Foundation pit rock-socketed support pile passive earth pressure calculation method

Abstract

The application provides a calculation method of passive earth pressure of a foundation pit rock-socketed support pile. The calculation of the passive earth pressure comprises the following steps: setting an angle between a passive sliding surface and a horizontal plane as θ, dividing the earth pressure calculation model into three cases according to the relative position relationship between the sliding surface and a reserved rock shoulder in the pit, and establishing equations according to the static equilibrium condition on the sliding body by using the limit equilibrium method to obtain the passive earth pressure expression of the three cases; deriving the earth pressure expression with respect to θ, setting the equation as 0 to obtain θ' of different cases, comparing θ' with limit angles θ1 and θ2 of the three cases, selecting a suitable θ value to be substituted into the corresponding passive earth pressure equation, respectively obtaining the passive earth pressure of the three cases, and taking the minimum value as the actual passive earth pressure. The application fully considers the passive earth pressure provided by the reserved rock shoulder in the soil-rock combined foundation pit, so that the calculated passive earth pressure is more in line with the field conditions, and the calculation formula is simple and practical.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, specifically to a method for calculating passive earth pressure on foundation pit embedded rock support piles. Background Technology

[0002] The problem of solving earth pressure has always been one of the hot topics in geotechnical engineering. At present, most traditional earth pressure calculations use classical Rankine and Coulomb earth pressure theories or expressions modified from classical earth pressure theories. However, all of the above theories are based on the basic assumption that the soil behind the wall is a semi-infinite space.

[0003] In deep foundation pit support engineering in soil-rock strata, pile-anchor support structures are commonly used. With the increase in underground space development projects, the excavation depth of foundation pits is getting greater and greater, and the support piles need to be embedded deep into the rock strata. However, considering factors such as economy and construction difficulty, the embedment depth of the support piles is limited and cannot reach the bottom of the foundation pit, thus forming a "suspended pile" support system. The calculation theory for this type of support system in the current specifications is not yet mature.

[0004] In "suspended pile" support systems, a rock shoulder of a certain width is often reserved in the pit to help constrain the displacement of the support piles. If the passive earth pressure in this situation is calculated using the classical Rankine and Coulomb earth pressure theories, the limited width of the reserved rock shoulder means that the straight slip surface, as assumed by the classical earth pressure theory, cannot extend to the soil surface, contradicting the assumption of a semi-infinite space. Clearly, the classical Rankine and Coulomb earth pressure theories are unsuitable for this specific working condition.

[0005] Therefore, it is hoped that a method for calculating earth pressure on rock-socketed retaining piles in soil-rock combined foundation pits can be found to improve the design level of existing foundation pit support structures. Summary of the Invention

[0006] The purpose of this invention is to provide a method for calculating passive earth pressure on foundation pit embedded rock support piles, aiming to optimize the limitations of existing earth pressure calculation theories, reduce support costs, and avoid resource waste.

[0007] To achieve the above technical objectives, this invention proposes a method for calculating passive earth pressure on foundation pit embedded rock support piles, specifically including the following steps:

[0008] Step 1: Determine the design calculation parameters for the rock-socketed support piles, including: the rock-socketing depth H of the support pile, the width of the reserved rock shoulder b, the height of the reserved rock shoulder h, the soil weight γ, the cohesion c, and the internal friction angle. Pile-soil cohesion c w Pile-soil external friction angle δ, passive earth pressure E p , ;

[0009] Step 2: The angle between the passive slip surface and the horizontal plane is θ. Based on the relative positional relationship between the slip surface and the reserved rock shoulder in the pit, an earth pressure calculation model is established. The earth pressure calculation model is divided into three types: slip surface through the top surface of the rock shoulder, slip surface through the side wall of the rock shoulder, and slip surface through the base.

[0010] Step 3: Perform force analysis on the passive lateral sliding soil wedge of the rock-socketed support pile under the ultimate state, and establish the static equilibrium equations in the horizontal and vertical directions:

[0011]

[0012] In the above formula: R is the supporting reaction force of the stationary soil mass on the sliding soil wedge, K is the cohesion of the stationary soil mass on the sliding soil wedge, K w W represents the adhesion force between the support pile and the sliding soil wedge, and W represents the weight of the sliding soil wedge.

