Long-term stability analysis method and its model for slope reinforced by prestressed anchor cable frame

Abstract

The application discloses a long-term stability analysis method of a prestressed anchor cable frame beam reinforced slope, which comprises the following steps: establishing a coupling analysis model; according to the deformation basic mechanism and characteristics of an anchoring system composed of an anchor cable body-frame beam-free section sliding body-anchoring section sliding bed of the prestressed anchor cable frame beam reinforced slope, the interaction relationship between the anchor cable body, the anchoring section sliding bed, the corresponding sliding body of the free section and the slope surface concrete frame beam is considered to establish the coupling analysis model, the coupling analysis model comprises a first part for describing the slope surface concrete frame beam, a second part for describing the sliding body of the anchor cable free section, a third part for describing the anchor cable body and a fourth part for describing the corresponding sliding bed of the anchor cable anchoring section; an anchor cable tension relaxation equation is established; and the influence of the anchor cable tension relaxation on the slope stability is analyzed. The application discloses a prestressed anchor cable tension loss aging analysis model for the above method. The application can solve the technical problem that it is difficult to reasonably determine the anchor cable tension relaxation effect of the prestressed anchor cable frame beam reinforced slope and the influence of the anchor cable tension relaxation effect on the slope stability in the prior art.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, and in particular to a method and model for analyzing the long-term stability of slopes reinforced by prestressed anchor cable frame beams. Background Technology

[0002] In the process of reinforcing slopes, the concrete frame beam-prestressed anchor cable system is affected by the material properties of the anchor cables, the construction quality, and the characteristics of the slope's soil and rock mass. This leads to a tension relaxation effect in the anchor cables, causing a cumulative reduction or loss of tension over time. The degree of tension loss directly determines the reinforcement effect and the safety of the project. Therefore, studying the interaction mechanism between the anchor cables and the soil and rock mass, the variation law of the anchoring force, and the calculation of the loss value is of great significance.

[0003] While most existing studies can reflect the characteristics of anchor cable tension gradually decreasing and then stabilizing over time to some extent, and there are some calculation models for anchor cable tension relaxation, there is no theoretical analysis model in the current technology that integrates the four elements of the slope frame beam, sliding body, sliding bed, and anchor cable for slope reinforcement by prestressed anchor cable frame beams. Therefore, it is impossible to determine the anchor cable tension relaxation effect of slope reinforcement by prestressed anchor cable frame beams and its impact on slope stability. Summary of the Invention

[0004] The main objective of this invention is to provide a long-term stability analysis method for slopes reinforced by prestressed anchor cable frame beams, in order to solve the technical problem in the prior art that it is difficult to reasonably determine the anchor cable tension relaxation effect and its impact on slope stability in slopes reinforced by prestressed anchor cable frame beams.

[0005] Therefore, in order to reflect the role of the slope frame beam in the creep coupling model, that is, to consider the interaction between the free section and anchored section of the anchor cable and the soil and rock mass, as well as the interaction between the slope frame beams, and to fully reflect the characteristics of the slope anchoring system composed of "anchor cable body - frame beam - free section sliding body - anchored section sliding bed", a coupled calculation model of anchor cable tension relaxation of the prestressed anchor cable frame beam for the reinforced slope is established, so as to provide a theoretical basis and calculation method for the long-term stability analysis of the slope reinforced by the prestressed anchor cable frame beam.

[0006] To achieve the above-mentioned objectives, this invention provides a method for analyzing the long-term stability of slopes reinforced by prestressed anchor cable frame beams:

[0007] This invention provides a method for long-term stability analysis of slopes reinforced by prestressed anchor cable frame beams, comprising the following steps:

[0008] Step 1: Establish a coupling analysis model. Based on the basic deformation mechanism and characteristics of the anchoring system consisting of "anchor body - frame beam - free section sliding body - anchoring section sliding bed" in the prestressed anchor cable frame beam reinforced slope, a coupling analysis model is established considering the interaction between the anchor cable, the corresponding sliding bed of the anchor cable fixed section, the corresponding sliding body of the anchor cable free section, and the corresponding frame beam of the slope. The coupling analysis model includes a first part for describing the concrete frame beam of the slope, a second part for describing the sliding body of the anchor cable free section, a third part for describing the anchor cable body, and a fourth part for describing the corresponding sliding bed of the anchor cable anchoring section.

[0009] Step 2: Establish the anchor cable tension relaxation equation. Without considering the influence of external factors such as rainfall and earthquakes on anchor cable deformation, establish a mechanical relationship equation between the anchor cable tension and the total tensile strain of the model to determine the relaxation variation law of the anchor cable tension over time.

[0010] Step 3: Analyze the impact of anchor cable tension relaxation on slope stability. Based on the proposed time-dependent analysis model of prestressed anchor cable tension loss, the calculation expression for anchor cable tension relaxation can be obtained. Then, based on the transfer coefficient method, the anchor cable tension can be introduced into the corresponding slope stability analysis, thereby analyzing and evaluating the time-dependent stability of the anchored slope.

[0011] The purpose of this invention is to establish an analytical method for the impact of anchor cable tension relaxation effect on slope stability in slopes reinforced with prestressed anchor cable frame beams. The main content is based on the fundamental deformation mechanism and characteristics of the anchoring system of a prestressed anchor cable frame beam reinforced slope, consisting of "anchor cable body - frame beam - free section sliding body - anchored section sliding bed". Considering the interaction relationships between the anchor cable, sliding body, sliding bed, and frame beam, a long-term stability analysis method for slopes reinforced with prestressed anchor cable frame beams is proposed. This invention establishes a coupled calculation model for slope anchor cable tension relaxation, based on the interaction between the free and anchored sections of the anchor cable and the soil, as well as the interaction relationship between the frame beam and the anchor cable. The calculation results of the proposed coupled model are compared with experimental measured data and the calculation results of existing models, demonstrating that the theoretical calculation results of this invention have high accuracy and can effectively predict anchor cable anchorage force loss, conforming to actual conditions and verifying the applicability of the theoretical calculation model of this invention. The long-term stability analysis method for slope reinforcement using prestressed anchor cable frame beams of the present invention can provide effective theoretical analysis guidance and engineering design methods for slope reinforcement using prestressed anchor cable frame beams.

