Method for determining structure plane parameters of rock mass reinforced by vertical deep small-diameter anti-slide pile

Abstract

The application provides a design method for vertical deep-buried small-diameter anti-slide pile reinforced rock mass outer-inclined structural surface, and belongs to the field of slope support. The method comprises the following steps: obtaining the inclination angle θ of the outer-inclined structural surface of the rock mass, the internal friction angle, the cohesion c, the sliding body specific gravity γ, the sliding body height H, and determining the sliding body width b and the horizontal extension length l borne by a single deep-buried small-diameter anti-slide pile; calculating the flexural inclination angle β1 of the deep-buried small-diameter anti-slide pile at the maximum anti-slide force, and then calculating the section parameter, the axial force and the anchoring length of the deep-buried small-diameter anti-slide pile. The application considers the positive role of the axial force of the deep-buried small-diameter anti-slide pile in anti-slide, deduces the maximum anti-slide force that can be provided by the deep-buried small-diameter anti-slide pile in the deformation process, can obtain more accurate design results, and can save resources compared with the empirical design method.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of slope support, in particular to a design method of vertical deep-buried small-diameter anti-slide pile reinforced rock mass outward-inclined structural plane. BACKGROUND

[0002] In recent years, deep-buried small-diameter anti-slide piles are used more and more in slope engineering. Unlike ordinary anti-slide piles, deep-buried small-diameter anti-slide piles have the characteristics of small diameter, large slenderness ratio, small bending stiffness, and complex pile-soil interaction between the deep-buried small-diameter anti-slide pile and the surrounding pile-soil mass during the anti-slide process. Therefore, the stress form and failure mechanism of deep-buried small-diameter anti-slide piles are more complex than those of ordinary anti-slide piles during the process of reinforcing the slope with deep-buried small-diameter anti-slide piles, and there is a lack of design method for deep-buried small-diameter anti-slide piles. Currently, designers can only estimate the design of deep-buried small-diameter anti-slide piles according to experience, and cannot accurately design the structural plane parameters of deep-buried small-diameter anti-slide piles, which may result in resource waste. SUMMARY

[0003] To solve the above technical problems, the embodiments of the present application provide a design method of vertical deep-buried small-diameter anti-slide pile reinforced rock mass outward-inclined structural plane.

[0004] In order to achieve the above purpose, the embodiments of the present application adopt the following technical solutions:

[0005] A design method of vertical deep-buried small-diameter anti-slide pile reinforced rock mass outward-inclined structural plane, the method comprises:

[0006] obtaining the inclination angle θ of the rock mass outward-inclined structural plane, the internal friction angle cohesion c, the specific gravity γ of the sliding body, the height H of the sliding body, and determining the sliding body width b and the horizontal extension length l borne by a single deep-buried small-diameter anti-slide pile;

[0007] calculating the deflection inclination angle β1 of the deep-buried small-diameter anti-slide pile when the anti-slide force is maximum;

[0008] calculating the cross-section parameters of the deep-buried small-diameter anti-slide pile using the following four formulas

[0009]

[0010] EA=E s A p +E m (A-A p )

[0011]

[0012]

[0013] 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 of the deep-buried small-diameter anti-slide pile; E s is the elastic modulus of the steel bar used for the deep-buried small-diameter anti-slide pile; E m is the elastic modulus of the mortar used for the deep-buried small-diameter anti-slide pile; A p is the cross-sectional area of the steel bar used for the deep-buried small-diameter anti-slide pile; F st is the cross-sectional area of the steel bar used for the deep-buried small-diameter anti-slide pile; F a is the safety factor of the slope stability;

[0014] The axial force F of the deep-buried small-diameter anti-slide pile is calculated using the following formula:

[0015]

[0016] The anchoring length of the deep-buried small-diameter anti-slide pile is calculated using the following two formulas:

[0017]

[0018]

[0019] Wherein, l a is the anchoring 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; f rbk is the standard value of the ultimate bonding strength between the rock layer and the deep-buried small-diameter anti-slide pile, f b is the standard value of the bonding strength between the steel bar and the mortar.

