A three-dimensional analysis method for creep rock mass reinforced with prestressed anchor cables

Abstract

The present invention belongs to the field of civil engineering, and specifically relates to a three-dimensional analysis method for creep rock mass reinforced with prestressed anchor cables, comprising the following steps: (1) considering the time-dependent change of the anchoring force of the prestressed anchor cables and the creep effect of the engineering rock mass, abstracting the anchoring project into a three-dimensional mechanical problem, and constructing a mechanical analysis model of a representative unit of the anchored rock mass; (2) deriving an elastic solution for the vertical displacement of any point deep in the rock mass within the load action range; (3) determining the constitutive model of the anchor cable and the anchored rock mass, using an elastic model for the anchor cable and a Burgers model for the rock mass; (4) deriving a viscoelastic solution for the creep deformation of the rock mass and the time-dependent change of the anchoring force of the anchor cable; and (5) selecting mechanical parameters of the anchored rock mass to perform computational analysis on the coupling problem between the creep deformation of the anchored rock mass and the change of the anchoring force of the anchor cable.

Description

Technical Field

[0001] The present invention belongs to the field of civil engineering, and in particular relates to a three-dimensional analysis method for prestressed anchor cable reinforcement of creep rock mass. Background Art

[0002] Anchor support is the primary support method for underground tunnels and coal mine roadways. After underground cavern excavation and support, the stress adjustment and deformation of the rock mass gradually develop and change, exhibiting significant time effects. In recent years, as rock mass engineering projects have gradually expanded deep underground, the rheological properties of the surrounding rock caused by deep high-altitude stresses have become increasingly pronounced. Consequently, failure of support systems and deformation and damage to caverns are common. In-depth research on the long-term deformation behavior and mechanical properties of the surrounding rock under the combined action of anchor cables has important theoretical and practical implications for the design and maintenance of underground projects.

[0003] In previous studies, the analytical method for anchor reinforcement of creep rock mass is still insufficient and there is little relevant data, which urgently needs in-depth research.

[0004] To this end, the present invention provides a three-dimensional analysis method for creep rock mass reinforced with prestressed anchor cables. This method, based on the Boussinesq problem, uses a semi-infinite elastic body model to study the coupling between the change in anchoring force of prestressed anchor cables and rock creep. The method derives an elastic solution for the anchoring force and deformation of the prestressed anchor cables in this coupling model. Furthermore, the viscoelastic solution for the anchoring force and deformation of the prestressed anchor cables in this coupling model, using Laplace and inverse transforms, is derived, considering viscoelastic theory. This method is expected to achieve promising results in the three-dimensional analysis of creep rock mass reinforced with prestressed anchor cables.

[0005] The current research status of related creep characteristics of anchor cable reinforced rock mass in China is as follows:

[0006] 1. "A new method of predicting the prestress variations in anchored cables with excavation unloading destruction" investigates the factors affecting prestress variations in anchor cables in EUD formations and proposes a model for predicting prestress variations in anchor cables and rock mass based on the equal strain assumption. The new model is validated using field data from a real case study, demonstrating its improved predictive capabilities and potential for broader application. (See Engineering Geology, 2018, 241:109-120. Chen G, Chen T, Chen Y, et al.)

[0007] 2. The article "Study on Prediction Models for Initial and Long-term Loss of Anchor Cable Prestress" considers the coupling effect between anchor cable prestress changes and slope creep, establishes two coupling models, and derives the model's constitutive equations and effective prestress change formulas. (See Rock and Soil Mechanics, 2020, 41(05):1663-1669. Xu Yiqing, Deng Shaoyu, Ge Qi.)

[0008] In some research results, the interaction between anchor cables and surrounding rocks was considered, but the research methods were too limited and failed to fully demonstrate the mechanism and law of coupled creep between anchor cables and anchored rock masses. Summary of the Invention

[0009] In order to overcome the deficiencies of the prior art, the present invention provides a three-dimensional analysis method for creep rock mass reinforced with prestressed anchor cables.

[0010] To achieve the above object, the present invention adopts the following technical solutions:

[0011] A three-dimensional analysis method for creep rock mass reinforced with prestressed anchor cables is based on a coupling model of the anchoring force variation of prestressed anchor cables and rock creep. The steps are as follows:

[0012] (1) Considering the time-dependent change of the anchoring force of the prestressed anchor cable and the creep effect of the engineering rock mass, the anchoring project is abstracted into a three-dimensional mechanical problem, and a mechanical analysis model of the representative unit of the anchoring rock mass is constructed;

[0013] (2) Derive the elastic solution for the vertical displacement of any point deep in the rock mass within the load range;

[0014] (3) Determine the constitutive model of the anchor cable and the anchored rock mass. The elastic model is used for the anchor cable and the Burgers model is used for the rock mass.