[0013] Step 4: Simplify the equations from Step 3 according to the three cases in Step 2 to obtain the passive earth pressure E under the three cases. p The calculation formula is as follows:

[0014] (1) When the slip surface passes through the top surface of the rock shoulder, i.e., Hcotθ≤b, the parameter values ​​are as follows:

[0015]

[0016] Obtain the passive earth pressure E p :

[0017]

[0018] (2) When the slip surface passes through the sidewall of the rock shoulder, i.e., b < Hcotθ ≤ b + hcotθ, the parameter values ​​are as follows:

[0019]

[0020] Obtain the passive earth pressure E p :

[0021]

[0022] (3) When the slip surface passes through the base, i.e., Hcotθ>b+hcotθ, the parameter values ​​are as follows:

[0023]

[0024] Obtain the passive earth pressure E p :

[0025]

[0026] Step 5: Apply passive earth pressure Ep Differentiating the angle θ between the passive slip surface and the horizontal plane, we obtain...

[0027]

[0028] Step Six: Establish the XY-axis plane coordinate system with the deepest point of the retaining pile embedded in the rock as the origin O. The top surface of the reserved rock shoulder in the pit intersects with the sidewall at point A, and the sidewall of the reserved rock shoulder in the pit intersects with the base at point B. Let the angle between OA and the negative X-axis be θ1, and the angle between OB and the negative X-axis be θ2. Calculate the three cases in Step Four respectively, substitute them into formula ④ in Step Five to obtain the corresponding θ', compare θ' with θ1 and θ2, and select the appropriate value to substitute into the corresponding formula in Step Four to calculate the corresponding passive earth pressure E. p1 E p2 E p3 The minimum value is taken as the actual passive earth pressure, and the specific process is as follows:

[0029] a. When the slip surface passes through the top surface of the rock shoulder, calculate the value of θ, i.e., θ', according to formulas ① and ④; compare the magnitude of θ' with θ1. If θ' > θ1, then substitute θ = θ' into formula ① to calculate E. p1 If θ'≤θ1, then substitute θ=θ1 into formula ① to calculate E. p1 ;

[0030] b. When the slip surface passes through the sidewall of the rock shoulder, calculate the value of θ, i.e., θ', according to formulas ② and ④; compare the magnitudes of θ' with θ1 and θ2. If θ2 < θ' < θ1, then substitute θ = θ' into formula ② to calculate E. p2 Otherwise, substitute θ = θ1 and θ = θ2 into formula ② respectively, and use the smaller value as E. p2 ;

[0031] c. When the slip surface passes through the substrate, calculate the value of θ, i.e., θ', according to formula ③; compare the magnitudes of θ' and θ2. If θ' < θ2, then substitute θ = θ' into formula ③ to calculate E. p3 If θ' ≥ θ2, then θ = θ2. Substitute this into formula ③ to calculate E. p3 .

[0032] A further technical solution of the present invention: the soil surface is horizontal and there is no load.

[0033] A further technical solution of the present invention: In step one, the pile-soil cohesion c w The formula for calculating the pile-soil external friction angle δ is as follows:

[0034]

[0035]

[0036] A further technical solution of the present invention: The passive earth pressure calculation formula obtained in step four is as follows, and the relevant parameters in the following formula are the same as those in claim 1:

[0037]

[0038] A further technical solution of the present invention: in step five It can be simplified as follows:

[0039]

[0040] To solve for the dip angle θ' of the slip surface, we should first substitute the known parameters to simplify the equation, and then use Matlab software to solve this complex trigonometric function equation.

