A new classification of failure mechanisms at tunnels in stratified rock masses through physical and numerical modeling

A new classification of failure mechanisms at tunnels in stratified rock masses through physical and numerical modeling

Tunnelling and Underground Space Technology 91 (2019) 103017 Contents lists available at ScienceDirect Tunnelling and Underground Space Technology j...

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Tunnelling and Underground Space Technology 91 (2019) 103017

Contents lists available at ScienceDirect

Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust

A new classification of failure mechanisms at tunnels in stratified rock masses through physical and numerical modeling

T



Nader Moussaeia, Mostafa Sharifzadehb, , Kourosh Sahriarc, Mohammad Hossein Khosravia a

School of Mining Engineering, University of Tehran, Iran Department of Mining Eng. Metallurgical Eng., Western Australian School of Mines; Mineral Energy and Chemical Eng. (WASM: MECE), Curtin University, Australia c Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran b

A R T I C LE I N FO

A B S T R A C T

Keywords: Tunneling Physical model Stratified rocks Ground behavior Failure mechanisms Collapsed zone Buckling zone

Stability of tunnels in stratified rock masses under low stress conditions is governed by the rock mass structure (blocks) and excavation geometry and dimension. A physical model was built and the effects of bedding dip, discontinuity spacing, and tunnel dimensions on tunnel failure mechanisms were examined. Based on the image analysis, three zones were recognized around the excavation consisting: stationary, collapsed and buckling zones. The buckling zone was more affected by layer dip angle. The collapsed zone occurred in three modes of block falls and sliding, and toppling. Also, numerical simulation using distinct element method was performed and verified. After model calibration, numerical simulations were extended to a wide range of block size and discontinuity gradients. Finally, considering physical test results, image analysis, and numerical simulation results, failure mechanisms in stratified rocks were classified using “bedding dip” and so called “dimensional ratio”. Results lead us to a deep insight of ground behavior around the shallow underground excavations in stratified blocky rock masses under low stress condition. Additionally the deformation mechanisms of blocks such as buckling, shearing, sliding are discussed in detail.

1. Introduction Shallow tunnels in rock masses are mostly excavated through geologically stratified and blocky structures with low in-situ stresses. Sedimentation, layering, tectonic activities, tensile jointing, and structures formed as a result of metamorphic or igneous rock flow are the main origins of such geologically stratified and blocky grounds. Generally, stratified structures are continuously extended and they have a planar geometry. Moreover, these structures do not sustain tensile stress in the direction perpendicular to the bedding plane, and shear strength of the bedding surface is remarkably lower than the intact rock (Brady and Brown, 2005). Due to the various tectonic forces in a geological lifetime, a stratified structure could possibly experience various conditions of fracturing such as masonry structures. In this case, two discontinuity sets cut perpendicularly through layers with particular spacing. Physical, numerical and analytical methods are often engaged to evaluate the behavior of excavation in such ground. Several assumptions have been involved in numerical and analytical methods which reduces the reliability of results. Hoek et al. (2000) was categorized the

instability mechanism based on the stress level and jointing condition. They classification is on based jointing condition and stress level. Physical, numerical and analytical methods were employed to simulate such structures so far. Fuenkajorn and Phueakphum (2010) used experimental studies to try and evaluate the influence of depth, discontinuity spacing, and dip on the maximum unsupported span of a shallow tunnel under static and cyclic loading in a blocky rock mass. They have found that maximum unsupported span increases with the decrease of vertical to horizontal discontinuity spacing ratio. The increase in discontinuity dip as well as depth contributes to the roof stability. The maximum accelerations of 0.225g reduced the maximum unsupported span up to 50%. Shen and Barton (1997) have determined the behavior of rock masses that included two joint sets with orthogonal discontinuities, based on numerical analysis. They found three zones: failure zone, open zone, and shear zone around a tunnel in various conditions of rock mass. Jiang et al. (2006) have evaluated the deformation of underground excavations at different discontinuity geometries. Jia and Tang (2008) have studied the influence of bedding dip on tunnel stability using rock failure process analysis (RFPA) code. Moyo and Stacey (2012) have studied mechanisms of rock bolts in

⁎ Corresponding author at: Department of Mining Eng. Metallurgical Eng., Western Australian School of Mines; Mineral Energy and Chemical Eng. (WASM: MECE), Curtin University, Kalgoorlie 6430, Australia. E-mail address: [email protected] (M. Sharifzadeh).

https://doi.org/10.1016/j.tust.2019.103017 Received 6 February 2018; Received in revised form 30 January 2019; Accepted 22 June 2019 Available online 01 July 2019 0886-7798/ © 2019 Published by Elsevier Ltd.

