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SAIMM, SANIRE and ISRM The 6th International Symposium on Ground Support in Mining and Civil Engineering Construction A Tavallali and A Vervoort FAILURE OF TRANSVERSELY ISOTROPIC ROCK MATERIAL: EFFECT OF LAYER ORIENTATION AND MATERIAL PROPERTIES A. Tavallali, A. Vervoort K.U.Leuven, Research Unit Mining, Belgium Abstract Although the property of anisotropy was in the past often not considered, it plays an important role in the behaviour of the rock mass. Hence, the knowledge of these anisotropic properties is more and more required as input for the design and/or for numerical modelling. Despite its importance, rock anisotropy is still poorly understood. In this study, one specific form of anisotropy is considered, namely transverse isotropy. The experimental research in this paper focuses at macro-scale on the effect of the layer orientation on failure strength and fractures induced for samples of sandstone from Modave in the South of Belgium. Although at first sight these samples look similar, their behaviour in a Brazilian test is different when focussing on their failure pattern. The failure through layer activation is not necessarily predominant for all these samples, e.g. for an inclination angle of 70°. The reasons for the different types of behaviour are further investigated by a detailed petrographical study. 1 Introduction In general, rock material near the earth’s surface has mechanical properties that can change as a function of the direction, or in other words are anisotropic. More and more this anisotropy is taken into account, as input for the design and for numerical modelling. Hence, the knowledge of the anisotropic properties is required in studies of civil, mining and petroleum engineering with applications like e.g. stability of underground excavations, slope stability and borehole deformation. Despite its importance, rock anisotropy is often poorly understood. In this study, one specific form of anisotropy is considered, namely transverse isotropy. The tests are conducted on stratified sandstone and the Brazilian tensile method is applied. Five blocks of sandstone are taken from a quarry in Modave in the South of Belgium. This type of sandstone is also known as “Psammite of Condroz” (Poty & Chevalier 2004). This sandstone is characterized by numerous thin and parallel layers. The plane of transverse isotropy is assumed to be parallel to the apparent direction of rock layering. Visual inspection (hand samples) would normally lead to the conclusion that they are all similar. The rock is cored in the laboratory using a 50 mm diameter drill bit. The direction of coring is parallel to the layering. For the test, a thickness-to-diameter ratio (t/D) of 0.5 is taken. All tests are carried out using a loading machine with a loading capacity of 100 kN, at a constant displacement rate of 1 mm/min. The disc shaped samples are positioned as in Figure 1 and compressed vertically until failure. The experimental research in this paper focuses at macro-scale on the effect of the layer orientation on failure strength and failure pattern of this transversely isotropic sandstone. First, the effect of the layer orientation is investigated in detail for samples cored in the same block (about 31 samples in total). The sandstone corresponding to this block is called “Type 1 sandstone” or “Reference”. These tests illustrate the effect of the layer orientation on the fracture patterns on macro-scale. However, test results of samples from the four other blocks Page 317 SAIMM, SANIRE and ISRM The 6th International Symposium on Ground Support in Mining and Civil Engineering Construction A Tavallali and A Vervoort do not show the same effect of layer orientation. Therefore further research on micro-scale is being conducted to quantify the reason for different behaviour on relatively similar rock materials. For each block of sandstone a thin section is prepared and studied under microscope (Ganne & Vervoort 2006 and Van de Steen et al. 2002). Their differences on micro-scale are discussed later in detail. Figure 1. Disc shape sample and configuration of layers in Brazilian tests. θ varies between 0° and 90°. 2 Brazilian test results for “Type 1 sandstone”: tensile strength and fracture analyses The rock layers are inclined at different angles (see Figure 1) ranging between 0° (perpendicular to the loading direction) and 90° (parallel to the loading direction). Nine different values are considered: 0, 15, 30, 45, 60, 65, 70, 80 and 90°. Since one sample is not necessarily representative for the failure behaviour corresponding to a specific inclination angle, two to five samples are tested per inclination angle value. Figure 2 presents the variation of the Brazilian tensile strength (BTS) with the inclination angle. This Figure shows that by increasing the inclination angle a slight decrease in tensile strength occurs. The average BTS varies between 15.1 MPa and 9.5 MPa. The smallest value corresponds to an inclination angle equal to 80°. This trend could be expected, because when the layers are horizontal or semi-horizontal the fracture is mainly through the stronger material, while by increasing the inclination angle the fracturing processes make use of the layers, of which one could expect that they have weaker mechanical properties. Also it is