Pouch-type Recyclable Pressure Anchor Bolt and Its Bearing Capacity Calculation Method

Abstract

The present invention discloses a bag-type recyclable pressure-type anchor rod, which includes an anchor head and anchor, a rod body, a carrier and an anchor solid. The rod body includes a steel strand and a protective casing, and the protective casing is sleeved around the steel strand. The carrier is located at the end of the anchor rod body and is connected to the steel strand. The anchor solid includes a cement-soil anchor solid and a cement slurry anchor solid. The cement-soil anchor solid is formed by high-pressure jet grouting of cement slurry and the surrounding soil, and the cement slurry anchor solid is formed by injecting cement slurry into a bag wrapped around the rod body through a reserved grouting pipe. This anchor rod makes the shear stress distribution at the interface between the anchor solid and the soil more uniform, effectively prevents the cement-soil anchor solid from being damaged under pressure, and fully exerts the bearing capacity of the anchor solid. The present invention also provides a method for calculating the bearing capacity of the above-mentioned bag-type recyclable pressure-type anchor rod, which can simply, efficiently and accurately obtain the ultimate bearing capacity data of the anchor rod.

Description

Technical Field

[0001] The present invention relates to a bag - type recyclable pressure - type anchor rod and a calculation method for its bearing capacity, mainly in the engineering field of applying bag - type recyclable prestressed anchor rods, including foundation pit engineering, slope engineering, tunnel engineering, etc. Background Technique

[0002] The tension - anchored support system is connected to the deep soil mass by setting prestressed anchor rods on the retaining structure, which can actively reinforce the rock and soil mass. Compared with other support forms such as row piles plus supports in foundation pit support, it has a larger construction operation surface, is more convenient for subsequent underground structure construction, saves the time for support construction and demolition, can improve the construction speed and efficiency, and has good economy, so it is applied in more and more foundation pit retaining projects.

[0003] Traditional prestressed anchor rods are divided into tension - type anchor rods and pressure - type anchor rods. The tension - type anchor rod transfers the applied external load to the rock and soil mass directly through the bonding action between the tendon and the anchor body. When designing a tension - type anchor rod, a relatively large anchorage length is often adopted. During use, it is easy to exceed the land use red line, and its tendon will become an obstacle to subsequent underground space development, so it is greatly restricted in practical applications, and then the pressure - type anchor rod was developed.

[0004] The pressure - type anchor rod transfers the load directly to the carrier composed of a bearing member, an unlocking anchor and its peripheral protective sleeve at the bottom end of the anchor rod (the end far from the free section) through a steel strand with a sleeve or a non - bonded prestressed steel strand. The pressure - type anchor rod can realize the recovery of the tendon through the unlocking device at the end of the tendon. After its use function is over, the anchor rod is recovered to solve the problem of the anchor rod exceeding the red line and avoid it becoming an underground obstacle to subsequent project construction, which meets the requirements of sustainable development and the "dual - carbon" goal, saves resources and is environmentally friendly. However, the pressure - type anchor rod will cause stress concentration at the position of the carrier, resulting in easy compression failure of the anchor body at the front end of the carrier and unable to fully exert the bearing performance of the anchor body.

[0005] To overcome the application defects of tension - type and pressure - type anchor rods, the present invention has developed a bag - type recyclable pressure - type anchor rod. However, there is currently no calculation method for bag - type recyclable pressure - type anchor rods at home and abroad. As a new type of anchor rod, the existing calculation formula for the bearing capacity of anchor rods in the current national standard is no longer applicable, and the existing theory cannot calculate the bearing capacity of each load transfer interface, so the bearing capacity of the bag - type recyclable pressure - type anchor rod cannot be accurately calculated.

[0006] Therefore, the present invention proposes a load transfer mechanism and a bearing capacity calculation method for bag - type recyclable pressure - type anchor rods. By analyzing the load transfer mechanism of tension - compression composite anchor rods, the ultimate bearing capacity of the anchor rod is obtained, providing a basis for engineering design. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a bag-type recyclable pressure-type anchor rod, which makes the shear stress distribution at the interface between the anchor solid and the soil more uniform, effectively prevents the cement-soil anchor solid from being damaged under pressure, and gives full play to the bearing capacity of the anchor solid. The present invention also provides a method for calculating the bearing capacity of the above-mentioned bag-type recyclable pressure-type anchor rod, which can simply, efficiently and accurately obtain the ultimate bearing capacity data of the anchor rod.