[0020] Wherein, the step of calculating the deflection angle β1 of the deep-buried small-diameter anti-slide pile at the maximum anti-slide force comprises:

[0021] The β value when the following formula is satisfied is used as β1 using Newton's method, wherein the initial value of β is assigned as 0°

[0022]

[0023] Wherein, the method further comprises:

[0024] The compressive bearing capacity of the small-diameter anti-slide pile is checked using the following formula:

[0025] F≤A p f y +(A-A p )f c

[0026] Wherein, f c is the compressive strength of the mortar used for the deep-buried small-diameter anti-slide pile; f y is the compressive strength of the steel bar used for the deep-buried small-diameter anti-slide pile.

[0027] The structural surface inclination angle theta is greater than the internal friction angle

[0028] The deep-buried small-diameter anti-slide pile bonding safety factor K is 2.6, 2.4 and 2.2 respectively according to the safety levels of the slope, i.e., first level, second level and third level.

[0029] The embodiment of the present application has the following beneficial effects:

[0030] The vertical deep-buried small-diameter anti-slide pile reinforced rock mass outward-inclined structural surface design method provided by the embodiment of the present application can consider the positive effect of the deep-buried small-diameter anti-slide pile shaft force on anti-slide, deduce the maximum value of the anti-slide force provided by the deep-buried small-diameter anti-slide pile in the deformation process, and obtain more scientific and accurate structural surface parameter values.

[0031] Of course, implementing any product or method of the present application does not necessarily require achieving all the advantages described above at the same time. BRIEF DESCRIPTION OF DRAWINGS

[0032] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description only represent some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative effort.

[0033] Figure 1 The vertical deep-buried small-diameter anti-slide pile reinforced rock mass outward-inclined structural surface design method flow chart of the embodiment of the present application is shown in the figure.

[0034] Figure 2 The figure is a schematic diagram of the deformation of the pile axis when the sliding block slides slightly in the embodiment of the present application. DETAILED DESCRIPTION

[0035] The present application will be further described below in combination with the drawings and specific embodiments. Obviously, the described embodiments only represent some embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations. It should be noted that the embodiments and features in the embodiments of the present application can be combined with each other without conflict, if possible.

[0036] It should be noted that: similar labels 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 application, the terms "first", "second", "third", "fourth" and the like are only used to distinguish the description, and cannot be understood as just or imply relative importance.

[0037] This invention provides a design method for reinforcing the outward-dipping structural surface of rock formations with vertically buried small-diameter anti-slide piles. The method first derives the formula for calculating the anti-slide force based on static equilibrium, the Mohr-Coulomb criterion, and the geometric relationship after the small-diameter pile undergoes minor deflection. Then, it differentiates the anti-slide force with respect to the deflection angle of the small-diameter pile, sets the derivative to zero, and obtains the maximum and maximum values ​​of the anti-slide force. By ensuring that the anti-slide force is greater than or equal to the product of the slope stability safety factor and the sliding force, the design section parameters and axial force of the small-diameter anti-slide pile are obtained. Based on the axial force, the compressive bearing capacity of the section of the small-diameter anti-slide pile is verified, and the anchorage length of the small-diameter anti-slide pile is calculated. This invention considers the positive effect of the axial force of the small-diameter anti-slide pile on anti-slide efforts and derives the maximum anti-slide force that the small-diameter anti-slide pile can provide during deformation, saving resources compared to empirical design methods.

[0038] like Figure 1 As shown in the figure, the design method for the externally inclined structural surface of rock mass reinforced by vertically buried small-diameter anti-slide piles provided in this embodiment of the invention includes the following steps:

[0039] Step S1: Obtain the dip angle θ and internal friction angle of the rock mass's outward-dipping structural surface. The factors include cohesion c, sliding weight γ, sliding height H, and the width b and horizontal extension l of the sliding body to be borne by a single deep-buried small-diameter anti-slide pile.

[0040] Among them, the dip angle θ of the rock external dip structure surface and the internal friction angle Parameters such as cohesion c, sliding mass weight γ, and sliding height H can be obtained through on-site measurement and experiments. The width b and horizontal extension l of the sliding mass supported by the single deeply buried small-diameter anti-slide pile can be determined according to design requirements.

