A design method for rock mass structural surface reinforcement using small diameter anti-slide piles considering axial deformation

Abstract

The present invention provides a design method for a small-diameter anti-slide pile with axial deformation considered for reinforcing a rock mass structural plane, belonging to the field of slope support. The method includes: obtaining the dip angle θ of the external inclined structural plane of the rock mass, the internal friction angle #imgabs0#, the cohesion c, the unit weight γ of the sliding mass, the height H of the sliding mass, and determining the width b of the sliding mass borne by a single deeply embedded small-diameter anti-slide pile and the horizontal extension length l; calculating the flexure inclination angle β1 of the deeply embedded small-diameter anti-slide pile when the anti-slide force is maximum, and then calculating the cross-section parameters, axial force and anchorage length of the deeply embedded small-diameter anti-slide pile. The present invention considers the positive effect of the axial force of the deeply embedded small-diameter anti-slide pile on anti-slide and the deformation amount of the pile body pressed into the rock mass during axial compression, and deduces the maximum value of the anti-slide force that the deeply embedded small-diameter anti-slide pile can provide during the deformation process, so as to obtain a more accurate design result and save resources compared with the empirical design method.

Description

Technical Field

[0001] The invention relates to the field of slope support, and in particular to a design method for reinforcing a rock mass structural surface with small-diameter anti-slide piles taking into account axial deformation. Background Art

[0002] In recent years, deep-buried small-diameter anti-slide piles have been used more and more in slope engineering. Different from ordinary anti-slide piles, deep-buried small-diameter anti-slide piles have the characteristics of small pile diameter, large aspect ratio, small bending stiffness, and complex pile-soil interaction between deep-buried small-diameter anti-slide piles and the surrounding inter-pile rock and soil during the anti-slide process. Therefore, in the process of slope reinforcement with deep-buried small-diameter anti-slide piles, the force form and failure mechanism of deep-buried small-diameter anti-slide piles are more complex than those of ordinary anti-slide piles. Due to the lack of design methods for deep-buried small-diameter anti-slide piles, designers can only estimate the design of deep-buried small-diameter anti-slide piles based on experience, and cannot accurately design deep-buried small-diameter anti-slide piles, which will result in a waste of resources. Summary of the invention

[0003] In order to solve the above technical problems, an embodiment of the present invention provides a design method for reinforcing a rock structure surface with small-diameter anti-slide piles taking into account axial deformation.

[0004] In order to achieve the above purpose, the embodiment of the present invention adopts the following technical solution:

[0005] A design method for reinforcing a rock mass structural surface by using small-diameter anti-slide piles taking into account axial deformation comprises the following steps:

[0006] Obtain the inclination angle θ and internal friction angle of the rock body Cohesion c, sliding mass γ, sliding height H, and the width b and horizontal extension length l of the sliding body borne by a single deep-buried small-diameter anti-sliding pile;

[0007] Calculate the deflection angle β of the deeply buried small diameter anti-slide pile when the anti-slide force is maximum 1 ;

[0008] Use the following formula to calculate the axial force of deeply buried small diameter anti-slide piles;

[0009]

[0010] Use the following four formulas to calculate the cross-sectional parameters of deeply buried small-diameter anti-slide piles;

[0011]

[0012] EA=E s A p +E m (AA p )

[0013]

[0014]

[0015] Wherein, E is the composite elastic modulus of the deep-buried small-diameter anti-slide pile; A is the cross-sectional area of ​​the deep-buried small-diameter anti-slide pile; D is the diameter of the deep-buried small-diameter anti-slide pile; d is the diameter of the steel bar in the deep-buried small-diameter anti-slide pile core; E s E is the elastic modulus of the steel bars used for deeply buried small-diameter anti-slide piles; m A is the elastic modulus of the mortar used for deeply buried small diameter anti-slide piles; p F is the cross-sectional area of ​​the steel bars used for deeply buried small-diameter anti-slide piles; st is the slope stability safety factor;

[0016] Use the following two formulas to calculate the anchorage length of deeply buried small diameter anti-slide piles;

[0017]

[0018]

[0019] Among them, l a is the anchorage length of the deep-buried small-diameter anti-sliding pile; K is the bonding safety factor of the deep-buried small-diameter anti-sliding pile, f rbk is the standard value of the ultimate bonding strength between the rock layer and the deeply buried small-diameter anti-slide pile, f b It is the standard value of the bond strength between steel bars and mortar.

