第三章 岩石的力学性质-4-练习
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6
Tang Lizhong .
Institute of Rock & Soil Mechanics and Engineering,
Central South University
Chapter 3 Mechanical Properties of Rock
3.6 问题/Problems
(9)
王文星,岩体力学,第一章练习一之第1题. (10)
3
Tang Lizhong .
Institute of Rock & Soil Mechanics and Engineering,
Central South University
Chapter 3 Mechanical Properties of Rock
Fra Baidu bibliotek
3.6 问题/Problems
(4) What causes a rock to break when it is compressed uniaxially to failure? Is it when the stress reaches a certain value or when the strain reaches a certain value? Or is it when some other parameter reaches a critical value, such as the energy input per unit volume, or the microcrack density per unit volume? (5) The geometry of the linear Mohr-Coulomb envelope is such that a number of useful relations between strength parameters canbe drawn from it. Derive an expression for the uniaxial compressive strength of rock in terms of the cohesion and angle of internal friction
Figure 2. Complete axial stress– axial strain curves obtained in triaxial compression tests on Tennessee Marble at the confining pressures indicated by the numbers on the curves.
王文星,岩体力学,第一章练习一之第2题.
(11) 王文星,岩体力学,第一章练习一之第4题.
Tang Lizhong .
Institute of Rock & Soil Mechanics and Engineering,
Central South University
7
Chapter 3 Mechanical Properties of Rock
Tang Lizhong .
Institute of Rock & Soil Mechanics and Engineering,
Central South University
2
Chapter 3 Mechanical Properties of Rock
3.6 问题/Problems
(3) (a) Establish an approximate peak strength envelope for the marble for which the data shown in figure 2 were obtained. (b) In what ways might the observed stress–strain behaviour of the specimens have differed had the tests been carried out in a conventional testing machine having a longitudinal stiffness of 2.0 GNm−1? Assume that all specimens were 50 mm in diameter and 100 mm long.
Chapter 3 Mechanical Properties of Rock
3.6 问题/Problems
(1) From the data given in Figure 1, calculate the tangent modulus and Poisson’s ratio for the initial elastic behaviour of the limestone with σ 3 = 2.0 MPa.
Tang Lizhong . Institute of Rock & Soil Mechanics and Engineering, Central South University
5
Chapter 3 Mechanical Properties of Rock
3.6 问题/Problems
(8)
Central South University
1
Chapter 3 Mechanical Properties of Rock
3.6 问题/Problems
(2) A porous sandstone has a uniaxial compressive strength of σ c = 75 MPa. The results of a series of triaxial compression tests plotted on shear stress–normal stress axes give a linear Coulomb peak strength envelope having a slope of 45◦. Determine the axial stress at peak strength of a jacketed specimen subjected to a confining pressure of σ 3 = 10 MPa. If the jacket had been punctured during the test, and the pore pressure had built up to a value equal to the confining pressure, what would the peak axial stress have been?
Figure 1. Results of triaxial compression tests on an oolitic limestone with volumetric strain measurement
Tang Lizhong .
Institute of Rock & Soil Mechanics and Engineering,
Tang Lizhong .
Institute of Rock & Soil Mechanics and Engineering,
Central South University
4
Chapter 3 Mechanical Properties of Rock
3.6 问题/Problems
(6) The linear Mohr-Coulomb envelope with a tensile cut-off sets a definite limit on the maximal uniaxial tensile strength of a material. By considering the largest uniaxial tensile Mohr circle that can be drawn, determine this tensile strength limit in terms of σ c and ϕ. (7) A firm whose judgement has been questioned on a previous occasion has been entrusted with the strength testing of rock in a site investigation project. During their first uniaxial compression test, the equipment failed to measure the peak axial load, but the technician did record that the specimen failed by the formation of a single fracture inclined at 20 ° to the loading axis. In a subsequent triaxial test, as the confining pressure was being increased before application of the axial stress, the specimen failed prematurely when the confining pressure in the Hoek cell was 85 MPa. On the basis of these results, propose a failure criterion of the form σ 1=aσ 3 + b for the rock.
3.6 问题/Problems
(12) The results in the table below show the axial displacement and radial strain induced in a cylindrical specimen of weak chalk during a uniaxial creep test. In this test, the specimen was initially 250 mm high and was subjected to an axial stress of 55 MPa. After 3 hours the test was stopped, at which stage creep had ceased and the displacement had become constant at 0.4545 mm.
A servo-controlled compression test has been conducted on a weak soapstone such that the specimen length remained unchanged throughout: as the axial stress, σ a, was increased, so the confining pressure, p, was increased so that no net axial strain resulted. A plot of axial stress (vertical axis) against confining pressure (horizontal axis) gave an initial straight line passing through the origin. At a critical confining pressure of p = 85 MPa (when σ a =39.1 MPa), the slope of the σ a - P plot suddenly changed to 29 °and remained constant for the remainder of the test. This change in slope may be taken to represent the onset of yield. (i) Determine an elastic constant from the slope of the initial portion of the σ a -- P curve. (ii) Assuming that the Mohr-Coulomb criterion is applicable, determine σ c, c and ϕ for the rock.