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(Fig. 1) was established to study the tunnel failure mechanisms under different tunnel size, rock mass block size and bedding inclination. Accordingly, at first the governing factors for stability analysis of underground excavations in stratified ground such as bedding dip, discontinuity spacing and tunnel dimensions were determined and classified. Physical and numerical tests were designed and implemented to cover all governing factors. For this purpose, a testing apparatus was developed and a wide range of experiments were designed and tested to study failure mechanisms for various ground conditions. Finally, considering test results tunnel failure mechanisms were identified and categorized based bedding dip and newly introduced dimensional ratio (DR).

jointed rock masses in deep mining, based on the small-scale models. Sagong et al. (2011) have presented a rock-like model under biaxial compressive loading to investigate the failure mechanism around a circular tunnel for various discontinuity dips. They revealed that tensile cracks initiated at low discontinuity dip and in a direction perpendicular to the discontinuity around the tunnel. Kulatilake et al. (2001) have examined the effect of discontinuity dip on failure modes of a rock-like cast (replica). They found three failure modes: tensile, shear and combined mode under uniaxial compression test. Mode 1 occurs at low dip of discontinuity (0–15 degree to the horizontal) as tensile fracture. Mode 2 is shear failure when discontinuity dip was greater than 35 degrees Mode 3 is the combined condition and occurs when discontinuity dip is 15–35 degrees. He et al. (2010, 2011) used physical model to study the behavior of the area around the roadway in Qishan underground coal mine. They built several model with various bedding dips. The test results show that the damaged zone is localized in a limited area around a tunnel in horizontal layers and damage zone is speared parallel to the layers in vertical bedding. Also, they compared full face and sequential excavation methods using Infrared Radiation Temperature (IRT) distributions. Whittaker and Reddish (1989) have investigated the propagation of fractures in overburden (long wall excavation) using the gravitational force as loading in a model. Despite the presented physical models to study the effect of block’s geometry and orientation improved our understanding, but most of the models so far have two main shortcoming consisting; firstly, they did not apply the influence of various effective factors in the models, and secondly, they are considered one aspect of instability mechanism such as maximum unsupported span or roof failure mechanism. To overcome these shortcomings, in this paper an comprehensive research procedure

2. Test setup 2.1. Test material The material properties used in physical modeling must be representative of the real material, which makes it possible to study the failure mechanism around underground excavations in stratified structures. Various materials such as concrete, aluminum blocks and rock blocks were used so far in the construction of physical models. There were many objections to using these materials because of a lack of representative properties. The main shortcomings of often used materials for physical modelling are listed in Table 1. One of the major concerns in physical modelling is material reproducibility properties which are defined as its properties that do not change significantly from one to another block. To overcome the shortcomings of the materials illustrated in

Fig. 1. Research procedure to study the failure mechanism of underground excavations in stratified structures using physical and numerical modeling. 2

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Table 1 Drawbacks of some commonly used materials in physical modeling. Materials Any kind of mixture (Concrete, chalk, …)

Aluminum block

Natural rock

Shortcoming

Advantage

1. Preparing and curing of mixture is time consuming process 2. Mechanical properties of block surfaces are not necessarily same (property anisotropy) 3. The properties in the prepared blocks are not reproducible 1. Cutting of the blocks with similar and equal dimensions are difficult and timeconsuming 2. Aluminum is expensive 1. The cutting of rocks to small blocks is difficult. So model size should be big enough to represent the real condition 2. Cutting and finishing of rock is expensive and time-consuming

1. MDF is relatively inexpensive and low-priced compared to alternative materials. 2. It is easy to cut down to a specified block size. 3. It is easy to reproduce several blocks with similar properties (All used blocks were cut from one sheet with same saw). 4. Strength parameters are not the same at cut surfaces (representative of joint surfaces) and smooth surfaces (representative of bedding surfaces). 5. MDF itself has a stratified structure. Therefore, its appearance is like the real stratified rock structures. 6. MDF is easily accessible and available with reasonable quality and price. Therefore, MDF was selected and then mechanical uniaxial and compressive tests were carried out in a laboratory to determine the blocks’ properties under normal stress and shear condition. To determine the mechanical properties of MDF, uniaxial compressive and direct shear tests were performed on blocks. The tests on MDF samples were performed according to ISRM Suggested Methods (Fairhurst and Hudson, 1999; and Muralha, 1974–2006). The experimental test results on MDF are illustrated in Table 2. Based on the minimum young modulus (435 MPa) and density (7 kN/m3) of the materials as well as the height of the model (85 cm), the maximum axial strain (contraction) will be almost 1.4e−5 during the physical model tests. This confirms that MDF blocks have enough rigidity as a test material. Purpose of the uniaxial test is to assure that, the block remains rigid under the applied tresses during the physical tests. The normal stress must be equal to the in-situ stress in direct-shear test. However, lateral

