joint plane. At α=0°, the compression stress is concentrated on the rock bridges which induces the Ⅰfailure mode (tensile failure across the joint plane); thus, the strength value of the jointed rock mass model is heavily reduced compared to intact rock model due to the fact that the rock bridges only occupy a little proportion of the total horizontal cross sectional area (i.e. 40%). Even though the interaction of joint interfaces could resist the compression loading somehow when the joints come to be closed, the rock bridges between pre-existing joints have already crushed then. The normalized strength value is 0.66. Similarly, at α=15° the jointed rock mass model fails in Ⅰfailure mode, and the normalized strength value is 0.63. The reason for this little reduction from 0.66 to 0.63 is the more non-uniform stress distribution in α=15° case compared to that of α=0° case. The shear failure along the joint plane mode (Ⅱ failure mode) produces low strength values, and the lowest uniaxial compressive strength occurs for α=45°. The normalized strength value for α=45° is only 0.45. At α=30° both Ⅰfailure mode and Ⅱ failure mode involve in the generation of failure planes through the jointed rock mass model (Fig. 5); therefore, the strength value is larger than that for α=45°. The normalized strength value for α=30° is 0.54.

Fig. 8. Normalized strength of jointed rock mass models with one joint plane.

Fig. 9. Displacement images of jointed rock mass models having one joint plane at the peak stress (Displacement unit: mm).

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Fig. 10. Failure modes of jointed rock mass models having different joint spacing (Lo=18 mm).

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of pre-existing joint interfaces at α=60° and 75° turns out to be worse with the maximum displacements along the joint plane of 2.24 mm and 1.89 mm; while at α=45° the maximum displacement along the joint plane is 1.68 mm. When the pre-existing joints are vertical (α=90°), the maximum displacement happens near the bottom end of the jointed rock mass model regardless of the joint plane. The maximum displacement value at α=90° is 1.97 mm.

induces the reduction of resistance capability of jointed rock mass models having low joint dip angle (α=0° and 15°), even no change of failure mode. At α=30°, the jointed rock mass model failure mode changes with the joint spacing variation. When the jointed rock mass models have one or two or three joint planes, a mixed mode of tensile failure across the joint plane (Ⅰfailure mode) and shear failure along the joint plane (Ⅱfailure mode) occurs (Figs. 5 and 10). With axial compression, rock blocks are generated to slide along the joint plane. Simultaneously, some wing cracks initiate and propagate along the loading directions. In the case of two joint planes (d=75 mm), the wing cracks only take place near the top and bottom ends of the jointed rock mass model; while there are no wing cracks observed in the middle region between the two parallel joint planes. That is to say the pre-existing joint planes have negligible interaction with each other. On the contrary, when the joint spacing, d, decreases to 50 mm (three joint planes) the wing cracks begin to appear in the middle region of the jointed rock mass model, which reduces the normalized strength values from 0.47 to 0.39. With the joint spacing, d, further decreasing to be 37.5 mm and 30 mm, only the Ⅰfailure mode occurs in the jointed rock mass models rather than a mixed mode of Ⅰfailure mode and Ⅱfailure mode. Once the jointed rock mass models are subjected to uniaxial compression, lots of tensile cracks (i.e. wing cracks) are initiated at the joint tips and propagate perpendicular to the joint plane. These tensile cracks reach the tips of adjacent parallel joint planes. As a result, some bocks are generated, and stress concentration at tips of joints leads to rotation of blocks, as shown in Fig. 10. The rotation of blocks increases deformation towards the lateral sides of the jointed rock mass model, and thus restrains the shear and sliding response along the joint planes. The normalized strength values are further reduced to be 0.35 and 0.30, respectively, in the cases of d=37.5 mm and d=30 mm. At α=45°, the joint spacing decrease has similar effect on the failure mode as at α=30°. Particularly, when joint plane number increases from one to two and three, the failure mode transforms from Ⅱ failure mode to a mixed mode of Ⅰfailure mode and Ⅱfailure mode. The corresponding normalized strength value changes from 0.45 to 0.41 and 0.35. Furthermore, the failure mode alerts to be Ⅰfailure mode (tensile failure across the joint plane) as the joint spacing, d, decreases as 37.5 mm and 30 mm. The normalized strength values are 0.33 and 0.29, respectively. The rotation of blocks is also observed in the case of d=30 mm, as displayed in Fig. 10 at α=45°. At α=60°, when the joint spacing is less than 75 mm (d≦75 mm) the jointed rock mass models fail in a mixed mode of Ⅰfailure mode and Ⅲ failure mode. Under the uniaxial compression, some tensile cracks (wing cracks) develop to link with the oblique secondary crack or the adjacent joint tips directly to form the failure mode of tensile failure along the joint plane (Ⅲ failure mode); whereas, some other tensile cracks keep propagating in the direction perpendicular to the joint plane to interact with parallel joint planes. When the joint spacing is 75 mm, the tensile cracks are rarely observed in the middle region between two parallel joint planes. With the decrease of joint spacing from 75 mm to 50 mm, 37.5 mm and 30 mm, increasing tensile cracks appear in the middle regions of the jointed rock mass models, which implies the increasing interaction of adjacent parallel joints and reduces the normalized strength values. The corresponding normalized strength values are 0.52, 0.41, 0.36 and 0.34, respectively (Fig. 11). At α=75°, regardless of the joint spacing decreasing from 75 mm to 30 mm through 50 mm and 37.5 mm, the jointed rock mass models all fail in tensile failure along the joint plane mode. After several macro failure planes formed, the whole jointed rock mass model break into multiple beams, as shown in Fig. 10. When the joint spacing is large, e.g., d=75 mm, the separated rock beams or blocks can still resist the compression loading because of their contacts with the loading plates at the ends. On the other hand, when the joint spacing is small, e.g., d=30 mm, some separated rock beams having no contact with the loading plates will lose their capability to resist the compression