[0012] Furthermore, in step one, the first part is the Hooke(H) body, the second part is the generalized Kelvin body (KH body), the third part is the Hooke(H) body with different parameters, and the fourth part is the generalized Kelvin body (KH body) with different parameters.

[0013] Furthermore, in step one, the H-body describing the slope frame beam, the KH-body describing the free section sliding body, the H-body describing the anchor cable body, and the KH-body describing the anchoring section sliding bed are connected in series.

[0014] Furthermore, in step two, according to the coupled mechanics analysis model, we can obtain:

[0015]

[0016] In the formula, P is the anchor cable tension; ε is the tensile strain; E a1 E a2 The elastic modulus E of the H-body, which simulates the properties of frame beams and anchor cables; k1 E h1 η1 and η2 are the hysteretic elastic modulus, instantaneous elastic modulus, and viscosity coefficient of the KH body simulating the rheological properties of the sliding body, respectively; E k2 E h2 η1 and η2 represent the hysteretic elastic modulus, instantaneous elastic modulus, and viscosity coefficient, respectively, of the simulated rheological properties of the slide bed in the anchorage section; A a1 Let A be the equivalent cross-sectional area of ​​a single-hole anchored cable frame beam. a1 =A s ·d / a, where A s d is the actual cross-sectional area of ​​the frame beam, d is the anchor hole spacing, and a is the cross-sectional width of the frame beam; A a2 A is the cross-sectional area of ​​a single-hole anchor cable; r1 The effective range of a single-hole anchor cable-frame beam on the soil and rock mass can be considered as the range of the "center-to-center" spacing between adjacent anchor cables; A r2 Let be the area of ​​the effective influence range of a single anchor cable on the slide bed. This influence range can be considered a circular region, and the diameter of this circular region can be taken as the center-to-center distance between the anchor holes; D is the calculation symbol, denoted as .

[0017] For relaxation problems, ε = constant (i.e., Dε = 0), therefore, multiplying both sides of the above equation by A a1 A a2 A r1 A r2 E a1 E a2 E h1 E h2 E k1 E k2 After finding a common denominator, the result can be simplified to:

[0018] k1P″+k2P′+k3P=k4ε (2)

[0019] In the formula, k1, k2, k3, and k4 are constant coefficients, respectively:

[0020]

[0021]

[0022]

[0023] k4=A a1 A a2 A r1 A r2 E a1 E a2 E h1 E h2 E k1 E k2 (2d)

[0024] Solving the differential equation shown in equation (2), we can obtain

[0025]

[0026] In the formula, t represents time; n1 and n2 are the equations k1r 2 The two real roots of +k2r+k3=0; b1, b2 and b3 are integration constants, where b1=k4 / k3;

[0027] Given the initial condition P(0) = P0, equation (3) can be solved to obtain

[0028]

[0029] In the formula, C is an arbitrary constant that can be obtained based on the known conditions in a specific example; ε can be determined based on the initial tension of the anchor cable, i.e.

[0030]

[0031] Furthermore, the step of determining the constant C in equation (4) in step two is as follows: by substituting the values ​​of t at different times after the anchor cable tensioning and locking... m The monitored anchor cable tension P m Where m is the number of monitoring times taken for calculation; thus, m C values ​​are obtained, and the calculated anchor cable tension curves at different C values ​​are compared with the measured curves. The C value that makes the correlation coefficient between the two the highest is the constant value to be obtained.

[0032] Furthermore, in step two, in order to improve the calculation accuracy, the value of m can be appropriately increased, that is, the number of typical observation times in the initial stage (a period of time after the anchor cable is tensioned and locked), with the correlation coefficient between the measured value curve of the anchor cable tension and the theoretical calculated value curve in the initial stage reaching a sufficiently large value as the control requirement.

[0033] Furthermore, step three specifically involves applying the time-dependent anchor cable tension P determined by equation (4) using the transfer coefficient method.i In the stability analysis of anchored slopes, the stability coefficient F of the anchored slope is solved. s The time-dependent stability of the slope is analyzed and evaluated. The calculation expression is as follows:

[0034] E i =W i sinα i -W i cosα i tanφ i / F s -c i l i / F s -P i [cos(α i +δ i )+sin(α i +δ i )tanφ i / F s ]+ψ i ′E i-1 (6)

[0035] In the formula, α i δ i W i l i c i φ i These are the sliding surface inclination angle, anchor cable inclination angle, gravity, sliding surface length, sliding surface cohesion, and internal friction angle of the i-th sliding block, respectively; P i Let ψ' be the time-dependent anchor cable tension corresponding to the i-th sliding block. i The transfer coefficient is calculated as follows:

[0036] ψ i ′=cos(α i-1 -α i )-sin(α i-1 -α i )tanφ i / F s (7)

[0037] Based on the remaining thrust E of the last segment at the leading edge of the slope. n =0, from equation (6), the recursive method can be used to calculate and determine the time (corresponding to different anchor cable tensions P) at different times. i The stability coefficient of the anchored slope.