[0008] To this end, the bag-type recyclable pressure-type anchor rod provided by the present invention includes an anchor head anchor, a rod body, a carrier and an anchor solid. The rod body includes a steel strand and a protective sleeve. The protective sleeve is sleeved around the steel strand. The carrier is located at the end of the anchor rod body and is connected to the steel strand. The anchor solid includes a cement-soil anchor solid and a cement slurry anchor solid. The cement-soil anchor solid is formed by high-pressure jet grouting of cement slurry and the surrounding soil, and the cement slurry anchor solid is formed by injecting cement slurry into the bag wrapped around the rod body through a reserved grouting pipe.

[0009] Preferably, a bearing member, an unlocking anchor and an unlocking anchor protective sleeve are provided at the rear end of the cement slurry anchor solid.

[0010] A method for calculating the bearing capacity of the above-mentioned bag-type recyclable pressure-type anchor rod provided by the present invention includes the following steps:

[0011] Step 1. Determine the critical anchorage length of the cement slurry anchor solid in the bearing area:

[0012] Its expression is:

[0013]

[0014] In the formula: l c1 is the critical anchorage length of the cement slurry anchor solid; d is the diameter of the cement slurry anchor solid; E c1 is the comprehensive elastic modulus of the cement slurry anchor solid; G b is the shear modulus of the cement-soil anchor solid;

[0015] According to this formula, the critical anchorage length of the cement slurry anchor solid can be determined;

[0016] Step 2. Determine the bearing capacity of the cement slurry anchor solid:

[0017] When the cement slurry anchor solid is in normal working condition, it should not be damaged under pressure, and should not slip off from the surrounding structure;

[0018] The bearing capacity of the cement slurry anchor solid is the smaller value of the bearing capacity of the cement slurry anchor solid at the front end of the carrier under pressure and the frictional resistance at the interface between the cement slurry anchor solid and the surrounding cement-soil anchor solid;

[0019] The bearing capacity of the cement slurry anchor solid at the front end of the carrier under pressure is calculated according to Equation (19) as:

[0020]

[0021] Where: σ maxr is the ultimate compressive stress that the cement slurry anchor solid can withstand, and d1 is the diameter of the cement slurry anchor solid;

[0022] The interfacial frictional resistance between the cement slurry anchor solid and the surrounding structure is:

[0023]

[0024] Where: τ u1 is the interfacial shear strength between the cement slurry anchor solid and the surrounding structure; l r1 is the length of the cement slurry anchor solid; l c1 is the critical length of the cement slurry anchor solid;

[0025] According to Eqs. (21) and (22), the bearing capacity of the cement slurry anchor solid is:

[0026] P3 = min{P1, P2} (23)

[0027] Step 3. Determine the critical anchorage length of the cement-soil anchor solid in Zone I:

[0028] Its expression is:

[0029]

[0030] Where: l c3 is the critical anchorage length of the cement-soil anchor solid in Zone I; d2 is the diameter of the cement-soil anchor solid; E m1 is the comprehensive elastic modulus of the cement-soil anchor solid in Zone I; G s is the shear modulus of the surrounding soil mass;

[0031] The critical anchorage length of the cement-soil anchor solid in Zone I can be determined according to this formula;

[0032] Step 4. Determine the bearing capacity of the cement-soil anchor solid in Zone I:

[0033] The bearing capacity of the cement-soil anchor solid in Zone I is the smaller value between the compressive bearing capacity of the cement-soil anchor solid in Zone I at the front end of the cement slurry anchor solid and the interfacial frictional resistance between the cement-soil anchor solid in Zone I and the surrounding rock and soil mass;

[0034] The compressive bearing capacity of the cement-soil anchor solid in Zone I at the front end of the cement slurry anchor solid is:

[0035]

[0036] Where: σ maxm is the ultimate compressive stress that the cement-soil anchor solid can withstand, and d2 is the diameter of the cement-soil anchor solid;

[0037] The interfacial frictional resistance between the cement-soil anchor body in Zone I and the surrounding rock and soil mass is:

[0038]

[0039] In the formula: τ u2 is the shear strength of the interface between the cement-soil anchor body and the surrounding rock and soil mass; l m1 is the length of the cement-soil anchor body in Zone I; l c3 is the critical length of the cement-soil anchor body in Zone I;

[0040] According to Eqs. (25) and (26), the bearing capacity of the cement-soil anchor body in Zone I is:

[0041] P6 = min{P4, P5} (27)

[0042] Step 5. Determine the critical anchorage length of the cement-soil anchor body in Zone II

[0043] Its expression is:

[0044]

[0045] In the formula: l c4 is the critical anchorage length of the cement-soil anchor body in Zone II; d2 is the diameter of the cement-soil anchor body; E m2 is the comprehensive elastic modulus of the cement-soil anchor body in Zone II; G s is the shear modulus of the surrounding soil mass;

[0046] According to this formula, the critical anchorage length of the cement-soil anchor body in Zone II can be determined;

[0047] Step 6. Determine the bearing capacity of the cement-soil anchor body in Zone II:

