Method for calculating bearing capacity of shear-yielding and pressure-yielding anchoring pile

Abstract

The invention provides a method for calculating the bearing capacity of a shear-yielding and pressure-yielding anchoring pile. The method is used for solving the technical problems that the bearing capacity of an existing shear-yielding and pressure-yielding anchoring pile is difficult to calculate, and popularization and application of the shear-yielding and pressure-yielding anchoring pile are not facilitated. The method comprises the specific steps that S1, initial data of the shear-yielding and pressure-yielding anchoring pile and a rock mass are obtained; s2, the anchor cable design tension A is calculated through a pile top displacement control method; s3, constructing a bending moment and shearing force equation of a cross section at any distance x from the anchoring end when the anchor cable design tension A and the landslide thrust are applied to the shear-yielding and pressure-yielding type anchoring pile; and S4, the internal force of the anchoring section of the shear-yielding and pressure-yielding type anchoring pile is calculated through a foundation coefficient K method. According to the method, the internal force of the anchoring section of the shear-yielding and pressure-yielding type anchoring pile is calculated, popularization and utilization of the method are facilitated, and meanwhile the internal force calculation method has the advantages of being high in accuracy and small in calculation amount.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering, and in particular to a method for calculating the bearing capacity of shear-compression type anchor piles. Background Technology

[0002] Anchored piles, as a traditional bedding slope support structure, can effectively improve slope stability. Currently, the structural calculations of anchored piles are mainly based on limit equilibrium theory, assuming that all points on the sliding surface simultaneously reach the critical stress state. However, the weak interfaces of bedding slopes exhibit strain softening characteristics during shearing. The limit equilibrium method neglects the influence of soil displacement on stability analysis and fails to consider the strain softening properties of soil and rock as deformation develops, which is inconsistent with the reality of most bedding slopes.

[0003] Based on the softening characteristics of soil and rock materials, anchor piles, as a rigid support structure, need to limit large deformations of the slope. However, neglecting the deformation of the reinforced slope and the shear strength interaction between the rock strata in the landslide area leads to the neglect of the slope's own shear capacity, resulting in amplified slope thrust. Therefore, existing research proposes a shear-yielding and compression-yielding anchor pile reinforcement structure. The compression and shear yielding layers in the structure can control the allowable deformation of the slope, thereby improving the slope's self-bearing capacity and effectively reducing the forces acting on the support structure. However, shear-yielding and compression-yielding anchor piles are a novel support structure, and a design and calculation method for them has not yet been established, hindering their widespread application. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the bearing capacity of shear-compression type anchored piles. This method addresses the technical problem of the difficulty in calculating the bearing capacity of existing shear-compression type anchored piles, which hinders their widespread application.

[0005] A method for calculating the bearing capacity of shear-compression type anchored piles is provided. The rock mass sliding force on the cantilever section of the pile is a uniformly distributed load. There is no rock mass in front of the pile. The cantilever section of the pile is subjected to landslide thrust and anchor cable tension. The specific steps of the bearing capacity calculation method are as follows:

[0006] S1: Obtain initial data on shear-compression type anchor piles and rock mass;

[0007] S2: The anchor cable design tension A is calculated using the controlled pile top displacement method;

[0008] S3: Construct the bending moment and shear force equations for the cross section at any distance x from the anchoring end when the anchor cable design tension A and the landslide thrust are applied to the shear-compression type anchor pile;

[0009] S4: The internal forces in the anchorage section of the shear-compression type anchor pile are calculated using the subgrade coefficient K method.

[0010] Optionally, obtaining the initial data of the shear-compression type anchor pile in step S1 includes: the dimensional parameters of the shear-compression type anchor pile and the pile stiffness EI;

[0011] The initial data of the rock mass include the shear stiffness Ks and displacement Δu0 of the potential sliding body layer, the sliding thrust F, the force-bearing area S0 of the potential sliding body layer, the elastic modulus E0 of the collapsible layer, the contact area S between the collapsible layer and the potential sliding body, and the rock layer dip angle θ.