[0015] (4) Derive the viscoelastic solution of rock mass creep deformation and anchoring force over time;

[0016] (5) Select the mechanical parameters of the anchoring rock mass and perform computational analysis on the coupling problem between the creep deformation of the anchoring rock mass and the change of the anchoring force of the anchor cable.

[0017] Compared with the prior art, the present invention has the following beneficial effects:

[0018] 1. Based on the Boussinesq problem, the present invention selects a semi-infinite elastic body model as the basic model for studying the coupling model of anchor cables and anchored rock mass. Taking into account the viscoelastic theory, it can more accurately analyze the mechanical properties of anchor cable reinforced creep rock mass, and play a certain guiding role in the anchoring of slopes and underground engineering.

[0019] 2. The invention method can be widely used in the study of the mechanical properties of creep rock mass reinforced by anchor cables in the fields of civil engineering, hydropower, mining, energy, etc., and has a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Schematic diagram of the boundary of a semi-infinite elastic body subjected to a normal concentrated force;

[0021] Figure 2 Equivalent schematic elevation drawing of the slope and anchor displacement calculation point positions;

[0022] Figure 3 This is an equivalent schematic cross-sectional diagram of the slope and anchor displacement calculation point positions;

[0023] Figure 4 It is the time history curve of rock deformation when P>F0;

[0024] Figure 5 is the time history curve of anchor cable anchoring force when P>F0;

[0025] Figure 6 is the time history curve of rock mass deformation when P<F0;

[0026] Figure 7 This is the time history curve of anchor cable anchoring force when P<F0. DETAILED DESCRIPTION

[0027] The three-dimensional analysis method of creep rock mass reinforced with prestressed anchor cables is based on the coupling model of the change of anchoring force of prestressed anchor cables and rock creep. The steps are as follows:

[0028] 1. Considering the time-dependent change of the anchoring force of the prestressed anchor cable and the creep effect of the engineering rock mass, the anchoring project is abstracted into a three-dimensional mechanical problem, and a mechanical analysis model of the representative unit of the anchored rock mass is constructed. The specific method is as follows:

[0029] like Figure 1 As shown in the figure, the coupling problem between the change of anchoring force of prestressed anchor cables and rock creep is simplified to the problem of local normal concentrated force on the boundary of a semi-infinite elastic body, which represents the vertical displacement of any point deep in the rock mass, that is:

[0030]

[0031] Where: ω is the vertical displacement of any point deep in the rock mass, m; E r is the elastic modulus of rock, kPa; μ is the Poisson's ratio of rock; z is the vertical depth of the measuring point, m; l is the distance from the concentrated force to the measuring point, m; F is the normal concentrated force acting on the rock mass, kN.

[0032] 2. Derive the elastic solution of the vertical displacement of any point deep in the rock mass within the load range. The specific method is as follows:

[0033] like Figure 2 、 Figure 3As shown, a micro unit is taken within the load range, the distance from the anchor point A is r, and the area of ​​the differential unit is dA = rdrdθ. Then the vertical displacement formula of point B can be obtained by integrating formula (1) within the load range to obtain the vertical displacement of any point deep in the rock mass:

[0034]

[0035] Where: q is the load released by rock mass excavation, kPa; R0 is the radius of the circular range of the load released by rock mass excavation, m; T is the anchoring force of the anchor cable, kN; F=(q-q0)πR0 2 ; dA=rdrdθ.

[0036] The top and tail ends of the anchor cable are marked as points A and B, and the vertical displacement of the two points is:

[0037]

[0038]

[0039] 3. Determine the constitutive model of the anchor cable and the anchored rock mass. The elastic model is used for the anchor cable and the Burgers model is used for the rock mass. The specific method is as follows:

[0040] A one-dimensional elastic body is used for the anchor cable, and a three-dimensional Burgers model is used for the rock mass.