[0020] Wherein, the structural surface inclination angle θ is greater than the internal friction angle

[0021] Wherein, the method further comprises:

[0022] Use the following formula to calculate the cross-sectional compressive bearing capacity of small diameter anti-slide piles;

[0023] F≤A p f y +(AA p )f c

[0024] Among them, f c The compressive strength of the mortar used for deeply buried small-diameter anti-slide piles; f y The compressive strength of the steel bars used for deeply buried small diameter anti-slide piles.

[0025] Wherein, when the calculated anti-sliding force is the maximum, the deflection angle β of the deeply buried small-diameter anti-sliding pile is 1 The steps include:

[0026] Let the value of β when the following equation is true be β 1 , where the initial value of β is set to 0°;

[0027]

[0028] Among them, the bonding safety factor K of the deeply buried small-diameter anti-sliding piles is taken as 2.6, 2.4, and 2.2 according to the safety level of the slope, level 1, level 2, and level 3, respectively.

[0029] The embodiments of the present invention have the following beneficial effects:

[0030] The embodiment of the present invention provides a method for designing a structural surface of a rock mass reinforced with small-diameter anti-sliding piles taking into account axial deformation. The method takes into account the positive effect of the axial force of the pile body of the deeply buried small-diameter anti-sliding pile on anti-sliding and the deformation of the pile body pressed into the rock mass during axial compression. The maximum value of the anti-sliding force that the deeply buried small-diameter anti-sliding pile can provide during the deformation is deduced, so that more scientific and accurate structural surface parameter values ​​can be obtained, which can save resources compared to empirical design methods.

[0031] Of course, it is not necessary to achieve all of the advantages described above at the same time to implement any product or method of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0033] Figure 1 This is a flow chart of a design method for strengthening a rock mass structural surface by small-diameter anti-slide piles taking into account axial deformation according to an embodiment of the present invention;

[0034] Figure 2 It is a schematic diagram of the pile axis deformation caused by a slight sliding movement of the slider in an embodiment of the present invention. DETAILED DESCRIPTION

[0035] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention generally described and shown in the accompanying drawings can be arranged and designed in various different configurations. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can also be combined with each other.

[0036] It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. In the description of the present invention, the terms "first", "second", "third", "fourth", etc. are only used to distinguish the description and cannot be understood as just or implying relative importance.

[0037] The embodiment of the present invention provides a design method for reinforcing the rock structure surface with small diameter anti-sliding piles considering axial deformation. The method first derives the relationship between the pile axis deflection angle, pile body cross-sectional parameters and pile body axial force after a small deflection of a deep buried small diameter pile according to the amount of compression in the rock mass during the compression process of the pile body and the amount of compression inside the structural surface; derives the anti-sliding force calculation formula according to static equilibrium and Mohr-Coulomb criterion; derivates the anti-sliding force with respect to the deflection angle of the deep buried small diameter pile, sets the derivative function equal to 0, and obtains the maximum point and maximum value of the anti-sliding force; sets the maximum value of the anti-sliding force to be greater than or equal to the product of the slope stability safety factor and the sliding force, and obtains the pile body axial force of the deep buried small diameter anti-sliding pile; calculates the pile body cross-sectional parameters according to the pile body axial force, verifies the cross-sectional compressive bearing capacity of the deep buried small diameter anti-sliding pile, and calculates the anchoring length of the deep buried small diameter anti-sliding pile. The present invention takes into account the positive effect of the axial force of the deeply buried small-diameter anti-slide pile on anti-slide and the deformation of the pile body pressed into the rock mass during axial compression, and derives the maximum anti-slide force that the deeply buried small-diameter anti-slide pile can provide during the deformation process. Compared with the empirical design method, it can save resources.

[0038] like Figure 1 As shown in the embodiment of the present invention, a design method for a rock mass structural surface reinforced with small-diameter anti-sliding piles considering axial deformation is provided, comprising the following steps:

[0039] Step S1, obtaining the inclination angle θ and internal friction angle of the outer inclined structural surface of the rock body Cohesion c, sliding mass γ, sliding height H, as well as the width b and horizontal extension length l of the sliding body borne by a single deeply buried small-diameter anti-sliding pile.

