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Geomechanics and Geotechnical Engineering
Bangbiao Wu, Kaiwen Xia
BANGBIAO WU, Ph.D. Candidate, e-mail: [email protected], KAIWEN XIA (corresponding author), Professor, e-mail: [email protected], Department of Civil Engineering and Lassonde Institute, University of Toronto. Ontario, M5S 1A4, Canada
Dynamic Brazilian test on Laurentian granite under pre-stress conditions
Abstract: In this paper, a modified split Hopkinson pressure bar (SHPB) system is utilized to load Brazilian disc (BD) Laurentian granite samples statically, and then exert dynamic load to the sample generated by impact. Five groups of samples are tested under the pre-tension of 0 MPa, 2 MPa, 4 MPa, 8 MPa, and 10 MPa; and five groups of samples are tested under the hydrostatic stress of 0 MPa, 5 MPa, 10 MPa, 15 MPa, and 20 MPa. The result shows that the rock dynamic tensile strength decreases with the pre-tension, but increases with loading rate and hydrostatic stress; however, the increment of the tensile strength decreases as the hydrostatic stress becomes higher.
Key words: Dynamic tensile strength, pre-tension, hydrostatic, Brazilian disc, SHPB.
Tensile failure is a main failure mode of rocks in underground rock engineering projects, in which rocks are subjected to dynamic disturbances while under in situ stresses. As is well known, pores and microcracks are potential sources of failure for rock materials because of stress concentration [1, 2, 9, 12]. When disturbed by dynamic loads from blasting, seismicity, or rockbursts, the underground rocks would be vulnerable to tensile failure. Even though the far-field load is compressive, the local stresses may be tensile as shown in Fig. 1. Therefore, it is necessary to investigate the dynamic tensile failure of rock materials under in situ stress state.
Introduction
Roof
(Macroscopic tension)
."HI
aMf
• In-situ Stress state (Microscopic tension)
Fig. 1. Potential tensile failure of rocks under in situ stress states.
© Bangbiao Wu, Kaiwen Xia, 2016
In this work, the Brazilian disc (BD) sample [14] is adopted for the measurement of dynamic tensile strength of rock materials under pre-tension and hydrostatic stress state. The Brazilian disc specimen is loaded by a modified split Hopkinson pressure bar (SHPB) system, using which static pre-tension and hydrostatic stress are applied to the rock sample and maintained before applying the dynamic load. The pre-tension and hydrostatic stress are applied through a hydraulic press, and the dynamic loading is exerted using a low speed gas gun, as in a conventional SHPB system.
Sample preparation and testing methodology
Specimen preparation. The rock samples are Laurentian granite (LG) taken from the Laurentian region of Grenville province, Canada. Special care was taken to prepare the Brazilian disc specimens with a diameter of 40 mm and thickness of 16 mm. All specimens are polished to have a surface roughness of less than 0.5% of the sample thickness [14]. The physical and mechanical properties of LG are summarized in Table 1 [8].
Table 1
Summary of physical and mechanical properties of Laurentian granite
Density Porosity Young's modulus Poisson's ratio Tensile strength UCS
2.63 g/cm3 0.64% 92 GPa 0.21 12.8 MPa 259 MPa
Experimental apparatus. The tests were conducted on the modified Split Hopkinson pressure bar (SHPB) system, which includes three bars (a striker bar, an incident bar, and a transmitted bar) [14] and the hydraulic system (Fig. 2). The hydraulic system is mainly composed of a pressure chamber that provides axial preload to the bars and sample, a cylinder that applies lateral confinement and a rigid mass at the incident bar end that is connected to the chamber by tie-rods.
Fig. 2. Schematics of the modified SHPB system with the Brazilian disc specimen.
Realize of the static pre-stress and data reduction. During the tests, the static pre-tension is applied to the sample by the pressure loading units attached to the end of the transmitted bar (cylinder 2 in Fig. 2) through the elastic bars and flange supported by a rigid mass. When the desired pre-tension is achieved, dynamic loading is applied from the impact of the striker bar on the free end of the incident bar. The incident pulse
propagates along the incident bar before it hits the sample, leading to a reflected stress wave and a transmitted stress wave that are recorded by the strain gauges attached on the incident and transmitted bar surfaces. The
strains of incident wave, reflected wave and transmitted wave are denoted by s1, sr and st, respectively.