[0041] The form of the elastic model operator function in Laplace space is:

[0042]

[0043] The form of the Burgers model operator function in Laplace space is:

[0044]

[0045] Where: are all operator functions of the viscoelastic model of surrounding rock in Laplace space; G 1r is the elastic shear modulus of the rock mass, MPa; G 2r is the viscoelastic shear modulus of the rock mass, MPa; K is the bulk modulus, MPa; η 1r is the viscosity coefficient in the first creep stage, MPa·h; η 2r is the viscosity coefficient in the second creep stage, MPa·h; s is the independent variable in Laplace space.

[0046] 4. Derive the viscoelastic solution for the creep deformation of rock mass and the time-dependent change of anchoring force of anchor cables. The specific method is as follows:

[0047] When the rock excavation release force P is greater than the initial anchoring force F0 of the anchor cable, that is, P>F0:

[0048]

[0049] The deformation of the anchor cable is equal to the deformation of the rock mass, that is:

[0050]

[0051] The elastic solution of the rock mass deformation Δω and the anchoring force T under the coupled model are sorted out as follows:

[0052]

[0053]

[0054] Where: ΔL is the deformation of the anchor cable, m; Δω is the deformation of the rock mass, m; F0 is the initial prestress of the anchor rod, kN; L is the length of the prestressed anchor cable, m; E b is the elastic modulus of the anchor cable, MPa; A b is the cross-sectional area of ​​the anchor cable, m 2 .

[0055] In three-dimensional space, the relationship between elastic modulus E, Poisson's ratio μ, elastic shear modulus G, and elastic bulk modulus K is:

[0056]

[0057]

[0058] Substituting equations (11) and (12) into equations (9) and (10), we obtain:

[0059]

[0060]

[0061] Where:

[0062] a3=πR0 2 L b1=P b2=(P-F0)πR0 2 L b3=πR0 2 L

[0063] Performing Laplace transform on equation (13) yields:

[0064]

[0065] Substituting equations (5) and (6) into equation (15), we can obtain:

[0066]

[0067] Where:

[0068] c1=3(a1-2a2)Kp 2r 2 +2(2a1-a2)p 2r q 2r

[0069] c2=6(a1-2a2)Kp 1r p 2r +2(2a1-a2)(p 2r q 1r +p 1r q 2r )

[0070] c3=3(a1-2a2)(Kp 1r 2 +2Kp 2r )+2(2a1-a2)(p 1r q 1r +5q 2r )

[0071] c4=6(a1-2a2)Kp 1r +2(2a1-a2)q 1r

[0072] c5=3(a1-2a2)K

[0073] c6=3(a4-2a5)Kp 2r 2 E b +12a3Kp 2r q 2r +2(2a4-a5)p 2r q 2r E b +4a3q 2r 2

[0074] c7=6(a4-2a5)Kp 1r q 2r E b +(12a3K+2(2a4-a5)E b )(p 2r q 1r +p 1r q 2r )+8a3q 1r q 2r

[0075] c8=3(a4-2a5)KE b (p 1r 2 +2p 2r )+(12a3K+2(2a4-a5)E b )(p 1r q 1r +q 2r )+4a3q 1r 2

[0076] c9=6(a4-2a5)Kp 1r E b +12a3Kq 1r +2(2a4-5a5)q 1r E b

[0077] c 10 =3(a4-2a5)KE b

[0078] Where: s1, s2, s3, s4, s5 are the characteristic equations c6s 5 +c7s 4 +c8s 3 +c9s 2 +c 10 s=0; r1, r2, r3, r4, r5 are the unknown coefficients, which is called equation c6s 5 +c7s 4 +c8s 3 +c9s 2 +c 10 The residue of s at s1, s2, s3, s4, and s5 can be calculated as follows:

[0079]

[0080] Through the inverse Laplace transform, we can get:

[0081]

[0082] Where: t is the time of aging change of anchoring force of prestressed anchor cable, d.

[0083] Performing Laplace transform on equation (17) yields:

[0084]

[0085] Substituting equations (5) and (6) into equation (19), we can obtain:

[0086]

[0087] where:

[0088] d1 = b1 d2 = 12b2Kp 2r q 2r + 4b2q 2r 2 d3 = 12b2K(p 1r q 2r + p 2r q 1r ) + 8b2q 1r q 2r

[0089] d4 = 12b2K(q 2r + p 1r q 1r ) + 4b2q 1r 2 d5 = 12b2Kp 1r

[0090] d6 = 3(b4 - 2b5)Kp 2r 2 E b + 12b3Kp 2r q 2r + 2(2b4 - b5)p 2r q 2r E b + 4b3q 2r 2

