The calculation method of stability coefficient of rock mass horizontal resistance for unequal-depth anchorage anti-slide stability

Abstract

The application discloses a kind of unequal-depth anchorage anti-sliding stability coefficient calculation method considering rock mass horizontal resistance, including the simplified analysis model of the calculation of middle wall step horizontal resistance is constructed according to the limit failure mode of middle wall rock mass, the force balance equation when wedge limit failure is obtained;The force balance equation parallel to the direction of sliding surface and perpendicular to the direction of sliding surface is constructed according to the force balance equation when wedge limit failure, and the expression of the horizontal limit bearing capacity of middle wall rock mass is derived and obtained;Middle wall rock mass horizontal limit bearing capacity is substituted into the anti-sliding stability coefficient calculation formula of anchoring foundation as anti-sliding stability horizontal force, and the anti-sliding stability coefficient of anchoring foundation considering the influence of rock mass horizontal resistance on unequal-depth excavation anchoring foundation anti-sliding stability is obtained;The application considers the resistance contribution of middle wall rock mass when calculating anchoring anti-sliding, can more accurately calculate anchoring anti-sliding safety factor, provides theoretical basis for optimizing anchoring foundation design scale and pit excavation size.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical mechanics, and more specifically, relates to a method for calculating the anti-sliding stability coefficient of unequal-depth anchorages that takes into account the horizontal resistance of rock mass. Background Technology

[0002] The stability analysis of anchor foundations includes two parts: anti-overturning stability analysis and anti-sliding stability analysis. The anti-sliding stability analysis mainly prevents sliding between the base surface and the base soil under horizontal thrust.

[0003] According to the "Design Code for Highway Suspension Bridges" (JTG D65T), the anti-sliding stability coefficient of anchorage foundations has its own inherent calculation expression. For stepped anchorage foundations with unequal excavation depths, since there is currently no calculation formula or design basis for the horizontal resistance of the stepped middle wall, current designs generally do not consider the horizontal resistance of the middle wall step, but only regard it as a safety reserve, assuming it as a flat-bottomed anchorage for calculation and analysis. However, the bottom slab of the anchorage foundation often uses moderately weathered rock strata as the bearing layer, and the horizontal resistance provided by the stepped rock mass with unequal depth middle walls cannot be ignored.

[0004] Therefore, there is an urgent need for a calculation method that takes into account the resistance contribution of the central rock mass and can more accurately calculate the anchorage anti-slip safety factor. Summary of the Invention

[0005] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a method for calculating the anti-sliding stability coefficient of unequal-depth anchorages that considers the horizontal resistance of rock mass. It derives a calculation formula for the horizontal resistance of the central wall step. By considering the resistance contribution of the central wall rock mass when calculating the anti-sliding of the anchorage, the anti-sliding safety factor of the anchorage can be calculated more accurately. Furthermore, it provides a theoretical basis for optimizing the design scale of the anchorage foundation and the excavation size of the foundation pit, thereby saving project costs, shortening the construction period, and making the anchorage foundation design more scientific and reasonable, resulting in significant economic and social benefits.

[0006] To achieve the above objectives, the present invention provides a method for calculating the anti-sliding stability coefficient of anchorages of unequal depths that considers the horizontal resistance of rock mass, comprising the following steps:

[0007] S1: Based on the ultimate failure mode of the central wall rock mass, a simplified analytical model for calculating the horizontal resistance of the central wall steps is constructed to obtain the force balance equation at the ultimate failure of the wedge-shaped body;

[0008] S2: Based on the force balance equation at the ultimate failure of the wedge, construct the force balance equations parallel to the slip surface and perpendicular to the slip surface, and derive the expression for the horizontal ultimate bearing capacity of the middle wall rock mass;

[0009] S3: Substitute the horizontal ultimate bearing capacity of the middle wall rock mass as the anti-sliding stability horizontal force into the calculation formula of the anti-sliding stability coefficient of the anchor foundation to obtain the anti-sliding stability coefficient of the anchor foundation considering the influence of the horizontal resistance of the rock mass on the anti-sliding stability of the anchor foundation in unequal depth excavation.

[0010] Furthermore, the force balance equation for the ultimate failure of the wedge in step S1 is specifically expressed by equation (1):

[0011] F 滑动 =F 抗滑 (1),

[0012] Among them, F 滑动 F represents the sliding force of the wedge at ultimate failure. 抗滑 This represents the anti-slip force of the wedge at the point of ultimate failure.