3.2. Effect of joint spacing on mechanical behavior of a jointed rock mass model In order to investigate the effect of joint spacing on the mechanical behavior of a jointed rock mass model, the joint spacing value was varied to be 75 mm, 50 mm, 37.5 mm and 30 mm, as shown in Fig. 3. Correspondingly, the jointed rock mass models have two, three, four and five joint planes, respectively. As aforementioned, the effect of joint spacing is studied in a range of joint dip angle, from 0° to 90° with an interval of 15°. The other geometric parameters are kept constant, i.e. Lj=18 mm, Lr=12 mm, Lo =18 mm. Figs. 10 and 11, respectively, display the failure modes and uniaxial compression strength values of jointed rock mass models having different joint spacing. Figs. 10 and 11 show that the joint spacing has a significant influence on the mechanical behavior of jointed rock mass models. Particularly, when the pre-existing joints are horizontal (α=0°), even though all the jointed rock mass models fail in tensile failure across the joint plane mode (Ⅰfailure mode) regardless of the spacing values between parallel joint planes, the normalized strength reduces with the decrease of joint spacing (Fig. 11). As the joint spacing, d, decreases from 75 mm to 50 mm, 37.5 mm and 30 mm, the corresponding normalized strength value reduces from 0.55 to 0.48, 0.41 and 0.38, respectively, which are all less than that of jointed rock mass model having just one joint plane. As shown in Fig. 5, under compression wing cracks initiate from the joint tips and develop along the loading direction. When these wing cracks develop to form a through-going macro plane, the whole rock model having one pre-existing joint plane fails. As the jointed rock models which have multiple joint planes (d≦75 mm) are subjected to compression loading, wing cracks initiate from the joint tips belonging to different joint planes almost at the same time (Fig. 10). The decrease of joint spacing reduces the energy required for wing cracks to rupture the intact materials by coalescence with each other, which further reduce the global strength of the jointed rock model. Moreover, the jointed rock models with joint dip angle of 15° also fails in tensile failure across the joint plane (Ⅰfailure mode) no matter how the joint spacing changes, as shown in Fig. 10. However, as the joint spacing, d, decreases from 75 mm to 50 mm, 37.5 mm and 30 mm, the corresponding normalized strength values are 0.54, 0.45, 0.40 and 0.36, respectively. The interaction of parallel joint planes

Fig. 11. Normalized strength of jointed rock mass models having different joint spacing (Lo=18 mm).

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Fig. 12. Displacement images of jointed rock mass models with different joint spacing at the peak stress (Lo=18 mm, displacement unit: mm).