[0091] d7 = 6(b4 - 2b5)Kp 1r q 2r E b +(12b3K + 2(2b4 - b5)E b )(p 2r q 1r + p 1r q 2r ) + 8b3q 1r q 2r

[0092] d8 = 3(b4 - 2b5)KE b (p 1r 2 + 2p 2r )+(12b3K + 2(2b4 - b5)E b )(p 1r q 1r + q 2r ) + 4b3q 1r 2 ]>

[0093] d9 = 6(b4 - 2b5)Kp1r E b +12b3Kq 1r +2(2b4-b5)q 1r E b d 10 =3(b4-2b5)KE b

[0094] in:

[0095]

[0096] Through the inverse Laplace transform, we can get:

[0097]

[0098] When the rock excavation release force P is less than the initial anchoring force F0 of the anchor cable, that is, P<F0:

[0099]

[0100] The elastic solution of the rock mass deformation Δω and the anchoring force T under the coupled model are sorted out as follows:

[0101]

[0102]

[0103] Substituting equations (11) and (12) into equations (24) and (25), we obtain:

[0104]

[0105]

[0106] Where: a 33 =πR0 2 L b 22 =(F0-P)πR0 2 L b 33 =πR0 2 L

[0107] Performing Laplace transform on equation (26) yields:

[0108]

[0109] Substituting equations (5) and (6) into equation (28), we can obtain:

[0110]

[0111] In the formula:

[0112] c 11 = 3(a 11 - 2a 22 )Kp 2r 2 + 2(2a 11 - a 22 )p 2r q 2r

[0113] c 22 = 6(a 11 - 2a 22 )Kp 1r p 2r + 2(2a 11 - a 22 )(p 2r q 1r + p 1r q 2r )

[0114] c 33 = 3(a 11 - 2a 22 )(Kp 1r 2 + 2Kp 2r + 2(2a 11 - a 22 )(p 1r q 1r + 5q 2r )

[0115] c 44 = 6(a 11 - 2a 22 )Kp 1r + 2(2a 11 - a 22 )q 1r

[0116] c 55 = 3(a 11 - 2a 22 )K

[0117] c 66 = 3(a 44 - 2a 55 )Kp 2r 2 E b + 12a 33 Kp 2r q 2r + 2(2a 44 - a 55 )p 2r q2r E b +4a 33 q 2r 2

[0118] c 77 =6(a 44 -2a 55 )Kp 1r q 2r E b +(12a 33 K+2(2a 44 -a 55 )E b )(p 2r q 1r +p 1r q 2r )+8a 33 q 1r q 2r

[0119] c 88 =3(a 44 -2a 55 )KE b (p 1r 2 +2p 2r )+(12a 33 K+2(2a 44 -a 55 )E b )(p 1r q 1r +q 2r )+4a 33 q 1r 2

[0120] c 99 =6(a 44 -2a 55 )Kp 1r E b +12a 33 Kq 1r +2(2a 44 -5a 55 )q 1r E b

[0121] c 1010 =3(a 44 -2a 55 )KE b

[0122] in: s i is the characteristic equation c66 s 5 +c 77 s 4 +c 88 s 3 +c 99 s 2 +c 1010 The root of s=0.

[0123] Through the inverse Laplace transform, we can get:

[0124]

[0125] Performing Laplace transform on equation (27) yields:

[0126]

[0127] Substituting equations (5) and (6) into equation (31), we can obtain:

[0128]

[0129] Where:

[0130] d 11 =b 11 d 22 =12b 22 Kp 2r q 2r +4b 22 q 2r 2 d 33 =12b 22 K(p 1r q 2r +p 2r q 1r )+8b 22 q 1r q 2r

[0131] d 44 =12b 22 K(q 2r +p 1r q 1r )+4b 22 q 1r 2 d 55 =12b 22 Kp 1r

[0132] d 66 =3(b 44 -2b 55 )Kp 2r 2 Eb +12b 33 Kp 2r q 2r +2(2b 44 -b 55 )p 2r q 2r E b +4b 33 q 2r 2

[0133] d 77 =6(b 44 -2b 55 )Kp 1r q 2r E b +(12b 33 K+2(2b 44 -b 55 )E b )(p 2r q 1r +p 1r q 2r )+8b 33 q 1r q 2r

[0134] d 88 =3(b 44 -2b 55 )KE b (p 1r 2 +2p 2r )+(12b 33 K+2(2b 44 -b 55 )E b )(p 1r q 1r +q 2r )+4b 33 q 1r 2