[0013] Furthermore, obtaining the expression for the ultimate horizontal bearing capacity of the middle wall rock mass in step S2 includes the following steps:

[0014] Step S21: Based on the fact that the sliding force of the wedge at the ultimate failure is equal to the component of the wedge's weight along the direction parallel to the slip surface, the cohesion between the wedge and the rock mass at the slip surface, the component of the wedge under the gravity load of the overlying anchor along the direction parallel to the slip surface, and the sliding friction force of the wedge on the slip surface, construct the force balance equation parallel to the slip surface.

[0015] Step S22: Construct a force balance equation perpendicular to the slip surface based on the fact that the component of the wedge's weight in the direction perpendicular to the slip surface is equal to the sum of the component of the anchor's gravity load in the direction perpendicular to the slip surface and the component of the horizontal ultimate bearing capacity of the central wall rock mass in the direction perpendicular to the slip surface.

[0016] Step S23: Let the sum of the weight of the wedge and the weight load of the overlying anchor on the wedge be a fixed value, and obtain the second form of the force balance equation perpendicular to the slip surface direction and the expression for the sum of the component of the wedge's weight along the direction parallel to the slip surface and the component of the wedge's weight along the direction parallel to the slip surface under the action of the overlying anchor weight.

[0017] Step S24: Based on the second form of the force balance equation perpendicular to the slip surface and the expression for the sum of the component of the wedge's weight along the direction parallel to the slip surface and the component of the wedge's weight along the direction parallel to the slip surface under the weight load of the overlying anchor, obtain the second expression for the anti-slip force of the wedge at ultimate failure.

[0018] Step S25: Based on the fact that the sliding force of the wedge at ultimate failure is the component of the horizontal ultimate bearing capacity of the middle wall rock mass in the direction parallel to the slip surface, the third expression for the sliding force of the wedge at ultimate failure is obtained;

[0019] Step S26: Substitute the second expression for the anti-sliding force of the wedge at ultimate failure and the third expression for the sliding force of the wedge at ultimate failure into the force balance equation at ultimate failure of the wedge to derive the expression for the horizontal ultimate bearing capacity of the middle wall rock mass.

[0020] Furthermore, the force balance equation parallel to the slip surface in step S21 is expressed by equation (2):

[0021]

[0022] Where τ is the direction parallel to the slip surface; g is the weight of the wedge; g τ σB is the component of the wedge's weight along the τ direction; c is the rock mass cohesion, in kPa; L is the slip surface length; cL is the cohesion between the wedge and the rock mass at the slip surface; σB is the anchorage gravity load; σB τ R is the component of the force on the wedge body under the gravity load of the overlying anchor along the direction parallel to the slip surface (τ direction); R is the component of the force between the wedge body and the slip surface of the rock mass in the direction perpendicular to the slip surface. The friction angle within the rock mass is expressed in degrees (°). The friction coefficient between the wedge and the rock mass slip surface.

[0023] Furthermore, the force balance equation perpendicular to the slip surface in step S22 is expressed by equation (3):

[0024] R=[(g+σB)cosθ+E pn (3)

[0025] Where n is the direction perpendicular to the slip surface; g is the weight of the wedge; θ is the dip angle of the slip surface, in degrees; g cosθ is the component of the wedge's weight in the n direction; σB is the anchorage gravity load; σB cosθ is the component of the anchorage gravity load in the n direction; E p E represents the ultimate horizontal bearing capacity of the rock mass in the middle wall. pn Let E be the component of the horizontal ultimate bearing capacity of the rock mass in the n-direction; where E pn =E p sinθ;

[0026] Furthermore, the second expression for the force balance equation perpendicular to the slip surface in step S23 is expressed by equation (5):

[0027] R = G cosθ + E p sinθ (5)

[0028] Where G is the sum of the weight of the wedge and the weight load of the overlying anchor on the wedge.

[0029] Furthermore, in step S24: the second expression for the anti-slip force of the wedge at ultimate failure is expressed by equation (7):

[0030]

[0031] Furthermore, in step S25: the third expression for the sliding force of the wedge at ultimate failure is expressed by equation (8):

[0032] F 滑动 =E pτ =E p cosθ (8)

[0033] Among them, E pτ This is the component of the horizontal ultimate bearing capacity of the rock mass in the middle wall in the τ direction.

[0034] Furthermore, the expression for the ultimate horizontal bearing capacity of the rock mass in the middle wall in step S26 is given by equation (10):

[0035]

[0036] In the formula: θ is the dip angle of the slip surface, in degrees; ω is the internal friction angle of the rock mass, in °; c is the cohesion of the rock mass, in kPa; L is the length of the slip surface; G is the sum of the weight of the wedge and the weight load of the overlying anchor on the wedge.