[0012] Optionally, in step S2, the anchor cable tension A is calculated as follows:

[0013]

[0014] In the formula, EI is the pile stiffness, δ QQ δ QM δ represents the displacement in the shear force direction at point O when M0 = 1 and Q0 = 1, respectively. MM δ MQ y1 and y2 are the turning angles generated at point 0 when M0=1 and Q0=1, respectively. Point 0 is the sliding surface point, y2 is the given allowable horizontal displacement of the pile top, and x0 is the distance from the point of application of the resultant force of the landslide thrust to the sliding surface.

[0015] Optionally, in step S3, the equations for bending moment and shear force of the cross-section at any distance x from the anchoring end are constructed as follows:

[0016]

[0017] Q(x) = qL - A - qx

[0018] In the formula, M(x) is the bending moment equation of the cantilever section of the shear-compression type anchored pile, Q(x) is the shear force equation of the cantilever section of the shear-compression type anchored pile, q is the uniformly distributed load of the slope sliding force, L is the length of the cantilever section of the anti-slide pile, and A is the tension of the prestressed anchor cable.

[0019] Optional, in the bending moment and shear force equations:

[0020]

[0021]

[0022] In the formula, E0 represents the elastic modulus of the compression layer and the shear layer, a is the thickness of the compression layer, S is the contact area between the compression layer and the potential sliding body, a0 is the compressible thickness of the compression layer when the material is in the elastic deformation stage, and K... s S is the shear stiffness, and S0 is the area of ​​the potential sliding body layer;

[0023] The equations for bending moment and shear force can be simplified using the above formula as follows:

[0024]

[0025] Optionally, the specific method for calculating the internal force of the anchorage section of the shear-compression type anchor pile is as follows:

[0026] By simultaneously solving the bending moment and shear force equations and integrating them, the deflection curve equation of the shear-compression type anchored pile can be obtained. Using the boundary conditions of the shear-compression type anchored pile cantilever beam, the deflection curve equation of the shear-compression type anchored pile cantilever beam is obtained. The internal forces in the anchorage section of the shear-compression type anchored pile are calculated using the subgrade coefficient K method.

[0027] Because of the adoption of the above technical solution, the present invention has the following advantages:

[0028] This application calculates the internal forces in the anchorage section of shear-compression type anchor piles, which is beneficial for their widespread application. At the same time, the internal force calculation method of this application has the advantages of high accuracy and small calculation amount.

[0029] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0030] The accompanying drawings of this invention are described below.

[0031] Figure 1 This is a flowchart of the load-bearing capacity calculation method of the present invention.

[0032] Figure 2 This is a curve showing the relationship between strain softening stress and displacement in this invention.

[0033] Figure 3 This is a simplified calculation diagram of the method for controlling pile top displacement according to the present invention.

[0034] Figure 4 This is a force analysis diagram of the shear-compression type anchor pile of the present invention.

[0035] Figure 5 This is a cross-sectional view of the shear-compression type anchor pile used in the experimental analysis of this invention.

[0036] Figure 6 This is a diagram of the internal forces in the shear-compression type anchor pile used in the experimental analysis of this invention. Detailed Implementation

[0037] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0038] Example:

[0039] like Figure 1The method for calculating the bearing capacity of a shear-compression type anchored pile is shown in this application. In this application, the rock mass sliding force on the cantilever section of the shear-compression type anchored pile is a uniformly distributed load. There is no rock mass in front of the pile. The cantilever section of the pile is subjected to the landslide thrust and the anchor cable tension. The specific steps of the bearing capacity calculation method are as follows:

[0040] S1: Obtain initial data on shear-compression type anchor piles and rock mass;

[0041] In this embodiment, the initial data for the shear-compression type anchor pile includes: the dimensional parameters of the shear-compression type anchor pile (cantilever beam length, pile embedment depth), and the pile stiffness EI;

[0042] The initial data of the rock mass include the shear stiffness Ks and displacement Δu0 of the potential sliding body layer, the sliding thrust F, the force-bearing area S0 of the potential sliding body layer, the elastic modulus E0 of the collapsible layer, the contact area S between the collapsible layer and the potential sliding body, and the rock layer dip angle θ.

[0043] S2: As Figure 3 As shown, the anchor cable design tension A is calculated using the controlled pile top displacement method;

[0044] In this embodiment, referring to the "Code for Design of Landslide Prevention" (GB / T 38509-2020) and the "Code for Design of Highway Landslide Prevention" (JTG / T 3334-2018) and commonly used engineering calculation methods, the anchor cable tension is usually calculated first using the method of controlling the horizontal displacement of the pile top when designing anchored piles. Under the combined action of the anchor cable tension A and the landslide thrust F, the allowable horizontal displacement y2 at the pile top is ultimately generated.