[0040] Among them, the inclination angle θ and the internal friction angle of the rock body are Parameters such as cohesion c, sliding mass γ, sliding height H, etc. can be obtained through on-site measurement and experiments. The sliding width b and horizontal extension length l borne by the single deep-buried small-diameter anti-sliding pile can be determined according to design requirements.

[0041] Step S2, calculating the deflection angle β of the deeply buried small-diameter anti-sliding pile when the anti-sliding force is maximum 1 ;

[0042] Since the deep-buried small-diameter anti-slide piles have low bending stiffness, the bending moment has little effect on the deformation process, and they play an anti-slide role. Therefore, for the sake of conservative design and calculation convenience, the bending moment effect is not taken into account. Figure 2 The figure shows the deformation of the pile axis when the slider slides slightly downward. When the slider is subjected to load, the slider will slide slightly along the sliding surface. During the sliding process, the deeply buried small-diameter anti-sliding pile will bend slightly. Assume that the angle between the pile body and the vertical direction after the deflection is β. According to the force balance in the direction perpendicular to the slider, equation (1) can be obtained:

[0043] Fcos(θ-β)+F N =γblHcosθ (1)

[0044] Where F is the axial force of the small-diameter anti-sliding pile buried deep at the structural surface, F N It is the supporting force of the lower rock mass on the sliding body.

[0045] The standard value of the ultimate bond strength between rock and anchor is f rbk , then the depth at which the axial force transmission of the deeply buried small-diameter pile is 0 can be expressed by the following formula:

[0046]

[0047] Where D is the diameter of the deeply buried small-diameter anti-slide pile.

[0048] Considering the standard value of the ultimate bond strength between rock and anchor body is f rbk , assuming that the axial force of the pile body decays linearly in the rock mass, the indentation deformation of the deeply buried small-diameter anti-slide pile in the rock on one side can be expressed by the following formula:

[0049]

[0050] Wherein, E is the composite elastic modulus of the deeply buried small-diameter anti-slide pile, and A is the cross-sectional area of ​​the deeply buried small-diameter anti-slide pile.

[0051] The distance between the bottom surface of the sliding body and the top surface of the lower rock mass (i.e., the width of the structural surface) is h. The deformation of the deeply buried small-diameter anti-sliding pile inside the structural surface can be expressed by the following formula:

[0052]

[0053] During the slight sliding of the sliding body, the distance between the bottom surface of the sliding body and the top surface of the lower rock mass remains unchanged. According to the geometric relationship before and after deformation, it can be obtained:

[0054]

[0055] By transforming formula (5), we can get:

[0056]

[0057] According to the Mohr-Coulomb strength criterion and the force decomposition of the axial force F of the deep-buried small-diameter anti-sliding pile, the anti-sliding force R along the sliding surface can be expressed by formula (7):

[0058]

[0059] The anti-sliding force R along the sliding surface direction obtained by solving equations (1), (6) and (7) is expressed by equation (8):

[0060]

[0061] In order to increase the maximum anti-sliding force generated by the anti-sliding pile when the angle between the pile body and the vertical direction after different deflections is β, the derivative of R with respect to β can be obtained.

[0062]

[0063] make

[0064] We can get formula (10)

[0065]

[0066] Use the iterative method to calculate the β value when equation (10) is true, let it be β 1 , where the initial value of β is 0°. During the solution process, it was found that the inclination angle θ of the inclined structural surface is greater than the internal friction angle When , equation (10) has a solution in the interval (0, θ). Therefore, in order for the axial force of the deeply buried small-diameter pile to play an anti-sliding role, it is necessary to require that the inclination angle θ of the structural surface is greater than the internal friction angle The specific derivation process is as follows:

[0067] To ensure that the following equation has a solution in the interval (0, θ):

[0068]

[0069] Assume the function:

[0070]

[0071] Since the function f(β) is a function formed by adding, subtracting, and multiplying trigonometric functions, it is a continuous function in the domain of definition. According to the zero point existence theorem, if the graph of the function y=f(x) on the interval [a,b] is a continuous curve, and f(a)f(b)<0, then the function y=f(x) must have a zero point in the interval (a,b), that is, there exists x 0 belongs to (a,b), so that f(x 0 )=0. According to the above theorem: for the function f(β), we only need to prove f(0)f(θ)<0 to prove that equation (7) has a solution.