[0037] Furthermore, the anti-sliding stability coefficient of the anchor foundation, which considers the influence of the horizontal resistance of the rock mass on the anti-sliding stability of the anchor foundation in step S3, is expressed by equation (13):

[0038]

[0039] Where, k d The sliding stability coefficient of the anchor foundation is given by considering the influence of horizontal rock mass resistance on the sliding stability of the anchor foundation in unequal depth excavation; μ is the friction coefficient between the foundation ground and the foundation soil; P i For the i-th vertical force; ∑P i E represents the total vertical force. p The ultimate horizontal bearing capacity of the rock mass in the middle wall; ∑E p H represents the total horizontal ultimate bearing capacity of the rock mass in the middle wall; iS For the i-th sliding horizontal force; ∑H iS This represents the sum of the sliding horizontal forces.

[0040] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects:

[0041] This invention provides a method for calculating the anti-sliding stability coefficient of anchorages at unequal depths, considering the horizontal resistance of rock mass. Based on the ultimate failure mode of the central wall rock mass, a simplified analytical model for calculating the horizontal resistance of the central wall steps is constructed to obtain the force balance equation at the ultimate failure of the wedge-shaped body. Based on the force balance equation at the ultimate failure of the wedge-shaped body, force balance equations parallel and perpendicular to the slip surface are constructed, deriving the expression for the ultimate horizontal bearing capacity of the central wall rock mass. The ultimate horizontal bearing capacity of the central wall rock mass is then substituted as the anti-sliding stability horizontal force into the formula for calculating the anti-sliding stability coefficient of the anchorage foundation, obtaining the anti-sliding stability coefficient of the anchorage foundation considering the influence of the horizontal resistance of rock mass on the anti-sliding stability of anchorages at unequal depths. This invention considers the resistance contribution of the central wall rock mass when calculating the anti-sliding of the anchorage, enabling more accurate calculation of the anti-sliding safety factor. This provides a theoretical basis for optimizing the design scale of the anchorage foundation and the excavation size of the foundation pit, thereby saving engineering costs, shortening the construction period, and making the anchorage foundation design more scientific and reasonable, resulting in significant economic and social benefits. Attached Figure Description

[0042] Figure 1 This is a structural schematic diagram of an anchor foundation with unequal depth excavation, which is based on the method for calculating the anti-sliding stability coefficient of anchors with unequal depth considering the horizontal resistance of rock mass in an embodiment of the present invention.

[0043] Figure 2 This is a schematic diagram of the mathematical model of the rock mass resistance wedge algorithm for the middle wall step, which is a method for calculating the anti-sliding stability coefficient of unequal-depth anchorage considering the horizontal resistance of rock mass in an embodiment of the present invention.

[0044] Figure 3 This is a flowchart illustrating the method for calculating the anti-sliding stability coefficient of unequal-depth anchorages considering the horizontal resistance of rock mass, as described in an embodiment of the present invention.

[0045] In all the accompanying drawings, the same reference numerals indicate the same technical features, specifically: 1-middle wall rock mass, 2-anchor body, 3-bottom plate, 4-compartment, 5-core filler, 6-top plate, 7-support pier, 8-front anchor chamber, 9-diaphragm wall, 10-inner lining. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0047] like Figure 1This is a structural diagram of an anchorage foundation with unequal depth excavation. The central rock mass 1 is moderately or slightly weathered. The anchor body 2 is made of concrete and embedded to a certain depth within the central rock mass 1. The bottom of the anchor body 2 is a base plate 3, and the top of the anchor body 2 is a top plate 6. Before excavating the anchorage pit, a diaphragm wall 9 is constructed. After the diaphragm wall 9 is completed, the anchorage pit is excavated in layers. After each layer of pit excavation is completed, the corresponding soil lining 10 is constructed. After the unequal depth pit is excavated to the design base elevation, the base plate 3 is constructed at the bottom of the pit. After the base plate 3 is poured, the anchor body 2 and the filler core 5 are constructed in layers. The filler core 5 is constructed up to the bottom of the compartment. After the elevation of the foundation pit is reached, the construction of the compartment 4, the anchor body 2 and the core filler 5 are carried out to the bottom elevation of the top plate 6, and then the top plate 6 is constructed and sealed. Among them, the diaphragm wall 9 is used for support and waterproofing during the excavation of the foundation pit and resists the lateral deformation of the soil around the foundation pit. The inner lining 10 is used to improve the support strength of the diaphragm wall 9. The compartment 4 is a closed space, and the compartments 4 are not interconnected. The outer wall is the concrete of the core filler 5. The support pier 7 is located on the top plate 6 of the anchor and is connected to the top plate 6. The front anchor chamber 8 is located inside the support pier 7. The front anchor chamber 8 is a thin-walled box structure. The bottom surface of the front end is connected to the support pier 7, and the side surface of the rear end is connected to the rear top plate 6.