[0048] When the cement-soil anchor body in Zone II is in normal working condition, there should be no slippage between the cement-soil anchor body in Zone II and the surrounding rock and soil mass. At the same time, the cement slurry anchor body inside the cement-soil anchor body in Zone II should also be in normal working condition;

[0049] The bearing capacity of the cement-soil anchor body in Zone II is the smaller value between the interfacial frictional resistance between the cement-soil anchor body in Zone II and the surrounding rock and soil mass and the bearing capacity of the cement slurry anchor body inside the cement-soil anchor body in Zone II;

[0050] In practical engineering applications, the anchorage length of the cement slurry anchor body is much smaller than its critical anchorage length. Therefore, the shear stress distribution at the interface between the cement slurry anchor body and the cement-soil anchor body tends to be uniform. The anchorage length of the cement-soil anchor body in Zone II is also much smaller than the critical anchorage length of the cement-soil anchor body in Zone II. The shear stress distribution at the interface between the cement-soil anchor body in Zone II and the surrounding rock and soil mass can be simplified to a uniform distribution. For the sake of safety, a corresponding reduction coefficient β = 0.75 is multiplied by the ultimate shear stress at the interface;

[0051] The interface frictional resistance between the cement-soil anchor body in Zone II and the surrounding rock and soil mass is:

[0052] P7 = βπd2τ u2 l m2 (29)

[0053] Where: l m2 is the length of the cement-soil anchor body in Zone II;

[0054] According to Eqs. (23) and (29), the bearing capacity of the cement-soil anchor body in Zone II is:

[0055] P8 = min{P7, P 11} (30)

[0056] Step 7. Determine the bearing capacity of the overall anchor body

[0057] According to Eqs. (27) and (30), the bearing capacity of the bag-type recoverable pressure-type anchor rod is:

[0058] P9 = P6 + P8 (31)

[0059] Step 8. Determine the bearing capacity of the bag-type recoverable pressure-type anchor rod:

[0060] The overall bearing capacity of the bag-type recoverable pressure-type anchor rod should be the smaller value among the overall bearing capacity of the anchor body, the bearing capacity of the steel strand, and the normal working ultimate bearing capacity of the unlocking anchor;

[0061] The bearing capacity of the steel strand is:

[0062] P 10 = ξf py A s (32)

[0063] Where: ξ is the strength reduction coefficient of the steel strand, which can be taken as 0.80 - 0.95; f py is the design value of the tensile strength of the steel strand; A s is the effective cross-sectional area of the steel strand;

[0064] The overall bearing capacity of the bag-type recoverable pressure-type anchor rod is:

[0065] P 12= min{P9, P 10 , P 11} (33)

[0066] where: P 11 is the normal working ultimate bearing capacity of the unlocking anchor, provided by the manufacturer's test report.

[0067] Technical effects of the present invention:

[0068] 1. The action mechanism of the bag-type recoverable pressure-type anchor is more complex than that of traditional tension-type and pressure-type anchors, and there are many load transfer interfaces. Without the bag, the load is directly transferred to the cement-soil anchor through the carrier, causing point displacement of the cement-soil anchor at the carrier position, and the stress level of the cement-soil anchor in front of the carrier is high, making it prone to compressive failure. The interfacial shear stress between the cement-soil anchor and the soil reaches its peak at the carrier position and rapidly decays towards the front end of the cement-soil anchor, with a small distribution range. By setting up the bag to form a cement slurry anchor, the external load is first transferred to the cement slurry anchor through the carrier and then to the cement-soil anchor. The load received by the cement slurry anchor is jointly borne by the interfacial shear stress between the cement slurry and the cement-soil anchor and the cement-soil anchor in front of the cement slurry anchor. Since the deformation modulus of the cement slurry anchor is much larger than that of the cement-soil anchor, when an external load acts, the point displacement originally generated at the carrier position inside the cement-soil anchor becomes a uniformly distributed linear displacement along the interface between the cement slurry and the cement-soil anchor, thus generating corresponding uniform shear stress. According to the Mindlin displacement solution and the generalized Hooke's law, the interfacial shear stress between the cement-soil anchor and the surrounding soil is also uniformly distributed. Therefore, the shear stress between the cement-soil anchor and the surrounding soil within the range where the cement slurry anchor is set tends to be averaged, greatly improving the contribution of the cement-soil anchor within this range to the overall bearing capacity of the anchor. The existence of the cement slurry anchor increases the compressive area of the cement-soil anchor at the front end and reduces its stress level, making it not easily prone to compressive failure. Moreover, the cement slurry anchor has a high compressive strength and is not easily prone to compressive failure when bearing the load from the carrier, and can make full use of the bearing performance of each part of the anchor.