possible that in the latter cases samples fail also in shear and not purely in tension. This seems to be consistent with the experimental results of Chen et al. (1998) on two kinds of transversely isotropic sandstone. However, the difference between the maximum and minimum value of BTS was considerable for the experiments of Chen et al. (1998), while in this study a relatively small difference is observed. In the experiments of Chen et al. (1998), the BTS-values for an angle of 0° and 90° were close. Page 318 SAIMM, SANIRE and ISRM The 6th International Symposium on Ground Support in Mining and Civil Engineering Construction A Tavallali and A Vervoort BTS (MPa) 20 15 10 5 0 0 15 30 45 60 75 90 Inclination angle, θ (°) Figure 2. Variation of Brazilian tensile strength, BTS, as a function of the inclination angle for all the samples. Similar to the idea introduced by Szwedzicki (2007) for UCS-tests, different failure modes are suggested. By considering the samples after failure, different types of fractures are observed (see Figure 3): (1) Some fractures are parallel to the isotropic layers which are further called “layer activation”; (2) Some fractures are roughly parallel to the loading direction and they are located in the central part of the sample between the two loading lines. The central part is defined as 10% of the diameter on both sides of the central line. These fractures are further called “central fractures”; (3) Fractures outside the central part are also observed. If they do not correspond to layer activation, they are further called “non-central fractures”. The latter are often curved lines, starting at or around the loading platens. In most cases, two or three different fracture types occur in the same experiment (Tavallali et al. 2007). It is to be noted that, in the case of θ = 90° and when a straight fracture between both loading platens is induced, this is classed as layer activation and not as central fracture. Figure 3. Schematic representation of different fracture types in Brazilian test. (1) Layer activation, (2) Central fracture, (3) Non-central fracture. The predominant failure modes of the samples are observed as follows: (1) central fracture(s) when inclination angle is equal to 0°, 15° or 30°, (2) combination of central fracture(s) and layer activation when this angle is equal to 45° or 60° and (3) layer activation when the inclination angle is equal to 65°, 70°, 80° or 90°. Some typical samples after failure are shown in Figure 4 for each inclination angle. Apart from the predominant failure mode some secondary fractures are also observed. The failure patterns corresponding to 0° and 90° look similar. However for 0° (layers perpendicular to the loading direction) the average BTS is 14.1 MPa which should rather correspond to the tensile strength of the “intact” material, while for 90° (layers parallel to the loading direction), the average BTS is 10.4 MPa. The latter should rather correspond to the tensile strength of the “layers”. Figure 4 shows that for inclination angles situated between 45° and 60°, both failure modes (central fracture and layer activation) are present, but as this angle increases, layer activation becomes more dominant. So it can be concluded for this transversely isotropic sandstone that below a certain transition Page 319 SAIMM, SANIRE and ISRM The 6th International Symposium on Ground Support in Mining and Civil Engineering Construction A Tavallali and A Vervoort angle, fractures are mainly in the central zone (central fracture mode). Above that transition angle, fractures are parallel to the isotropic layers (layer activation mode). To determine more precisely the transition angle, the failure modes are quantified by estimating the fracture length. Figure 4. Observed failure patterns of Brazilian test for different values of the inclination angle (one typical sample for each group). The predominant mode is put in parentheses, CF = Central fracture, LA = Layer activation. The fracture length within the various rock samples is estimated and used as a tool to distinguish between the different failure modes. First, the length of all fractures in the sample is measured. Second, the length corresponding to the various fracture types is considered. When a fracture is classified as layer activation the entire length, including the part within the central zone, is put into the total sum of layer activation. In a similar way, if the major part of a curved shape fracture (e.g. the non-central fracture in Figure 3) is outside the central zone, the entire length including the small portion in the central zone is put into the total sum of non-central fractures. The fracture pattern in some of the samples is true three dimensional and on both sides of the sample, the fracture pattern is different. In such cases, averages of the fracture lengths on both sides are considered. Variation of the fracture length corresponding to layer activation and central fracture(s) as a function of the inclination angle are plotted in Figure 5 for individual samples. Figure 5a shows that when the inclination angle exceeds 60°, a considerable decrease in the length corresponding to central fracture(s) is observed. Figure 5b shows that for inclination angle smaller than 45°, the length corresponding to layer activation is very small, sometimes even negligible. When this angle