[0038] This invention also provides a time-dependent analysis model for the tensile stress loss of prestressed anchor cables. Based on the basic deformation mechanism and characteristics of the anchoring system consisting of "anchor cable body - frame beam - free section sliding body - anchoring section sliding bed" in the prestressed anchor cable frame beam reinforced slope, a coupled analysis model is established considering the interaction between the anchor cable, the corresponding sliding bed of the anchor cable fixed section, the corresponding sliding body of the anchor cable free section, and the corresponding frame beam of the slope. The coupled analysis model includes a first part for describing the concrete frame beam of the slope, a second part for describing the sliding body of the anchor cable free section, a third part for describing the anchor cable, and a fourth part for describing the corresponding sliding bed of the anchor cable anchoring section.

[0039] Furthermore, the first part is the Hooke(H) body, the second part is the generalized Kelvin body (KH body), the third part is the Hooke(H) body with different parameters, and the fourth part is the generalized Kelvin body (KH body) with different parameters.

[0040] Furthermore, the H-body describing the slope frame beam, the KH-body describing the free section sliding body, the H-body describing the anchor cable, and the KH-body describing the anchoring section sliding bed are connected in series.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0042] The purpose of this invention is to determine the anchor cable tension relaxation effect of prestressed anchor cable frame beam reinforced slopes and its impact on slope stability. The innovative approach is based on the fundamental deformation mechanism and characteristics of the anchoring system of prestressed anchor cable frame beam reinforced slopes, consisting of "anchor cable body - frame beam - free section sliding body - anchored section sliding bed." Considering the interaction relationships between the anchor cable, sliding body, sliding bed, and slope frame beam, a long-term stability analysis method for prestressed anchor cable frame beam reinforced slopes is proposed. This invention establishes a coupled calculation model for anchor cable tension relaxation of slopes, based on the interaction between the free and anchored sections of the anchor cable and the soil, as well as the interaction relationship between the frame beam and the anchor cable. This model, with four elements connected in series, yields the anchor cable tension decay function over time, which is then used for long-term stability analysis of anchored slopes. Comparison of the calculation results of the proposed series model with experimental data and existing models demonstrates that the theoretical calculation results of this invention have high accuracy, can effectively predict anchor cable anchorage force loss, conform to actual conditions, and verify the applicability of the theoretical calculation model of this invention. The four-in-one serial creep coupling model of anchor cable, sliding body, sliding bed and slope frame beam established in this invention, along with the calculation method for determining the relaxation of anchor cable tension, can analyze the long-term stability of anchored slopes. It can effectively prevent the instability and failure of prestressed anchor cable frame beam reinforced slopes over time by analyzing and predicting the long-term stability of the slopes. It has important theoretical and practical significance.

[0043] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached image description:

[0044] Figure 1 This is a schematic diagram of the overall stress analysis of the anchor cable in the prestressed anchor cable frame beam for slope reinforcement in this invention (taking a single-hole anchor cable as an example).

[0045] Figure 2 This is a schematic diagram of the anchor cable tension relaxation analysis model for slope reinforcement using a prestressed anchor cable frame beam in this invention.

[0046] Figure 3 This is a schematic diagram of the slope reinforcement using a prestressed anchor cable frame beam in Embodiment 1 of the present invention.

[0047] Figure 4 This is the relaxation curve of the anchor cable tension over time calculated in Embodiment 1 of the present invention.

[0048] Figure 5 This is the curve showing the change of slope stability coefficient over time in Embodiment 1 of the present invention.

[0049] Figure 6 This is a schematic diagram of the slope reinforcement using a prestressed anchor cable frame beam in Embodiment 2 of the present invention.

[0050] Figure 7 This is the relaxation curve of the anchor cable tension over time calculated in Embodiment 2 of the present invention.

[0051] Figure 8 This is the curve showing the change of slope stability coefficient over time in Embodiment 2 of the present invention.

[0052] The markings in the diagram are: Ⅰ-anchor cable, Ⅱ-frame beam, Ⅲ-free section of anchor cable, Ⅳ-anchor cable anchorage section, Ⅴ-slide bed, Ⅵ-slide body, and 1 to 7 are sliders. Detailed Implementation

[0053] The present invention will now be clearly and completely described in conjunction with the accompanying drawings. Those skilled in the art will be able to implement the present invention based on these descriptions. Before describing the present invention in conjunction with the accompanying drawings, it should be particularly noted that:

[0054] The technical solutions and features provided in the various parts of this invention, including the following description, can be combined with each other without conflict.

[0055] Furthermore, the embodiments of the present invention described below are generally only some, not all, of the embodiments of the present invention. Therefore, all other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0056] This invention provides a method for long-term stability analysis of slopes reinforced by prestressed anchor cable frame beams, comprising the following steps:

[0057] Step 1: Establish a coupling analysis model. Based on the basic deformation mechanism and characteristics of the anchoring system consisting of "anchor body - frame beam - free section sliding body - anchoring section sliding bed" in the prestressed anchor cable frame beam reinforced slope, a coupling analysis model is established considering the interaction between the anchor cable, the corresponding sliding bed of the anchor cable fixed section, the corresponding sliding body of the anchor cable free section, and the corresponding frame beam of the slope. The coupling analysis model includes a first part for describing the concrete frame beam of the slope, a second part for describing the sliding body of the anchor cable free section, a third part for describing the anchor cable body, and a fourth part for describing the corresponding sliding bed of the anchor cable anchoring section.

[0058] Step 2: Establish the anchor cable tension relaxation equation. Without considering the influence of external factors such as rainfall and earthquakes on anchor cable deformation, establish a mechanical relationship equation between the anchor cable tension and the total tensile strain of the model to determine the relaxation variation law of the anchor cable tension over time.