[0135] d 99 =6(b 44 -2b 55 )Kp 1r E b +12b 33 Kq 1r +2(2b 44 -b 55 )q 1r E b d 1010 =3(b 44 -2b 55)KE b

[0136] in:

[0137] Through the inverse Laplace transform, we can get:

[0138]

[0139] 5. Select the mechanical parameters of the anchored rock mass to perform calculation and analysis on the coupling problem between the creep deformation of the anchored rock mass and the change of the anchoring force of the anchor cable. The specific method is as follows:

[0140] An analysis is conducted on typical anchored rock projects to determine relevant parameters, such as initial anchoring force and rock excavation release force. The deformation of the anchored rock and anchor cables is calculated and analyzed using the established prestressed anchor force change and rock creep coupling model, and the deformation curves of the anchored rock and anchor cables are drawn.

[0141] For example, for the analysis of a typical anchoring rock mass project, the parameter values ​​are shown in Table 1.

[0142] Table 1 Parameter values

[0143]

[0144]

[0145] When the calculated rock mass excavation release force is greater than the initial anchoring force of the anchor cable, the time history curve of the anchor cable deformation is as follows: Figure 4 As shown in the figure, the time history curve of anchor cable anchoring force is as follows: Figure 5 shown.

[0146] When the calculated rock mass excavation release force is less than the initial anchoring force of the anchor cable, the time history curve of the anchor cable deformation is as follows: Figure 6 As shown in the figure, the time history curve of anchor cable anchoring force is as follows: Figure 7 shown.

Claims

1. A three-dimensional analysis method for creep rock mass reinforced with prestressed anchor cables, characterized in that: Here are the steps: (1) Considering the time-dependent change of the anchoring force of the prestressed anchor cable and the creep effect of the engineering rock mass, the anchoring project is abstracted into a three-dimensional mechanical problem, and a mechanical analysis model of the representative unit of the anchoring rock mass is constructed; (2) Derive the elastic solution for the vertical displacement of any point deep in the rock mass within the load range; (3) Determine the constitutive model of the anchor cable and the anchored rock mass. The elastic model is used for the anchor cable and the Burgers model is used for the rock mass. (4) Derive the viscoelastic solution of rock mass creep deformation and anchoring force over time; (5) Select the mechanical parameters of the anchored rock mass and perform computational analysis on the coupling problem between the creep deformation of the anchored rock mass and the change of the anchoring force of the anchor cable; The coupling problem between the change of anchoring force of prestressed anchor cables and rock creep is simplified to the problem of local normal concentrated force on the boundary of a semi-infinite elastic body, which is expressed as the vertical displacement of any point deep in the rock mass, namely: Where: ω is the vertical displacement of any point deep in the rock mass, m; E r is the elastic modulus of rock, kPa; μ is the Poisson's ratio of rock; z is the vertical depth of the measuring point, m; l is the distance from the concentrated force to the measuring point, m; F is the normal concentrated force acting on the rock mass, kN.

2. The three-dimensional analysis method for creep rock mass reinforced with prestressed anchor cables according to claim 1, characterized in that: The elastic solution of the vertical displacement of any point deep in the rock mass within the load range is derived as follows: take a micro unit within the load range, the distance from the anchor point A on the rock mass surface is r, and the area of ​​the differential unit is dA = rdrdθ. Then, the vertical displacement formula of point B inside the rock mass can be integrated within the load range to obtain the vertical displacement of any point deep in the rock mass: Where: ω is the vertical displacement of any point deep in the rock mass, m; E r is the elastic modulus of rock, kPa; μ is the Poisson's ratio of rock; z is the vertical depth of the measuring point, m; is the distance from the concentrated force to the measuring point, m; F=(q-q0)πR0 2 , is the normal concentrated force on the rock mass, kN; q is the load released by rock mass excavation, kPa; R0 is the radius of the circular range of the load released by rock mass excavation, m; T is the anchoring force of the anchor cable, kN; is the equivalent load strength of the anchoring force of the anchor cable within the circular range, kPa.