[0041] Step S2: Calculate the deflection angle β1 of the deeply buried small-diameter anti-sliding pile when the anti-sliding force is maximum;

[0042] Because deeply buried small-diameter anti-slide piles have low bending stiffness and minimal influence of bending moment during deformation, and because they play an anti-slide role, their bending moment is neglected for conservative design and calculation convenience. For example... Figure 2 The diagram shows a small deformation of the anti-slide pile axis caused by the sliding block. When the sliding body is subjected to a load, it will undergo a small downward displacement along the sliding surface. During the sliding process, the deeply buried small-diameter anti-slide pile will undergo a small deflection. Assume that the angle between the pile body and the vertical direction after deflection is β. According to the force balance in the direction perpendicular to the sliding body, we can obtain equation (1):

[0043] Fcos(θ-β)+F N =γblHcosθ (1)

[0044] Where F is the axial force of the deeply buried small-diameter anti-slide pile at the structural surface, FN supporting force of the lower rock mass to the sliding mass.

[0045] Assuming the distance between the bottom surface of the sliding mass and the top surface of the lower rock mass (i.e., the width of the structural plane) is h, during the process of the sliding mass sliding slightly, the distance between the bottom surface of the sliding mass and the top surface of the lower rock mass is unchanged, according to the geometric relationship before and after deformation, the strain of the deep small-diameter anti-slide pile at the structural plane can be calculated by formula (2),

[0046]

[0047] In the formula, ε is the strain of the deep small-diameter anti-slide pile at the structural plane, l is the length of the deep small-diameter anti-slide pile located in the structural plane before deformation, and Δl is the deformation amount of the deep small-diameter anti-slide pile in the structural plane before and after deformation.

[0048] The shaft force F of the deep small-diameter anti-slide pile at the structural plane can be represented by formula (3):

[0049] F = εEA (3)

[0050] In the formula, E is the composite elastic modulus of the deep small-diameter anti-slide pile, and A is the cross-sectional area of the deep small-diameter anti-slide pile.

[0051] According to the Mohr-Coulomb strength criterion and the force decomposition of the shaft force F of the deep small-diameter anti-slide pile, the anti-slide force R in the direction of the sliding surface can be represented by formula (4):

[0052]

[0053] The anti-slide force R in the direction of the sliding surface can be represented by formula (5) by jointly solving formula (1), formula (2), formula (3), and formula (4):

[0054]

[0055] In order to find the maximum anti-slide force generated by the anti-slide pile under the condition that the angle between the deflected pile body and the vertical direction is β, the derivative of R with respect to β is taken, and formula (6) is obtained.

[0056]

[0057] Let

[0058] Formula (7) is obtained

[0059]

[0060] The value of β when formula (7) is established is calculated using the iterative method, and it is denoted as β1, where the initial value of β is 0°. During the solving process, it is found that the inclination angle θ of the structural plane is greater than the internal friction angle At this time, formula (7) has a solution in the interval (0, θ), and the specific derivation process is as follows:

[0061] To ensure that the following formula has a solution in the interval (0, θ):

[0062]

[0063] Let the function be:

[0064]

[0065] Since the function f(β) is a function formed by adding, subtracting and multiplying trigonometric functions, it is a continuous function in the domain. According to the zero point existence theorem, if the graph of the function y=f(x) in the interval [a, b] is a continuous curve, and f(a)f(b)<0, then the function y=f(x) in the interval (a, b) must have a zero point, i.e. there exists x0 in (a, b) such that f(x0)=0. According to the above theorem, for the function f(β), it is only necessary to prove that f(0)f(θ)<0, that is, to prove that formula (7) has a solution.

[0066] Because:

[0067]

[0068] Therefore, as long as f(0)>0, it can be proved that f(0)f(θ)<0, which ensures that formula (7) has a solution, and the following can be obtained:

[0069]

[0070] From the above formula, we have:

[0071]

[0072] That is,

[0073]

[0074] When the above formula is true, formula (7) has a solution in the interval in the interval (0, θ), so the structural surface inclination angle θ needs to be greater than the internal friction angle

[0075] The value of β1 calculated is brought into formula (5) to calculate the maximum value of the anti-sliding force R max The stability coefficient of the sliding block is:

[0076]

[0077] Ensure that the stability coefficient f s calculated is greater than or equal to the stability coefficient f st, the safety level of the slope is determined by the stability coefficient f st According to the specification "Technical Code for Building Slope Engineering GB50330-2013", the stability coefficient f

[0078] Step S3, the section parameters of the deep small diameter anti-slide pile are calculated;

[0079] The calculation formula of the section parameter EA of the deep small diameter anti-slide pile can be obtained from formula (5), (8), and formula (9):

[0080]

[0081] The section parameter of the deep small diameter anti-slide pile can be represented by formula (10), (11), (12).