[0069] 2) In the present invention, by analyzing the stress mechanism of each part of the bag-type recoverable pressure-type anchor and calculating the bearing capacity of each part, the ultimate bearing capacity data of the anchor can be obtained simply, efficiently and accurately, overcoming the defect that there is no calculation method for bag-type recoverable pressure-type anchors at home and abroad, and providing a reliable basis for engineering design, reducing construction costs while improving safety. Description of the Drawings

[0070] Figure 1 is the overall structure diagram of the bag-type recoverable pressure-type anchor.

[0071] Figure 2It is the sectional view of each position of the bag-type recyclable pressure-type anchor rod.

[0072] Figure 3 It is the schematic diagram of the partition of the cement-soil anchor body.

[0073] Figure 4 It is the force mechanism diagram of the tensile-type anchor rod.

[0074] Figure 5 It is the model diagram of the shear displacement of the soil around the tensile-type anchor rod.

[0075] Figure 6 It is the diagram of the shear stress distribution mode within the critical anchorage length.

[0076] Figure 7 It is the simplified calculation diagram of the failure body.

[0077] Figure 8 It is the force diagram of the failure body in area ①.

[0078] Figure 9 It is the force diagram of the failure body in area ②.

[0079] Figure 10 It is the force diagram of a micro-segment of the failure body in area ②.

[0080] Figure 11 It is the force mechanism diagram of the cement-soil anchor body of the bag-type recyclable pressure-type anchor rod.

[0081] Figure 12 It is the force mechanism diagram of the cement slurry anchor body of the bag-type recyclable pressure-type anchor rod.

[0082] Figure 13 It is the diagram of the shear stress distribution at the interface of the cement-soil anchor body of the bag-type recyclable pressure-type anchor rod.

[0083] Figure 14 It is the diagram of the shear stress distribution at the interface of the cement slurry anchor body of the bag-type recyclable pressure-type anchor rod.

[0084] Reference signs:

[0085] 1. Anchor head and anchor; 2. Steel strand; 3. Protection sleeve; 4. Cement-soil anchor body; 5. Bag; 6. Cement slurry anchor body; 7. Carrier; 8. Unlocking anchor protection sleeve. Detailed implementation manners

[0086] To further elaborate on the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following, in combination with the accompanying drawings and preferred embodiments, details the specific implementation manners, structures, features and their effects of the present invention as follows.

[0087] Refer to Figures 1-3As shown in the figure, the bag-type recyclable pressure-type anchor rod provided by the present invention includes an anchor head anchor 1, a rod body, a carrier 7 and an anchor solid. The rod body includes a steel strand 2 and a protective sleeve 3. The protective sleeve 3 is sleeved around the steel strand 2. The carrier 7 is located at the end of the anchor rod body and is connected to the steel strand 2. The inner end of the sleeve 3 is fixed on the carrier 7, and the joint between the two is sealed to ensure that the slurry will not enter. The carrier 7 is a component that converts the tension received by the steel strand 2 into the pressure acting on the anchor solid. The anchor solid includes a cement-soil anchor solid 4 and a cement slurry anchor solid 6. The cement-soil anchor solid 4 is formed by high-pressure jet grouting of cement slurry and the surrounding soil. The cement slurry anchor solid 6 is formed by injecting cement slurry into the bag 5 wrapped around the rod body through a reserved grouting pipe. The rear end of the cement slurry anchor solid 6 is provided with the bearing member 7, an unlocking anchor and an unlocking anchor protection sleeve 8. The unlocking anchor is located in the carrier 7 at the end of the steel strand 2, which connects the steel strand 2 and the carrier 7, and is a component that can be separated from the carrier 7 through an unlocking action. The unlocking anchor protection sleeve 8 is located outside the unlocking anchor and is connected to the bearing plate 7, and should have good sealing performance to prevent the slurry from leaking into the unlocking device during grouting, resulting in the inability to recycle the anchor rod in the later stage.

[0088] Referring to Figures 1-14 As shown in the figure, when the anchor rod is subjected to an external load, the external load is finally transmitted to the rock and soil mass through the interfacial shear stress between the anchor solid and the rock and soil mass. This interfacial shear stress decays along the length direction of the anchor rod. After exceeding a certain length, the shear stress is zero. Therefore, the shear stress of the anchor rod is only distributed within a certain length, and the length from the peak point of the shear stress to the zero point of the shear stress is the critical anchorage length. Within the critical anchorage length range, the distribution pattern of the shear stress is triangular, as shown in Figure 6 .

[0089] Within the critical anchorage length range, the magnitude of the shear stress at any point x away from the top end around the anchor solid is:

[0090]

[0091]

[0092] In the formula: l c is the critical anchorage length of the anchor solid; d is the diameter of the anchor solid; R is the load at the front end of the anchor solid; x is the distance from the load-bearing end of the anchor solid; τ u is the interfacial shear stress between the top end of the anchor solid and the surrounding soil.