[0048] Currently, there is no calculation formula or design basis for the horizontal resistance of the central wall of the stepped structure. Existing designs generally do not consider the horizontal resistance of the central wall stepped structure, but only regard it as a safety reserve. The design assumes that it is a flat-bottomed anchor for calculation and analysis. However, the anchor foundation slab is often based on moderately weathered rock strata as the bearing layer. The horizontal resistance that the stepped rock mass of the central wall with unequal depth can provide cannot be ignored.

[0049] Based on the above reasons, such as Figure 2 As shown, this invention provides a method for calculating the anti-sliding stability coefficient of anchorages of unequal depths that considers the horizontal resistance of rock mass, comprising the following steps:

[0050] S1: Based on the ultimate failure mode of the central wall rock mass, a simplified analytical model for calculating the horizontal resistance of the central wall steps is constructed to obtain the force balance equation at the ultimate failure of the wedge-shaped body;

[0051] S2: Based on the force balance equation at the ultimate failure of the wedge, construct the force balance equations parallel to the slip surface and perpendicular to the slip surface, and derive the expression for the horizontal ultimate bearing capacity of the middle wall rock mass;

[0052] S3: Substitute the horizontal ultimate bearing capacity of the middle wall rock mass as the anti-sliding stability horizontal force into the calculation formula of the anti-sliding stability coefficient of the anchor foundation to obtain the anti-sliding stability coefficient of the anchor foundation considering the influence of the horizontal resistance of the rock mass on the anti-sliding stability of the anchor foundation in unequal depth excavation.

[0053] Furthermore, in step S1, based on the ultimate failure mode of the central wall rock mass, a simplified analytical model for calculating the horizontal resistance of the central wall steps is constructed (e.g., Figure 3As shown), determine the force state, force equilibrium conditions, and deformation characteristics of the wedge at its critical passive limit failure; among which, Figure 2 In this context, B represents the width of the wedge's top surface; L represents the length of the wedge's slip surface; assuming that the rock mass step in the anchorage wall undergoes slip failure at a certain angle θ, the direction parallel to the slip surface is defined as the τ direction, and the direction perpendicular to the slip surface is defined as the n direction; the anchorage undergoes horizontal displacement under the action of cable force, and the middle wall step generates passive pressure. As the cable force increases, the resistance of the middle wall step gradually increases. When the rock mass in the middle wall reaches its ultimate failure (critical failure), according to the force equilibrium condition, the sliding force of the wedge is equal to the anti-slip force; the force equilibrium equation at the ultimate failure of the wedge is obtained, specifically expressed by equation (1):

[0054] F 滑动 =F 抗滑 (1),

[0055] Among them, F 滑动 F represents the sliding force of the wedge at ultimate failure. 抗滑 This represents the anti-slip force of the wedge at the ultimate failure point;

[0056] Furthermore, obtaining the expression for the ultimate horizontal bearing capacity of the middle wall rock mass in step S2 includes the following steps:

[0057] Step S21: Based on the fact that the sliding force of the wedge at the ultimate failure is equal to the component of the wedge's weight along the direction parallel to the slip surface, the cohesion between the wedge and the rock mass at the slip surface, the component of the wedge under the gravity load of the overlying anchor along the direction parallel to the slip surface, and the sliding friction force of the wedge on the slip surface, construct the force balance equation parallel to the slip surface.

[0058] Step S22: Construct a force balance equation perpendicular to the slip surface based on the fact that the component of the wedge's weight in the direction perpendicular to the slip surface is equal to the sum of the component of the anchor's gravity load in the direction perpendicular to the slip surface and the component of the horizontal ultimate bearing capacity of the central wall rock mass in the direction perpendicular to the slip surface.

[0059] Step S23: Let the sum of the weight of the wedge and the weight load of the overlying anchor on the wedge be a fixed value, and obtain the second form of the force balance equation perpendicular to the slip surface direction and the expression for the sum of the component of the wedge's weight along the direction parallel to the slip surface and the component of the wedge's weight along the direction parallel to the slip surface under the action of the overlying anchor weight.

[0060] Step S24: Based on the second form of the force balance equation perpendicular to the slip surface and the expression for the sum of the component of the wedge's weight along the direction parallel to the slip surface and the component of the wedge's weight along the direction parallel to the slip surface under the weight load of the overlying anchor, obtain the second expression for the anti-slip force of the wedge at ultimate failure.