Based on the one dimensional stress wave theory, and assuming stress equilibrium during loading [14]
(i.e., s + sr = st), the history of the force on the sample is:
P(t) = P0 + Pd(t), (1)
where P0 is the static preload on the bars, Pd (t) is the dynamic force history on the bars after the impact. The tensile stress history at the center of the disc sample can be determined as:
a(t) = a0 +ad (t) =
tTRB ^ (2)
where a0 is the pre-tension at the center of the disc, and
P
' 0 tTRB
^o = ^7 • (3)
ad(t) is the dynamic tensile stress, E0 is the Young's Modulus of the bars, A is the cross-sectional
area of the bars; R is the radius of the sample and B is the thickness of the sample. The tensile strength is the maximum value of the tensile stress when the rock sample is damaged.
As shown in Fig. 2, the two cylinders are connected to the same hydraulic oil pump by separate valves. When the two valves are open at the same time, the rock sample would be in hydrostatic stress state, regardless of the shape of the rock sample.
The tensile stress history at the center of the sample is the same as shown in Eq. (2).
Testing results
Five groups of samples are tested under the pre-tension of 0 MPa, 2 MPa, 4 MPa, 8 MPa, and 10 MPa; and five groups of samples are tested under the hydrostatic stress of 0 MPa, 5 MPa, 10 MPa, 15 MPa, and 20 MPa. The pulse shaper technique is applied to achieve the force balance in the specimen during the experiments. This technique was discussed by Frew et al. [6] in details for SHPB compressive tests of brittle materials.
Effect of loading rate. Fig. 3 illustrates the dynamic tensile strength versus loading rate. And Fig. 4 shows the dynamic tensile strength of the rock under different hydrostatic stresses. It is obvious from the two figures that the dynamic tensile strength increases with the loading rate, revealing the phenomenon of rate dependency that is common for engineering materials, such as rock [13], concrete [4, 7], ceramic [3, 11].
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Loading Rate (GPa/s)
3. Dynamic strength versus loading rate for different pre-tensions.
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1800
600 900 1200 1500 Loading rate (GPa/s) Fig. 4. Dynamic tensile strength of rocks under different hydrostatic stresses.
Effect of pre-stress. Apart from the rate dependency mentioned above, what can be seen from Fig. 3 is that the dynamic tensile strength of the rock decreases with the increase of the pre-tension when subjected to the same loading rate. The decrease of dynamic tensile strength is caused by the opening of microcracks when the specimen bears the pre-tension stress. Which is consistent to the results reported by Xia et al. that the microstructures affect the dynamic stress of rock specimens [10].
The effect of hydrostatic stress is also obvious as can be seen from Fig. 4 that the dynamic tensile strength increases with the hydrostatic stress. However, the increment decreases with the increases of the hydrostatic stress. For example, as shown in Table 2, when the loading rate is approximately 1220 GPa/s, the dynamic tensile strength is 38.6 MPa when the specimen is loaded stress-free being subjected to dynamic loading; and the dynamic tensile strength of the one with 10 MPa hydrostatic stress is 50.0 MPa, which is 11.4 MPa higher than the former. However, when the hydrostatic stress grows to 20 MPa, the dynamic tensile strength becomes 56.4 MPa. The increment of 6.4 MPa is much smaller than 11.4 MPa with equivalent increase of the hydrostatic stress.
Table 2
Example of dynamic tensile strength when the loading rate is about 1220 GPa/s
Hydrostatic stress (MPa) 0 5 10 15 20
Tensile strength (MPa) 38.6 48.3 50.0 55.5 56.4
Interpretation and discussion
The failure pattern of specimens can be an important indicator in revealing the failure mechanism of rocks, so it would be useful to analyze the failure pattern of the recovered samples. Fig. 5 shows typical recovered samples from dynamic tests, samples a ~ c are the ones under pre-tension and d ~ f are the ones under hydrostatic stress. It shows that all of the samples were fractured diametrically into two halves. The difference between static and dynamic failure of rock materials is that the microcracks do not have enough time to
propagate and coalescence until failure under dynamic loadings, that is why the rock failure is involved with only the most vulnerable crack under static loadings but all of the microcracks are involved in the dynamic fragmentation process. The two fragments in sample 2-2 and sample 4-2 can be explained as the microcracks activated by the pre-tension are all involved in the fragmentation process. It is also obvious that more microcracks are involved in the process in sample 4-9, which can be seen from the crushed strap along the loading diameter and the cracks on the sample surface.