[0045]

[0046] In the formula, This refers to the horizontal displacement of the pile top under the action of the landslide thrust F. Let A be the horizontal displacement of the pile top under the action of anchor cable tension A, where:

[0047] Combining the above formulas, the anchor cable tension A is calculated as follows:

[0048]

[0049] In the formula, EI represents the pile stiffness, and y0 F Φ0 F y0 A and Φ0 A These represent the horizontal displacement and rotation of the pile at the anchorage point under the action of landslide thrust F and anchor cable tension A, respectively, Φ1 F Let δ be the rotation angle of the pile at point 1 under the action of landslide thrust F, where point 1 is the point of application of the resultant force of the landslide thrust. QQδ QM δ represents the displacement in the shear force direction at point O when M0 = 1 and Q0 = 1, respectively. MM δ MQ y1 represents the turning angle generated at point 0 when M0=1 and Q0=1, respectively. Point 0 is the intersection of the sliding surfaces, y2 is the given allowable horizontal displacement of the pile top, and x0 is the distance from the point of application of the resultant force of the landslide thrust to the sliding surface.

[0050] S3: As Figure 4 As shown, when the anchor cable design tension A and the landslide thrust are applied to the shear-compression type anchor pile, the bending moment and shear force equations for the cross section at any distance x from the anchoring end are as follows:

[0051]

[0052] Q(x) = qL - A - qx

[0053] In the formula, M(x) is the bending moment equation of the cantilever section of the shear-compression type anchored pile, Q(x) is the shear force equation of the cantilever section of the shear-compression type anchored pile, q is the uniformly distributed load of the slope sliding force, L is the length of the cantilever section of the anti-slide pile, and A is the tension of the prestressed anchor cable.

[0054] By simultaneously solving the equations for bending moment and shear force and integrating them, we can obtain the equation for the deflection curve:

[0055]

[0056] Based on the boundary conditions of the cantilever beam, y = 0 and y' = 0 at x = 0. Substituting these into the above equation, we get C1 = C2 = 0. Substituting these back into the above equation, we obtain the deflection curve equation of the cantilever segment of the pile:

[0057]

[0058] In this embodiment, the elastic modulus of the compression layer and the shear layer is:

[0059]

[0060] In the formula, ε represents the strain of the compressive layer, σ represents the stress of the compressive layer, a represents the thickness of the compressive layer, and a0 represents the compressive thickness of the compressive layer; combining the above formulas, we get:

[0061]

[0062] The magnitude of the horizontal force on the pressure layer is:

[0063]

[0064] In the formula, S represents the contact area between the pressure layer and the potential sliding body. At this stage, the sliding force generated by the sliding body is F. The magnitude of the force in the horizontal direction is determined by both the sliding force of the sliding body and the anti-sliding force F′ between the rock strata, i.e.:

[0065] F x = (FF′)cosθ

[0066] In the formula, θ is the dip angle of the rock strata. Combining the above formulas, we can obtain:

[0067]

[0068] At this stage, such as Figure 3 As shown, the anti-slip force F' of the sliding surface can be obtained from the shear strain curve, and the shear stiffness is K. s This ensures that the shear-pressure type anti-slide pile retaining bedding rock slope remains in a stable state.

[0069] τ=ΔuK S (0≤Δu≤Δu0)F=τS

[0070] In the formula: Δu is the displacement of the sliding body, Δu0 is the displacement corresponding to the peak shear force, and τ is the shear force. Combining the above formulas, we can obtain:

[0071]

[0072] In the formula, S0 is the force-bearing area of ​​the potential sliding body layer, and qL=F x Substitute into the above equation:

[0073]

[0074] Finally, by combining the above equations, we can obtain the bending moment equation and shear force equation for the pile body under pressure:

[0075]

[0076] S4: The internal forces in the anchorage section of the shear-compression type anchor pile are calculated using the subgrade coefficient K method.