[0082] EA=E s A p +E m (A-A p ) (10)

[0083]

[0084]

[0085] Wherein, E is the composite elastic modulus of the deep small diameter anti-slide pile; A is the section area of the deep small diameter anti-slide pile; D is the diameter of the deep small diameter anti-slide pile; d is the diameter of the steel reinforcement of the deep small diameter anti-slide pile; E s is the elastic modulus of the steel reinforcement used by the deep small diameter anti-slide pile; E m is the elastic modulus of the mortar used by the deep small diameter anti-slide pile; A p is the section area of the steel reinforcement used by the deep small diameter anti-slide pile.

[0086] Step S4, the axial force of the deep small diameter anti-slide pile is calculated;

[0087] The calculation formula of the axial force F of the deep small diameter anti-slide pile can be obtained from formula (2), formula (3), formula (5), formula (8), and is shown in formula (13):

[0088]

[0089] Wherein, the following formula is used to check the compressive bearing capacity of the small diameter anti-slide pile section.

[0090] F≤A p f y +(A-A p )f c (14)

[0091] Wherein, f c is the compressive strength of the mortar used by the deep small diameter anti-slide pile; fy The compressive strength of the steel bar for the deep-buried small-diameter anti-slide pile.

[0092] In step S5, the anchoring length of the deep-buried small-diameter anti-slide pile is calculated.

[0093]

[0094]

[0095] Wherein, l a The anchoring 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 respectively according to the safety level of the slope, i.e. first level, second level and third level; f rbk The standard value of the ultimate bonding strength between the rock layer and the deep-buried small-diameter anti-slide pile; f b The standard value of the bonding strength between the steel bar and the mortar, which can be determined according to the standard "Technical Code for Building Slope Engineering GB 50330-2013".

[0096] Taking the actual design process of a project as an example, the bulk density of the sliding rock mass is 26.5 kN / m 3 , the thickness of the sliding rock mass is 28.5736 m, the width of the sliding rock mass is 1 m, the horizontal extension length is 1 m, the inclination angle of the outward-inclined structural surface is 11°, the internal friction angle of the structural surface is 6°, and the cohesion of the structural surface is 20 kPa. The safety level of the slope is first level.

[0097] Substituting the above formula and the specific parameters into formula (9), the following formula can be obtained:

[0098] cos11°-cos 3 (11°-β)-tan6°sin(11°-β)cos 2 (11°-β)=0

[0099] The solution is:

[0100] β1=β=2.3357°

[0101] Substituting the above formula and the specific parameters into formula (9), the following formula can be obtained:

[0102]

[0103] The diameter of the deep-buried small-diameter anti-slide pile is 0.15 m, the elastic modulus of the steel bar is 2×10 8 kPa, and the elastic modulus of the mortar is 3×10 7 kPa. Substituting the above formula and the specific parameters into formula (10), (11) and (12), the following formula can be obtained:

[0104]

[0105] ​Solving: the diameter of the reinforcing steel d is greater than or equal to 0 mm.

[0106] The formula (13) can obtain the shaft force of the deep-buried small-diameter anti-slide pile body, and is as follows:

[0107]

[0108] The elastic compressive strength of the reinforcing steel is 300 MPa, the elastic modulus of the mortar is 14.3 MPa, and the formula (14) is as follows:

[0109]

[0110] Solving: the diameter of the reinforcing steel d is greater than or equal to 92.55 mm, and the diameter of the reinforcing steel is 95 mm.

[0111] The standard value of the ultimate bond strength between the rock and the anchoring body is 1000 kPa, and the formula (15) can obtain the anchoring length of the deep-buried small-diameter anti-slide pile, and is as follows:

[0112]

[0113] The standard value of the bond strength between the reinforcing steel and the mortar is 2100 kPa, and the formula (16) can obtain the anchoring length of the deep-buried small-diameter anti-slide pile, and is as follows:

[0114]

[0115] The anchoring length is 12 m.