exceeds 45°, layer activation becomes significant. For an inclination angle between 45° and 90°, there is an increasing trend for this length. For all samples corresponding to a single angle value, the average fracture length is calculated. Variation of the three types of fractures, as well as the total fracture length is plotted as a function of the inclination angle in Figure 6. It shows that for angles smaller than 30° the fractures parallel to the isotropic layers are small and when the inclination angle exceeds 70° the fracture length corresponding to central fracture(s) becomes small. This Figure also illustrates that the non-central fracture length is nearly constant and thus Page 320 SAIMM, SANIRE and ISRM The 6th International Symposium on Ground Support in Mining and Civil Engineering Construction A Tavallali and A Vervoort Fracture length of central fracture (mm) independent at least for the interval 0° to 65°. When the inclination angle increases from 30° to 90°, the length of central fracture(s) decreases while the length corresponding to layer activation increases. From the above explanation, it can be concluded that the transition angle, which indicates the change of failure mode from central fracture to layer activation, is in the range of 45° and 60° for this type of transversely isotropic sandstone. 200 (a) 150 100 50 0 0 10 20 30 40 50 60 70 80 90 Fracture length of layer activation (mm) Inclination angle, θ (°) 200 (b) 150 100 50 0 0 10 20 30 40 50 60 70 80 90 Inclination angle, θ (°) Figure 5. Variation of fracture length as a function of the inclination angle (a) Central fracture(s), (b) Layer activation. 3 Brazilian test results for the other four types of Modave sandstone For Type I, nine groups of the inclination angle are tested. In five groups (60°, 65°, 70°, 80° and 90°) layer activation is the predominant failure mode (see Figure 4). It was decided to verify this for one inclination angle (i.e. 70°) using samples of the other four blocks. As for the first block of sandstone, four samples are tested under an angle of 70° for each block. Page 321 Average fracture length (mm) SAIMM, SANIRE and ISRM The 6th International Symposium on Ground Support in Mining and Civil Engineering Construction A Tavallali and A Vervoort Total Layer activation Central fracture Non-central fracture 150 100 50 0 0 10 20 30 40 50 60 70 80 90 Inclination angle, θ (°) Figure 6. Variation of average fracture length as a function of the inclination angle. The average value of Brazilian tensile strength for the additional four blocks are 7.9 MPa, 14.5 MPa, 11.4 MPa and 12.8 MPa respectively while for the first block this value is 10.7 MPa. On a macroscopic scale the blocks look similar, but there is about 5 MPa difference between smallest and largest average value of BTS. Some typical samples after failure are shown in Figure 7 for each block of sandstone. By observing the fracture patterns in Figure 7 it is clearly understood that the predominant failure mode is not only layer activation as for Type 1. All the samples from the four blocks show a failure by either central fracture(s) only (3, 4 and 5) or a combination of central fracture(s) and layer activation (2). In Figure 8 the percentage of layer activation, central fracture(s) and non-central fracture(s) compared to the total fracture length is given as a function of the sandstone type. Central fracture(s) is predominant for all four types (2, 3, 4, and 5) of sandstone, while layer activation is the main failure mode for the reference sandstone. From the above explanation, it can be concluded that samples from different blocks (which are relatively similar) behave differently at macro-scale. Therefore further study on microscale by preparing thin sections is necessary to be able to explain the differences. (1) (2) (3) (4) (5) Figure 7. Observed failure patterns of samples from different blocks of sandstone under Brazilian test (one typical sample for each block; inclination angle of 70° for all samples). Sandstone type number and the predominant failure mode are put in parentheses, CF = Central fracture, LA = Layer activation. Page 322 SAIMM, SANIRE and ISRM The 6th International Symposium on Ground Support in Mining and Civil Engineering Construction A Tavallali and A Vervoort Relative fracture length (%) 100 Non-central fracture Central fracture 80 Layer activation 60 40 20 0 1 2 3 4 Sandstone type 5 Figure 8. Variation of fracture length percentage corresponding to layer activation, central fracture(s) and non-central fracture(s) as a function of sandstone type. 4 Micro-scale quantification of sandstone types To explain the reason for the differences in macro-scale behaviour, as illustrated above, micro-scale quantification is necessary. Therefore, thin sections are prepared for the five untested sandstone samples and analysed. The diameter of the samples is 50 mm. Thin sections with a thickness of 30 µm are prepared. Figure 9 shows the position of these thin sections in a sample. Figure 10 presents digital photos which are taken from parts of the thin section of the first block. In all the samples, quartz, feldspar, carbonate and mica are observed but they are different in quantity. Also pores, organic material and clay minerals are observed, although in a very small quantity. In Figure 10a layer boundaries are indicated by vertical