Effect of Displacement Loading Rate on Mechanical Properties of Sandstone Jinghu Yang School of Resource and Safety Engineering, China University of Mining and Technology (Beijing) Ding No.11 Xueyuan Road, Haidian District, Beijing 100083 P. R. China e-mail:852275223@qq.com ABSTRACT In order to obtain the mechanical properties of sandstone under different displacement loading rates, the uniaxial compression, shear and Brazilian split test were carried out on nearly 150 pieces of standard specimens by the WAW-600B electro-hydraulic servo. And it s explained how displacement loading rate influence the physical and mechanical properties of sandstone such as uniaxial compressive strength, elastic modulus, cohesion, internal friction angle, tensile strength and failure modes, etc. The results show that, while the displacement loading rate is small, the test results are susceptible to the effect of joint fissures in the specimens, and express high volatility. While the rate reaching a certain range, the greater the displacement loading rate is, the bigger all the tested parameters become. At last, a mechanical model was built by work-energy theorem on the molecular scale, explaining the displacement loading rate s mechanism of action. KEYWORDS: displacement loading rate; mechanical properties; joint fissures; molecular scale INTRODUCTION With the implementation of the western development strategy in China, the underground mining intensity increases gradually, and working face has a higher advancing speed than ever before, which inevitably leads to higher loading rate on stope space. As shown in Figure 1, overlying strata presses the roof like a loader. And the quicker the working face advances, the faster the overlying strata sinks and the bigger the displacement loading rate gets. Rock mass under high loading rate shows different mechanical properties. Then the traditional rock mechanics analysis based on conventional loading rate is not accurate, even incorrect. So, it s very necessary to study the mechanical properties of rock mass under different loading rates. - 591 -
Vol. 20 [2015], Bund. 2 592 Overlying strata Sinkage z Coal Main roof Immediate roof Figure 1: The overlying strata s pressure on roof At present, the domestic and foreign scholars have done some useful related researches on the mechanical properties of rock under different loading rate. For example, XI [7], WANG [5], LIANG [4], et al studied the influence of loading rate on the rock acoustic emission activities. LI [3], GONG [2], WU [6], et al analyzed the influence of loading rate on the rock fracture toughness. XIAO [8] studied the tensile strength of concrete under different loading form. YIN [9] got the rock failure pattern under different loading rate. CHEN [1] analyzed the influence of loading rate on the Kaiser effect of rock. These studies analyze the effects of loading rate on rock s mechanical properties most by using stress loading rate instead of displacement loading rate. Therefore, we do this rock mechanical property test for exploring more about the properties of the sandstone under different displacement loading rates. Specimen preparation and testing scheme Sandstone is common in underground coal mine, so we choose it as test material. And the perfect, compact and less surface crack specimens are needed for reducing the influence of joints and fissures on test accuracy. Based on the rock physical and mechanical properties test specification, we prepare the three styles as shown in table 1, respectively for the uniaxial compression, shear and Brazilian split rock tests. Table 1: The size of specimens Test name uniaxial compression (mm) Shear(mm) Brazilian split(mm) Size φ50 100 50 50 50 φ50 25 The main test equipment is the WAW-600B electro-hydraulic servo loading system, supplemented by the shearing mold, a set of electronic extensometer, pressure dynamic record system and corresponding data analysis software. As shown in Figure 2 is the test platform.
Vol. 20 [2015], Bund. 2 593 Figure 2: The WAW-600B electro-hydraulic servo WAW-600B electro-hydraulic servo test system has eight kinds of displacement loading rate inbuilt (0.5 mm/min, 1 mm/min, 2 mm/min, 5 mm/min, 10 mm/min, 20 mm/min, 50 mm/min, 100 mm/min), which meets the test requirements properly. In order to test as many loading rates as possible and eliminate samples individual differences, we made a large number of specimens, as shown in table 2. Test name uniaxial compression Table 2: Test scheme Quantity of specimen Loading rate(mm/min) 48 All the 8 inbuilt shear 48 All the 8 inbuilt except 1 and 5 Brazilian split 50 All the 8 inbuilt RESULTS AND DISCUSSION The uniaxial compression test The Figure 3 shows the specimen and its test process. In the test, we found that, the destruction of the sandstone under different displacement loading rate is obviously different. Faster loading rate causes more rapidly rock damage, greater speed of the damage pieces to fly out and more noise generated.