[0041] The beneficial effects of this invention are as follows: The passive earth pressure calculation method for rock-embedded support piles in foundation pits provided by this invention can take into account the soil resistance provided by the pre-reserved rock shoulder in the pit, resulting in a more accurate and reasonable passive earth pressure. The calculation formula is simple and practical, and can be applied to the calculation of passive earth pressure of rock-embedded support piles in soil-rock combined foundation pits. The simple and practical calculation formula has certain promotion and application value for optimizing the design of support structures and reducing the cost of foundation pit projects. Attached Figure Description

[0042] Figure 1 This is a flowchart illustrating the earth pressure calculation method described in this invention;

[0043] Figure 2 This is the earth pressure calculation and analysis model for three cases of slip surface in this invention;

[0044] Figure 3 These are force analysis diagrams for three types of sliding soil wedges;

[0045] Figure 4 This is a diagram illustrating the earth pressure calculation steps in this invention;

[0046] Figure 5 This is the earth pressure calculation and analysis model in the embodiment.

[0047] In the diagram: 1—Ground surface, 2—Support structure, 3—Reserved rock shoulder, 4—Base, 5—Slip surface. Detailed Implementation

[0048] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. Figures 1 to 5 The accompanying drawings are all embodiments of the present invention, simplified to concisely and clearly illustrate the purpose of the embodiments. However, it should be understood that the scope of the specific implementation of the present invention is not limited to the content of the embodiments and can be implemented in various forms. These embodiments are provided solely for the purpose of more fully disclosing the content of the present invention.

[0049] In this invention, the same parameter symbols refer to the same parameter.

[0050] This invention provides a method for calculating passive earth pressure on foundation pit embedded rock support piles. Specifically, addressing the limitations of the semi-infinite space assumption in traditional earth pressure theory, it designs a passive earth pressure calculation method that considers the soil resistance of the reserved rock shoulder. The calculation method is described in [reference needed]. Figure 1 This includes the following steps:

[0051] Step 1: Determine the design calculation parameters for the rock-socketed support piles, assuming the soil surface is horizontal and unloaded; including: the rock-socketing depth H of the support pile, the width b of the reserved rock shoulder, the height h of the reserved rock shoulder, the soil weight γ, the cohesion c, and the internal friction angle. Pile-soil cohesion c w The external friction angle δ between the pile and the soil, and the magnitude of the passive earth pressure are represented by E. p This indicates that the parameters in the following formulas all match the parameters mentioned above, and the mechanical parameters appearing in the following formulas are all consistent with those in step one; wherein the pile-soil cohesion c w The formula for calculating the pile-soil external friction angle δ is as follows:

[0052]

[0053]

[0054] Step Two: Let θ be the angle between the passive slip surface and the horizontal plane. Based on the relative positional relationship between the slip surface and the reserved rock shoulder in the pit, the earth pressure calculation model is divided into three forms, as detailed below. Figure 2 The above, Figure 2 The number 5 in the figure represents the slip surface corresponding to the three calculation models, which are, from top to bottom, the slip surface passing through the top surface of the rock shoulder, the slip surface passing through the sidewall of the rock shoulder, and the slip surface passing through the basement.

[0055] Step 3: Perform stress analysis on the passive lateral sliding soil wedge of the rock-socketed support pile under the ultimate state, such as... Figure 3 ,in Figure 3 (a) is a force analysis diagram of the passive lateral sliding soil wedge of the rock-embedded support pile under the ultimate state of the slip surface passing through the top surface of the rock shoulder; Figure 3 (b) is a force analysis diagram of the passive lateral sliding soil wedge of the rock-embedded support pile under the ultimate state of the slip surface passing through the rock shoulder sidewall; Figure 3 (c) is a force analysis diagram of the passive lateral sliding soil wedge of the rock-socketed support pile under the ultimate state of the slip surface passing through the base;

[0056] Establish the static equilibrium equations in the horizontal and vertical directions:

[0057]

[0058] In the formula: R is the supporting reaction force of the stationary soil mass on the sliding soil wedge, K is the cohesion of the stationary soil mass on the sliding soil wedge, K w W represents the adhesion force between the support pile and the sliding soil wedge, and W represents the weight of the sliding soil wedge.