[0093] According to formula (1), the axial force of the anchor solid is obtained as:

[0094]

[0095] According to formula (3) and Hooke's law, the displacement at the top end of the anchor solid is obtained as:

[0096]

[0097] Where: Δ Top is the displacement at the load acting end of the anchor solid; E b is the elastic modulus of the anchor solid;

[0098] A b is the cross-sectional area of the anchor solid.

[0099] Based on the similarity of the uplift bearing mechanism and deformation characteristics between the anchor rod and the uplift pile, without considering the increase of the vertical stress of the surrounding soil, the surrounding soil can adopt a shear displacement model similar to that of the uplift pile, as shown in Figure 5 .

[0100] According to the shear displacement model, the shear stress of the soil at a distance x from the top of the anchor solid and a distance r from the axis of the anchor solid is:

[0101]

[0102] The corresponding shear strain at this position is:

[0103]

[0104] Where: U is the soil displacement along the axis of the anchor solid; V is the soil displacement along the diameter of the anchor solid; G s is the shear modulus of the soil.

[0105] According to Eqs. (5) and (6), it can be obtained that:

[0106]

[0107] Where: r m is the influence radius of the anchor rod.

[0108] When r = d and x = 0:

[0109]

[0110] According to the deformation coordination condition, the displacement at the front end of the anchor solid is equal to the displacement of the surrounding soil, that is:

[0111] Δ Top = U(0, d) (9)

[0112] According to engineering experience, taking r m ≈ 20d, the critical anchorage length of the anchor solid is obtained as:

[0113]

[0114] When calculating the critical anchorage length, a simplified model is adopted for the shear stress distribution, which is more uniform than the actual distribution pattern. Therefore, the critical anchorage length obtained from Equation (10) is less than the actual value. For the sake of safety, multiply by the correction factor α = 1.2 to obtain:

[0115]

[0116] According to the calculation formula of the critical anchorage length and the distribution pattern of the shear stress, the interfacial frictional resistance between the anchor body and the surrounding structure can be calculated.

[0117] The failure mode of the cement slurry anchor body at the front end of the load-bearing body and the cement-soil anchor body at the front end of the cement slurry anchor body (hereinafter referred to as the failure body) under compression is similar to the failure mode of the rock foundation of a circular shallow foundation, which is overall shear failure. The force diagram at the time of failure of the failure body under compression is shown in Figure 7 When the cement slurry anchor body or the cement-soil anchor body at the time of failure is divided into three parts: ①, ②, and ③. The force analysis diagrams of parts ① and ② are shown in Figure 8 、 Figure 9 、 Figure 10 respectively.

[0118] By performing an axial equilibrium analysis on the forces acting on area ①, the following can be obtained:

[0119]

[0120]

[0121] In the formula: σ max is the compressive bearing capacity of the failure body; σ s is the side wall pressure received by the failure body;

[0122] σ1 is the normal stress between the failure bodies in areas ① and ②; τ1 is the shear stress between the failure bodies in areas ① and ②; α is the angle between the failure edge of the shear failure body ① and the horizontal direction; c is the cohesion of the failure body; is the internal friction angle of the failure body; D1 is the diameter of the failure body; D2 is the diameter of the compression zone.

[0123] By performing an axial equilibrium analysis on the forces acting on area ②, the following can be obtained:

[0124]

[0125] In the formula: σ2 is the normal stress between the failure bodies in areas ② and ③; τ2 is the shear stress between the failure bodies in areas ② and ③.

[0126] For the forces acting on area ②, ∑M = 0, and the following can be obtained:

[0127]

[0128] where: \(l_1\) is the distance of AC; \(l_2\) is the distance of EC;

[0129] Using the elastic mechanics solution of the cylinder and the generalized Hooke's law, according to the deformation coordination conditions of the anchor solid and the sidewall soil mass, we can obtain:

[0130] \(\sigma\) z \(= k\sigma\) max (16)

[0131] where: \(E\) m is the elastic modulus of the structure around the failure body; \(\mu\) m is the Poisson's ratio of the structure around the failure body; \(E\) r is the elastic modulus of the failure body; \(\mu\) r is the Poisson's ratio of the failure body.