[0077] In this embodiment, the K-method is used to solve for the internal forces and deformations of the anchorage section:

[0078] When shear compression type anchor piles satisfy When it is an elastic pile, the flexural differential equation for an elastic anti-slip pile is:

[0079]

[0080] y(x)=e βz (C1 cosβx+C2 sinβx)+e -βx (C3 cosβx + C4 sinβx)

[0081]

[0082] Based on the boundary conditions, solve for the integration constants C1, C2, C3, and C4, and calculate the internal forces and displacements of the pile:

[0083]

[0084] In the formula, Z is the embedment depth of the shear-compression type anchor pile.

[0085] S5: Experimental Analysis: Taking the right-side rock strata of the No. 2 bedding slope at Changtan Interchange as an example, although the rock strata on the right side of the No. 2 bedding slope at Changtan Interchange have a relatively stable attitude, there is a weak layer between the rock strata that serves as a potential sliding surface. The sliding surface has poor bonding, a thickness of about 10cm, and its dip is oblique to the route and tends towards the roadbed. Under the condition of excavation at the toe of the slope, it will have a significant impact on the stability of the slope. Therefore, this section of the bedding slope is unstable after excavation. This section of the slope starts at K30+534 and ends at K30+622, with a length of 88m. The lithology of the slope body is siltstone and sandstone. The elevation of the top of the slope is about 406.66m, the elevation of the bottom is about 335.73m, and the height is about 70.93m. When this section of the bedding rock slope is excavated to the design elevation, a high slope of 15m-35m will be formed. Since this section of the slope is a rock slope, the use of anchor piles can make full use of the advantages of the rock strata. Therefore, in order to prevent the slope from sliding along the weak surface during the slope excavation process, shear-pressure type anchor piles are used as a treatment method.

[0086] like Figure 5 As shown, the road cut slope is excavated in two stages. The first-stage slope has a gradient of 1:0.75 and a height of 10m. The second-stage slope has a gradient of 1:1 and is excavated to the top. A 2m wide platform is constructed at the top of the first-stage slope. C30 prestressed anchor cable anti-slide piles are installed at the second-stage platform. The anti-slide piles have a cross-section of 2.0m × 3.0m and a length of 22m. Two rows of prestressed anchor cables are installed on top of the anti-slide piles. The upper row of anchor cables is located 1m from the top of the pile, with a length of 34m and a downward inclination angle of 24°. The lower row of anchor cables is located 2m from the top of the pile, with a length of 32m and a downward inclination angle of 26°. There are 8 anchor cables in total. Composed of high-strength, low-relaxation 1860 grade steel strands, each anchorage section is 10m long, with a prestress locking value of 400kN. An anchor frame is installed on the first-level slope surface, with anchor lengths of 9m, 6m, and 9m from bottom to top. The frame cross-section is 0.4m × 0.4m, constructed using C30 reinforced concrete cast in-situ, and the anchors are made of Φ25mm HRB400 threaded steel bars. The cross-sectional view of the right slope and slope support structure layout of slope #2 is shown below. Figure 5 As shown.

[0087] The calculations were based on a two-dimensional plane. In-situ direct shear tests were conducted to obtain the shear stiffness Ks and Δu0 of the weak interlayer in the slope as 1.7 × 10⁻⁶. 6N / m 3 With a slope depth of 0.012m, the slope sliding thrust F is 7015.09kN / m, and the stress-bearing area S0 of the potential sliding mass layer is 80.25m². 2 The elastic modulus E0 of the laminated EPS material and the contact surface S are set to 5MPa and 18m, respectively. 2 The rock strata dip angle θ is 12°. The physical and mechanical parameters of each material are shown in Table 1.

[0088] Table 1 Physical and mechanical parameters of each material

[0089]

[0090] Using the above parameters, the thickness 'a' of the laminate is calculated as follows:

[0091]

[0092] To facilitate calculation and analysis and to follow actual engineering applications, the thickness of the shear-compression layer is taken as a = 0.2m. Substituting a into the expressions for M(x) and Q(x), the internal forces M(x) and deformation Q(x) of the cantilever section of the shear-compression type anchor pile can be obtained. According to the boundary conditions, M = M at the sliding surface. A Q = Q A The bottom of the pile is a fixed end with y = 0 and θ = 0. The internal forces and deformations M(z) and Q(z) of the anchorage section are solved using the K method.