[0059] Step 4: Simplify the equations from Step 3 according to the three cases in Step 2 to obtain the passive earth pressure E under the three cases. p The calculation formula is as follows:

[0060] (1) When the slip surface passes through the top surface of the rock shoulder, i.e., Hcotθ≤b, the parameter values ​​are as follows:

[0061]

[0062] Substituting and simplifying, we get the passive earth pressure E. p :

[0063]

[0064] (2) When the slip surface passes through the sidewall of the rock shoulder, i.e., b < Hcotθ ≤ b + hcotθ, the parameter values ​​are as follows:

[0065]

[0066] Substituting and simplifying, we get the passive earth pressure E. p :

[0067]

[0068] (3) When the slip surface passes through the substrate, i.e., Hcotθ>b+hcotθ, the parameter values ​​are as follows:

[0069] Substituting and simplifying, we get the passive earth pressure E. p :

[0070]

[0071] Step 5: Place E p Differentiating with respect to θ, we get as follows:

[0072]

[0073] make

[0074] Substitute the known parameters into the formula for simplification. Based on the location of the slip surface, select the corresponding formula from step four, substitute the known parameters into the formula for simplification, and use Matlab software to solve the problem. At this point, calculate the θ value (θ') for the three cases, and the corresponding E. p This is the resultant force of passive earth pressure.

[0075] Step Six: As Figure 4 As shown, establish the XY-axis plane coordinate system with the deepest point of the retaining pile embedded in the rock as the origin O. The top surface of the reserved rock shoulder in the pit intersects with the sidewall at point A, and the sidewall of the reserved rock shoulder in the pit intersects with the base at point B. Let the angle between OA and the negative X-axis be θ1, and the angle between OB and the negative X-axis be θ2. Calculate the three cases in step four respectively, substitute them into formula ④ in step five to obtain the corresponding θ', compare θ' with θ1 and θ2, and select the appropriate value to substitute into the corresponding formula in step four to calculate the corresponding passive earth pressure E. p1 E p2 E p3 The minimum value is taken as the actual passive earth pressure, and the specific process is as follows:

[0076] a. When the slip surface passes through the top surface of the rock shoulder, i.e., the slip surface is located to the right of the straight line OA, calculate the value of θ, i.e., θ', according to formulas ① and ④; compare the magnitude of θ' with θ1. If θ' > θ1, it indicates that there is a minimum slip surface location. Then substitute θ = θ' into formula ① to calculate E. p1 Otherwise, substitute θ = θ1 into formula ① to calculate E. p1 ;

[0077] b. When the slip surface passes through the rock shoulder sidewall, i.e., when the slip surface is located between lines OA and OB, calculate the value of θ, i.e., θ', according to formulas ② and ④; compare the magnitudes of θ' with θ1 and θ2. If θ2 < θ' < θ1, it indicates the existence of a minimum slip surface location. Then, substitute θ = θ' into formula ② to calculate E. p2 Otherwise, substitute θ = θ1 and θ = θ2 into formula ② respectively, and use the smaller value as E. p2 ;

[0078] c. When the slip surface passes through the base, i.e., the slip surface is located to the left of line OB, calculate the value of θ, i.e., θ', according to formula ③; compare the magnitudes of θ' and θ2. If θ' < θ2, it indicates the existence of a minimum slip surface location. Then, substitute θ = θ' into formula ③ to calculate E. p3 Otherwise, substitute θ = θ² into formula ③ to calculate E. p3 .

[0079] The invention will be further described below with reference to specific embodiments. The embodiments are for a foundation pit in Wuhan with a soil-rock combined stratum structure. The foundation pit is 10m deep, and the support method is bored piles + internal bracing. The exposed rock layer on the south side is relatively shallow, 7m below the ground. The overlying soil layer consists of miscellaneous fill, medium-fine sand, and silty clay, while the underlying rock layer is mainly weathered rock. To save construction costs and reduce construction difficulty, a suspended pile support method is adopted. The pile bottom rock embedment depth H = 2.5m, the reserved rock shoulder width b = 1m, and the height h = 3m. According to the geological survey report, the relevant foundation pit support design parameters are shown in Table 1.