[0132] According to equations (12)-(16), we can obtain:

[0133]

[0134] where: \(m_1 = \cos\alpha+\tan\alpha\sin\alpha\);

[0135] According to equations (12) and (17), the compressive bearing capacity of the failure body can be determined as:

[0136]

[0137]

[0138] Referring to Figures 1-14 as shown, the bearing capacity calculation method of the above-mentioned bag-type recoverable pressure-type anchor rod provided by the present invention includes the following steps:

[0139] Step 1. Determine the critical anchorage length of the cement slurry anchor solid:

[0140] Its expression is:

[0141]

[0142] where: \(l\) c1 is the critical anchorage length of the cement slurry anchor solid; \(d\) is the diameter of the cement slurry anchor solid; \(E\) c1 is the comprehensive elastic modulus of the cement slurry anchor solid; \(G\) b is the shear modulus of the cement-soil anchor solid;

[0143] The critical anchorage length of the cement slurry anchor solid can be determined according to this formula;

[0144] Step 2. Determine the bearing capacity of the cement slurry anchor solid:

[0145] When the cement slurry anchor solid is in normal working condition, it should not be damaged by compression, and at the same time, it should not slip off from the surrounding structure.

[0146] The bearing capacity of the cement slurry anchor solid is the smaller value of the compressive bearing capacity of the cement slurry anchor solid at the front end of the bearing body and the frictional resistance at the interface between the cement slurry anchor solid and the surrounding cement-soil anchor solid.

[0147] The compressive bearing capacity of the cement slurry anchor solid at the front end of the bearing body is calculated according to Equation (19) as follows:

[0148]

[0149] In the formula: σ maxr is the ultimate compressive stress that the cement slurry anchor solid can withstand, and d1 is the diameter of the cement slurry anchor solid.

[0150] The frictional resistance at the interface between the cement slurry anchor solid and the surrounding structure is:

[0151]

[0152] In the formula: τ u1 is the interface shear strength between the cement slurry anchor solid and the surrounding structure; l r1 is the length of the cement slurry anchor solid; l c1 is the critical length of the cement slurry anchor solid.

[0153] According to Equations (21) and (22), the bearing capacity of the cement slurry anchor solid is:

[0154] P3 = min{P1, P2} (23)

[0155] Step 3. Determine the critical anchorage length of the cement-soil anchor solid in Zone I:

[0156] Its expression is:

[0157]

[0158] In the formula: l c3 is the critical anchorage length of the cement-soil anchor solid in Zone I; d2 is the diameter of the cement-soil anchor solid; E m1 is the comprehensive elastic modulus of the cement-soil anchor solid in Zone I; G s is the shear modulus of the surrounding soil.

[0159] The critical anchorage length of the cement-soil anchor solid in Zone I can be determined according to this formula.

[0160] Step 4. Determine the bearing capacity of the cement-soil anchor solid in Zone I:

[0161] The bearing capacity of the cement-soil anchor body in Zone I is the smaller value between the compressive bearing capacity of the cement-soil anchor body in Zone I at the front end of the cement slurry anchor body and the interfacial frictional resistance between the cement-soil anchor body in Zone I and the surrounding rock and soil mass;

[0162] The compressive bearing capacity of the cement-soil anchor body in Zone I at the front end of the cement slurry anchor body is:

[0163]

[0164] In the formula: σ maxm is the ultimate compressive stress that the cement-soil anchor body can bear, and d2 is the diameter of the cement-soil anchor body;

[0165] The interfacial frictional resistance between the cement-soil anchor body in Zone I and the surrounding rock and soil mass is:

[0166]

[0167] In the formula: τ u2 is the interfacial shear strength between the cement-soil anchor body and the surrounding rock and soil mass; l m1 is the length of the cement-soil anchor body in Zone I; l c3 is the critical length of the cement-soil anchor body in Zone I;

[0168] According to formulas (25) and (26), the bearing capacity of the cement-soil anchor body in Zone I is:

[0169] P6 = min{P4, P5} (27)

[0170] Step 5. Determine the critical anchorage length of the cement-soil anchor body in Zone II

[0171] Its expression is:

[0172]

[0173] In the formula: l c4 is the critical anchorage length of the cement-soil anchor body in Zone II; d2 is the diameter of the cement-soil anchor body; E m2 is the comprehensive elastic modulus of the cement-soil anchor body in Zone II; G s is the shear modulus of the surrounding soil mass;

[0174] The critical anchorage length of the cement-soil anchor body in Zone II can be determined according to this formula;

[0175] Step 6. Determine the bearing capacity of the cement-soil anchor body in Zone II:

[0176] When the cement-soil anchor body in Zone II is in normal working condition, there should be no slippage between the cement-soil anchor body in Zone II and the surrounding rock and soil mass. At the same time, the cement slurry anchor body inside the cement-soil anchor body in Zone II should also be in normal working condition;

[0177] The bearing capacity of the soil-cement anchor body in Zone II is the smaller value between the interfacial frictional resistance between the soil-cement anchor body in Zone II and the surrounding rock and soil masses and the bearing capacity of the cement slurry anchor body inside the soil-cement anchor body in Zone II;