[0059] Step 3: Analyze the impact of anchor cable tension relaxation on slope stability. Based on the proposed time-dependent analysis model of prestressed anchor cable tension loss, the calculation expression for anchor cable tension relaxation can be obtained. Then, based on the transfer coefficient method, the anchor cable tension can be introduced into the corresponding slope stability analysis, thereby analyzing and evaluating the time-dependent stability of the reinforced slope.

[0060] The purpose of this invention is to establish an analytical method for the impact of anchor cable tension relaxation effect on slope stability in slopes reinforced with prestressed anchor cable frame beams. The main content is based on the fundamental deformation mechanism and characteristics of the anchoring system of a prestressed anchor cable frame beam reinforced slope, consisting of "anchor cable body - frame beam - free section sliding body - anchored section sliding bed". Considering the interaction relationships between the anchor cable, sliding body, sliding bed, and frame beam, a long-term stability analysis method for slopes reinforced with prestressed anchor cable frame beams is proposed. This invention establishes a coupled calculation model for slope anchor cable tension relaxation, based on the interaction between the free and anchored sections of the anchor cable and the soil, as well as the interaction relationship between the frame beam and the anchor cable. The calculation results of the proposed coupled model are compared with experimental measured data and the calculation results of existing models, demonstrating that the theoretical calculation results of this invention have high accuracy and can effectively predict anchor cable anchorage force loss, conforming to actual conditions and verifying the applicability of the theoretical calculation model of this invention. The long-term stability analysis method for slope reinforcement using prestressed anchor cable frame beams of the present invention can provide effective theoretical analysis guidance and engineering design methods for slope reinforcement using prestressed anchor cable frame beams.

[0061] In step one, the first part is the Hooke(H) body, the second part is the generalized Kelvin body (KH body), the third part is the Hooke(H) body with different parameters, and the fourth part is the generalized Kelvin body (KH body) with different parameters.

[0062] In step one, the H-body describing the slope frame beam, the KH-body describing the free section sliding body, the H-body describing the anchor cable body, and the KH-body describing the anchoring section sliding bed are connected in series.

[0063] In step two, according to the coupled mechanics analysis model, we can obtain:

[0064]

[0065] In the formula, P is the anchor cable tension; ε is the tensile strain; E a1 E a2 The elastic modulus E of the H-body, which simulates the properties of frame beams and anchor cables; k1 E h1 η1 and η2 are the hysteretic elastic modulus, instantaneous elastic modulus, and viscosity coefficient of the KH body simulating the rheological properties of the sliding body, respectively; E k2 E h2 η1 and η2 are the hysteretic elastic modulus, instantaneous elastic modulus, and viscosity coefficient of the KH body simulating the rheological properties of the slide bed in the anchorage section, respectively; A a1 Let A be the equivalent cross-sectional area of ​​a single-hole anchored cable frame beam. a1 =A s ·d / a, where A s d is the actual cross-sectional area of ​​the frame beam, d is the anchor hole spacing, and a is the cross-sectional width of the frame beam; Aa2 A is the cross-sectional area of ​​a single-hole anchor cable; r1 The effective range of a single-hole anchor cable-frame beam on the soil and rock mass can be considered as the range of the "center-to-center" spacing between adjacent anchor cables; A r2 Let be the area of ​​the effective influence range of a single anchor cable on the slide bed. This influence range can be considered a circular region, and the diameter of this circular region can be taken as the center-to-center distance between the anchor holes; D is the calculation symbol, denoted as .

[0066] For the relaxation problem, the tensile strain ε = constant (i.e., Dε = 0). Therefore, multiplying both sides of the above equation by A... a1 A a2 A r1 A r2 E a1 E a2 E h1 E h2 E k1 E k2 After finding a common denominator, the result can be simplified to:

[0067] k1P″+k2P′+k3P=k4ε (2)

[0068] In the formula, k1, k2, k3, and k4 are constant coefficients, respectively:

[0069]

[0070]

[0071]

[0072] k4=A a1 A a2 A r1 A r2 E a1 E a2 E h1 E h2 E k1 E k2 (2d)

[0073] Solving the differential equation shown in equation (2), we can obtain

[0074]

[0075] In the formula, t represents time; n1 and n2 are the equations k1r 2 The two real roots of +k2r+k3=0; b1, b2 and b3 are integration constants, where b1=k4 / k3.

[0076] Given the initial condition P(0) = P0, equation (3) can be solved to obtain

[0077]

[0078] In the formula, C is an arbitrary constant that can be obtained based on the known conditions in a specific example; the tensile strain ε can be determined based on the initial tension of the anchor cable, i.e.

[0079]

[0080] The steps for determining the constant C in equation (4) in step two are as follows: by substituting the constant C into the constant C at different times t after the anchor cable tensioning and locking. m The monitored anchor cable tension P m Where m is the number of monitoring times taken for calculation; thus, m C values ​​are obtained, and the calculated anchor cable tension curves at different C values ​​are compared with the measured curves. The C value that makes the correlation coefficient between the two the highest is the constant value to be obtained.

[0081] In step two, in order to improve the calculation accuracy, the value of m can be appropriately increased, that is, the number of typical observation times in the initial stage, so that the correlation coefficient between the measured value curve of the anchor cable tension and the theoretical calculated value curve in the initial stage reaches a sufficiently large value as the control requirement.