[0072] because:

[0073]

[0074] Therefore, as long as f(0)>0 is guaranteed, it can be proved that f(0)f(θ)<0, and equation (7) has a solution, and we can get:

[0075]

[0076] From the above formula, we can get:

[0077]

[0078] Right now,

[0079]

[0080] When the above equation is established, equation (10) must have a solution in the interval (0, θ). Therefore, the structural surface inclination angle θ needs to be greater than the internal friction angle

[0081] The calculated β 1 Substituting the value into formula (8) can calculate the maximum anti-slip force R max , then the stability coefficient of the slider is:

[0082]

[0083] Ensure that the stability factor f obtained by calculation s ≥ According to the stability factor f determined by the safety level of the slope st , the stability factor f determined by the safety level of the slope st It can be determined according to the specification "Technical Specification for Building Slope Engineering GB 50330-2013".

[0084] Step S3, calculating the axial force of the deeply buried small-diameter anti-sliding pile;

[0085] From equations (8), (9) and (11), the calculation formula for the axial force F of the deep-buried small-diameter anti-sliding pile can be obtained, as shown in equation (12):

[0086]

[0087] Step S4, calculating the cross-sectional parameters of the small-diameter anti-slide pile;

[0088] The cross-sectional dimensions of small diameter anti-slide piles can be calculated using the following formula:

[0089] F≤A p f y +(AA p )f c (13)

[0090] Among them, f c The compressive strength of the mortar used for deeply buried small-diameter anti-slide piles; f y It is the compressive strength of the steel bars used for deeply buried small diameter anti-slide piles. p is the cross-sectional area of ​​the steel bars used for the deep-buried small-diameter anti-sliding piles; A is the cross-sectional area of ​​the deep-buried small-diameter anti-sliding piles, which can be calculated by equations (14) and (15) respectively.

[0091]

[0092]

[0093] Using equations (2) and (6), the calculation formula for the buried small diameter section parameter EA can be obtained, equation (16):

[0094]

[0095] According to the cross-sectional parameters of the deeply buried small-diameter anti-slide pile, it can be expressed by formula (17):

[0096] EA=E s A p +E m (AA p ) (17)

[0097] Wherein, E is the composite elastic modulus of the deep-buried small-diameter anti-slide pile; A is the cross-sectional area of ​​the deep-buried small-diameter anti-slide pile; D is the diameter of the deep-buried small-diameter anti-slide pile; d is the diameter of the steel bar in the deep-buried small-diameter anti-slide pile core; E s E is the elastic modulus of the steel bars used for deeply buried small-diameter anti-slide piles; m A is the elastic modulus of the mortar used for deeply buried small diameter anti-slide piles; p The cross-sectional area of ​​the steel bars used for deeply buried small-diameter anti-slide piles.

[0098] Step S5, calculating the anchorage length of the deeply buried small-diameter anti-slide pile

[0099]

[0100]

[0101] Among them, l a is the anchorage length of the deep-buried small-diameter anti-slide pile; K is the bonding safety factor of the deep-buried small-diameter anti-slide pile, which can be taken as 2.6, 2.4, and 2.2 according to the safety level of the slope, level 1, level 2, and level 3, respectively; f rbk is the standard value of the ultimate bonding strength between the rock layer and the deeply buried small-diameter anti-slide pile, f b It is the standard value of the bond strength between steel bars and mortar, which can be determined according to the specification "Technical Specification for Building Slope Engineering GB 50330-2013".

[0102] It can be seen from the above technical scheme that an embodiment of the present invention provides a method for designing a rock structure surface reinforced with small-diameter anti-sliding piles taking into account axial deformation. The method first derives the relationship between the pile axis deflection angle, pile body cross-sectional parameters and pile body axial force after a small deflection of the deeply buried small-diameter pile occurs according to the compression amount of the pile body in the rock mass during compression and the compression amount inside the structural surface; derives the anti-sliding force calculation formula according to static equilibrium and the Mohr-Coulomb criterion; differentiates the anti-sliding force with respect to the deflection angle of the deeply buried small-diameter pile, sets the derivative function equal to 0, and obtains the maximum point and maximum value of the anti-sliding force; sets the maximum value of the anti-sliding force greater than or equal to the product of the slope stability safety factor and the sliding force, and obtains the axial force of the pile body of the deeply buried small-diameter anti-sliding pile; calculates the pile body cross-sectional parameters according to the pile body axial force, verifies the cross-sectional compressive bearing capacity of the deeply buried small-diameter anti-sliding pile, and calculates the anchoring length of the deeply buried small-diameter anti-sliding pile. The present invention takes into account the positive effect of the axial force of the deeply buried small-diameter anti-slide pile on anti-slide and the deformation of the pile body pressed into the rock mass during axial compression, and derives the maximum anti-slide force that the deeply buried small-diameter anti-slide pile can provide during the deformation process. Compared with the empirical design method, it can save resources.