[0061] Step S25: Based on the fact that the sliding force of the wedge at ultimate failure is the component of the horizontal ultimate bearing capacity of the middle wall rock mass in the direction parallel to the slip surface, the third expression for the sliding force of the wedge at ultimate failure is obtained;

[0062] Step S26: Substitute the second expression for the anti-sliding force of the wedge at ultimate failure and the third expression for the sliding force of the wedge at ultimate failure into the force balance equation at ultimate failure of the wedge to derive the expression for the horizontal ultimate bearing capacity of the middle wall rock mass;

[0063] Specifically, a wedge-shaped algorithm is used to perform force analysis on the wedge. In step S21, the force balance equation parallel to the slip surface direction is determined by the sum of four factors: the component of the wedge's weight along the slip surface direction at ultimate failure, the cohesion between the wedge and the rock mass at the slip surface, the component of the wedge along the slip surface direction under the gravity load of the overlying anchor, and the sliding friction force of the wedge at the slip surface. The force balance equation parallel to the slip surface direction is expressed by equation (2).

[0064]

[0065] Where τ is the direction parallel to the slip surface; g is the weight of the wedge; g τ σB is the component of the wedge's weight along the τ direction; c is the rock mass cohesion, in kPa; L is the slip surface length; cL is the cohesion between the wedge and the rock mass at the slip surface; σB is the anchorage gravity load; σB τ R is the component of the force along the τ direction of the wedge body under the gravity load of the overlying anchor; R is the component of the force between the wedge body and the rock mass slip surface in the direction perpendicular to the slip surface. The friction angle within the rock mass is expressed in degrees (°). The friction coefficient between the wedge and the rock mass slip surface;

[0066] Furthermore, the force balance equation perpendicular to the slip surface in step S22 is determined based on the fact that the component of the wedge and the rock mass slip surface perpendicular to the slip surface is equal to the sum of the component of the wedge's weight perpendicular to the slip surface, the component of the anchorage's gravity load perpendicular to the slip surface, and the component of the horizontal ultimate bearing capacity of the central wall rock mass perpendicular to the slip surface; the force balance equation perpendicular to the slip surface is expressed by equation (3):

[0067] R=[(g+σB)cosθ+E pn (3)

[0068] Where, n is the direction perpendicular to the slip surface; R is the component of the force between the wedge and the rock mass slip surface in the n direction; g is the weight of the wedge; θ is the dip angle of the slip surface, in °; g cosθ is the component of the wedge weight g in the n direction; σB is the anchorage gravity load; σB cosθ is the component of the anchorage gravity load in the n direction; E p E represents the ultimate horizontal bearing capacity of the rock mass in the middle wall. pn Let E be the component of the horizontal ultimate bearing capacity of the rock mass in the n-direction; where E pn =E p sinθ;

[0069] Further, in step S23, let the sum of the weight of the wedge and the weight load of the overlying anchor on the wedge be G, that is, g + σB = G, to obtain another form of expression for the component force of the wedge and the rock mass slip surface in the direction perpendicular to the slip surface (n direction), that is, the second expression of the force balance equation perpendicular to the slip surface, which is expressed by equation (4):

[0070] R = G n +E p sinθ (4)

[0071] Among them, G n Let g be the component of the wedge's weight g in the n direction. n The sum of the components of the gravity load σB borne by the overlying anchor on the wedge-shaped body in the n-direction; where G n =G cosθ;

[0072] Therefore, the second expression for the force balance equation perpendicular to the slip surface direction can also be expressed by equation (5):

[0073] R = G cosθ + E p sinθ (5)

[0074] Based on g + σB = G, we can similarly obtain the component of the wedge's weight along the direction parallel to the slip surface, gτ, and the component of the wedge's weight along the direction parallel to the slip surface, σB, under the weight load of the overlying anchor. τ The expression for the sum is given by equation (6):

[0075] g τ +σB τ =G sinθ (6);

[0076] Furthermore, in step S24: the second expression for the anti-slip force of the wedge at ultimate failure is expressed by equation (7):

[0077]

[0078] That is, by substituting formulas (5) and (6) into formula (2), we can obtain the second expression for the anti-slip force of the wedge at the ultimate failure point - formula (7);

[0079] Furthermore, in step S25, based on the fact that the sliding force of the wedge at ultimate failure is the component of the horizontal ultimate bearing capacity of the middle wall rock mass in the direction parallel to the slip surface, a third expression for the sliding force of the wedge at ultimate failure is obtained, which is expressed by equation (8):

[0080] F 滑动 =E pτ =E p cosθ (8)

[0081] Among them, E pτ This is the component of the horizontal ultimate bearing capacity of the central wall rock mass in the direction parallel to the slip surface (τ direction);

[0082] In step S26, the second expression for the anti-sliding force of the wedge at ultimate failure and the third expression for the sliding force of the wedge at ultimate failure are substituted into the force balance equation at ultimate failure of the wedge to derive the horizontal ultimate bearing capacity E of the middle wall rock mass. p The expression;

[0083] That is, by substituting formulas (7) and (8) into formula (1), we can obtain formula (9):

[0084]

[0085] Further derivation shows that the horizontal ultimate bearing capacity E of the middle wall rock mass... p Equation (10) represents:

[0086]

[0087] In the formula: θ is the dip angle of the slip surface, in degrees; ω is the internal friction angle of the rock mass, in °; c is the cohesion of the rock mass, in kPa; L is the length of the slip surface; G is the sum of the weight of the wedge and the weight load of the overlying anchor on the wedge.