[0178] In practical engineering applications, the anchorage length of the cement slurry anchor body is much smaller than its critical anchorage length. Therefore, the shear stress distribution at the interface between the cement slurry anchor body and the soil-cement anchor body tends to be uniform; the anchorage length of the soil-cement anchor body in Zone II is also much smaller than the critical anchorage length of the soil-cement anchor body in Zone II, and the shear stress distribution at the interface between the soil-cement anchor body in Zone II and the surrounding rock and soil masses can be simplified to a uniform distribution. For the sake of safety, a corresponding reduction coefficient β = 0.75 is multiplied by the ultimate shear stress at the interface;

[0179] The interfacial frictional resistance between the soil-cement anchor body in Zone II and the surrounding rock and soil masses is:

[0180] P7 = βπd2τ u2 l m2 (29)

[0181] Where: l m2 is the length of the soil-cement anchor body in Zone II;

[0182] According to Eqs. (23) and (29), the bearing capacity of the soil-cement anchor body in Zone II is:

[0183] P8 = min{P7, P 11} (30)

[0184] Step 7. Determine the bearing capacity of the overall anchor body

[0185] According to Eqs. (27) and (30), the bearing capacity of the bag-type recoverable pressure-type anchor rod is:

[0186] P9 = P6 + P8 (31)

[0187] Step 8. Determine the bearing capacity of the bag-type recoverable pressure-type anchor rod:

[0188] The overall bearing capacity of the bag-type recoverable pressure-type anchor rod should be the smaller value among the overall bearing capacity of the anchor body, the bearing capacity of the steel strand, and the normal working ultimate bearing capacity of the unlocking anchor;

[0189] The bearing capacity of the steel strand is:

[0190] P 10 = ξf py A s (32)

[0191] Where: ξ is the strength reduction coefficient of the steel strand, which can be taken as 0.80 - 0.95; f py is the design value of the tensile strength of the steel strand; A sis the effective cross-sectional area of the steel strand;

[0192] The overall bearing capacity of the bag-type recoverable pressure-type anchor bolt is:

[0193] P 12 = min{P9, P 10 , P 11} (33)

[0194] Where: P 11 is the normal working ultimate bearing capacity of the unlocking anchor, provided by the manufacturer's test report.