3. The three-dimensional analysis method for creep rock mass reinforced with prestressed anchor cables according to claim 1, characterized in that: Determine the constitutive model of the anchor cable and the anchored rock mass. The elastic model is used for the anchor cable and the Burgers model is used for the rock mass. The specific method is as follows: For the anchor cable, a one-dimensional elastic body is used, and for the rock mass, a three-dimensional Burgers model is used; The form of the elastic model operator function in Laplace space is: in, is the operator function of the anchor cable elastic model in Laplace space; E b is the elastic modulus of the anchor cable, MPa; the operator function of the Burgers model in Laplace space is: Where: are all operator functions of the viscoelastic model of surrounding rock in Laplace space; G 1r is the elastic shear modulus of the rock mass, MPa; G 2r is the viscoelastic shear modulus of the rock mass, MPa; K is the bulk modulus, MPa; η 1r is the viscosity coefficient in the first creep stage, MPa·h; η 2r is the viscosity coefficient in the second creep stage, MPa·h; s is the independent variable in Laplace space; q 1r =η 2r , 4. The three-dimensional analysis method for creep rock mass reinforced with prestressed anchor cables according to claim 3, characterized in that: The viscoelastic solution for the creep deformation of rock mass and the time-dependent change of anchor force is derived as follows: (1) When the rock excavation release force P is greater than the initial anchoring force F0 of the anchor cable, that is, P>F0 Where, F is the normal concentrated force on the rock mass, kN; q is the load released by rock excavation, kPa; R0 is the radius of the circular range of the load released by rock excavation, m; E is the equivalent load strength of the anchor force within the circular range, kPa; b is the elastic model of the anchor cable, MPa; A b is the cross-sectional area of ​​the anchor cable, m 2 The deformation of the anchor cable is equal to the deformation of the rock mass, that is: Where: ΔL is the deformation of the anchor cable length, m; L is the length of the prestressed anchor cable, m; Δω is the rock mass deformation, m; the elastic solution of the rock mass deformation Δω and the anchoring force T under the coupling model is: Where: F0 is the initial anchoring force of the anchor cable, kN; E r is the elastic modulus of the rock mass, MPa; Performing a three-dimensional Laplace transform yields: Where: is the form of rock mass deformation in Laplace space; is the operator function of Laplace space; s is the independent variable of Laplace space; a3=πR0 2 L, is the form of the anchoring force of the anchor cable in Laplace space; b1=P, b2=(P-F0)πR0 2 L, b3=πR0 2 L, Through sorting, we can get: Where: <h2 style=";text-align:left;direction:ltr">c1 = 3(a1 - 2a2)Kp<h2 style=";text-align:left;direction:ltr"> 2r <h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +2(2a1-a2)p<h2 style=";text-align:left;direction:ltr"> 2r <h2 style=";text-align:left;direction:ltr"> q<h2 style=";text-align:left;direction:ltr"> 2r <h2 style=";text-align:left;direction:ltr"> , c2=6(a1-2a2)Kp 1r p 2r +2(2a1-a2)(p 2r q 1r +p 1r q 2r ), <h2 style=";text-align:left;direction:ltr">c3 = 3(a1 - 2a2)(Kp)<h2 style=";text-align:left;direction:ltr"> 1r <h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +2Kp<h2 style=";text-align:left;direction:ltr"> 2r <h2 style=";text-align:left;direction:ltr"> )+2(2a1-a2)(p<h2 style=";text-align:left;direction:ltr"> 