arrows. In the sedimentation process as water flow becomes stable, very fine grains such as clay minerals deposit. The colour of clay minerals is black. As it can be observed in Figure 10b the number of weak elements such as carbonates increases in the layer boundary. In the layer boundaries of the five types of sandstone, the density of weak minerals (carbonate and mica) increase (see also further). As indicated in Figure 10b the grains which are white, gray and dark gray are quartz. Carbonates have rhombic shape and their colour is light gray. Micas are very thin (20-30 µm) and long. Figure 9. Location of thin section in an untested sample. Page 323 SAIMM, SANIRE and ISRM The 6th International Symposium on Ground Support in Mining and Civil Engineering Construction A Tavallali and A Vervoort (a) (b): Detail of (a) Figure 10. Digital photos of part of the thin section from the first block of sandstone (type 1). (a) Layer boundaries are indicated by arrows (pixel resolution is 2.69 µm), (b) Magnified layer boundary, Q: Quartz, C: Carbonate, M: Mica (pixel resolution is 1.31 µm) 4.1 Number of layer boundaries In all the samples the number of layer boundaries is counted. In Figure 11 the number of layer boundaries over one centimetre is given as a function of sandstone type. Graded bedding of shallow-water environments is generally composed of thin layers from a few millimetres to 1 or 2 cm, and seldom makes sequences more than 10 or 20 cm thick (Reineck & Singh 1986). Therefore from Figure 11 it can be concluded that all the blocks are from shallow-water environments as their layer thicknesses are from 1.1 mm for the reference type to 6.4 mm for sandstone type 5. Normally layer boundaries are planes of weakness because the quantity of clay mineral, mica and carbonate increase in this zone (see Figure 10b). Therefore it is important to note that for example in type 1, the number of weak planes is more than three times this number in type 3. 4.2 Grain size In sandstone the majority of the grains are quartz. The quartz grain size is not the same and this is also the case for the different sandstone types studied here. To have an estimation of the grain size, 20 grains in a width of 250 µm on both sides of a layer boundary (0.5 mm) of each sample are measured. The smallest dimension of the grains is considered. The average (and maximum, minimum) grain size values in µm for the sandstone types one to five are 79 (104, 55), 67 (98, 48), 107 (152, 64), 80 (124, 51) and 75 (135, 47) respectively. By considering the British Standards (Craig, 1990), all grains of these five sandstone types are in the size range of fine sand. The third group has the highest average grain size (107 µm) and the second group has the lowest average grain size (67 µm). It is interesting to note that the Page 324 SAIMM, SANIRE and ISRM The 6th International Symposium on Ground Support in Mining and Civil Engineering Construction A Tavallali and A Vervoort Number of layer boundaries per cm average value of the Brazilian tensile strength (BTS), the total fracture length and fracture length corresponding to non-central fracture(s) are the largest for the third type of sandstone, while these three parameters are the lowest for sandstone type two, which corresponds to the lowest average grain size. Although the grain size of the five groups is not identical, the shape and roundness of the grains are the same. For roundness of sand grains, Shepard (1963) and Powers (1953) distinguish six groups (Reineck & Singh 1986). All grains of these five sandstone types are in the class of subangular. 10 8 6 4 2 0 1 2 3 4 Sandstone type 5 Figure 11. Number of layer boundaries per one centimetre in different types of sandstones. 4.3 Presence of ripples It has already been mentioned that layer orientation affects the fracture pattern. When other planes of weakness besides the layer boundaries exist, both of these types of weak planes can affect the fracture behaviour. In sandstone type 5, ripples are observed as the secondary plane of weakness (see Figure 12). Ripples are a series of parallel or sub-parallel ridges in sand or sediment that is caused by the rhythmic or directional movement of wind or water. The mica lines in Figure 12 show such ripples. 4.4 Presence of weak minerals In the thin sections of all the sandstone types, weak minerals such as mica and carbonate are observed, especially in the layer boundaries themselves, but not only there. To be able to quantify the relative amount of weak minerals, the point-counting method is applied. 500 points in each thin section are counted in a regular pattern with a fixed interval of 400 µm between the points. Direction of counting is perpendicular to the layers. Figure 13 presents the percentage of different minerals in each sandstone type. The amount of weak minerals (mainly mica and carbonate) is different for the five types, but it is the largest for type 1 (Reference). This could be the reason why the effect of layer orientation for type 1 is much more pronounced than for the other types (see Figure 7). The amount of weak minerals as a function of the number of layer boundaries is also remarkable (Figure 14). Page 325 SAIMM, SANIRE and ISRM The 6th International Symposium on Ground Support in Mining and Civil Engineering Construction A Tavallali and A Vervoort Observed mineral percentage (%) Figure 12. Digital picture of thin section of sandstone type 5 (pixel resolution is 1.31 µm). Direction of layers is vertical, while direction of ripples is different. Direction of ripples corresponds to the mica-lines. Micas are indicated by white arrows or by M next to it. 100 Others Mica Carbonate 80 Feldspar Quartz 60 40 20 0 1 2 3 Sandstone type 4 5 Figure 13. Observed mineral percentage in different sandstone types by 500 counted points. Category ‘Others’ corresponds to pores, organic material and clay minerals. As the grains are counted perpendicular to the layers and the number of weak elements increases in the layer boundary, therefore sandstone with more layer boundaries should have a larger percentage of weak elements (see Figure 14). Apart from type 5, this corresponds to a very good correlation. The presence of ripples as second planes of weakness in sandstone type 5 is probably the reason for this exception. Page 326 SAIMM, SANIRE and ISRM The 6th International Symposium on Ground Support in Mining and Civil Engineering Construction A Tavallali and A Vervoort Weak element percentage (%) 40 30 1 2 3 4 5 20 10 0 0 2 4 6 8 Number of layer boundaries per cm 10 Figure 15. Variation of weak elements (carbonate and mica) percentage as a function of number of layer boundaries per centimetre in different sandstone types. 5 Discussion and conclusions In experimental studies on transversely isotropic rocks, the number of required specimens to be able to evaluate a property is much more than that required for isotropic rock. For example the typical fracture pattern of isotropic rocks in Brazilian test is a central fracture, while in transversely isotropic rocks many fracture patterns can occur. Because of high variability of the natural rock due to their formation process, geological environment, weathering and mineral composition, texture, fracture, crystal orientation and joint characteristics, it is difficult to obtain a large number of field specimens with uniform properties (Tien et al. 2006). This is something that became very obvious during the process of the research presented here. A certain correlation was developed between fracture pattern and inclination angle based on samples from one single block of Modave sandstone (Tavallali et al. 2007). As more samples were needed to carry on the research project, other blocks in the neighbourhood were taken. By being over-critical, a few tests were repeated on the additional blocks, just to verify that they showed the same behaviour, which was not the case. This led to a more detailed microscopic study of the sandstone, which did not completely answer the question “Why relatively similar natural rocks behave differently ?”. By comparing the five sandstone types which are macroscopically relatively similar it is observed that their Brazilian tensile strengths are different, but mainly that the fracture patterns are different. Thin sections show that samples have different microscopic parameters such as number of layer boundaries per cm, grain size, quantity and quality of weak elements, etc. Also one type (5) has second planes of weakness, namely ripples. It is too early to derive any final conclusions, but it is certainly worthwhile to note that type (1), with the largest number of layer boundaries per cm, has the largest amount of weak minerals, and that most likely this results in more layer activation during the failure process (i.e. for inclination angles of 45° or more). This process is most likely caused by shear failure instead of tensile splitting. It is also observed that the average value of the Brazilian tensile strength (BTS), the total fracture length and fracture length corresponding to non-central fracture(s) is the largest for the type of sandstone (3) with the largest grain size, while these three parameters are the lowest for sandstone type 2 which corresponds to the lowest average grain size. In a next step, thin sections will be prepared from samples after a Brazilian test is completed, but also from samples which are stopped prior to final failure (Van de Steen et al. 2002). This Page 327 SAIMM, SANIRE and ISRM The 6th International Symposium on Ground Support in Mining and Civil Engineering Construction A Tavallali and A Vervoort information, together with acoustic emission measurements should lead to a visualisation of some of the explanations given above. Acknowledgement The financial support of the Research Council of the Katholieke Universiteit Leuven (OTproject OT/03/35) is gratefully appreciated. The work is part of the PhD study by A. Tavallali. References Chen C. S., Pan E., Amadei B. Determination of deformability and tensile strength of anisotropic rock using Brazilian tests, Int. J. Rock Mech. Min. Sci. Vol. 35 (1): 43-61, 1998. Craig R. F. Soil mechanics, 4th ed. London, Chapman and Hall, 410 p., 1990. Ganne P., Vervoort A. Characterisation of tensile damage in rock samples induced by different stress paths. Pure appl. geophys. Vol. 163: 2153-2170, 2006. Poty E., Chevalier E. L’activité extractive en Wallonie, Situation actuelle et perspectives. Belgium, Ouvrage publié par le Ministère de la Region wallonne, 85 p., 2004. Powers M.C. A new roundness scale for sedimentary particles. J. Sediment. Petrol. Vol. 23: 117-119, 1953. Reineck H.-E., Singh I.B. 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