[0082] The third step specifically involves using the transfer coefficient method to determine the time-dependent anchor cable tension P per hole, as determined by equation (4). i In the stability analysis of anchored slopes, the stability coefficient F of the anchored slope is solved. s The time-dependent stability of the slope is analyzed and evaluated. The calculation expression is as follows:

[0083]

[0084] In the formula, α i δ i W i l i c i φ i These are the sliding surface inclination angle, anchor cable inclination angle, gravity, sliding surface length, sliding surface cohesion, and internal friction angle of the i-th sliding block, respectively; P i Let ψ' be the time-dependent anchor cable tension corresponding to the i-th sliding block. i The transfer coefficient is calculated as follows:

[0085] ψ i ′=cos(α i-1 -α i )-sin(α i-1 -α i )tanφ i / F s (7)

[0086] Based on the remaining thrust E of the last segment at the leading edge of the slope. n =0, from equation (6), the recursive method can be used to calculate and determine the time (corresponding to different anchor cable tensions P) at different times. i The stability coefficient of the anchored slope.

[0087] This invention also provides a time-dependent analysis model for the tensile stress loss of prestressed anchor cables. Based on the basic deformation mechanism and characteristics of the anchoring system consisting of "anchor cable body - frame beam - free section sliding body - anchoring section sliding bed" in the prestressed anchor cable frame beam reinforced slope, a coupled analysis model is established considering the interaction relationship between the anchor cable, the corresponding sliding bed of the anchor cable fixed section, the corresponding sliding body of the anchor cable free section, and the corresponding frame beam of the slope. The coupled analysis model includes a first part for describing the concrete frame beam of the slope, a second part for describing the sliding body of the anchor cable free section, a third part for describing the anchor cable, and a fourth part for describing the corresponding sliding bed of the anchor cable fixed section.

[0088] The first part is the Hooke(H) body, the second part is the generalized Kelvin body (KH body), the third part is the Hooke(H) body with different parameters, and the fourth part is the generalized Kelvin body (KH body) with different parameters.

[0089] The H-body describing the slope frame beam, the KH-body describing the free section sliding body, the H-body describing the anchor cable, and the KH-body describing the anchoring section sliding bed are connected in series.

[0090] The invention will be further illustrated below through its practical applications.

[0091] This invention provides a method for long-term stability analysis of slopes reinforced by prestressed anchor cable frame beams, comprising the following steps:

[0092] Step 1: Establish an anchor cable tension coupling analysis model

[0093] like Figure 1 As shown, the overall stress analysis of the anchor cable in the prestressed anchor cable frame beam reinforced slope is as follows: Anchor cable body I consists of two sections: free section III and fixed section IV. Free section III is within the sliding body VI, and fixed section IV is within the sliding bed V. Frame beam II is set on the slope surface, i.e., the outer surface of sliding body VI.

[0094] Combination Figure 1 , Figure 2 , Figure 3 , Figure 6As shown, based on the basic deformation mechanism and characteristics of the anchoring system consisting of "anchor body - frame beam - free section sliding body - anchoring section sliding bed" in the prestressed anchor frame beam reinforced slope, and considering the interaction relationship between anchor body I, anchoring section sliding bed V, free section sliding body VI, and slope frame beam II, the overall series model for coupled calculation consists of four parts: the first part is the Hooke (H) body, used to describe the frame beam II of the slope concrete; the second part is the generalized Kelvin body (KH body), used to describe the sliding body VI of the free section III of the anchor cable; the third part is the Hooke (H) body with different parameters, used to describe the anchor cable body; and the fourth part is the generalized Kelvin body (KH body) with different parameters, used to describe the sliding bed V of the fixed section IV of the anchor cable.

[0095] Step 2: Establish the anchor cable tension relaxation equation

[0096] Without considering the influence of external factors such as rainfall and earthquakes on anchor cable deformation, a mechanical equation can be established between the anchor cable tension P and the total tensile strain ε of the model to determine the relaxation variation law of the anchor cable tension with time t.

[0097] The equation relating the anchor cable tension P and the total tensile strain ε of the model is expressed as follows:

[0098]

[0099] In the formula, P is the anchor cable tension; ε is the tensile strain; E a1 E a2 The elastic modulus E of the H-body, which simulates the properties of frame beams and anchor cables; k1 E h1 η1 and η2 are the hysteretic elastic modulus, instantaneous elastic modulus, and viscosity coefficient of the KH body simulating the rheological properties of the sliding body, respectively; E k2 E h2 η1 and η2 are the hysteretic elastic modulus, instantaneous elastic modulus, and viscosity coefficient of the KH body simulating the rheological properties of the slide bed in the anchorage section, respectively; A a1 Let A be the equivalent cross-sectional area of ​​a single-hole anchored cable frame beam. a1 =A s ·d / a, where A s d is the actual cross-sectional area of ​​the frame beam, d is the anchor hole spacing, and a is the cross-sectional width of the frame beam; A a2 A is the cross-sectional area of ​​a single-hole anchor cable; r1 The effective range of a single-hole anchor cable-frame beam on the soil and rock mass can be considered as the range of the "center-to-center" spacing between adjacent anchor cables; A r2 Let be the area of ​​the effective influence range of a single anchor cable on the slide bed. This influence range can be considered a circular region, and the diameter of this circular region can be taken as the center-to-center distance between the anchor holes; D is the calculation symbol, denoted as .

[0100] For the relaxation problem, the tensile strain ε = constant (i.e., Dε = 0). Therefore, both sides of equation (1) are multiplied by A. a1 A a2 A r1 A r2 E a1 E a2 E h1 E h2 E k1 E k2 After finding a common denominator, the result can be simplified to:

[0101] k1P″+k2P′+k3P=k4ε (2)

[0102] In the formula, k1, k2, k3, and k4 are constant coefficients, respectively:

[0103]

[0104]

[0105]

[0106] k4=A a1 A a2 A r1 A r2 E a1 E a2 E h1 E h2 E k1 E k2 (2d)

[0107] Solving the differential equation shown in equation (2), we can obtain

[0108]

[0109] In the formula, t represents time; n1 and n2 are the equations k1r 2 The two real roots of +k2r+k3=0; b1, b2 and b3 are integration constants, where b1=k4 / k3.