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0.34 and 0.30, respectively, as shown in Fig. 14. At α=15° and 30°, with the decrease of joint overlap the failure mode changes from tensile failure across the joint plane mode (Ⅰfailure mode) to a mixed mode of tensile failure across the joint plane mode and shear failure along the joint plane mode (Ⅱ failure mode). As aforesaid in Section 3.1, the shear failure along the joint plane mode corresponds to low strength behavior. Thus, the normalized strength value is reduced with the decrease of joint overlap from 18 mm to 3 mm through 10.5 mm, as shown in Fig. 14. In addition, at α=45° the failure mode changes from tensile failure across the joint plane mode (Ⅰfailure mode) to a mixed mode of tensile failure across the joint plane mode (Ⅰ failure mode) and tensile failure along the joint plane mode (Ⅲ failure mode) with the joint overlap decrease. The tensile failure along the joint plane mode involves the generation of macro failure plane by coalescence of wing cracks and pre-existing joints in a short path compared to that by coalescence of wing cracks from different planes. The decrease of joint overlap advanced the generation of though-going macro failure plane. Therefore, with the joint overlap decreasing from 18 mm to 3 mm through 10.5 mm, the corresponding normalized strength value reduces from 0.29 to 0.25 through 0.26, respectively. When the joint dip angle is high (i.e. α=60°, 75° and 90°), the failure mode of jointed rock mass models does not change with the variation of joint overlap. And the joint overlap has negligible influence on the normalized strength value (Fig. 14). Fig. 15 displays the displacement distribution in the surface of jointed rock mass models with different joint overlap, Lo, at the peak stress stage. As aforementioned, when the joint dip angle is high (i.e. α=60°, 75° and 90°) the joint overlap has negligible effect on the mechanical behavior of jointed rock mass models. Thus, the displacement distribution for α=0°, 15°, 30° and 45° is analyzed herein, as shown in Fig. 15. This figure shows that the joint overlap has pronounced effect on the displacement distribution in the surface during compression test. At α=0°, the maximum displacement occurs near the lateral sides of jointed rock mass models. With the decrease of joint overlap, wing cracks (tensile cracks) distribute more extensively around the whole rock mass model, as shown in Fig. 13, which reduces the deformation near the lateral sides at peak stress. At α=15° and 30°, when the joint overlap is high, i.e. Lo=18 mm, the rotation of rock blocks happens, which leads to high displacement. As the joint overlap decreases, the rotation of rock blocks response eliminates, and further decreases the maximum displacement value, as shown in Fig. 15. Moreover, the tensile failure along the joint plane mode (Ⅲ failure mode) induces less dilation deformation than that of tensile failure across the joint plane mode (Ⅰfailure mode). As a result, when the joint dip angle increases to be 45° the mixed model of Ⅰfailure mode and Ⅲ failure mode induces less displacement in the surface than that of justⅠfailure mode. With the joint overlap, Lo, decreasing from 18 mm to 3 m through 10.5 mm, the corresponding maximum displacement value reduces from 4.07 mm to 1.88 mm through 2.27 mm, respectively, as displayed in Fig. 15.

