Questions and Answers of Geological Engineering

Considering the data and results from Problem 20, determine the shaft wall safety factors in tension and compression.
Given the stresses relative to compass coordinates (x = east, y = north, z = sup), σxx = 2,155, σyy = 3,045, σzz = 4,200, τyx = −1,222, τxz = 0, τyz = 0 in psi with compression positive, find
A rectangular shaft 6 × 8 m is planned for a depth of 1,500 m where the premining stresses relative to compass coordinates (x=east, y =north, z = up) are given by: σxx = 1,724 + 11.3h, σyy = 5,517
Considering the data and results from Problem 23, determine the shaft wall safety factors in tension and compression.
Given the stresses relative to compass coordinates (x=east, y=north, z =up), σxx = 14.9, σyy = 21.0, σzz = 29.0, τyx = −8.4, τxz = 0, τyz = 0 in MPa with compression positive, find the
A large vertical shaft is planned for an underground hard rock mine. Laboratory tests on core from exploration drilling show thatCo = 21,500 psi, To = 1,530 psi, E = 6.25(106) psi,G = 2.5(106) psi,
A large vertical shaft is planned for an underground hard rock mine. Laboratory tests on core from exploration drilling show thatCo = 148.3, To = 10.6, E = 43.10GPa, G = 17.24GPa,γ = 22.78kN/m3
Laboratory tests on core from exploration drilling show thatCo = 21,500 psi, To = 1,530, E = 6.25(106) psi,G = 2.5(106) psi, γ = 144pcf, while premining stress measurements can be fit to the
A rectangular shaft 12 ft by 24 ft is planned for deepening from a depth of 3,200 to 4,800 ft in ground where the pre-shaft stress state relative to compass coordinates (x = east, y = north, z = up)
Laboratory tests on core from exploration drilling show thatCo = 148.3 MPa, To = 10.55 MPa, E = 43.10GPa,G = 17.24GPa, γ = 22.78kN/m3, while premining stress measurements can be fit to the
A rectangular shaft 3.7 × 7.4 m is planned for deepening from a depth of 975 to 1,463 m in ground where the pre-shaft stress state relative to compass coordinates (x = east, y = north, z = up) is
A vertical circular shaft will pass through a water bearing stratum at a depth of 2,780 ft where the water pressure is estimated to be 210 psi. Finished shaft diameter must be 18 ft. The pre-shaft
A three-compartment rectangular shaft 12 × 24 ft in cross section is planned for a depth of 3,000 ft. The pre-sinking stress field is assumed to be caused by gravity only. The weakest rock along the
The pre-sinking stress field assumed to be caused by gravity alone (Problem 3.33) turns out to be wrong. The actual stress field has a tectonic component that adds a constant 1,250 psi to the
A circular shaft 18 ft in diameter is decided upon rather than the proposed rectangular shaft. Determine the unlined shaft wall safety factors. Note: The stress field from Problem 3.34 applies.
The in situ stress field for Problems 34 and 35 changes between 3,000 and 3,500 ft to one described by the formulas σv = 1.125h, σH = 3,500 + 0.33h, σh = 3,500 + 0.33h, where the stresses are in
A three-compartment rectangular shaft 3.7 × 7.4 m in cross section is planned for a depth of 914 m. The pre-sinking stress field is assumed to be caused by gravity only. The weakest rock along the
The pre-sinking stress field assumed to be caused by gravity alone (Problem 3.37) turns out to be wrong. The actual stress field has a tectonic component that adds a constant 8.62 MPa to the
A circular shaft 5.5min diameter is decided upon rather than the proposed rectangular shaft. Determine the unlined shaft wall safety factors. Note: The stress field from Problem 3.38 applies.
The in situ stress field for Problems 38 and 39 changes between 914 and 1,067 m to one described by the formulas σv = 25.45h, σH = 24,138 + 7.47h, σh = 24,138 + 7.47h where the stresses are in kPa
A circular shaft liner is sunk to a depth of 3,750 ft (1,143 m). If the premining stress field is caused by gravity alone, what unconfined compressive rock strength in psi (MPa) is needed for a rock
A circular vertical shaft is planned to have a finished, inside diameter of 19 ft in an underground hard rock mine. Rock properties are: Co = 23,700 psi, To = 1,480 psi, E = 5.29(106 psi), ν = 0.27,
With reference to the previous problem data, if changes in the inside diameter of the lined shaft are monitored for safety, what “reading” in inches would indicate impending failure of the liner?