[0110] Given the initial condition P(0) = P0, equation (3) can be solved to obtain

[0111]

[0112] In the formula, C is an arbitrary constant that can be obtained based on the known conditions in a specific example; the tensile strain ε can be determined based on the initial tension of the anchor cable, i.e.

[0113]

[0114] Step 3: Determine the integration constant

[0115] To determine the constant C in equation (4), it can be obtained by substituting the values ​​of t at different times after the anchor cable is tensioned and locked. m The monitored anchor cable tension P m Where m is the number of monitoring times taken for calculation; thus, m C values ​​are obtained, and the calculated anchor cable tension curves at different C values ​​are compared with the measured curves. The C value that makes the correlation coefficient between the two the highest is the constant value to be obtained.

[0116] To improve the accuracy of the calculation, the value of m can be appropriately increased, that is, the number of typical observation times in the initial stage can be increased, and the correlation coefficient between the measured value curve of the anchor cable tension and the theoretical calculated value curve in the initial stage should reach a sufficiently large value (e.g., 0.92) as the control requirement.

[0117] Step 4: Long-term stability analysis of anchored slopes

[0118] According to the transfer coefficient method, the time-dependent anchor cable tension P in each hole, determined by equation (4), is... i In the stability analysis of anchored slopes, the stability coefficient F of the anchored slope is solved. s The time-dependent stability of the slope is analyzed and evaluated. The calculation expression is as follows:

[0119]

[0120] In the formula, α i δ i W i l i c i φ i These are the sliding surface inclination angle, anchor cable inclination angle, gravity, sliding surface length, sliding surface cohesion, and internal friction angle of the i-th sliding block, respectively; P i Let ψ' be the time-dependent anchor cable tension corresponding to the i-th sliding block. i The transfer coefficient is calculated as follows:

[0121] ψ i ′=cos(α i-1 -α i )-sin(α i-1 -α i )tanφ i / F s (7)

[0122] Based on the remaining thrust E of the last segment at the leading edge of the slope. n =0, from equation (6), the recursive method can be used to calculate and determine the time (corresponding to different anchor cable tensions P) at different times. i The stability coefficient of the anchored slope.

[0123] The present invention will be further described below in conjunction with actual measurements, Comparative Examples 1, 2, 3, and 4, as well as Examples 1 and 2. The test conditions and test objects of Comparative Examples 1, 2, 3, and 4, as well as Examples 1 and 2, are the same. The difference lies in the analysis method and model for the long-term stability of the slope reinforced by the prestressed anchor cable frame beam.

[0124] Comparative Example 1

[0125] The long-term stability analysis of the slope reinforced by the prestressed anchor cable frame beam was carried out using the analysis model and method in the literature "Coupling Analysis of Long-term Prestress Loss and Slope Creep" [Zhu Hanya, Shang Yuequan, Lu Ximing, et al. Coupling Analysis of Long-term Prestress Loss and Slope Creep of Anchor Cable [J]. Chinese Journal of Geotechnical Engineering, 2005(04):464-467].

[0126] Comparative Example 2

[0127] The long-term stability analysis of the slope reinforced by the prestressed anchor cable frame beam was carried out using the analysis model and method in the literature "Prestressed Anchor Cable Tension Relaxation Analysis Model" [Xiao Shiguo, Cao Shunli, Zhao Linzhi. Prestressed Anchor Cable Tension Relaxation Analysis Model for Reinforced Rock Mass [J]. Journal of Beijing University of Technology, 2020, 46(08): 940-947].

[0128] Comparative Example 3

[0129] The long-term stability analysis of the slope reinforced by a prestressed anchor cable frame beam was conducted using the analytical model and method in the literature "Coupled calculation model for anchoring force loss in aslope reinforced by a frame beam and anchor cables" [Shi K, Wu X, Liu Z, et al. Coupled calculation model for anchoring force loss in a slope reinforced by a frame beam and anchor cables[J]. Engineering Geology, 2019, 260(3):105245].

[0130] Comparative Example 4

[0131] The long-term stability analysis of the slope reinforced by the prestressed anchor cable frame beam was carried out using the analysis model and method in the literature "Research on Coupled Model of Anchoring Force Loss and Time-dependent Deformation of Soil and Rock Mass" [Dong Xuguang, Ma Zihan, Li Zheng, et al. Research on Coupled Model of Anchoring Force Loss and Time-dependent Deformation of Soil and Rock Mass [J]. Chinese Journal of Rock Mechanics and Engineering, 2022, 41(06):1093-1102].

[0132] Example 1

[0133] Combination Figure 1 , Figure 2 , Figure 3 A slope in a certain project was reinforced using prestressed anchor cable frame beams. The sliding mass and the sliding bed have similar properties. According to the geological survey, the slope rock strata are mainly weathered argillaceous shale with a unit weight of 21 kN / m³. 3 The cohesion of the potential sliding surface is taken as 60 kPa and the internal friction angle is 21°. Two prestressed anchor cables are selected as test anchor cables with a tensioning tonnage of 600 kN. The anchor cable length is 25-30 m and the anchor cable inclination angle is 20°. The anchor cable is composed of 4 high-strength, low-relaxation, unbonded steel strands with an ultimate tensile strength of 1860 MPa, a diameter of 15.24 mm, an anchor hole diameter of 110 mm, an anchor cable elastic modulus of 195 GPa, an anchor hole spacing of 4 m, and a frame beam cross-sectional dimension of 0.5 × 0.6 m. The numbers 1 to 7 represent the various sliding body blocks. There are a total of 7 sliding body blocks, i.e., the value of i in formula (6) is 1 to 7.