loading. This, to some extent, explains the reduction of jointed rock mass model strength with the decrease of joint spacing. As the joint spacing, d, decreases from 75 mm to be 50 mm, 37.5 mm and 30 mm, the normalized strength value changes from 0.78 to 0.72, 0.67 and 0.65, respectively (Fig. 11). Moreover, at α=90° the jointed rock mass models fail in intact material failure mode (Ⅳ failure mode) in spite of the variation of joint spacing. However, the decrease of joint spacing from 75 mm to 30 mm still induces a slight reduction of normalized strength from 0.92 to 0.85, which might be because of the increase of flaws (pre-existing joints) in the rock-like materials. Fig. 12 displays the displacement distribution in the surface of jointed rock mass models with different joint spacing at the peak stress stage. In accordance with this figure, the variation of joint spacing has different influence on the displacement distribution in the surface of jointed rock mass models depending on the joint orientation. To be specific, the maximum displacement value reduces with the decrease of joint spacing when the joint dip angle is horizontal, i.e. α=0°. In this case, when the joint spacing is large, for example d=75 mm，the macro failure plane comprised by wing cracks mainly concentrate on the lateral sides of the jointed rock mass models to produce large deformation. When the joint spacing is less, the wing cracks distribute more uniformly to reduce the deformation near the lateral sides, and further reduce the maximum deformation value. As the joint dip angle increases to 15°, the tensile cracks distribute uniformly regardless of the joint spacing. With the decrease of joint spacing, the developed wing crack number increases, which further increases the maximum displacement value, as shown in Fig. 12. At α=30° and 45°, with the decrease of joint spacing the rotation of blocks separated by tensile cracks between parallel joint planes begins to dominate the failure and deformation behavior of jointed rock mass models. The rotation of blocks significantly increases the maximum deformation values, as shown in Fig. 12. Furthermore, at α=60° and 75° the tensile failure along the joint plane mode (Ⅲ failure mode) becomes dominant to influence the jointed rock mass model deformability. The generated macro failure plane induces the detachment of pre-existing joint interfaces. Thus, more joint planes produce larger deformation values (Fig. 12). Similarly, at α=90° the maximum deformation value increases with the decrease of joint spacing. 3.3. Effect of joint overlap on mechanical behavior of a jointed rock mass model Joint overlap, Lo, represents the position of joints with respect to adjacent parallel joints along the joint orientation (Fig. 4). To consider the effect of joint overlap on failure mode, strength and deformation behavior of jointed rock mass models, the other geometrical parameters except for α are kept constant (Lj=18 mm, Lr=12 mm, d=30 mm) and joint overlap is varied from 18 mm to 3 mm through 10.5 mm. Figs. 13 and 14, respectively, display the failure modes and normalized strength of jointed rock mass models having different joint overlap. As shown in Fig. 13, the joint dip angle dominates the failure behavior of jointed rock mass models, whereas the effect of joint overlap on the failure mode is less significant. Nevertheless, the variation of joint overlap still induces some failure characteristics even with the same failure mode, and further induces the slight difference in uniaxial compression strength (Fig. 14). For example, at α=0° even though all jointed rock mass models having different joint overlap fail inⅠfailure mode (tensile failure across the joint plane), there are more tensile cracks (wing cracks) generated with decreasing joint overlap, Lo. The tensile cracks not only initiate from joint tips but also from the middle of joints. This phenomenon implies the weakness of resistance capability of intact materials between parallel joint planes under compression when the joint overlap value is small. Correspondingly, the normalized strength of jointed rock mass model reduces with the decrease of joint overlap. As the joint overlap, Lo, decreases from 18 mm to 10.5 mm and 3 mm, the normalized strength values are 0.37,

3.4. Effect of parallel joint interaction on mechanical behavior of a jointed rock mass model According to the aforesaid laboratory testing results, both of the joint spacing and joint overlap have significant effect on the mechanical behavior of jointed rock mass models. The joint spacing, d, and the joint overlap, Lo, describe the geometric position of pre-existing joints with respect to that of adjacent parallel joints perpendicular to the joint orientation and along the joint orientation, respectively. The variation of these two geometric parameters, joint spacing and joint overlap, is supposed to affect the interaction between adjacent parallel joints. In present study, it is found that the wing cracks (tensile cracks) developed from joint tips tend to connect any two of the parallel joint planes, as shown in Figs. 10 and 13. In accordance with Sections 3.2 49

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Fig. 13. Failure modes of jointed rock mass models having different joint overlap (d=30 mm).

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and 3.3, the variation of joint spacing and joint overlap induces the variation of wing crack amount at certain joint dip angles, and further induces the change of failure mode, normalized strength and displacement of jointed rock mass models. Therefore, we could suppose that the wing crack development and coalescence represent the interaction of parallel joints. The more wing cracks (tensile cracks) generated between parallel joint planes, the more significance of parallel joint interaction. According to Prudencio and Van Sint Jan,2 the rotational failure, that happens when the wing cracks of parallel joints coalesce and the model fractures into a series of blocks, is associated with a very low strength, ductile behavior, and large deformation. Bahaaddini et al.3 explains that the controlling effect of tensile wing cracks in block rotation and step-path failure mode results in a significant reduction in strength and Young's modulus. Cording and Jamil 27 claimed that for step-path failure mode the tensile strength of intervening rock bridges has a controlling effect on the failure strength of jointed rock samples. The wing cracks deteriorate the global strength of the whole rock models.

Fig. 14. Normalized strength of jointed rock mass models having different joint overlap (d=30 mm).

Fig. 15. Displacement images of jointed rock mass models with different joint overlap at the peak stress (d=30 mm, displacement unit: mm).