[0080] Table 1 Design parameters for foundation pit support

[0081]

[0082] The analysis is performed on a unit length of soil. Assuming the angle between the passive slip surface and the horizontal plane is θ, the calculation and analysis model is as follows: Figure 5 ,pass Figure 5 It can be seen that the slip surface in the embodiment will only have two cases: passing through the top surface of the reserved rock shoulder and the side wall of the reserved rock shoulder. There is no case where it passes through the base. Therefore, at this time, we only need to consider the two cases when the slip surface passes through the top surface of the rock shoulder and when the slip surface passes through the side wall of the rock shoulder.

[0083] The following parameters have been determined in the embodiments: the rock embedment depth H of the retaining pile, the width b of the reserved rock shoulder, the height h of the reserved rock shoulder, the soil weight γ, the cohesion c, and the internal friction angle. And according to the formula Calculate the pile-soil cohesion c w According to the formula Calculate the pile-soil external friction angle δ, and use E to represent the magnitude of the passive earth pressure. p express;

[0084] Substitute the relevant parameters from the examples into formulas ① and ② respectively, and E p Differentiate with respect to θ, let Combining formulas ① and ②, we can calculate that θ' = 58° when the slip surface passes through the top surface of the rock shoulder, and θ' = 31° when the slip surface passes through the sidewall of the rock shoulder.

[0085] In the first scenario, when the slip surface passes through the top surface of the rock shoulder, the line connecting the pile bottom to the top of the rock shoulder intersects with the horizontal line at the pile bottom (i.e., ...). Figure 4 Given that the angle between OA and the negative x-axis is θ1 = 68.2°, comparing θ' = 58° and θ1 = 68.2°, we can see that θ' < θ1. Therefore, substituting θ = 68.2° into formula ①, we can calculate E. p1 =1265.2kN / m;

[0086] In the second scenario, when the slip surface passes through the sidewall of the rock shoulder, the line connecting the pile bottom to the top of the rock shoulder intersects with the horizontal line at the pile bottom (i.e., ...). Figure 4 The angle between OA and the negative x-axis) θ1 = 68.2°, and the line connecting the bottom of the pile to the bottom of the rock shoulder (i.e. Figure 4 Since OB is located below the negative x-axis, it is clear that θ2 < θ' < θ1, indicating the existence of a minimum slip surface location. Substituting θ = 31° into formula ②, we can calculate E. p2 = 705.4 kN / m.

[0087] Therefore, comparing E p1 and E p2 The size of its E p2The smaller the value, the better option is E. p2 E can be calculated from the actual passive earth pressure value. p = 705.4 kN / m.

[0088] The inventors of this application also used the traditional Coulomb earth pressure theory to calculate the passive earth pressure E for this embodiment. p =586.7 kN / m. Compared with traditional methods, the passive earth pressure calculated by this invention is larger and more in line with the actual situation. In the design of foundation pit support, more consideration can be given to the passive earth pressure provided by the reserved rock shoulder, thereby optimizing the support structure design and reducing the project cost.

[0089] Finally, it should be noted that the above embodiments are only used to illustrate specific implementations of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above examples, those skilled in the art should understand that various modifications and changes in form and detail can be made without departing from the spirit of the present invention and without deviating from the scope defined by the claims of the present invention.