[0195] The above are only the preferred embodiments of the present invention and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to equivalent embodiments by using the disclosed technical content within the scope of the technical solution of the present invention. However, as long as it does not depart from the content of the technical solution of the present invention, any brief modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A method for calculating the bearing capacity of a pouch-type recyclable pressure-type anchor rod, characterized in that: The described bag-type recyclable pressure-type anchor rod includes an anchor head anchor, a rod body, a carrier, and an anchor solid. The rod body includes a steel strand and a protective casing. The protective casing is sleeved around the steel strand. The carrier is located at the end of the anchor rod body and is connected to the steel strand. The anchor solid includes a cement-soil anchor solid and a cement slurry anchor solid. The cement-soil anchor solid is formed by high-pressure jet grouting of cement slurry and the surrounding soil. The cement slurry anchor solid is formed by injecting cement slurry into the bag wrapped around the rod body through a reserved grouting pipe. The described calculation method includes the following steps: Step 1. Determine the critical anchorage length of the cement slurry anchor solid in the bearing area: Its expression is: where: l c1 is the critical anchorage length of the cement slurry anchor solid; d is the diameter of the cement slurry anchor solid; E c1 is the comprehensive elastic modulus of the cement slurry anchor solid; G b is the shear modulus of the cement-soil anchor solid; The critical anchorage length of the cement slurry anchor solid can be determined according to this formula; Step 2. Determine the bearing capacity of the cement slurry anchor solid: When the cement slurry anchor solid is in a normal working state, it should not be damaged by compression, and at the same time, it should not slip off from the surrounding structure; The bearing capacity of the cement slurry anchor solid is the smaller value of the compressive bearing capacity of the cement slurry anchor solid at the front end of the carrier and the interfacial frictional resistance between the cement slurry anchor solid and the surrounding cement-soil anchor solid; The compressive bearing capacity of the cement slurry anchor solid at the front end of the carrier is: Where: σ maxr is the ultimate compressive stress that the cement slurry anchor can withstand, and d1 is the diameter of the cement slurry anchor; The interfacial frictional resistance between the cement slurry anchor solid and the surrounding structure is: Where: τ u1 is the interfacial shear strength between the cement slurry anchor solid and the surrounding structure; l r1 is the length of the cement slurry anchor solid; l c1 is the critical length of the cement slurry anchor solid; According to formulas (21) and (22), the bearing capacity of the cement slurry anchor solid is: P3 = min{P1, P2} (23) Step 3. Determine the critical anchorage length of the cement-soil anchor solid in Zone I. The cement-soil anchor solid in Zone I is the transverse length section of the cement-soil anchor solid excluding the section with the cement slurry anchor solid: Its expression is: Where: l c3 is the critical anchorage length of the cement-soil anchor body in Zone I; d2 is the diameter of the cement-soil anchor body; E m1 is the comprehensive elastic modulus of the cement-soil anchor body in Zone I; G s is the shear modulus of the surrounding soil; The critical anchorage length of the cement-soil anchor solid in Zone I can be determined according to this formula; Step 4. Determine the bearing capacity of the cement-soil anchor solid in Zone I: The bearing capacity of the cement-soil anchor solid in Zone I is the smaller value of the compressive bearing capacity of the cement-soil anchor solid in Zone I at the front end of the cement slurry anchor solid and the interfacial frictional resistance between the cement-soil anchor solid in Zone I and the surrounding rock and soil; The compressive bearing capacity of the cement-soil anchor solid in Zone I at the front end of the cement slurry anchor solid is: The interfacial frictional resistance between the cement-soil anchor solid in Zone I and the surrounding rock and soil is: Where: σ maxm is the ultimate compressive stress that the cement-soil anchor body can withstand, and d2 is the diameter of the cement-soil anchor body; According to formulas (25) and (26), the bearing capacity of the cement-soil anchor solid in Zone I is: Where: τ u2 is the shear strength of the interface between the cement-soil anchor body and the surrounding rock and soil mass; l m1 is the length of the cement-soil anchor body in Zone I; l c3 is the critical length of the cement-soil anchor body in Zone I; P6 = min{P4, P5} (27) Step 5. Determine the critical anchorage length of the cement-soil anchor solid in Zone II. The cement-soil anchor solid in Zone II is the transverse length section of the cement-soil anchor solid with the cement slurry anchor solid Its expression is: According to this formula, the critical anchorage length of the cement-soil anchor solid in Zone II can be determined; Where: l c4 is the critical anchorage length of the soil-cement anchor body in Zone II; d2 is the diameter of the soil-cement anchor body; E m2 is the comprehensive elastic modulus of the soil-cement anchor body in Zone II; G s is the shear modulus of the surrounding soil; Step 6. Determine the bearing capacity of the cement-soil anchor solid in Zone II: When the cement-soil anchor solid in Zone II is in a normal working state, there should be no slippage between the cement-soil anchor solid in Zone II and the surrounding rock and soil. At the same time, the cement slurry anchor solid inside the cement-soil anchor solid in Zone II should also be in a normal working state; The bearing capacity of the cement-soil anchor solid in Zone II is the smaller value of the interfacial frictional resistance between the cement-soil anchor solid in Zone II and the surrounding rock and soil and the bearing capacity of the cement slurry anchor solid inside the cement-soil anchor solid in Zone II; ​ In practical engineering applications, the anchorage length of the cement slurry anchor body is much smaller than its critical anchorage length. Therefore, the shear stress distribution at the interface between the cement slurry anchor body and the cement soil anchor body tends to be uniform. The anchorage length of the cement soil anchor body in Zone II is also much smaller than the critical anchorage length of the cement soil anchor body in Zone II. The shear stress distribution at the interface between the cement soil anchor body in Zone II and the surrounding rock and soil mass can be simplified as a uniform distribution. For safety considerations, a corresponding reduction coefficient β = 0.75 is multiplied by the ultimate shear stress at the interface. The interface frictional resistance between the cement soil anchor body in Zone II and the surrounding rock and soil mass is: P7 = βπd2τ u2 l m2 (29) where: l m2 is the length of the soil-cement anchor solid in Zone II; According to Eqs. (23) and (29), the bearing capacity of the cement soil anchor body in Zone II is: P8 = min{P7, P 11} (30) Step 7. Determine the bearing capacity of the overall anchor body According to Eqs. (27) and (30), the bearing capacity of the bag-type recoverable pressure-type anchor rod is: P9 = P6 + P8 (31) Step 8. Determine the bearing capacity of the bag-type recoverable pressure-type anchor rod: The overall bearing capacity of the bag-type recoverable pressure-type anchor rod should be the smaller value among the overall bearing capacity of the anchor body, the bearing capacity of the steel strand, and the normal working ultimate bearing capacity of the unlocking anchor tool; The bearing capacity of the steel strand is: P 10 = ξf py A s (32) Where: ξ is the strength reduction factor of the steel strand, taking values from 0.80 to 0.95; f py is the design value of the tensile strength of the steel strand; A s is the effective cross-sectional area of the steel strand; The overall bearing capacity of the bag-type recoverable pressure-type anchor rod is: P 12 = min{P9, P 10 , P 11}} (33) Where: P 11 is the normal working ultimate bearing capacity of the unlocking anchor, provided by the manufacturer's test report.

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