2.2. Test setup Stainless steel was used for the test apparatus frame with the dimensions of 1000 mm × 1100 mm. Three loading jaws were placed in the framework; these jaws were used to provide zero displacement at the boundaries. Internal dimensions of framework, including the jaws, are 850 mm in height by 650 mm in width. The details of the framework are shown in Fig. 2. Blocks with various shapes and dimensions such as cubes and prisms were used to construct the stratified structure models with different bedding inclinations. Small blocks are used to fill the outer and inner boundaries in the model as shown in Fig. 3. The stratified structure models are made out of 1500 blocks on average. Tunnel shape was considered as rectangular and full face excavation was adapted in the model. The tunnel axis alignment and strike of the bedding plane were considered as parallel. Tunnel excavation process was simulated using three distinct plastic beams as shown in Fig. 4. The horizontal plastic beam was set at 5 mm distance from tunnel walls, to

Table 2 Mechanical properties of MDF blocks under normal and shear loads. 7

Mechanical properties perpendicular to bedding Young’s modulus (MPa) Poisson’s ratio Uniaxial compressive strength (MPa)

435 0.08 70

Mechanical properties Parallel to bedding Young’s modulus (MPa) Poisson’s ratio Uniaxial strength (MPa)

1800 0.25 20

Mechanical properties of joint surfaces Surface friction angle (deg) Surface cohesion (MPa) Shear Stiffness (MPa/mm)

34 0.05 3.5

Mechanical properties of bedding surfaces Surface friction angle (deg) Surface cohesion (MPa) Shear Stiffness (MPa/mm)

18 0 1.2

1. It is made from natural material, 2. The properties in the prepared blocks are reproducible

stress only generated based on confinement and there is low stress between block due to the gravity force. Thus, the direct shear test was carried out applying probable ranges of normal stresses (normal force is below 1.5 kN), which gives a reliable shear strength parameter. Based on the direct shear test, mechanical properties of the bedding (layer) surfaces are relatively weaker than the joint surfaces. This property is appropriate representative of the joint and bedding surfaces in rock masses. This is expected for the stratified structure and it could reasonably represent the rock behavior (Brady and Brown, 2005) (Table 2). A tunnel excavated in stratified sandstone was scaled down to study in this research as detailed in Table 3. Density, young’s modulus, and the normal stiffness of the typical discontinuous of sandstone uttered as 19.3 kN/m3, 15 GPa, and 1.3 GPa/m respectively [Zhang, 2017]. Scale factor for length considered as 50 dimensions of smallest block are 16 * 16 mm, and then, block size will be 0.8 * 0.8 m in prototype; therefore, the equivalent elastic modulus for rock mass will be 1 GPa in prototype. On the other hand, based on the Table 2, the equivalent Elastic modulus is 6.3 MPa for model material. Table 3 shows the scale factor of the material. It should be noted that, minimum tunnel dimensions will be equal to 8 * 8 m2 in prototype.

Table 1, in this research, Medium-Density Fiberboard (MDF) is used. The main advantages of MDF are:

MDF Unit weight (kN/m3)

1. It is made from natural material, 2. Various type of mixture with different strength can be built, 3. It is inexpensive. 1. The properties in the prepared blocks are reproducible

Table 3 Considered scale factor for physical model.

3

No.

Parameter

Scale factor

1 2 3 4 5 6 7

Length Density Acceleration Stiffness Displacement Strain Stress

0.02 0.36 1 6.25E−03 2.30E−02 1.15E−03 6.00E−03

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Fig. 2. Physical test apparatus frame (a): Front view (b): Side view structures (dimensions are in mm).

prevent its contact and possible interaction with tunnel walls once it dropped down. To prevent upward force in tunnel roof, the upper edge of the plastic beams were cut obliquely. During the model test, these internal frames (three separate plastic beams) slowly rotated until they separated completely from the tunnel walls (Fig. 4). Therefore, the tunnel excavation is considered fast by removing the beams in physical model which takes only few seconds. The high speed camera was used to record the video from the front view of the model before and during the test process. Numerical simulation where considered two dimensional plane strain which is common way to simulate long tunnel. Presented physical model is two dimensional model simulated as plane strain condition. The tunnel axis assumed to be parallel to layers strike in the model. The test preparation procedure for physical model tests was as follows: 1. The blocks were arranged and placed next to each other to build a stratified model, the tunnel was left empty and blocks around the tunnel were supported by the plastic beam frame. 2. The back glass was placed in the model framework (front glass was

Fig. 4. Schematic view of plastic beam to simulate full face tunnel excavation (dimensions are in mm).