[0093] The theoretical calculation model proposed in this invention is used to calculate the internal forces of shear-compression type anchored piles. For example... Figure 6 As shown, the bending moment and shear force of the shear-compression type anchored pile are significantly smaller than those of the traditional anchored pile. The maximum shear force of the pile is reduced by approximately 26.2%, and the maximum bending moment is reduced by approximately 24.6%. The peak values ​​of the internal forces in the pile occur around a pile depth of 8-10m, i.e., near the potential slip surface. The peak bending moment and the zero point of the shear force are basically at the same location, both occurring near the potential slip surface.

[0094] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for calculating the bearing capacity of a shear-compression type anchored pile, wherein the rock mass sliding force on the cantilever section of the pile body is a uniformly distributed load, there is no rock mass in front of the pile, and the cantilever section of the pile is subjected to the action of landslide thrust and anchor cable tension, characterized in that... The specific steps for calculating bearing capacity are as follows: S1: Obtain initial data on shear-compression type anchor piles and rock mass; S2: The anchor cable design tension A is calculated using the controlled pile top displacement method; S3: Construct the bending moment and shear force equations for the cross section at any distance x from the anchoring end when the anchor cable design tension A and the landslide thrust are applied to the shear-compression type anchor pile; S4: The internal forces in the anchorage section of the shear-compression type anchor pile are calculated using the subgrade coefficient K method.

2. The method for calculating the bearing capacity of a shear-compression type anchored pile according to claim 1, characterized in that, The initial data for the shear-compression type anchor pile obtained in step S1 includes: the dimensional parameters of the shear-compression type anchor pile and the pile stiffness EI; The initial data of the rock mass include the shear stiffness Ks and displacement Δu0 of the potential sliding body layer, the sliding thrust F, the force-bearing area S0 of the potential sliding body layer, the elastic modulus E0 of the collapsible layer, the contact area S between the collapsible layer and the potential sliding body, and the rock layer dip angle θ.

3. The method for calculating the bearing capacity of a shear-compression type anchored pile according to claim 1 or 2, characterized in that, In step S2, the anchor cable tension A is calculated as follows: In the formula, EI is the pile stiffness, δ QQ δ QM δ represents the displacement in the shear force direction at point O when M0 = 1 and Q0 = 1, respectively. MM δ MQ y1 and y2 are the turning angles generated at point 0 when M0=1 and Q0=1, respectively. Point 0 is the sliding surface point, y2 is the given allowable horizontal displacement of the pile top, and x0 is the distance from the point of application of the resultant force of the landslide thrust to the sliding surface.

4. The method for calculating the bearing capacity of a shear-compression type anchored pile according to claim 3, characterized in that, In step S3, the equations for bending moment and shear force of the cross section at any distance x from the anchorage end are as follows: Q(x) = qL - A - qx In the formula, M(x) is the bending moment equation of the cantilever section of the shear-compression type anchored pile, Q(x) is the shear force equation of the cantilever section of the shear-compression type anchored pile, q is the uniformly distributed load of the slope sliding force, L is the length of the cantilever section of the anti-slide pile, and A is the tension of the prestressed anchor cable.

5. The method for calculating the bearing capacity of a shear-compression type anchored pile according to claim 3, characterized in that, In the equations for bending moment and shear force: In the formula, E0 represents the elastic modulus of the compression layer and the shear layer, a is the thickness of the compression layer, S is the contact area between the compression layer and the potential sliding body, a0 is the compressive thickness of the compression layer when the material is in the elastic deformation stage, and K... s S0 is the shear stiffness, and S0 is the area of ​​the potential sliding body layer. The equations for bending moment and shear force can be simplified using the above formula as follows:

6. The method for calculating the bearing capacity of a shear-compression type anchored pile according to claim 2, characterized in that, The specific method for calculating the internal force of the anchorage section of a shear-compression type anchored pile is as follows: By simultaneously solving the bending moment and shear force equations and integrating them, the deflection curve equation of the shear-compression type anchored pile can be obtained. Using the boundary conditions of the shear-compression type anchored pile cantilever beam, the deflection curve equation of the shear-compression type anchored pile cantilever beam is obtained. The internal forces in the anchorage section of the shear-compression type anchored pile are calculated using the subgrade coefficient K method.

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