[0116] As can be seen from the above technical scheme, the design method of the vertical deep-buried small-diameter anti-slide pile reinforcing rock mass outward tilting structural surface provided by the embodiment of the present application firstly derives the anti-slide force calculation formula according to the static force balance, the Mohr-Coulomb criterion and the geometric relationship after the deep-buried small-diameter pile is slightly deflected; the derivative of the anti-slide force with respect to the deflection angle of the deep-buried small-diameter pile is calculated, the derivative function is set to 0, the maximum point and the maximum value of the anti-slide force are obtained; the anti-slide force is set to be greater than or equal to the product of the safety factor of the slope stability and the sliding force, the design section parameters and the shaft force of the deep-buried small-diameter anti-slide pile are obtained; according to the shaft force of the pile body, the compressive bearing capacity of the section of the deep-buried small-diameter anti-slide pile is calculated, and the anchoring length of the deep-buried small-diameter anti-slide pile is calculated. The present application considers the positive role of the shaft force of the deep-buried small-diameter anti-slide pile on the anti-slide, derives the maximum value of the anti-slide force that can be provided by the deep-buried small-diameter anti-slide pile in the deformation process, can obtain more scientific and accurate structural surface parameter values, and can save resources compared with the empirical design method.

[0117] The above description is only the preferred embodiment of the present application and the explanation of the technical principles applied, and is not intended to limit the scope of the application claimed, but only represents the preferred embodiment of the present application. Those skilled in the art should understand that the scope of the application involved in the present application is not limited to the technical solutions formed by the specific combinations of the above technical features, and should also cover other technical solutions formed by the combinations of the above technical features or their equivalent features without departing from the inventive concept. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of the present application.

Claims

1. A design method for reinforcing an outwardly inclined structural plane of a rock mass by vertical deep-buried small-diameter anti-slide piles, characterized in that, The method comprises: Obtaining the dip angle θ of the outer-dipping structural plane of the rock mass, the internal friction angle The cohesion c, the bulk density γ of the sliding mass, the height H of the sliding mass, and the sliding mass width b and the horizontal extension length l borne by a single deep-buried small-diameter anti-slide pile are determined. calculating the flexural inclination β1 of the deep-buried small-diameter anti-slide pile when the anti-slide force is maximum; calculating the section parameter of the deep-buried small-diameter anti-slide pile by using the following four formulas: EA = E s A p +E m (A-A 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 of the deep-buried small-diameter anti-slide pile; E s is the elastic modulus of the steel bar used for the deep-buried small-diameter anti-slide pile; E m is the elastic modulus of the mortar used for the deep-buried small-diameter anti-slide pile; A p is the cross-sectional area of the steel bar used for the deep-buried small-diameter anti-slide pile; F st is the safety factor of the slope stability; calculating the axial force F of the deep-buried small-diameter anti-slide pile by using the following formula: calculating the anchoring length of the deep-buried small-diameter anti-slide pile by using the following two formulas: Wherein, l a is the anchoring 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; f rbk is the standard value of the ultimate bonding strength between the rock layer and the deep-buried small-diameter anti-slide pile, f b is the standard value of the bonding strength between the steel bar and the mortar.

2. The method according to claim 1, wherein, The step of calculating the flexural inclination β1 of the deep-buried small-diameter anti-slide pile when the anti-slide force is maximum comprises: iteratively calculating the β value by using the Newton method when the following formula is established, and letting it be β1, wherein the initial value of β is 0° 3. The method according to claim 1, wherein, The structural plane inclination angle θ is greater than the internal friction angle 4. The method according to claim 1, wherein, The method further comprises: checking the compression bearing capacity of the small-diameter anti-slide pile section by using the following formula: F ≤ A p f y + (A - A p )f c wherein f c is the compressive strength of the mortar used for the deep-buried small-diameter anti-slide pile; f y is the compressive strength of the steel used for the deep-buried small-diameter anti-slide pile.

5. The method according to claim 1, wherein, The bond safety factor K of the deep-buried small-diameter anti-slide pile is respectively taken as 2.6, 2.4 and 2.2 according to the safety levels of the slope, i.e. level one, level two and level three.

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