Fig. 3. Various shapes and sizes of blocks to build different structures (dimensions are in mm). 4

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Fig. 5. Beam structure in inclined bedding.

fixed on the outer frame). 3. The camera was set to record during testing. 4. The tunnel frame was removed from behind the model to simulate full face excavation. 5. Visual recordings were carried out during the test and observations filled in predesigned forms. 6. The camera recording was stopped after the test. 7. All recorded images were processed to calculate total displacement fields in model building blocks.

Table 4 Conditions for physical test designed using Taguchi’s experiment design method.

2.3. Experiment design The discontinuity dip and spacing, and tunnel height and span are considered as main variables and the experiments were designed to capture a reasonable range of these variables. The inclination of the bedding was considered from horizontal to vertical (0, 30, 60 and 90 degrees with thickness of 16 mm). The discontinuities’ spacing was determined based on layer thickness from 1 and 2 times bedding thickness. The continuity factor (the ratio of tunnel diameter to block diameter) is between 6 and 15 for discontinuous area; because in this case tunnel and block weren’t circular, the authors introduced so called “dimension ratio” as the ratio of tunnel to block hydraulic radius. Therefore, tunnel dimensions are considered as 160, 192, and 224 mm so that the value of continuity factor remained between 6 and 15. According to variance range of several effective factors, 72 physical test models were designed to study the failure mechanisms at different tunnel sizes and structural conditions. Each test condition was carried out at least twice to assure its consistency of results and reproducibility. Therefore, huge number of tests were needed, which would be timeconsuming and expensive. To overcome such a situation, experiment design methods were engaged to optimize test numbers. Based on Taguchi’s experimental design method (Roy, 2010), 16 test models were predicted. The test details are illustrated in Table 4.

Test number

Joint spacing (Bedding thickness) (mm)

Tunnel height (mm)

Tunnel span (mm)

Bedding dip (deg)

T.1 T.2 T.3 T.4 T.5 T.6 T.7 T.8 T.9 T.10 T.11 T.12 T.13 T.14 T.15 T.16

16 16 32 32 16 16 32 32 32 32 16 16 32 32 16 16

160 192 224 160 160 192 224 160 160 192 224 160 160 192 224 160

160 160 160 160 192 192 192 192 224 224 224 224 160 160 160 160

0 30 60 90 60 90 0 30 90 60 30 0 30 0 90 60

trajectory. The imaging activity is similar under all test conditions and was captured using a high-speed camera (60 frames per second). But the available image processing methods was so far only compatible with homogeneous areas. Therefore, the conventional method was updated and customized for our test condition. To capture block displacement, white colored spot marks were fixed on each block on the front side of block surfaces. Therefore, the displacement of each white spot represents the corresponding block displacement. Then, photographs were taken before and during test of the model by the high-speed camera. To achieve high accuracy, the camera was set perpendicular to the physical model. The particle image velocity (PIV) computer code (acronym MatPIV v.1.6.1, and developed by Sveen, 2004) was updated and adapted to catch the marks and processing blocks’ movement path. Each photograph’s global coordinate system (pixel) is transferred to a model global coordinate system (metric) for displacement to be in the metric scale. Finally, displacement of the surrounding area of the tunnel is determined by comparison of sequential photographs.

2.4. Model monitoring using photogrammetric and image processing techniques There is a broad failure zone and blocks’ movement due to tunnel excavation in discontinuous structures during physical tests. A photogrammetric technique is used to capture the displacement of blocks in failure zones. Photogrammetric techniques were developed in recent years, and used both in some physical models and practical geotechnical engineering investigations (Yuanhai et al., 2004; Kirsch, 2010). This method consists of two main activities: at first, photographs are taken consecutively (by recording movie) during testing, and then the recorded image series are processed to follow the blocks’ movement

3. Test results and discussion 3.1. Testing and modeling conditions In deep underground excavations, stability depends on stresses 5

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a) Physical model

b) Image analysis

c) Numerical model

Fig. 6. Model test for horizontal bedding (Numbers refer to test conditions in Table 4).

and lateral boundaries are fixed and the upper boundary is left free (Fig. 2). More tests were carried out utilizing numerical modeling using the universal distinct element code (UDEC) were carried out (Itasca, 2004), numerical model simulated and calibrated according to the 16 different

concentration level and stress orientation with respect to the excavation profile, but in shallow and low stress conditions, the stability is governed by discontinuities’ structures and geometrical settings. To evaluate the failure mechanisms in shallow tunnels in such conditions, a two-dimensional physical model were built. In these models, the lower

6

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a) Physical model

b) Image analysis

c) Numerical model

Fig. 7. Model test for 30 degrees bedding (Numbers refer to test conditions in Table 4).

according to test results, as illustrated in Table 2. According to the iterative back-analysis of numerical results, discontinuity and bedding normal stiffness were calculated to be 400 and 500 MPa/mm, respectively. The block constitutive model is considered as elastic-isotropic because all blocks in the physical model behave like rigid-elastic

conditions similar to the physical models illustrated in Table 4. In Figs. 6–9, all calibrated numerical model showed beside the final physical model. Numerical model geometry and boundary conditions are exactly simulated similar to physical models as shown in Fig. 2. The physical and mechanical properties of materials are considered 7

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a) Physical model

b) Image analysis

c) Numerical model

Fig. 8. Model test for 60 degrees bedding (Numbers refer to test conditions in Table 4).