1r <h2 style=";text-align:left;direction:ltr"> q<h2 style=";text-align:left;direction:ltr"> 1r <h2 style=";text-align:left;direction:ltr"> +5q<h2 style=";text-align:left;direction:ltr"> 2r <h2 style=";text-align:left;direction:ltr"> ), <h2 style=";text-align:left;direction:ltr">c4 = 6(a1 - 2a2)Kp<h2 style=";text-align:left;direction:ltr"> 1r <h2 style=";text-align:left;direction:ltr"> +2(2a1-a2)q<h2 style=";text-align:left;direction:ltr"> 1r <h2 style=";text-align:left;direction:ltr"> , c5=3(a1-2a2)K, c6=3(a4-2a5)Kp 2r 2 E b +12a3Kp 2r q 2r +2(2a4-a5)p 2r q 2r E b +4a3q 2r 2 , c7⼝6(a4-2a5)Kp 1r q 2r E b +(12a3K+2(2a4-a5)E b )(p 2r q 1r +p 1r q 2r )+8a3q 1r q 2r , <h2 style=";text-align:left;direction:ltr">c8 = 3(a4 - 2a5)KE<h2 style=";text-align:left;direction:ltr"> b <h2 style=";text-align:left;direction:ltr"> (p<h2 style=";text-align:left;direction:ltr"> 1r <h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +2p<h2 style=";text-align:left;direction:ltr"> 2r <h2 style=";text-align:left;direction:ltr"> )+(12a3K+2(2a4-a5)E<h2 style=";text-align:left;direction:ltr"> b <h2 style=";text-align:left;direction:ltr"> )(p<h2 style=";text-align:left;direction:ltr"> 1r <h2 style=";text-align:left;direction:ltr"> q<h2 style=";text-align:left;direction:ltr"> 1r <h2 style=";text-align:left;direction:ltr"> +q<h2 style=";text-align:left;direction:ltr"> 2r <h2 style=";text-align:left;direction:ltr"> )+4a3q<h2 style=";text-align:left;direction:ltr"> 1r <h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> , c9=6(a4-2a5)Kp 1r E b +12a3Kq 1r +2(2a4-5a5)q 1r E b , c 10 =3(a4-2a5)KE b ; d1=b1,d2=12b2Kp 2r q 2r +4b2q 2r 2 ,d3=12b2K(p 1r q 2r +p 2r q 1r )+8b2q 1r q 2r , d4=12b2K(q 2r +p 1r q 1r )+4b2q 1r 2 ,d5=12b2Kp 1r , d6=3(b4-2b5)Kp 2r 2 E b +12b3Kp 2r q 2r +2(2b4-b5)p 2r q 2r E b +4b3q 2r 2 , d7=6(b4-2b5)Kp 1r q 2r E b +(12b3K+2(2b4-b5)E b )(p 2r q 1r +p 1r q 2r )+8b3q 1r q 2r , d8=3(b4-2b5)KE b (p 1r 2 +2p 2r )+(12b3K+2(2b4-b5)E b )(p 1r q 1r +q 2r )+4b3q 1r 2 , d9=6(b4-2b5)Kp 1r E b +12b3Kq 1r +2(2b4-b5)q 1r E b ,d 10 =3(b4-2b5)KE b ; Where: K is the bulk modulus, MPa; q 1r =η 2r , G 1r is the elastic shear modulus of the rock mass, MPa; G 2r is the viscoelastic shear modulus of the rock mass, MPa; η 1r is the viscosity coefficient in the first creep stage, MPa·h; η 2r is the viscosity coefficient of the second creep stage, MPa·h; s ωi , s Ti is the characteristic equation c6s 5 +c7s 4 +c8s 3 +c9s 2 +c 10 s=0 and d6s 4 +d7s 3 +d8s 2 +d9s+d 10 = the root of 0; r ωi , r Ti is the unknown coefficient, called equation c6s 5 +c7s 4 +c8s 3 +c9s 2 +c 10 s=0 and d6s 4 +d7s 3 +d8s 2 +d9s+d 10 =0 in s ωi , s Ti The residue at can be calculated as follows: Through the inverse Laplace transform, we can get: Where: t is the time of the change of anchoring force of prestressed anchor cable, d; (2) When the rock excavation release force P is less than the initial anchoring force F0 of the anchor cable, that is, P<F0: The deformation of the anchor cable is equal to the deformation of the rock mass, that is: The elastic solution of rock mass deformation Δω and anchor force T under the coupling model is: Performing a three-dimensional Laplace transform yields: Where: a 33 =πR0 2 L, b 11 =P,b 22 =(F0-P)πR0 2 L, b 33 =πR0 2 L, Through sorting, we can get: Where: c 11 =3(a 11 -2a 22 )Kp 2r 2 +2(2a 11 -a 22 )p 2r q 2r , c 22 =6(a 11 -2a 22 )Kp 1r p 2r +2(2a 11 -a 22 )(p 2r q 1r +p 1r q 2r ), <h2 style=";text-align:left;direction:ltr">c<h2 style=";text-align:left;direction:ltr"> 33 <h2 style=";text-align:left;direction:ltr"> =3(a<h2 