[0088] Furthermore, the formula for calculating the anti-sliding stability coefficient of the anchorage foundation in step S3, according to the "Design Code for Highway Suspension Bridges" (JTG D65T), is expressed by equation (11):

[0089]

[0090] In the formula: k c P is the anti-sliding stability coefficient of the anchorage foundation. i For the i-th vertical force; ∑Pi H represents the total vertical force. iP For the i-th anti-slip stabilizing horizontal force; ∑H iP The sum of horizontal forces resisting sliding and stabilizing; H iS For the i-th sliding horizontal force; ∑H iS Let H be the sum of the sliding horizontal forces; μ be the friction coefficient between the foundation surface and the subgrade soil; where ∑H iP and ∑H iS Let H be the sum of the horizontal forces in each of the two opposing directions, with the larger absolute value representing the total sliding horizontal force. iS The other is the sum of anti-slip stabilizing forces ∑H iP ;μ∑P i It is the sum of the anti-sliding stabilizing forces;

[0091] Using the ultimate horizontal bearing capacity of the central wall rock mass as the anti-sliding stability horizontal force, we can see that:

[0092] E p =H ip (12)

[0093] Among them, H ip To provide anti-slip stability and horizontal force;

[0094] Substituting the ultimate horizontal bearing capacity of the rock mass in the middle wall as the anti-sliding stability horizontal force into the formula for calculating the anti-sliding stability coefficient of the anchor foundation, it can be seen that the anti-sliding stability coefficient of the anchor foundation considering the influence of the horizontal resistance of the rock mass on the anti-sliding stability of the anchor foundation in unequal depth excavation is expressed by equation (13):

[0095]

[0096] Where, k d The sliding stability coefficient of the anchor foundation, E, is given to account for the influence of horizontal rock mass resistance on the sliding stability of anchor foundations in unequal-depth excavation. p The ultimate horizontal bearing capacity of the rock mass in the middle wall; ∑E p It is the sum of the horizontal ultimate bearing capacity of the rock mass in the middle wall.

[0097] Result verification:

[0098] To study the impact of the step effect on the bearing capacity of anchorages, the applicant previously conducted numerical simulations and indoor scaled-down model tests. The results showed that the displacement and safety factor of the stepped anchorage foundation are higher than those of the flat-bottomed anchorage foundation, and the ultimate bearing capacity and safety factor can be increased by about 15%.

[0099] Specifically, the preliminary design of the anchorage foundation of a certain river-crossing passage recommends the use of a gravity anchorage scheme as an example. Based on the calculation parameters such as rock mechanics indices, physical properties, anchorage base stress, rock mass dimensions of the central wall, and step height, the horizontal ultimate resistance value that the central wall step can provide is calculated.

[0100] The anchorage design features a figure-eight shape with a total length of 158m, formed by two 100m diameter arcs on the anchorage plane. The base is embedded in moderately weathered argillaceous sandstone. The moderately weathered rock has a saturated uniaxial compressive strength of 9.67MPa and a preferred bearing capacity characteristic value of 1000kPa. It belongs to soft rock geological mass. The elevations of the front and rear bottom plates of the anchorage are -31m and -35m, respectively. Unequal excavation depths at the front and rear form a 4m high central wall step. The basic quality classification of the rock mass is Class IV. According to Appendix D of the "Engineering Rock Mass Classification Standard" GB50218-2014, the values ​​of the peak shear strength parameters of the rock mass structural plane are given, as shown in Table 1. The internal friction angle of the rock mass is 27°, and the cohesion is 200kPa.