A circular vertical shaft is planned to have a finished, inside diameter of 5.8 m in an underground hard rock mine. Rock properties are: Co = 163.5 MPa, To = 10.21 MPa, E = 36.48GPa, ν = 0.27, γ =
With reference to the previous problem data, if changes in the inside diameter of the lined shaft are monitored for safety, what “reading” in centimeters would indicate impending failure of the
A circular vertical shaft is planned to have a finished, inside diameter of 26 ft in an underground hard rock mine. Rock properties are: Co = 27,400 psi, To = 1,840 psi, E = 6.19(106 psi), ν = 0.22,
With reference to the previous problem data, if changes in the inside diameter of the lined shaft are monitored for safety, what “reading” in inches would indicate impending failure of the liner?
A circular vertical shaft is planned to have a finished, inside diameter of 8 m in an underground hard rock mine. Rock properties are: Co = 189.0 MPa, To = 12.69 MPa, E = 42.69GPa, ν = 0.22, γ =
With reference to the previous problem data, if changes in the inside diameter of the lined shaft are monitored for safety, what “reading” in cm would indicate impending failure of the liner?
A vertical unlined 22 ft diameter circular shaft is fitted with a concrete shaft liner to withstand water pressure of 123 psi in a massive sandstone aquifer at a depth of 2,890 ft. Liner properties
Show why the weight of a concrete shaft liner that is poured to the walls of the unlined shaft is not important to liner stress
A large vertical finished (inside) shaft diameter of 32 ft is required for hoisting capacity in a planned high volume underground oil shale mine. An aquifer is encountered at a depth of 1,270 ft
A vertical circular shaft will pass through a water-bearing stratum at a depth of 2,780 ft where the water pressure is estimated to be 210 psi. Finished shaft diameter must be 18 ft. The pre-shaft
A large vertical finished (inside) shaft diameter of 9.75mis required for hoisting capacity in a planned high volume underground oil shale mine. An aquifer is encountered at a depth of 387 m where
A vertical circular shaft will pass through a water-bearing stratum at a depth of 847 m where the water pressure is estimated to be 1.45 MPa. Finished shaft diameter must be 5.5 m. The pre-shaft
An in situ stress field between 3,000 ft and 3,500 ft is fit to the formulas σv = 1.125h, σH = 3,500 + 0.33h, σh = 3,500 + 0.33h where the stresses are in psi and the depth h is in ft. Stresses
With reference to the previous problem, determine the reduction in diameter of the liner when the liner first fails.
With reference to Problem 56, determine the radial displacement of the interface between the liner and shaft wall when the liner first fails.
With reference to Problem 56 data, water pressure of 80 psi is anticipated at 4,500 ft. What liner thickness is indicated, if a liner safety factor of 2.5 is required, note: Minimum thickness is 1 ft.
If a steel liner is used in Problem 59 instead of concrete and the steel strength is 36,000 psi (compressive and tensile strengths are equal), what is the corresponding steel liner thickness?
An in situ stress field between 914 and 1,067 m is fit to the formulas σv = 25.45h, σH = 24,138 + 7.47h, σh = 24,138 + 7.47h, where the stresses are in kPa and the depth h is in m. Stresses σv,
With reference to the previous problem, determine the reduction in diameter of the liner when the liner first fails. Discuss.
With reference to Problem 61, determine the radial displacement of the interface between the liner and shaft wall when the liner first fails.
With reference to Problem 61 data, water pressure of 0.552 MPa is anticipated at 1,372 m. What liner thickness is indicated, if a liner safety factor of 2.5 is required, note: Minimum thickness is
If a steel liner is used in Problem 64 instead of concrete and the steel strength is 248 MPa (compressive and tensile strengths are equal), what is the corresponding steel liner thickness?