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Fig. 16. Failure modes of jointed rock mass models having different joint overlap (α=30°, d=70 mm).

interaction works not only when the joint dip angle is relative low, e.g., α=0°, 15°, 30°, 45° and 60°, but also when the joint spacing is properly low. With proper joint dip angle and joint spacing values, the joint overlap is further considered to affect jointed rock mass behavior. The joint spacing has significant influence on the mechanical behavior of jointed rock mass models. With the decrease of joint spacing, the normalized strength value and the maximum displacement value at peak stress reduces except at α=0°. The parallel joint interaction increases with the decrease of joint spacing when the joint dip angle is less than 60°. The joint overlap also has significant influence on the mechanical behavior of jointed rock mass models when the joint dip angle is less than 45° at d=30 mm. The normalized strength value and the maximum displacement value at peak stress reduces with the decrease of joint overlap except at α=0°.

TheⅠfailure mode (tensile failure across the joint plane mode) leads to the generation of wing cracks (tensile cracks). TheⅠfailure mode occurs when the joint dip angle is not high enough, i.e. α=0°, 15°, 30°, 45° and 60°, as shown in Fig. 10. That is to say, the parallel joint interaction is significantly influenced by the joint orientation. With the increase of joint dip angle, the parallel joint interaction decreases. The initiation of wing cracks from pre-existing joints is driven by the normal stress component applied on the joint interfaces. With smaller joint dip angle, the more normal stress component is applied on the joint interfaces, and it is easier to develop wing cracks from joint dips; and vice verse. Furthermore, to enable the generation of wing cracks between two parallel joint planes a proper joint spacing value is also required. For example, when the joint spacing is large, e.g., d=75 mm, there are no wing cracks generated between the two parallel joint planes, even though at α=30°, 45° and 60° (Fig. 10). The coalescence of new cracks to form a macro failure plane prefers a short path. A further test, as shown in Fig. 16, shows that the variation of joint overlap, Lo, cannot induce wing cracks (interaction) between the parallel joint planes when the joint spacing, d, is 75 mm at α=30°. Therefore, the effect of joint overlap on interaction behavior of parallel joints depends not only the joint orientation but also on the joint spacing. So it is reasonable to consider the effect of joint overlap on mechanical behavior of jointed rock mass models with a proper joint spacing, e.g., d=30 mm. The joint overlap influences the parallel joint interaction through the modification of normal stress component applied on the joint interfaces. At low joint dip angle, e.g., α=0°, 15° and 30°, with the decrease of joint overlap, there are more normal stress component applied on the joint interfaces transferred from that applied on the rock bridges. Thus, it is easier to develop wing cracks (tensile cracks).

Acknowledgement This research was supported by the National Basic Research 973 Program of China (Grant Nos. 2013CB036003), the National Natural Science Foundation of China (Grant No. 51374198), Natural Science Foundation of Jiangsu Province for Distinguished Young Scholars (BK20150005). Special thankfulness are given to Professor Yuan-Hai Li for his technical support on using PhotoInfor system. References 1 Kim BH, Kaiser PK, Grasselli G. Influence of persistence on behavior of fractured rock masses., London: Geological Society; 2007, pp.p161–p173 [Special Publications]. 2 Prudencio M, Van Sint Jan M. Strength and failure modes of rock mass models with non-persistent joints. Int J Rock Mech Min Sci. 2007;44(6):890–902. 3 Bahaaddini M, Sharrock G, Hebblewhite BK. Numerical investigation of the effect of joint geometrical parameters on the mechanical properties of a non-persistent jointed rock mass under uniaxial compression. Comput Geotech. 2013;49:206–225. 4 Itasca Consulting Group Inc., PFC3D Manual, Version 4.0.Minneapolis, Minnesota, 2008. 5 Fan X, Kulatilake PHSW, Chen X. Mechanical behavior of rock-like jointed blocks with multi-non-persistent joints under uniaxial loading: a particle mechanics approach. Eng Geol. 2015;190:17–32. 6 Yang XX, Kulatilake PHSW, Jing HW, Yang SQ. Numerical simulation of a jointed rock block mechanical behavior adjacent to an underground excavation and comparison with physical model test results. Tunn Under Space Techn. 2015;50:129–142. 7 Ghazvinian A, Sarfarazi V, Schubert W, Blumel M. A study of the failure mechanism of planar non-persistent open joints using PFC2D. Rock Mech Rock Eng. 2012;45:677–693. 8 Wasantha PLP, Ranjith PG, Viete DR, Luo L. Influence of the geometry of partiallyspanning joints on the uniaxial compressive strength of rock. Int J Rock Mech Min Sci. 2012;50:140–146. 9 Xu T, Ranjith PG, Wasantha PLP, Zhao J, Tang CA, Zhu WC. Influence of the geometry of partially-spanning joints on mechanical properties of rock in uniaxial compression. Eng Geol. 2013;167:134–147.