[0101] Table 1 Appendix D of GB50218-2014 "Standard for Classification of Engineering Rock Mass"

[0102]

[0103] Table 2 shows the values ​​of the physical and mechanical parameters of the rock mass, including the dip angle of the slip surface. The rock mass is 26 kN / m 3 The effective unit weight is taken as 16 kN / m3 in the calculation; the average stress σ on the top surface of the wedge is taken as the average effective stress of the front and rear toes of the base, which is (1103+772) / 2=937 kPa when the cable is in operation; the base is located 35m underwater, and the effective stress is taken as 937-350=587 kPa; the values ​​of the wedge top surface width B, the wedge longitudinal length L, the slip surface width, etc. are shown in Table 2 below;

[0104] Table 2 Theoretical Calculation Values

[0105]

[0106]

[0107] Based on the above calculations, the horizontal resistance value provided by the rock mass of the central wall step is 759753 kN, which is the ultimate horizontal bearing capacity of the central wall rock mass. Without considering the horizontal resistance of the central wall, the current anti-sliding safety factor of the anchor foundation, calculated using the formula for the anti-sliding stability coefficient, is 2.07, which just meets the requirement of not less than 2.0 in the code. However, when considering the resistance of the central wall, according to the formula for calculating the anti-sliding stability coefficient of the anchor foundation considering the influence of the horizontal resistance of the rock mass on the anti-sliding stability of the anchor foundation in unequal depth excavation, the anti-sliding stability safety factor of the anchor foundation in unequal depth excavation considering the horizontal resistance of the rock mass is 2.42 (as shown in Table 3). Therefore, there is considerable room for optimization in terms of scale. This verifies the contribution of the horizontal resistance of the central wall rock mass to the anti-sliding safety factor of the base.

[0108] Table 3 Experimental Results

[0109]

[0110] This invention provides a method for calculating the anti-sliding stability coefficient of anchorages at unequal depths, considering the horizontal resistance of rock mass. Based on the ultimate failure mode of the central wall rock mass, a simplified analytical model for calculating the horizontal resistance of the central wall steps is constructed, yielding the force balance equation at the ultimate failure of the wedge-shaped body. Based on this equation, force balance equations parallel and perpendicular to the slip surface are constructed, deriving the expression for the ultimate horizontal bearing capacity of the central wall rock mass. This ultimate horizontal bearing capacity is then substituted into the formula for calculating the anti-sliding stability coefficient of the anchorage foundation, resulting in an anti-sliding stability coefficient that considers the influence of the horizontal resistance of rock mass on the anti-sliding stability of anchorages at unequal depths. This invention considers the resistance contribution of the central wall rock mass during anchorage anti-sliding calculations, enabling more accurate calculation of the anchorage anti-sliding safety factor and providing a theoretical basis for optimizing the design scale of anchorage foundations and the excavation dimensions of the foundation pit.

[0111] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating the anti-sliding stability coefficient of unequal-depth anchorages considering the horizontal resistance of rock mass, characterized in that, Includes the following steps: S1: Based on the ultimate failure mode of the central wall rock mass, a simplified analytical model for calculating the horizontal resistance of the central wall steps is constructed to obtain the force balance equation at the ultimate failure of the wedge-shaped body; S2: Based on the force balance equation at the ultimate failure of the wedge, construct the force balance equations parallel to the slip surface and perpendicular to the slip surface, and derive the expression for the horizontal ultimate bearing capacity of the middle wall rock mass; S3: Substitute the horizontal ultimate bearing capacity of the middle wall rock mass as the anti-sliding stability horizontal force into the calculation formula of the anti-sliding stability coefficient of the anchor foundation to obtain the anti-sliding stability coefficient of the anchor foundation considering the influence of the horizontal resistance of the rock mass on the anti-sliding stability of the anchor foundation in unequal depth excavation. The horizontal ultimate bearing capacity of the middle wall rock mass mentioned in step S2 This can be expressed by equation (10): （10） In the formula: The dip angle of the slip surface is expressed in degrees (°). The friction angle within the rock mass is expressed in degrees (°). Rock mass cohesion, expressed in kPa; The length of the slip surface; It is the sum of the weight of the wedge and the weight load of the overlying anchor on the wedge. In step S3, the anti-sliding stability coefficient of the anchor foundation, which considers the influence of the horizontal resistance of the rock mass on the anti-sliding stability of the anchor foundation in unequal-depth excavation, is expressed by equation (13): (13) in, The sliding stability coefficient of the anchor foundation, which takes into account the influence of the horizontal resistance of the rock mass on the sliding stability of the anchor foundation in unequal depth excavation; It is the coefficient of friction between the base surface and the foundation soil; For the first A vertical force; This represents the sum of vertical forces. The ultimate horizontal bearing capacity of the rock mass in the middle wall; This represents the sum of the horizontal ultimate bearing capacities of the rock mass in the central wall. For the first A sliding horizontal force; This represents the sum of the sliding horizontal forces.

2. The method for calculating the anti-sliding stability coefficient of unequal-depth anchorages considering the horizontal resistance of rock mass according to claim 1, characterized in that, The force balance equation for the ultimate failure of the wedge in step S1 is specifically expressed by equation (1): （1）， in, This represents the sliding force of the wedge at the point of ultimate failure; This represents the anti-slip force of the wedge at the point of ultimate failure.