Tang Lizhong .
Institute of Rock & Soil Mechanics and Engineering,
Central South University
Chapter 3 Mechanical Properties of Rock
3.6 问题/Problems
(9)
王文星,岩体力学,第一章练习一之第1题. (10)
3
Tang Lizhong .
Institute of Rock & Soil Mechanics and Engineering,
Central South University
Chapter 3 Mechanical Properties of Rock
Fra Baidu bibliotek
3.6 问题/Problems
(4) What causes a rock to break when it is compressed uniaxially to failure? Is it when the stress reaches a certain value or when the strain reaches a certain value? Or is it when some other parameter reaches a critical value, such as the energy input per unit volume, or the microcrack density per unit volume? (5) The geometry of the linear Mohr-Coulomb envelope is such that a number of useful relations between strength parameters canbe drawn from it. Derive an expression for the uniaxial compressive strength of rock in terms of the cohesion and angle of internal friction
Figure 2. Complete axial stress– axial strain curves obtained in triaxial compression tests on Tennessee Marble at the confining pressures indicated by the numbers on the curves.
王文星,岩体力学,第一章练习一之第2题.
(11) 王文星,岩体力学,第一章练习一之第4题.
Tang Lizhong .
Institute of Rock & Soil Mechanics and Engineering,
Central South University
7
Chapter 3 Mechanical Properties of Rock
Tang Lizhong .
Institute of Rock & Soil Mechanics and Engineering,
Central South University
2
Chapter 3 Mechanical Properties of Rock
3.6 问题/Problems
(3) (a) Establish an approximate peak strength envelope for the marble for which the data shown in figure 2 were obtained. (b) In what ways might the observed stress–strain behaviour of the specimens have differed had the tests been carried out in a conventional testing machine having a longitudinal stiffness of 2.0 GNm−1? Assume that all specimens were 50 mm in diameter and 100 mm long.
Chapter 3 Mechanical Properties of Rock
3.6 问题/Problems
(1) From the data given in Figure 1, calculate the tangent modulus and Poisson’s ratio for the initial elastic behaviour of the limestone with σ 3 = 2.0 MPa.
Tang Lizhong . Institute of Rock & Soil Mechanics and Engineering, Central South University
5
Chapter 3 Mechanical Properties of Rock
3.6 问题/Problems
(8)
Central South University
1
Chapter 3 Mechanical Properties of Rock
3.6 问题/Problems
(2) A porous sandstone has a uniaxial compressive strength of σ c = 75 MPa. The results of a series of triaxial compression tests plotted on shear stress–normal stress axes give a linear Coulomb peak strength envelope having a slope of 45◦. Determine the axial stress at peak strength of a jacketed specimen subjected to a confining pressure of σ 3 = 10 MPa. If the jacket had been punctured during the test, and the pore pressure had built up to a value equal to the confining pressure, what would the peak axial stress have been?
Figure 1. Results of triaxial compression tests on an oolitic limestone with volumetric strain measurement
Tang Lizhong .
Institute of Rock & Soil Mechanics and Engineering,
Tang Lizhong .
Institute of Rock & Soil Mechanics and Engineering,
Central South University
4
Chapter 3 Mechanical Properties of Rock
3.6 问题/Problems
(6) The linear Mohr-Coulomb envelope with a tensile cut-off sets a definite limit on the maximal uniaxial tensile strength of a material. By considering the largest uniaxial tensile Mohr circle that can be drawn, determine this tensile strength limit in terms of σ c and ϕ. (7) A firm whose judgement has been questioned on a previous occasion has been entrusted with the strength testing of rock in a site investigation project. During their first uniaxial compression test, the equipment failed to measure the peak axial load, but the technician did record that the specimen failed by the formation of a single fracture inclined at 20 ° to the loading axis. In a subsequent triaxial test, as the confining pressure was being increased before application of the axial stress, the specimen failed prematurely when the confining pressure in the Hoek cell was 85 MPa. On the basis of these results, propose a failure criterion of the form σ 1=aσ 3 + b for the rock.
3.6 问题/Problems
(12) The results in the table below show the axial displacement and radial strain induced in a cylindrical specimen of weak chalk during a uniaxial creep test. In this test, the specimen was initially 250 mm high and was subjected to an axial stress of 55 MPa. After 3 hours the test was stopped, at which stage creep had ceased and the displacement had become constant at 0.4545 mm.
A servo-controlled compression test has been conducted on a weak soapstone such that the specimen length remained unchanged throughout: as the axial stress, σ a, was increased, so the confining pressure, p, was increased so that no net axial strain resulted. A plot of axial stress (vertical axis) against confining pressure (horizontal axis) gave an initial straight line passing through the origin. At a critical confining pressure of p = 85 MPa (when σ a =39.1 MPa), the slope of the σ a - P plot suddenly changed to 29 °and remained constant for the remainder of the test. This change in slope may be taken to represent the onset of yield. (i) Determine an elastic constant from the slope of the initial portion of the σ a -- P curve. (ii) Assuming that the Mohr-Coulomb criterion is applicable, determine σ c, c and ϕ for the rock.