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Fig. 5. Typical failure patterns of the tested samples. (a) Sample 2-2 is loaded the pre-tension of 2 MPa and impact loading rate of 193.5 GPa/s Sample 0-0 is the sample damaged by static BD test; (b) Sample 4-2 is loaded the pre-tension of 4 MPa and impact loading rate of 289.6 GPa/s; (c) Sample 4-9 is loaded the pre-tension of 4 MPa and impact loading rate of 1292.9 GPa/s; (d) Sample 10-11 is loaded the hydrostatic stress of 10 MPa; (e) Sample 15-12 is loaded the hydrostatic stress of 15 MPa; (f) Sample 20-12 is loaded the
hydrostatic stress of 20 MPa.
Both sample 4-2 and sample 4-9 have a small wedge shaped crushed zone, which is a result of secondary fracture after the main fracture from the center of the disc as discussed in the literature [5]. The secondary fracture is mainly caused by the further movement of the incident bar towards the transmitted bar after the initial impact. With the increase of the loading rate, the impact velocity of the striker bar on the incident bar gets higher, leading to higher moving velocity of the incident bar. This is why the angle of the crushed zone is larger in higher loading rates than in lower ones.
Different from the pre-tension tests, there is no wedge at the recovered samples under hydrostatic stress. It is obvious that samples d ~ f are damaged along the loading axis even when the loading rate is really high. The reason is that under hydrostatic stress, the propagation and coalescence of microcracks are held back by the confinement. Thus the microcracks propagates along the most vulnerable direction, which is the loading axis in the test. And this is also the reason why the dynamic tensile strength increases with the hydrostatic stress.
Conclusions
In this paper, we propose a modified SHPB testing technique with a Brazilian disc specimen to measure the dynamic tensile strength with different pre-tension and hydrostatic stress. The following conclusions are obtained:
1. The dynamic tensile strength of rocks decreases with the pre-tension.
2. The dynamic tensile strength of rocks increases with loading rate and hydrostatic stress.
3. The increment of the tensile strength decreases as the hydrostatic stress becomes higher.
4. The modified SHPB system is approved applicable to be used as a testing methods considering pre-stress such as pre-tension and hydrostatic.
REFERENCES
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The report was delivered at the 5th Russian-Chinese Scientific Technical Forum Deep Level Rock Mechanics and Engineering, August, 5-7th, 2015, Weihai, CPR. On its basis, the author has written an article especially for FEFU: School of Engineering Bulletin.
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ВЕСТНИК ИНЖЕНЕРНОЙ ШКОЛЫ ДВФУ. 2016. № 2 (27)
НАУКИ О ЗЕМЛЕ. Геомеханика и строительная геотехнология
УДК 622.831
Банбяо У, Кайвэнь Ся
БАНБЯО У - докторант, e-mail: [email protected]; КАЙВЕНЬ СЯ - профессор -Департамент гражданского строительства, Институт Лассонда, Университет Торонто. Онтарио, M5S 1A4, Канада
Динамические испытания предварительно напряженного гранита Laurentian «бразильским» методом
Аннотация: В статье приведены результаты испытаний гранита Laurentian «бразильским» методом. Показано, что с ростом предварительного напряжения предел динамической прочности снижается. При испытании использовалась усовершенствованная система разрезного стержня Гопкинсона (SHPB) для статичного размещения образцов гранита Laurentian в форме бразильского диска (BD), с последующим приложением динамической нагрузки на образец, вызываемой воздействием. Были протестированы пять групп образцов под предварительным напряжением 0 МПа, 2 МПа, 4 МПа, 8 МПа и 10 МПа и пять групп образцов под гидростатическим напряжением 0 МПа, 5 МПа, 10 МПа, 15 МПа и 20 МПа. Результаты показали, что при предварительном напряжении предел динамической прочности образцов гранита снижается, но он возрастает с ростом предварительного напряжения и гидростатического напряжения. Тем не менее приращение предела динамической прочности снижается по мере увеличения гидростатического напряжения.
Ключевые слова: предел динамической прочности, предварительное напряжение, гидростатическое напряжение, «бразильский» метод, разрезной стержень Гопкинсона (SHPB).
Здесь и далее: статьи китайских авторов этого номера первоначально были представлены как доклады и сообщения на 5-й Российско-Китайской научной конференции «Нелинейные геомеханико-геодинамические процессы при отработке месторождений полезных ископаемых на больших глубинах», 5-7 августа 2015, Вэйхай, КНР. На их основе авторы подготовили публикации специально для «Вестника Инженерной школы ДВФУ».