[0134] Based on the results of the slope rock creep test, the KH body parameters of the sliding bed in the anchored section were obtained: H body elastic modulus, K body elastic modulus, and viscosity coefficient were 15790 MPa, 46 MPa, and 657 MPa·d⁻¹, respectively. 1 Since the slope is entirely composed of shale rock, the rheological properties of the sliding body where the free section of the anchor cable is located and the sliding bed of the anchored section are approximately the same, and both can be taken from this test value. Taking the anchor cable tension monitoring value at t=4d (the calculated value is relatively optimal), the constant C with the highest calculation accuracy is -41.312kN. Substituting the relevant parameters into equation (4), the expressions for the anchor cable tension are as follows:

[0135] P(t) = 448.797 + 192.515e -0.0700t -41.312e -0.0936t (7)

[0136] The calculated relaxation curve of anchor cable tension over time is shown below. Figure 4 As shown in the figure, the calculation results of Comparative Examples 1, 2, and 3, as well as the converted results from existing measurements using multi-point displacement gauges, are also presented. It is evident that the calculation results of the method of this invention are closer to the measured values ​​and are therefore reasonable.

[0137] The slope stability coefficient calculated using equation (6) as a function of time is shown in the curve. Figure 5 As shown.

[0138] Example 2

[0139] Combination Figure 1 , Figure 2 , Figure 6 A high slope in a certain project was reinforced using prestressed anchor cable frame beams. The potential landslide body on this slope was in a fractured state, with obvious signs of loosening and deformation. The exposed strata in the slope area were Upper Jurassic welded tuff, with a single lithology and a landslide mass of 19 kN / m. 3 The cohesion is 110 kPa and the internal friction angle is 20°. The cohesion of the potential sliding surface is 80 kPa and the internal friction angle is 17°. The anchor cable tensioning tonnage is 850 kN, the length is about 22.5 m, the inclination angle is 15°, the anchor cable is composed of 6 high-strength, low-relaxation, unbonded steel strands, the ultimate tensile strength is 1860 MPa, the diameter is 15.24 mm, the anchor hole diameter is 110 mm, the anchor cable elastic modulus is 195 GPa, the anchor hole spacing is 4 m in the transverse direction and 6 m in the longitudinal direction, the cross-sectional dimensions of the reinforced concrete frame beam are 0.45 × 0.45 m, the cross-sectional dimensions of the longitudinal beam are 0.60 × 0.45 m, and its elastic modulus is 30 GPa. Among them, the numbers 1 to 7 represent each sliding body block. There are a total of 7 sliding body blocks, that is, i in formula (6) takes the value of 1 to 7.

[0140] Based on the creep formula of the KH model, and through back analysis of on-site displacement and anchor cable tension monitoring data, the elastic modulus of the H-body of the slope sliding body was obtained as 60 MPa, the elastic modulus of the K-body as 46 MPa, and the viscosity coefficient as 657 MPa·d. -1 For a relatively intact slide (rock mass), based on relevant indoor triaxial creep test results, the rheological parameters of the KH body are taken as follows: H body elastic modulus of 550 MPa, K body elastic modulus of 4680 MPa, and viscosity coefficient of 734400 MPa·d. -1 When t = 13h (the calculated value is relatively optimal), the constant C1 = 106.397kN can be calculated. Therefore, substituting the relevant parameters into equation (4), the expression for the tension of the BZ16-23 anchor cable as a function of time is obtained as follows:

[0141] P(t) = 753.434 - 9.831e -0.0064t +106.397e -0.0788t (7)

[0142] The relaxation curve of the anchor cable tension over time obtained using the method described in this application is calculated as follows: Figure 7As shown in the figure, the calculation results of Comparative Examples 1, 2, 3, and 4, as well as the measured conversion results using existing multi-point displacement gauges, are presented simultaneously. It is evident that the calculation results of the method of this invention agree better with the measured values ​​and possess good rationality.

[0143] The slope stability coefficient calculated using equation (6) as a function of time is shown in the curve. Figure 8 As shown.

[0144] The anchor cable tension relaxation curve over time, the slope rock creep test results, and the relevant indoor triaxial creep test results mentioned in Examples 1 and 2 above were obtained from the existing technical literature "Research on the Quantitative Loss Law of Anchor Cable Prestress in Soft Rock Slopes" [Chen Yuanjiang, Yin Jin, Hu Yifu. Research on the Quantitative Loss Law of Anchor Cable Prestress in Soft Rock Slopes [J]. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(08):1685-1691] and "Coupling Analysis of Long-Term Loss of Anchor Cable Prestress and Slope Creep" [Zhu Hanya, Shang Yuequan, Lu Ximing, et al. Coupling Analysis of Long-Term Loss of Anchor Cable Prestress and Slope Creep [J]. Chinese Journal of Geotechnical Engineering, 2005(04):464-467.], as well as the rheological characteristics parameters of the rock and soil obtained from the field creep test.

[0145] The above embodiments are merely illustrative of the present invention and are not intended to limit the technical solutions described herein. Although this specification has described the present invention in detail with reference to the various embodiments described above, the present invention is not limited to the specific embodiments described above. Therefore, any modifications or equivalent substitutions to the present invention, without departing from the spirit and scope of the present invention, should be covered within the scope of the claims of the present invention.