4. Conclusions Jointed rock mass specimens prepared with rock-like materials consisted of plaster and water are utilized to investigate the effect of parallel joint interaction on the mechanical behavior of a rock mass model having non-persistent open joints under uniaxial compression. The failure mode of jointed rock mass models is in significant dependence of the joint orientation. Four basic failure modes identified from the testing results are tensile failure across the joint plane (Ⅰfailure mode), shear failure along the joint plane (Ⅱ failure mode), tensile failure along the joint plane (Ⅲ failure mode), and intact material failure (Ⅳ failure mode). The parallel joint planes interact with each other through the wing cracks developed from the pre-existing joints. Under uniaxial compression the parallel joint interaction shows a significant dependence on the joint dip angle, joint spacing and joint overlap. The parallel joint 52

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18 Chen X, Liao ZH, Peng X. Deformability characteristics of jointed rock masses under uniaxial compression. Int J Min Sci Technol. 2012;22(2):213–221. 19 Dershowitz WS, Einstein HH. Characterizing rock joint geometry with joint system models. Rock Mech Rock Eng. 1988;21:21–51. 20 Bahaaddini M, Hagan P, Mitra R, Hebblewhite BK. Numerical study of the mechanical behavior of non-persistent jointed rock masses. Int J Geomech. 2016;15:04015035. 21 Kulatilake PHSW, Malama B, Wang JL. Physical and particle flow modeling of jointed rock block behavior under uniaxial loading. Int J Rock Mech Min Sci. 2001;38(5):641–657. 22 Yang XX, Kulatilake PHSW, Chen X, Jing HW, Yang SQ. Particle flow modeling of rock blocks with non-persistent open joints under uniaxial compression. Int J Geomech. 2016:04016020. 23 Li YH, Zhu HH, Ueno K. Deformation field measurement for granular soil model using image analysis. Chin J Geotech Eng. 2004;26(1):36–41. 24 Griffith AA. The phenomena of rupture and flow in solids. Philos Trans R Soc Lond. 1921;221A:163–198. 25 Jamil SM. Strength of non-persistent rock joints [Ph.D. thesis], Urbana, Illinois: University of Illinois; 1992. 26 Sagong M, Bobet M. Coalescence of multiple flaws in a rock-model material in uniaxial compression. Int J Rock Mech Min Sci. 2002;39:229–241. 27 Cording EJ, Jamil SM. Slide geometrieson rock slopes and walls. In: 4th South American congress on rock mechanics, Santiago, Chile. p. 199–221; 1997.

10 Sarfarazi V, Ghazvinian A, Schubert W, Blumel M, Nejati HR. Numerical simulation of the process of fracture of echelon rock joints. Rock Mech Rock Eng. 2014;47:1355–1371. 11 Tang CA, Lin P, Wong RHC, Chau KT. Analysis of crack coalescence in rock-like materials containing three flaws-Part Ⅱ: numerical approach. Int J Rock Mech Min Sci. 2001;38(7):925–939. 12 Zhang XP, Wong LNY. Crack initiation, propagation and coalescence in rock-like material containing two flaws: a numerical study based on bonded-particle model approach. Rock Mech Rock Eng. 2013;46:1001–1021. 13 Mughieda O, Omar MT. Stress analysis for rock mass failure with offset joints. Geotech Geol Eng. 2008;26(5):543–552. 14 Wong LNY, Einstein HH. Crack coalescence in molded gypsum and Carrara marble: Part 1. Macroscopic observations and interpretation. Rock Mech Rock Eng. 2009;42(3):475–511. 15 Yang SQ, Yang DS, Jing HW, Li YH, Wang SY. An experimental study of the fracture coalescence behavior of brittle sandstone specimens containing three fissure. Rock Mech Rock Eng. 2012;45(4):563–582. 16 Yang SQ, Huang YH, Jing HW, Liu XR. Discrete element modeling on fracture coalescence behavior of red sandstone containing two unparallel fissures under uniaxial compression. Eng Geol. 2014;178:28–48. 17 Chen X, Liao ZH, Li DJ. Experimental study on the effect of joint orientation and persistence on the strength and deformation properties of rock masses under uniaxial compression. Chin J Rock Mech Eng. 2011;30(4):781–789.

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