Vol. 20 [2015], Bund. 2 594 Figure 3: The uniaxial compression test What s more, the rock s uniaxial compressive strength and elastic modulus under different loading rate are also different. While the rate is 0.5 mm/min, the result is volatile, as shown in table 3. That s because there are many preexisting fissures in specimen, and it will take a very long time for the specimen s deformation and failure when the loading rate is small (as shown in table 4), which gives the fractures enough time to extent and generate new cracks who will repeat this process. The interaction gradually accumulates and has a greater impact on the test result of the rock s uniaxial compressive strength and elastic modulus within enough time. So the result is volatile in the rate of 0.5 mm/min, and should be ignored when studying the loading rate s function. Also as shown in table 4, the mean time to rock s failure gets very short when the rate is over 20 mm/min, resulting no enough record data to reflect the intrinsic properties of the rock, and should be ignored, too. Table 3: The result of uniaxial compression test while loading rate is 0.5 mm/min Specimen number uniaxial compressive strength (MPa) elastic modulus (10 4 MPa) 1 38.89 4.10 2 36.5 4.86 3 48.64 4.96 4 33.06 5.83 5 28.71 3.68 6 36.69 3.93 Table 4: Mean time to failure Loading rate (mm/min) Time (s) Loading rate (mm/min) Time (s) 0.5 208 10 10 1 100 20 7 2 49 50 <3 5 21 100 <2 While the loading rate increases from 1 mm/min to 10mm/min, mechanical properties of sandstone perform as shown in Figure 4 and Figure 5. That is, the bigger the rate is, the greater the
Vol. 20 [2015], Bund. 2 595 compressive strength becomes, and the larger the elastic modulus gets. Explained from the perspective of rock deformation and failure, while the rate gets bigger within 1 mm/min to 10 mm/min, the time to failure becomes shorter, the preexisting fissures interaction gets weaker and less new crack generated, resulting in smaller rock deformation and less weakening to the compressive strength, which causes the greater uniaxial compressive strength and larger elastic modulus. 40 Uniaxial compression strength 36 32 ( M Pa) 28 0 3 6 9 Loading rate (mm/min) Figure 4: Uniaxial compression strength under different loading rates Elastic modulus (10 4 MPa) 5.6 5.2 4.8 4.4 0 3 6 9 Loading rate (mm/min) Figure 5: Elastic modulus of sandstone under different loading rates The shear test As shown in Figure 6, we use four kinds of shearing molds for testing the shear strength, whose angles are 20, 30, 40 and 45 respectively. Then according to the coulomb's law τ=σtanφ+c, we draw all the measured results under the same loading rate on the same curve and figure out cohesion and internal friction angle later.
Vol. 20 [2015], Bund. 2 596 Figure 6: The shear test The cohesion of sandstone under different loading rates varies as shown in Figure 7. That is, the greater the loading rate gets, the lager the cohesion becomes. As shown in Figure 8, within 0.5 mm/min to 100 mm/min, the greater the loading rate, the bigger the internal friction angle. So according to the coulomb's law, we know that shear strength will become bigger along with the loading rate s increasing. 25 Cohesion (MPa) 20 15 10 0 30 60 90 Loading rate (mm/min) Figure 7: Cohesion of sandstone under different loading rates 42 Internal friction angle ( ) 39 36 33 0 30 60 90 Loading rate (mm/min) Figure 8: Internal friction angle under different loading rates
Vol. 20 [2015], Bund. 2 597 The Brazilian split test As shown in Figure 9, the specimen has a regular failure, and generates breakage on the diameter of the rock in the direction parallel to the external force. The two pieces produced after breaking have an initial velocity to the opposite side, and fly out with larger noise. And the same as the two tests above, the bigger the loading rate, the greater the fragments initial velocity and the more intense the noise. Figure 9: The Brazilian split test But different from the uniaxial compression test, even after the loading rate up to 20 mm/min, the measured tensile strength of sandstone under the same loading rate is still volatile, just as shown in Table 5. Table 5: Tensile strength of sandstone while loading rate is 20 mm/min Specimen Tensile strength (MPa) Specimen Tensile strength (MPa) B-16 4.6 B-20 2.5 B-17 3.6 R-5 3.9 B-18 2.1 R-6 3.7 B-19 4.1 R-7 2.1 After proper processing, we get the variation as shown in Figure 10. That is to say, within 2 mm/min to 10 mm/min, the greater the loading rate, the bigger the tensile strength. 3.5 Tensile strength (MPa) 3.4 3.3 3.2 3.1 3.0 0 5 10 15 20 Loading rate (mm/min) Figure 10: Tensile strength under different loading rates
Vol. 20 [2015], Bund. 2 598 In the experiment, we found that the stress and displacement change with the loading time regularly, as shown in Figure 11. Due to the constant displacement loading rate, the change of displacement with time is a straight line in the curve, and the slope is the loading rate. And the change of stress with time is also very regular: there is a long adjustment stage AB, followed by the steady growth BC approximating a straight line, the last is a sudden lowering CD indicating the rock s failure. In BC, the slope is the stress rate, symbolized by v f. We can see that there are several stress rates under the same displacement loading rate from table 6, and the bigger the displacement loading rate, the greater the stress rates in general. 6 4 2 Stress (kn) Fitting line Displacement (mm) y=0.823x-10.11 R 2 =0.987 C A 0 B D 4 8 12 16 20 Loading time (s) Figure 11: Loading curve in Brazilian split test Table 6: The stress rates under different displacement loading rates Displacement loading rate (mm/min) Stress rate (MPa/s) 1 0.1 0.2 2 0.2 0.3 0.4 5 0.5 0.9 10 1.2 1.7 1.9 20 2.0 3.0 3.7 And under the same displacement loading rate, the greater the stress rate, the larger the tensile strength of the sandstone, just as shown in Figure 12. And the result is less volatile.