Each physical model given in Table 4 has been tested at least twice. If trial test results were close to each other, then the results were recorded, otherwise, extra trial tests were conducted to reach stationary results. At each trial test, the errors that occurred were identified and

material. The Mohr-Coulomb shear failure model was assumed for discontinuities’ surfaces. The numerical models were simulated under two dimensional plane strain conditions which is popular in simplifying engineering analysis. 8

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Fig. 9. Model test for vertical bedding (Numbers refer to test conditions in Table 4).

9

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that critical dip and the stress arching doesn’t occur, so buckling won’t be expected in this condition (Figs. 8 and 9). Critical dip for creation of the stress arch is)(∅/2 ) + (π/4 )) as shear plane degree in uniaxial test, where ∅ is bedding surface friction angle, and stress arch could occur in 30 degree and horizontal bedding because bedding dip in lower than critical dip. Therefore, there will be a distressed zone in tunnel roof which has buckling potential. In steeper bedding (60 and 90 degree bedding), joint spacing and tunnel dimensions are not dominant factors for buckling failure occurrence.

resolved. Then, remaining conditions were simulated numerically to complete the database. 72 different models were used for analysis. 3.2. Physical and numerical test results at different conditions Physical tests were carried out according to the designed test schedule, as illustrated in Table 4, at bedding inclinations of horizontal 0 degrees, 30 degrees, 60 degrees and vertical 90 degrees, with different discontinuity spacing and tunnel sizing. Additionally, image processing results and numerical test results were provided for similar conditions to the physical test. Fig. 6 illustrates the test results for physical tests (left view), image analysis (middle view) and numerical results (right view), for horizontal bedding. Each test condition of horizontal bedding, such as spacing and tunnel size, was set according to Table 4 (test number is shown in the lower left side of physical test picture in Fig. 6). Similarly, test results for bedding inclinations of 30 degrees, 60 degrees, and 90 degrees (vertical bedding) are illustrated in Figs. 7–9, respectively. Based on the test results main types of failures were categorized as stationary, buckling and collapsed zones. The stationary zone does not influenced by the tunnel excavation procedure. Consistent bending of layers occur in the buckling zone. The collapsed zone is an area that has moved from its host (initial condition) and fallen into the tunnel. The detail of each condition are discussed below.

3.2.2. Collapsed zone Collapsed zone itself consists of three failure modes: falling, sliding and toppling. Bedding dip has major impact than other factors on the type of the collapsed zone. Tunnel span and discontinuity spacing control the extent of the collapsed zone in horizontal bedding. In this condition, collapsed zone occurs as falling roof beam (Fig. 6). When layers’ dip is 30 degrees, all three modes of collapsed zone happened. Tunnel dimensions, as well as the bedding dip, affect the collapsed zone development. From comparison of all model tests when bedding was 30 degrees, it is obvious that joint spacing significantly limited the collapsed zone. Also, when joint spacing to layer thickness ratio is 1, increasing the tunnel dimensions expanded the collapsed zone considerably, but when this ratio is equal to 2, the variation of the tunnel dimensions didn’t result in a significant change in the collapsed zone. This shows that the joint spacing is more dominant factor on collapsed zone extension than tunnel dimensions (Fig. 7). When bedding dip is 60 or 90 degrees, occurrence of different collapse modes was observed, but sliding is the principal event. As mentioned earlier, these bedding dip values are bigger than the critical dip for development of stress arch, thus high normal stress between blocks will not be generated and the shear strength of the bedding surface will be low and leads to instability of the blocks. Tunnel dimensions also affects the collapsed zone because when the tunnel dimensions are at their smallest value (square tunnel which its height or its span is ten times as big as bedding thickness), there is partial instability as shown in test number 16 in Fig. 8, but in general, tunnel dimensions and joint spacing didn’t have a significant impact on collapsed zone and in all model tests, except test number 16, sliding over bedding surface occurred. In this condition, blocks slides based on their own weight and the shear strength of the bedding surface determined stability of the layers (Figs. 8 and 9).