[0103] The above description is only a preferred embodiment of the present invention and an explanation of the technical principles used. It is not intended to limit the scope of the invention claimed for protection, but only represents the preferred embodiment of the present invention. Those skilled in the art should understand that the scope of the invention involved in the present invention is not limited to the technical solution formed by a specific combination of the above-mentioned technical features, but should also cover other technical solutions formed by any combination of the above-mentioned technical features or their equivalent features without departing from the inventive concept. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present invention.

Claims

1. A design method for strengthening rock mass structural surface with small diameter anti-slide piles considering axial deformation. It is characterized in that The following steps are involved: Obtain the inclination angle θ and internal friction angle of the rock body Cohesion c, sliding mass γ, sliding height H, and the width b and horizontal extension length l of the sliding body borne by a single deep-buried small-diameter anti-sliding pile; Calculate the deflection angle β of the deeply buried small diameter anti-slide pile when the anti-slide force is maximum 1 ; Use the following formula to calculate the axial force of deeply buried small diameter anti-slide piles; Use the following four formulas to calculate the cross-sectional parameters of deeply buried small-diameter anti-slide piles; EA=E s A p +E m (CHALLENGE ACCEPTED p ) Wherein, E is the composite elastic modulus of the deep-buried small-diameter anti-slide pile; A is the cross-sectional area of ​​the deep-buried small-diameter anti-slide pile; D is the diameter of the deep-buried small-diameter anti-slide pile; d is the diameter of the steel bar in the deep-buried small-diameter anti-slide pile core; E s E is the elastic modulus of the steel bars used for deeply buried small-diameter anti-slide piles; m A is the elastic modulus of the mortar used for deeply buried small diameter anti-slide piles; p F is the cross-sectional area of ​​the steel bars used for deeply buried small-diameter anti-slide piles; st is the slope stability safety factor; Use the following two formulas to calculate the anchorage length of deeply buried small diameter anti-slide piles; Among them, l a is the anchorage length of the deep-buried small-diameter anti-sliding pile; K is the bonding safety factor of the deep-buried small-diameter anti-sliding pile; f rbk is the standard value of the ultimate bonding strength between the rock layer and the deeply buried small-diameter anti-slide pile, f b It is the standard value of the bond strength between steel bars and mortar.

2. According to claim 1, a design method for strengthening rock mass structural surface by small diameter anti-slide piles taking into account axial deformation, It is characterized in that The structural surface inclination angle θ is greater than the internal friction angle 3. According to the design method of the small diameter anti-slide pile reinforcement rock structure surface considering axial deformation according to claim 1, It is characterized in that The method further comprises: Use the following formula to calculate the cross-sectional compressive bearing capacity of small diameter anti-slide piles; F≤A p f y +(A-A p )f c Among them, f c The compressive strength of the mortar used for deeply buried small-diameter anti-slide piles; f y The compressive strength of the steel bars used for deeply buried small diameter anti-slide piles.

4. According to the design method of the rock mass structural surface reinforced by small diameter anti-slide piles considering axial deformation according to claim 1, It is characterized in that When the calculated anti-sliding force is the maximum, the deflection angle β of the deeply buried small-diameter anti-sliding pile is 1 The steps include: Use Newton's method to iteratively calculate the β value when the following equation is true, let it be β 1 , where the initial value of β is set to 0°; 5. According to the design method of the small diameter anti-slide pile reinforcement rock structure surface considering axial deformation according to claim 1, It is characterized in that The bonding safety factor K of deeply buried small-diameter anti-slide piles is taken as 2.6, 2.4, and 2.2 according to the safety level of the slope, level 1, level 2, and level 3, respectively.

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