Claims

1. A method for analyzing long-term stability of a slope reinforced by prestressed cable frame beams, characterized in that, The method comprises the following steps: Step one: establishing a prestressed anchor cable tension loss aging analysis model, according to the deformation basic mechanism and characteristics of the anchoring system composed of the "anchor cable body-frame beam-free section sliding body-anchoring section sliding bed" of the prestressed anchor cable frame beam reinforced slope, considering the interaction relationship between the anchor cable, the corresponding sliding bed of the anchor cable fixed section, the corresponding sliding body of the anchor cable free section and the corresponding frame beam of the slope surface, a coupling analysis model is established, the coupling analysis model comprises a first part for describing the slope surface concrete frame beam, a second part for describing the corresponding sliding body of the anchor cable free section, a third part for describing the anchor cable, and a fourth part for describing the corresponding sliding bed of the anchor cable anchoring section, the coupling analysis model is the prestressed anchor cable tension loss aging analysis model; Step two: establishing an anchor cable tension relaxation equation, under the condition of not considering the influence of rainfall and earthquake on the deformation of the anchor cable, a mechanical relationship equation between the anchor cable tension and the total tensile strain of the model is established, and the relaxation change rule of the anchor cable tension with time is determined; Step three: analyzing the influence of anchor cable tension relaxation on the stability of the slope, according to the proposed prestressed anchor cable tension loss aging analysis model, the calculation expression of anchor cable tension relaxation is derived, then the anchor cable tension is introduced into the corresponding slope stability analysis based on the transfer coefficient method, and then the time-dependent stability of the reinforced slope is analyzed and evaluated. 2.The method for analyzing long-term stability of a slope reinforced by prestressed cable frame beams according to claim 1, wherein, In step one, the first part is a Hooke (H) body, the second part is a generalized Kelvin body, the third part is a Hooke (H) body with different parameters, and the fourth part is a generalized Kelvin body with different parameters.

3. The method for analyzing long-term stability of a slope reinforced by prestressed cable frame beams according to claim 2, wherein In step one, the H body describing the slope surface frame beam, the K-H body describing the free section sliding body, the H body describing the anchor cable and the K-H body describing the anchoring section sliding bed are connected in series.

4. The method for analyzing long-term stability of a slope reinforced by prestressed cable frame beams according to claim 1, wherein In step two, according to the coupling mechanical analysis model, the following equation can be obtained: where P is the anchor cable tension; ε is the tensile strain; E a1 , E a2 is the elastic modulus of the H-body simulating the frame beam and anchor cable properties; E k1 , E h1 , η1 are the hysteresis elastic modulus, instantaneous elastic modulus and viscous coefficient of the K-H body simulating the rheological properties of the sliding body, respectively; E k2 , E h2 , and η2 are the hysteresis elastic modulus, instantaneous elastic modulus and viscous coefficient of the K-H body simulating the rheological properties of the anchor segment sliding bed, respectively; A a1 is the equivalent cross-sectional area of the single-hole anchor cable frame beam, denoted as A a1 = A s · d / a, where A s is the actual cross-sectional area of the frame beam, d is the anchor hole spacing, and a is the cross-sectional width of the frame beam; A a2 is the cross-sectional area of the single-hole anchor cable; A r1 is the effective range of the single-hole anchor cable-frame beam on the rock-soil mass, which can be considered as the range of the "mid-mid" spacing of adjacent anchor cables; A r2 is the effective influence area of the single-hole anchor cable on the sliding bed, and the influence range can be considered as a circular area, and the diameter of the circular area can be taken as the center-to-center spacing of the anchor holes; D is a calculated symbol, denoted as For the relaxation problem, there is a constant tensile strain ε = constant, that is, Dε = 0, so multiply both sides of the above equation by A a1 A a2 A r1 A r2 E a1 E a2 E h1 E h2 E k1 E k2 After passing through the division, it can be simplified as: k1P″+k2P′+k3P=k4ε (2) In the equation, k1, k2, k3 and k4 are constant coefficients, which are respectively: k4 = A a1 A a2 A r1 A r2 E a1 E a2 E h1 E h2 E k1 E k2 (2d) Solving the differential equation shown in equation (2), the following equation can be obtained: where t is time; n1, n2 are the two real roots of the equation k1r 2 +k2r+k3=0; b1, b2 and b3 are integration constants, where b1=k4 / k3; According to the initial condition P(0)=P0, equation (3) can be solved as follows: In the equation, C is an arbitrary constant, which can be obtained according to the known conditions in the specific example; ε can be determined according to the initial tension of the anchor cable, that is:

5. The method for analyzing long-term stability of a slope reinforced by prestressed cable frame beams according to claim 4, wherein The step of determining the constant C in equation (4) in step two is as follows: by substituting the anchor cable tension at different times t after the anchor cable tension is locked m The monitored anchor cable tension P m wherein m is the number of monitoring times taken for calculation; thereby solving m C values, comparing the anchor cable tension calculation curves at different C times with the measured curves, and determining the C value that makes the correlation coefficient of the two highest as the constant value to be solved.

6. The method for analyzing long-term stability of a slope reinforced by prestressed cable frame beams according to claim 1, wherein In step two, in order to improve the calculation accuracy, the value of m can be appropriately increased, that is, the number of typical observation time points in the initial stage after the anchor cable is tensioned and locked, so that the correlation coefficient of the anchor cable tension measured value curve and the theoretical calculation value curve in the initial stage reaches a large enough value as the control requirement.

7. The method for analyzing long-term stability of a slope reinforced by prestressed cable frame beams according to claim 4, wherein In step three, according to the transfer coefficient method, the anchor cable tension related to time determined by equation (4) is introduced into the anchoring slope stability analysis, the anchoring slope stability coefficient is solved, and the time-dependent stability of the anchoring slope is analyzed and evaluated.

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