Claims

1. A method for calculating passive earth pressure on foundation pit embedded rock support piles, characterized in that, The method includes the following steps: Step 1: Determine the design calculation parameters for the rock-socketed support piles, including: the rock-socketing depth H of the support pile, the width of the reserved rock shoulder b, the height of the reserved rock shoulder h, the soil weight γ, the cohesion c, and the internal friction angle. Pile-soil cohesion c w Pile-soil external friction angle δ, passive earth pressure E p , ; Step 2: The angle between the passive slip surface and the horizontal plane is θ. Based on the relative positional relationship between the slip surface and the reserved rock shoulder in the pit, an earth pressure calculation model is established. The earth pressure calculation model is divided into three types: slip surface through the top surface of the rock shoulder, slip surface through the side wall of the rock shoulder, and slip surface through the base. Step 3: Perform force analysis on the passive lateral sliding soil wedge of the rock-socketed support pile under the ultimate state, and establish the static equilibrium equations in the horizontal and vertical directions: In the above formula: R is the supporting reaction force of the stationary soil mass on the sliding soil wedge, K is the cohesion of the stationary soil mass on the sliding soil wedge, K w W represents the adhesion force between the support pile and the sliding soil wedge, and W represents the weight of the sliding soil wedge. Step 4: Simplify the equations from Step 3 according to the three cases in Step 2 to obtain the passive earth pressure E under the three cases. p The calculation formula is as follows: (1) When the slip surface passes through the top surface of the rock shoulder, i.e., Hcotθ≤b, the parameter values ​​are as follows: Obtain the passive earth pressure E p : (2) When the slip surface passes through the sidewall of the rock shoulder, i.e., b < Hcotθ ≤ b + hcotθ, the parameter values ​​are as follows: Obtain the passive earth pressure E p : (3) When the slip surface passes through the base, i.e., Hcotθ>b+hcotθ, the parameter values ​​are as follows: Obtain the passive earth pressure E p : Step 5: Apply passive earth pressure E p Differentiating the angle θ between the passive slip surface and the horizontal plane, we obtain... Step Six: Establish the XY-axis plane coordinate system with the deepest point of the retaining pile embedded in the rock as the origin O. The top surface of the reserved rock shoulder in the pit intersects with the sidewall at point A, and the sidewall of the reserved rock shoulder in the pit intersects with the base at point B. Let the angle between OA and the negative X-axis be θ1, and the angle between OB and the negative X-axis be θ2. Calculate the three cases in Step Four respectively, substitute them into formula ④ in Step Five to obtain the corresponding θ', compare θ' with θ1 and θ2, and select the appropriate value to substitute into the corresponding formula in Step Four to calculate the corresponding passive earth pressure E. p1 E p2 E p3 The minimum value is taken as the actual passive earth pressure, and the specific process is as follows: a. When the slip surface passes through the top surface of the rock shoulder, calculate the value of θ, i.e., θ', according to formulas ① and ④; compare the magnitude of θ' with θ1. If θ' > θ1, then substitute θ = θ' into formula ① to calculate E. p1 If θ'≤θ1, then substitute θ=θ1 into formula ① to calculate E. p1 ; b. When the slip surface passes through the sidewall of the rock shoulder, calculate the value of θ, i.e., θ', according to formulas ② and ④; compare the magnitudes of θ' with θ1 and θ2. If θ2 < θ' < θ1, then substitute θ = θ' into formula ② to calculate E. p2 Otherwise, substitute θ = θ1 and θ = θ2 into formula ② respectively, and use the smaller value as E. p2 ; c. When the slip surface passes through the substrate, calculate the value of θ, i.e., θ', according to formula ③; compare the magnitudes of θ' and θ2. If θ' < θ2, then substitute θ = θ' into formula ③ to calculate E. p3 If θ' ≥ θ2, then θ = θ2. Substitute this into formula ③ to calculate E. p3 .

2. The method for calculating passive earth pressure on foundation pit embedded rock support piles according to claim 1, characterized in that: The soil surface is horizontal and there is no load acting on it.

3. The method for calculating passive earth pressure on rock-socketed support piles in foundation pits according to claim 1, characterized in that: In step one, the soil-pile cohesion c w The formula for calculating the pile-soil external friction angle δ is as follows:

4. The method for calculating passive earth pressure on foundation pit embedded rock support piles according to claim 1, characterized in that: The formula for calculating passive earth pressure obtained in step four is as follows:

5. The method for calculating passive earth pressure on foundation pit embedded rock support piles according to claim 1, characterized in that: In step five The calculation process is as follows: The solution process for the sixth type of slip surface dip angle θ' is as follows: first, based on the location of the slip surface, substitute each known parameter into the above formula to simplify, and then use Matlab software to solve this complex trigonometric function equation.

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