style=";text-align:left;direction:ltr"> 11 <h2 style=";text-align:left;direction:ltr"> -2a<h2 style=";text-align:left;direction:ltr"> 22 <h2 style=";text-align:left;direction:ltr"> (Kp)<h2 style=";text-align:left;direction:ltr"> 1r <h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +2Kp<h2 style=";text-align:left;direction:ltr"> 2r <h2 style=";text-align:left;direction:ltr"> )+2(2a<h2 style=";text-align:left;direction:ltr"> 11 <h2 style=";text-align:left;direction:ltr"> -a<h2 style=";text-align:left;direction:ltr"> 22 <h2 style=";text-align:left;direction:ltr"> )(p<h2 style=";text-align:left;direction:ltr"> 1r <h2 style=";text-align:left;direction:ltr"> q<h2 style=";text-align:left;direction:ltr"> 1r <h2 style=";text-align:left;direction:ltr"> +5q<h2 style=";text-align:left;direction:ltr"> 2r <h2 style=";text-align:left;direction:ltr"> ), c 44 =6(a 11 -2a 22 )Kp 1r +2(2a 11 -a 22 )q 1r , c 55 =3(a 11 -2a 22 )K, c 66 =3(a 44 -2a 55 )Kp 2r 2 E b +12a 33 Kp 2r q 2r +2(2a 44 -a 55 )p 2r q 2r E b +4a 33 q 2r 2 , c 77 =6(a 44 -2a 55 )Kp 1r q 2r E b +(12a 33 K+2(2a 44 -a 55 )E b )(p 2r q 1r +p 1r q 2r )+8a 33 q 1r q 2r , c 88 =3(a 44 -2a 55 )KE b (p 1r 2 +2p 2r )+(12a 33 K+2(2a 44 -a 55 )E b )(p 1r q 1r +q 2r )+4a 33 q 1r 2 ,c 99 =6(a 44 -2a 55 )Kp 1r E b +12a 33 Kq 1r +2(2a 44 -5a 55 )q 1r E b , c 1010 =3(a 44 -2a 55 ) b ; d 11 =b 11 ,d 22 =12b 22 Kp 2r q 2r +4b 22 q 2r 2 ,d 33 =12b 22 K(p 1r q 2r +p 2r q 1r )+8b 22 q 1r q 2r , d 44 =12b 22 K(q 2r +p 1r q 1r )+4b 22 q 1r 2 ,d 55 =12b 22 Kp 1r , d 66 =3(b 44 -2b 55 )Kp 2r 2 E b +12b 33 Kp 2r q 2r +2(2b 44 -b 55 )p 2r q 2r E b +4b 33 q 2r 2 , d 77 =6(b 44 -2b 55 )Kp 1r q 2r E b +(12b 33 K+2(2b 44 -b 55 )E b )(p 2r q 1r +p 1r q 2r )+8b 33 q 1r q 2r , d 88 =3(b 44 -2b 55 )KE b (p 1r 2 +2p 2r )+(12b 33 K+2(2b 44 -b 55 )E b )(p 1r q 1r +q 2r )+4b 33 q 1r 2 , d 99 =6(b 44 -2b 55 )Kp 1r E b +12b 33 Kq 1r +2(2b 44 -b 55 )q 1r E b , d 1010 =3(b 44 -2b 55 )KE b ;Where: K is the bulk modulus, MPa; q 1r =η 2r , G 1r is the elastic shear modulus of the rock mass, MPa; G 2r is the viscoelastic shear modulus of the rock mass, MPa; η 1r is the viscosity coefficient in the first creep stage, MPa·h; η 2r is the viscosity coefficient of the second creep stage, MPa·h; s ωii , s Tii is the characteristic equation c 66 s 5 +c 77 s 4 +c 88 s 3 +c 99 s 2 +c 1010 s = 0 and d 66 s 4 +d 77 s 3 +d 88 s 2 +d 99 s+d 1010 = the root of 0; r ωii , r Tii is the unknown coefficient, called equation c 66 s 5 +c 77 s 4 +c 88 s 3 +c 99 s 2 +c 1010 s = 0 and d 66 s 4 +d 77 s 3 +d 88 s 2 +d 99 s+d 1010 =0 in s ωii , s Tii The residue at can be calculated as follows: Through the inverse Laplace transform, we can get:

5. The three-dimensional analysis method for creep rock mass reinforced with prestressed anchor cables according to claim 1, characterized in that: The mechanical parameters of the anchored rock mass are selected to perform calculation and analysis on the coupling problem between the creep deformation of the anchored rock mass and the change of the anchoring force of the anchor cable. The specific method is as follows: An analysis is conducted on typical anchored rock projects to determine the parameters of initial anchoring force and rock excavation release force. The deformation of the anchored rock and anchor cables is calculated and analyzed using the established prestressed anchor force change and rock creep coupling model, and the deformation curves of the anchored rock and anchor cables are drawn.

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