A circular concrete shaft liner with a Young’s modulus of 3.4 million psi, Poisson’s ratio of 0.25, unconfined compressive strength 3,500 psi and tensile strength 350 psi is considered for
A circular concrete shaft liner with Young’s modulus of 3.4 million psi, Poisson’s ratio of 0.25, unconfined compressive strength 3,500 psi and tensile strength 350 psi is loaded to the verge of
With reference to Problem 67, measurements are made between points on the inside of the liner on opposite ends of a diametral line. What change in diameter from the no-load condition is indicated at
A circular concrete shaft liner with a Young’s modulus of 23.45GPa, Poisson’s ratio of 0.25, unconfined compressive strength 24.1 MPa, and tensile strength 2.41 MPa is considered for control of
A circular concrete shaft liner with Young’s modulus of 23.45GPa, Poisson’s ratio of 0.25, unconfined compressive strength 24.1 MPa, and tensile strength 2.41 MPa is loaded to the verge of
With reference to Problem 70, measurements are made between points on the inside of the liner on opposite ends of a diametral line. What change in diameter from the no-load condition is indicated at
A 12 ft by 24 ft rectangular shaft is sunk to a depth of 3,000 ft in ground where the premining stress field is given by formulas Sv = 1.2h, Sh = 120 + 0.5h, SH = 3, 240 + 0.3h, where h is depth in
A 3.7 × 7.4 m rectangular shaft is sunk to a depth of 914 m in ground where the premining stress field is given by formulas, Sv = 27.2h, Sh = 828 + 11.3h, SH = 22, 345 + 6.8h, where h is depth in m
A rectangular shaft 10 ft by 20 ft with the long axis parallel to the N–S line exists at a depth of 950 ft. The mining plan calls for deepening the shaft to 1,800 ft. The premining stress state
Given the stresses relative to compass coordinates (x = east, y = north, z = up), σxx = 2,155, σyy = 3,045, σzz = 4,200, τyx = −1,222, τxz = 0, τyx = 0 in psi with compression positive, find
A rectangular shaft 3 m × 6 m with the long axis parallel to the N–S line exists at a depth of 290 m. The mining plan calls for deepening the shaft to 550 m. The premining stress state relative to
Given the stresses relative to compass coordinates (x = east, y = north, z = up), σxx = 14.86, σyy = 21.00, σzz = 29.00, τyx = −8.43, τxz = 0, τyx = 0 in MPa with compression
The stresses relative to compass coordinates (x = east, y = north, z = up) are σxx = 2,155, σyy = 3,045, σzz = 4,200, τyx = −1,222, τxz = 0, τyx = 0, in psi with compression positive. Suppose
Consider a horizontal, rectangular opening that is 10 ft high and 20 ft wide and driven due north 5,000 ft. Rock properties are, Co = 23,700 psi, To = 1,480 psi, E = 5.29(106 psi), ν = 0.27, γ =
A tabular ore body 15 ft thick is mined full-seam height at a depth of 2,300 ft by repeated slices 20 ft wide and 5,000 ft long, so the first drive is simply a 20 ft wide tunnel from the rock
The stresses relative to compass coordinates (x = east, y = north, z = up) are σxx =14.86, σyy = 21.00, σzz =28.97, τyy= −8.43, τxz = 0, τyx = 0 in MPa with compression positive. Suppose a
Consider a horizontal, rectangular opening that is 3 m high and 6 m wide and driven due north 1,524 m. Rock properties are, Co = 163.5 MPa, To = 10.2 MPa, E = 36.48GPa, ν = 0.27, γ = 25.34kN/m3.
A tabular ore body 4.6 m thick is mined full-seam height at a depth of 700 m by repeated slices 6 m wide and 1,520 m long, so the first drive is simply a 6 m ft wide tunnel from the rock mechanics
Consider a pin-connected, two-segment, semi-circular steel rib shown in the sketch.(a) If the bearing ends are free to rotate, find the thrust and moment in the steel. Data are: Hp = 10 ft, Ht=18 ft,
Two-piece continuous steel sets are to support a tunnel with a semi-circular roof having a radius of 12 ft and a straight leg section of 13 ft. The tunnel is therefore 24 ft wide by 25 ft high. The
Two-piece continuous steel sets are to support a tunnel with a semi-circular roof having a radius of 12 ft and a straight leg section of 13 ft. The tunnel is therefore 24 ft wide by 25 ft high. The
Two-piece continuous steel sets are to support a tunnel with a semi-circular roof having a radius of 3.5 m, and a straight leg section of 4 m. The tunnel is therefore 7 m wide by 7.5 m high. The
Consider the analysis of tunnel bolting leading to the equation If bolting is on a square pattern of spacing S and a 45? cone of influence is assigned to the bolt forces, show that this equation is
Layout an equivalent bolting pattern for the crown portion of the tunnel in Problem 8 using 1 inch diameter rebar tensioned to 60,000 psi, specify bolt spacing and length.
Yieldable steel arches are used to control squeezing ground in a tunnel where the rock pressure corresponds to a rock “head” of 15 ft. Estimate the steel area needed for this situation. What
Layout an equivalent bolting pattern for the crown portion of the tunnel in Problem 10 using 2.5 cm diameter rebar tensioned to 410 MPa. Specify bolt spacing and length.
Yieldable steel arches are used to control squeezing ground in a tunnel where the rock pressure corresponds to a rock “head” of 4.6 m. Estimate the steel area needed for this situation. What
An arched tunnel is driven in moderately blocky and seamy, wet ground at a depth of 1,970 ft. The tunnel is 14 ft wide by 11 ft high; the back arch is semi-circular.(a) Specify a suitable steel set
For Problem 4.16 conditions, find an equivalent bolting pattern (bolt diameter, strength, length, and spacing), that provides the same approximate thrust capacity.