3.2.1. Buckling zone Buckling failure, lateral compressive failure at mid-span and abutments, abutment slip and diagonal fracturing are general modes of roof beam failure (Brady and Brown, 2005). Buckling failure occurs for high ratios of tunnel span to layer thickness, and at low ratios, sliding at abutments is likely to happen. In the model tests, when the tunnel span was 10 times larger than the bedding thickness, only two stationary and buckling zones occurred in horizontal bedding. However, by increasing the tunnel span up to 14 times the thickness of bedding, buckling failure occurred. Based on the stable beam above collapsed beams at tunnel roof as shown in test number 12 (Fig. 6), maximum unsupported span is 13 times as big as layer thickness. Also, buckling limit for this span is 6 mm which is equal to 37.5% of layer thickness. However, the ultimate deflection that causes a failure was expressed as 25% of layer thickness by Brady and Brown (2005). Deflection of layers is significantly decreased due to the increase of discontinuity spacing because equivalent Young’s Modulus increased by the rise of the discontinuity spacing. Based on Fig. 6, if the ratio of discontinuity spacing to the layer thickness increases from one to two; a variation of the tunnel span will has low influence on a layer’s deflection. (Compare tests results in Fig. 6). Beam deflection decreases with an increase of its dip up to 30 degrees because the effective unit weight is reduced in this way. Additionally, in the inclined beam, an external force will contribute to the beam stability. If inclined bedding around tunnel is divide into three distinct parts as shown in Fig. 5, parts 1 and 3 have been reclined to the host beneath layers. However, part 2 can be deflected while the sinusoidal component of gravitational weight of part 3 acts on part 2, and this can make it more stable than when this force doesn’t act on it. In addition, layers’ deflections are dampened with low rate than horizontal bedding in the direction perpendicular to the layers as shown in test numbers 12 in Fig. 6 and test numbers 11 in Fig. 7. This event is due to the locking of blocks. In horizontal bedding, the gravitational force of the upper layer makes blocks lock strongly to each other but, in inclined bedding, only cosine component of it provides block locking, so buckling zone will be expanded further. Additionally, because of poor locking of blocks, variation on tunnel dimension has more influence on beam deflection (Compare Figs. 6 and 7), But this happens when layer dip is lower than critical dip. In steeper layers, such as for 60 and 90 degrees bedding, no deflection was observed in model tests because layer dip is bigger than

3.3. Classification of instability mechanisms Failure mechanisms were studied by many professionals such as Hoek et al. (2000) presented the failure mechanism for both low and high stress level in three general states of a massive, jointed and highly jointed rock masses. In this study authors try to add jointing geometry and tunnel dimension to update this classification for low stress condition. The maximum amount of the Depth to tunnel height ratio was considered 3.6 for Minimum dimensions of tunnel (16 * 16 cm2); therefore, it is reasonable to consider that all cases are representation of the tunnel which bored in shallow depth. A new quantitative category, in order to use by practitioners and engineers were introduced in this paper. Dimensional Ratio (DR) takes in to account the rock mass block size and tunnel dimensions and gives the combination factor represents the rock uniformity; which represents the ratio of tunnel to block size or degree of jointing (Eq. (1)).

DR =

⎛ tunnel hydraulic radius =⎜ block hydraulic radius ⎜ ⎝

( ) ⎞⎟ ( ) ⎟⎠ At Pt

Ab Pb

(1)

where At and Pt are tunnel cross section area and perimeter, 10

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Table 5 Instability mechanisms for shallow stratified structure. Low jointing

Medium jointing

High jointing

Dimensional Ratio (DR) >7

7–11

> 11

Areas around the tunnel do not be affected by tunnel excavation. Maybe, the low deflection occurs in tunnel roof beam. (T.14)

Bucking zone created in limited area above tunnel roof, but layers are still stable. (T.1, and T.7)

Layers deflection increased and buckling failure happened. Buck ling zone extended too. (T.12)

Tunnel is generally stable and falling of few small blocks may happen. (T.13)

Collapsed zone created around the tunnel. Also, there is stable limited buckling zone. (T.2, and T.8)

Collapsed zone increase with low rate, but buckling zone has significant growth. (T.11)

There is slight chance of collapse on tunnel walls when bedding dip is less than 90°. (T.16) Stationary zone

Area that lost its bearing is unstable. (T.3, and T.5) Buckling zone

Tunnel generally is unstable. (T.5, T.10, and vertical bedding) Collapsed zone

Layer with low dip 0 < dip < Φ

Layer with medium dip Φ < dip < (∅/2 ) + (π/4 )