3. The method for calculating the anti-sliding stability coefficient of unequal-depth anchorages considering the horizontal resistance of rock mass according to claim 2, characterized in that, Obtaining the expression for the ultimate horizontal bearing capacity of the middle wall rock mass in step S2 includes the following steps: Step S21: Based on the fact that the sliding force of the wedge at the ultimate failure is equal to the component of the wedge's weight along the direction parallel to the slip surface, the cohesion between the wedge and the rock mass at the slip surface, the component of the wedge under the gravity load of the overlying anchor along the direction parallel to the slip surface, and the sliding friction force of the wedge on the slip surface, construct the force balance equation parallel to the slip surface. Step S22: Construct a force balance equation perpendicular to the slip surface based on the fact that the component of the wedge's weight in the direction perpendicular to the slip surface is equal to the sum of the component of the anchor's gravity load in the direction perpendicular to the slip surface and the component of the horizontal ultimate bearing capacity of the central wall rock mass in the direction perpendicular to the slip surface. Step S23: Let the sum of the weight of the wedge and the weight load of the overlying anchor on the wedge be a fixed value, and obtain the second form of the force balance equation perpendicular to the slip surface direction and the expression for the sum of the component of the wedge's weight along the direction parallel to the slip surface and the component of the wedge's weight along the direction parallel to the slip surface under the action of the overlying anchor weight. Step S24: Based on the second form of the force balance equation perpendicular to the slip surface and the expression for the sum of the component of the wedge's weight along the direction parallel to the slip surface and the component of the wedge's weight along the direction parallel to the slip surface under the weight load of the overlying anchor, the second expression for the anti-slip force of the wedge at ultimate failure is obtained. Step S25: Based on the fact that the sliding force of the wedge at ultimate failure is the component of the horizontal ultimate bearing capacity of the middle wall rock mass in the direction parallel to the slip surface, the third expression for the sliding force of the wedge at ultimate failure is obtained. Step S26: Substitute the second expression for the anti-sliding force of the wedge at ultimate failure and the third expression for the sliding force of the wedge at ultimate failure into the force balance equation at ultimate failure of the wedge to derive the expression for the horizontal ultimate bearing capacity of the middle wall rock mass.

4. The method for calculating the anti-sliding stability coefficient of unequal-depth anchorages considering the horizontal resistance of rock mass according to claim 3, characterized in that, The force balance equation in step S21, parallel to the slip surface, is expressed by equation (2): （2） in, The direction is parallel to the slip surface; The weight of the wedge-shaped object; For the weight of the wedge along directional component; Rock mass cohesion, expressed in kPa; The length of the slip surface; This refers to the cohesion between the wedge and the rock mass at the slip surface; For anchorage gravity load; The component of the force along the direction parallel to the slip surface under the gravity load of the overlying anchor on the wedge-shaped body; This represents the component of the force between the wedge and the rock mass slip surface in the direction perpendicular to the slip surface; The friction angle within the rock mass is expressed in degrees (°). The friction coefficient between the wedge and the rock mass slip surface.

5. The method for calculating the anti-sliding stability coefficient of unequal-depth anchorages considering the horizontal resistance of rock mass according to claim 4, characterized in that, The force balance equation perpendicular to the slip surface in step S22 is expressed by equation (3): （3） in, The direction is perpendicular to the slip surface; The dip angle of the slip surface is expressed in degrees (°). For the weight of the wedge in The component of force in the direction; For anchorage gravity load in The component of force in the direction; The ultimate horizontal bearing capacity of the rock mass in the middle wall; For the ultimate horizontal bearing capacity of the middle wall rock mass in The component of the force in the direction, where, .

6. The method for calculating the anti-sliding stability coefficient of unequal-depth anchorages considering the horizontal resistance of rock mass according to claim 5, characterized in that, The second expression for the force balance equation perpendicular to the slip surface in step S23 is expressed by equation (5): （5） in, It is the sum of the weight of the wedge and the weight load of the overlying anchor on the wedge.

7. The method for calculating the anti-sliding stability coefficient of unequal-depth anchorages considering the horizontal resistance of rock mass according to claim 6, characterized in that, In step S24: the second expression for the anti-slip force of the wedge at ultimate failure is expressed by equation (7): （7）。 8. The method for calculating the anti-sliding stability coefficient of unequal-depth anchorages considering the horizontal resistance of rock mass according to claim 7, characterized in that, In step S25: the third expression for the sliding force of the wedge at ultimate failure is represented by equation (8): （8） in, This represents the component of the horizontal ultimate bearing capacity of the rock mass in the central wall in the direction of [the force].

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