For the same “rock pressure” and semi-circular arch in Problem 16, determine the cross-sectional area of yieldable steel arches for ground control.
An arched tunnel is driven in moderately blocky and seamy, wet ground at a depth of 600 m. The tunnel is 4.3 m wide by 3.4 m high; the back arch is semi-circular.(a) Specify a suitable steel set size
For Problem 19 conditions, find an equivalent bolting pattern (bolt diameter, strength, length, and spacing), that provides the same approximate thrust capacity.
For the same “rock pressure” and semi-circular arch in Problem 19, determine the cross-sectional area of yieldable steel arches for ground control.
An arched tunnel is driven in moderately blocky and seamy, wet ground at a depth of 970 ft. The tunnel is 18 ft wide by 21 ft high; the back arch is semi-circular.(a) Specify a suitable steel set
For the same “rock pressure” and semi-circular arch in Problem 4.22, determine the cross-sectional area of yieldable steel arches for ground control.
For Problem 22 conditions, find an equivalent bolting pattern (bolt diameter, strength, length, and spacing), that provides the same approximate thrust capacity.
An arched tunnel is driven in moderately blocky and seamy, wet ground at a depth of 297 m. The tunnel is 5.51 m wide by 61.4 m high; the back arch is semi-circular.(a) Specify a suitable steel set
For the same “rock pressure” and semi-circular arch in Problem 25, determine the cross-sectional area of yieldable steel arches for ground control.
For Problem 4.26 conditions, find an equivalent bolting pattern (bolt diameter, strength, length, and spacing), that provides the same thrust capacity.
Semi-circular yieldable steel arches with a nominal radius of 6.75 ft are used in main entries to a coal mine developed from outcrop under plateau overburden. Seam depth at a point of interest is
With reference to Problem 28, an alternative support system in the form of fixed steel sets is considered with entry height 11.75 ft. Select a suitable steel rib for this alternative specifying steel
With reference to Problem 29, develop an approximately equivalent bolting reinforcement system using one-inch diameter, Grade 60 steel (60,000 psi elastic limit) bolts. Rock properties are: E = 4.9
Semi-circular yieldable steel arches with a nominal radius of 2 m are used in main entries to a coal mine developed from outcrop under plateau overburden. Seam depth at a point of interest is 716 m
With reference to Problem 31, an alternative support system in the form of fixed steel sets is considered with entry height 3.6 m. Select a suitable steel rib for this alternative specifying steel
With reference to Problem 4.32, develop an approximately equivalent bolting reinforcement system using one-inch diameter, Grade 60 steel (410 MPa elastic limit) bolts. Rock properties are: E
An arched tunnel is driven in moderately blocky and seamy, wet ground at a depth of 2,830 ft where rock properties are: Co = 14,300 psi, To = 1,430 psi, E = 4.25 (106) psi, G = 1.8 (106) psi, γ =
With reference to Problem 4.34, specify support in the form of rock reinforcement by bolting on a square pattern that has the same support capacity (bolt diameter, spacing, length, steel strength).
With reference to Problem 7, specify support in the form of yieldable steel arches that support the same “rock pressure” (steel area, set spacing, steel strength).
An arched tunnel is driven in moderately blocky and seamy, wet ground at a depth of 863 m where rock properties are, Co = 98.6 MPa, To = 9.86 MPa, E = 29.3GPa, G = 12.4GPa, γ = 24.7kN/m3. The tunnel
With reference to Problem 4.37, specify support in the form of rock reinforcement by bolting on a square pattern that has the same support capacity (bolt diameter, spacing, length, steel strength).
With reference to Problem 37, specify support in the form of yieldable steel arches that support the same “rock pressure” (steel area, set spacing, steel strength).
An arched (semi-circle) rectangular tunnel 28 ft wide and 28 ft high is driven in dry, moderately blocky, and seamy ground.(a) Select a steel rib suitable for these conditions; specify flange width,
An arched (semi-circle) rectangular tunnel 8.5 m wide and 8.5 m high is driven in dry, moderately blocky, and seamy ground.(a) Select a steel rib suitable for these conditions; specify flange width,
Explain the objective of rock mass classification schemes, RMR and Q, why RQD is important to such schemes, what the main components are and what the main differences are. Organize your comparisons
Explain the objective of rock mass classification schemes, RMR and Q, why RQD is important to such schemes, what the main components are and what the main differences are. In a run of 1.5 m of NQ

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