Vol. 20 [2015], Bund. 2 599 1mm/min 2mm/min 5mm/min tensile strength /MPa 5.0 4.5 4.0 3.5 3.0 10mm/min 20mm/min 2.5 2.0 0.0 1.0 2.0 3.0 4.0 stress rate (kn/s) Figure 12: Tensile strength under different stress rates Theoretical analysis All the mechanical parameters of rock in the test must be achieved by the destruction of the specimen. And the essence of destruction is that, the external force overcomes the intermolecular force, making the intermolecular distance becoming bigger and bigger, finally molecular force disappear and rock breaks. As shown in Figure 13 is the block s molecular structure before destroying, and Figure 14 is the variation of molecular force with the distance. Postulating that the initial time t is zero, external force F is zero. For balance, molecular force f is also zero, molecular spacing r is r 0. And r is gradually becoming bigger along with the increasing of F. While r reaching s 0, f almost reduces to zero and the specimen breaks, at this moment, the time is t 0, external force is F 0. Because the specimen is loaded at a constant displacement loading rate, the deformation is uniform and the molecule moves at a constant speed and can be set to kv. The coefficient k varies with the specimen s shape, size and loading ways of the force. In the process of loading, the external force has done the work to overcome the intermolecular force s work, the rest turns into the molecules kinetic energy, just as shown in formula (1). 1 2 s0 s0 2 2 Ft dr ( ) r fdr = mk v (1) 0 r0 where m is molecular weight, r is molecular spacing in t time, and r=2kvt, dr=2kvdt. Integral for molecular force work in the equation is constant for the specified specimen, and symbolized by U. So the formula above can be simplified into formula (2). s0 U 1 F ( ) 0 tdt = + kmv (2) 2kv 4
Vol. 20 [2015], Bund. 2 600 In the experiment, the external force F changes over time as shown in Figure 11. In the real loading stage BC segment, F t = v f t, so the formula (2) can be further simplified into formula (3) and formula (4). 2 2 F0s 0 = (2 U + k mv ) (3) F v 2 0 U 1 f = ( + kmv) (4) kv 2 By the formula (3), we know that, the bigger the loading rate v, the greater the force F 0 needed for the damage, so the measured value of strength is larger and larger along with the increasing of loading rate. The speed of the debris is kv, so the bigger loading rate v causes the greater speed of the debris, much more noise and more instantaneous energy released. The measured value of tensile strength under the same loading rate is volatile, which is caused by the measurement error in the test and the individual differences of the specimens. Especially, the more fissures contained in the prospective fracture surface, the less effective m in the formulas above. And different m causes different F 0 and different strength. By the formula (4), it can be seen that, under the same displacement loading rate, the bigger the stress rate v f, the greater the strength measured. F = ² ²f mn m f mn(rmn) n Figure 13: The block s molecular structure before destroying
Vol. 20 [2015], Bund. 2 601 F F(repulsion) O r 0 U M f F(attraction) s 0 r Figure 14: Molecular force CONCLUSIONS The quicker the working face advances, the faster the overlying strata sinks and the bigger the displacement loading rate gets. And rock mass under high loading rate shows different mechanical properties. The destruction of the sandstone under different displacement loading rate is obviously different. While the rate is small, the result is volatile because of the preexisting fissures. And the faster loading rate causes much more energy released while breaking. Within a certain range, the larger the loading rate is, the bigger all the tested parameters become. And which can be explained by the mechanical model built by work-energy theorem on the molecular scale. ACKNOWLEDGEMENT The financial support from National Basic Research Program (973 Program) (2013CB227903) and the Joint Funds of the National Natural Science Foundation of China(U1361209 ) is greatly appreciated. The authors are grateful to the coal mine and my research group, particularly, Professor Wang Jia-chen. REFERENCES [1] CHEN Mian,ZHANG Yan,JIN Yan, Experimental Study of Influence of Loading Rate on Kaiser Effect of Different Litho Logical Rocks. Chinese Journal of Rock Mechanics and Engineering S1, 2599-2604(2009).
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