Layer with steep dip ((∅/2 ) + (π/4 )) < dip

heavily jointed by tectonism. So, columns define rock mass conditions by considering rock block size with respect to the tunnel dimension. In other words, for smaller rock blocks, the ground loses its strength and extends the collapsed zone further. The rows in Table 5 are divided based on the strata inclination considering the angle of repose for granular material and angle of failure (slide) for intact material since this classification is introduced for shallow tunnels in which shear strength of discontinuity is low due to the low normal stress acting on them). To this extent, three classes of “Low dip” (0 ≤ dip ≤ ∅) , “Moderate dip” (∅ ≤ dip ≤ ∅/2 + π /4) , and “Steep” (∅/2 + π /4 ≤ dip ≤ 90o) were proposed. In the first category, only the deflection of a layer is likely to occur and stress arch will be created. In moderate dip bedding, there is potential of both the sliding of rock block and layer deflection, thus stress arch will be created. Test results show that only sliding of blocks happens in the third category and stress arch will not be created. Therefore, type and capacity of tunnel reinforcement and support could be evaluated from this classification. Comparison of the failure mechanism in first and second rows with third row in Table 5, shows that an instability grows in direction of normal and parallel to the bedding respectively, this happen due to the stress arch. When bedding dip is lower (∅/2 + π/(4)) due to the

respectively. Also, Ab and Pb refer to block cross section area and perimeter, respectively. The physical and numerical test results were carried out over horizontal to vertical bedding inclinations, with various tunnel sizes and discontinuity spacing as summarized in Figs. 6–9. According to these studies, the failure mechanisms were generalized, categorized and illustrated in Table 5. Considering dimensional ratio (DR), three main classes of “Low”, “Medium”, and “High” fractured area were classified. This selection is well-suited to bedding reaction to the boring of the tunnel. Based on the results if DR is less than 7, the rock mass shows high strength resembled to intact rock and isn’t influenced by tunnel excavation, however random block fall probably happen from tunnel periphery. In field real conditions, this class is representative of massive ground with low tectonism. In the second category (Medium DR) where DR is in the range of 7–11, rock block is not very small versus tunnel dimensions and the ground experienced moderate tectonic intensity. In such condition, depends on discontinuity orientation, buckling, block fall, and collapse may occur. The third (high DR), where DR is greater than 11, high probability of instability expected due to tunnel excavation. This class is representative of the highly fractured ground which has been 11

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considered. Based on the dimensional ratio, which defines the relationship between block size and excavation size, three classes of low, medium and high jointed conditions were presented. The bedding gradient was also divided into three categories: low, medium and steep dipping based on repose and failure plane angle. According to “dimensional ratio” and “bedding dip” classes, the failure mechanisms were divided into nine individual categories, ranging from roof layers’ deflection mechanism in low jointing and nearly flat bedding, to global collapse with mixed failure modes consisting of blocks sliding and falling in highly jointed and nearly vertical bedding. These results could efficiently have applied in practice for shallow underground space design in stratified rocks.

creation of the stress concentration zone, shear strength of the bedding surface increases and prevents further extension of collapsed zone. In contrast, in the third row (steep bedding), stress arch will not be created around the tunnel and the collapsed zone will be extended. The presented categorization helps for choosing efficient support system; because it shows asymmetric loading will apply to support system and should be considered in design stage. The proposed classification will allow more sensible decisions about time for support system installation and excavation method, because if stable buckling is possible, it’s not necessary to install a support system immediately. The time of support system installation, affect the efficiency of tunnel excavation procedure. Mechanisms of tunnels instability in shallow stratified rock masses as classified as Table 5 were prepared based on results of models tested under real conditions and evaluated by numerical simulation, so it will be a rational guide for engineers to decide about time of support system installation and excavation methods. For example, if the case No.3 will likely occur, your support system will be installed as soon as tunnel bored for tunnel with small span with high jointing density or you may have to choose a sequential excavation method for large span tunnel for moderately jointed rock masses, because in both case, the behavior of the rock mass will be almost same. So, this classification can help engineers for more accurate decision. The effect of discontinues strength parameter is not covered in this paper since the blocks are considered as rigid. Based on the model tests, when the angle of the bedding is more than (∅/2 + π/4) the only resistance force will mobilize at the upper and lower boundary of failure zone. During tunnel excavation in this condition, the vast group of blocks lost their underneath base, then, they start to sliding together (Figs. 8 and 9). Therefore, the amount of the driving force will be much more than resistance force. Therefore, joint shear strength won’t play a significant role to make the rock mass to be stable. The second reason is that the masonry structure couldn’t sustain tensile stress in the direction perpendicular to the bedding plane, and shear strength of the bedding surface is remarkably lower than the intact rock (Brady and Brown, 2005), therefore, the bedding surface always has low shear strength; on the other hand, based on the test results, the joint shear strength has low effect; only its normal stiffness plays a role in horizontal bedding. So, the general output of these tests will not change versus various joint types in this case. It should be note that the effects of bedding dip, tunnel dimension and discontinuity spacing are considered in the presented classification (Table 5).

Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.tust.2019.103017. References Brady, B.H., Brown, E.T., 2005. Rock mechanics for underground mining. Springer Science & Business Media 224–241. Fairhurst, C., Hudson, J., 1999. Draft ISRM suggested method for the complete stressstrain curve for intact rock in uniaxial compression. Int. J. Rock Mech. Min. Sci. 36 (3), 279–289. Fuenkajorn, K., Phueakphum, D., 2010. Physical model simulation of shallow openings in jointed rock mass under static and cyclic loadings. Eng. Geol. 113 (1–4), 81–89. https://doi.org/10.1016/j.enggeo.2010.03.003. He, M., 2011. Physical modeling of an underground roadway excavation in geologically 45° inclined rock using infrared thermography. Eng. Geol. 121 (3–4), 165–176. https://doi.org/10.1016/j.enggeo.2010.12.001. He, M., Jia, X., Gong, W., Faramarzi, L., 2010. Physical modeling of an underground roadway excavation in vertically stratified rock using infrared thermography. Int. J. Rock Mech. Min. Sci. 47 (7), 1212–1221. https://doi.org/10.1016/j.ijrmms.2010.06. 020. Hoek, E., Kaiser, P.K., Bawden, W.F., 2000. Support of Underground Excavations in Hard Rock. CRC Press. Itasca, 2004. UDEC—Universal Distinct Element Code (version 4.0. ed.). Itasca Consulting Group, Minneapolis. Jia, P., Tang, C.A., 2008. Numerical study on failure mechanism of tunnel in jointed rock mass. Tunn. Undergr. Space Technol. 23 (5), 500–507. https://doi.org/10.1016/j. tust.2007.09.001. Jiang, Y., Tanabashi, Y., Li, B., Xiao, J., 2006. Influence of geometrical distribution of rock joints on deformational behavior of underground opening. Tunn. Undergr. Space Technol. 21 (5), 485–491. https://doi.org/10.1016/j.tust.2005.10.004. Kirsch, A., 2010. Experimental investigation of the face stability of shallow tunnels in sand. Acta Geotech. 5 (1), 43–62. Kulatilake, P.H.S.W., Malama, B., Wang, J., 2001. Physical and particle flow modeling of jointed rock block behavior under uniaxial loading. Int. J. Rock Mech. Min. Sci. 38 (5), 641–657. https://doi.org/10.1016/S1365-1609(01)00025-9. Moyo. T., Stacey. T.R., 2012. Mechanisms of rock bolt support in jointed rock masses Paper presented at the Deep mining 2012, Perth, Australia. Muralha, J., 1974–2006. SRM Suggested Method for Laboratory Determination of the Shear Strength of Rock Joints: Revised Version. In: R. Ulusay (Ed.), The ISRM Suggested Methods for Rock Characterization, Testing and Monitoring (Vol. 1). Cham Heidelberg New York Dordrecht London: Springer. Roy, R., 2010. A Primer on the Taguchi Method. 2nd ed. vol. 1. Society of Manufacturing Engineers. Sagong, M., Park, D., Yoo, J., Lee, J.S., 2011. Experimental and numerical analyses of an opening in a jointed rock mass under biaxial compression. Int. J. Rock Mech. Min. Sci. 48 (7), 1055–1067. https://doi.org/10.1016/j.ijrmms.2011.09.001. Shen, B., Barton, N., 1997. The disturbed zone around tunnels in jointed rock masses. Int. J. Rock Mech. Min. Sci. 34 (1), 117–125. https://doi.org/10.1016/S1365-1609(97) 80037-8. Sveen, J.K., 2004. An introduction to MatPIV v. 1.6. 1. Preprint series. Mechanics and Applied Mathematics http://urn. nb.no/URN: NBN: no-23418. Whittaker, B., Reddish, D., 1989. Subsidence: Occurrence, Prediction and Control. Elsevier. Yuanhai, L., Hehua, Z., Ueno, K., Mochizuki, A., 2004. Deformation field measurement for granular soil model using image analysis. Chinese J. Geot. Eng 26, 36–41. Zhang, L., 2017. Engineering Properties of Rocks. Second ed. Butterworth-Heinemann, 173–338.

4. Conclusions The physical and numerical modeling of stratified jointed rock masses were investigated to evaluate the effects of discontinuity inclination and thickness represented by block size as well as opening size on the failure mechanisms around underground excavations. Based on physical modeling fundamentals so far, a physical modeling procedure was adopted and physical tests designed and carried out. An image processing technique with a new approach was introduced and employed to capture blocks’ displacements precisely during the tests. To verify the physical test results, numerical simulation were performed using the distinct element method, and then the models were extended for a wide range of ground conditions. Based on all the physical, numerical and image analysis results, the failure mechanisms around underground excavations were categorized using the so called “dimensional ratio” and “bedding dip”. In the newly defined dimensional ratio, the effect of the opening size as well as the joint spacing were

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