Method for calculating passive earth pressure of finite soil body considering narrow foundation pit space effect, storage medium and application

Abstract

This invention relates to a method, storage medium, and application for calculating passive earth pressure on finite soil considering the spatial effect of narrow foundation pits. The method includes: acquiring calculation parameters for the narrow foundation pit, determining the spatial effect amplification factor, and obtaining the passive earth pressure of the soil taking into account the spatial effect. The spatial effect amplification factor is calculated based on a fitting formula. The fitting formula is obtained by: establishing a passive earth wedge mechanical model of the finite soil, calculating the passive earth pressure of the finite soil at different depths, and then calculating the passive earth pressure intensity of the finite soil; defining the ratio of the passive earth pressure intensity of the finite soil to the improved Rankine passive earth pressure intensity as the spatial effect amplification factor; plotting the spatial effect amplification factor curves for different foundation pit widths, and establishing the fitting formula for the spatial effect amplification factor. Compared with existing technologies, this invention can more accurately and quantitatively assess the spatial effect, thereby obtaining more precise passive earth pressure. It can be used to optimize the penetration depth of retaining piles in narrow foundation pits and has significant engineering application value.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, and in particular to a method, storage medium, and application for calculating passive earth pressure in finite soil considering the spatial effect of narrow foundation pits. Background Technology

[0002] The overturning stability safety factor is a key control indicator for the penetration depth of foundation pit support piles in soft soil areas. Current specifications are based on classical earth pressure theory, which is simple to calculate but does not consider the beneficial effects of narrow foundation pit space.

[0003] Engineering practice shows that the smaller the width of the foundation pit, the more significant the spatial effect, the smaller the deformation of the retaining structure, the better the stability, and the shallower the required embedment depth. The original Shanghai Municipal Standard for Foundation Pit Engineering Design (DBJ08-61-97), Article 10.2.3.3, stipulated that the insertion ratio of the pipeline trench could be 0.5 to 0.8, and a large amount of monitoring data verified its reliability. However, the 2010 version of the standard deleted this clause, leading to a significant increase in the embedment depth of the pipeline trench retaining piles. This resulted in waste and increased the adverse effects of temporary sheet pile driving and extraction.

[0004] The narrow foundation pit has a small width-to-depth ratio, which does not satisfy the basic assumption of the passive zone soil being a semi-infinite body in classical earth pressure theory. Under the ultimate condition, the passive slip surface will extend to the retaining piles on the opposite side, making it unreasonable to continue using Rankine's theory for calculations.

[0005] Existing research indicates that the stability analysis methods for foundation pits, proposed earlier by Terzaghi, Peck, and others, which consider the width of the foundation pit, have significant limitations because they do not take into account the influence of the embedded section of the retaining piles. The literature "Influence of Foundation Pit Width on the Stability of Retaining Structures" (Wang Hongxin. Journal of Civil Engineering, 2011, 44(6): 120-126.) classifies foundation pits based on the width-to-depth ratio and proposes a corresponding method for calculating the overturning safety factor. However, its inference regarding the "tightening effect of trapezoidal passive soil wedges" is based on the rigid body assumption and ignores the secondary slip surfaces that may be generated inside the soil, leading to an overestimation of the beneficial influence of the narrow foundation pit space effect on the stability against overturning.

[0006] Numerous studies on the theory of earth pressure in finite soil have shown that classical Rankine or Coulomb theories tend to lead to conservative foundation pit designs. The literature "Analysis of Passive Earth Pressure on Rigid Retaining Walls in Translational Mode of Narrow Foundation Pit" (Ying Hongwei, Rock and Soil Mechanics, 2011, 32(12): 3755-3762) establishes a calculation model for passive earth pressure in finite soil within narrow foundation pits based on the Coulomb plane wedge assumption. It assumes that the passive zone generates associated broken-line slip surfaces and derives analytical solutions for the slip surface inclination angle and the passive earth pressure coefficient. Although this research has made significant progress in understanding the mechanism of earth pressure increase, its calculation formula requires complex iterative solutions. Furthermore, the use of a small-scale model with aspect ratio as the main parameter results in the earth pressure coefficient being concentrated in the steeply descending section of the curve, making it difficult to establish a quantitative relationship with spatial effects and limiting its engineering applications. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a simplified calculation method, a highly reliable method for calculating passive earth pressure in finite soil that considers the spatial effect of narrow foundation pits, as well as its storage medium and application, which can be used to optimize the depth of retaining piles.

[0008] The objective of this invention can be achieved through the following technical solutions:

[0009] A method for calculating passive earth pressure in finite soil considering the spatial effects of narrow foundation pits includes the following steps:

[0010] Obtain the calculation parameters for narrow foundation pits, and determine the spatial effect amplification factor based on the calculation parameters for narrow foundation pits;

[0011] The passive earth pressure intensity of the soil is obtained by calculating the spatial effect amplification factor and the improved Rankine method, and then the passive earth pressure of the soil is obtained.

[0012] The spatial effect amplification coefficient is calculated based on a fitting formula, which is specifically obtained by:

[0013] A finite soil passive earth wedge mechanical model is established. Based on the mechanical model, the passive earth pressure of the finite soil at different depths is simulated and calculated. Based on the passive earth pressure, the passive earth pressure intensity of the finite soil is calculated. The ratio of the simulated passive earth pressure intensity of the finite soil to the improved Rankine passive earth pressure intensity is defined as the spatial effect amplification factor.

[0014] Plot the spatial effect amplification coefficient curves for different foundation pit widths, introduce the ultra-deep adjacency ratio as the independent variable, merge the spatial effect amplification coefficient curves for different foundation pit widths into one, and establish a fitting formula for the spatial effect amplification coefficient.

[0015] Furthermore, this calculation method satisfies the following assumptions:

[0016] a) The retaining piles are rigid retaining walls, and the retaining piles undergo translational displacement into the foundation pit;

[0017] b) The passive zone soil produces associated broken-line slip surfaces;

[0018] c) All slip surfaces simultaneously reach the passive limit state;

[0019] d) Consider the external friction angle between the pile and the soil, and ignore the cohesion between the pile and the soil.

[0020] Furthermore, the calculation parameters for the narrow foundation pit include soil cohesion, foundation pit width, depth of retaining piles, internal friction angle, and reduction factor for pile-soil external friction angle.

[0021] Furthermore, when constructing the fitting formula for the spatial effect amplification coefficient, the pit width and the depth of the retaining piles are parameterized as the ultra-deep adjacent ratio, and the fitting formula for the spatial effect amplification coefficient is constructed as a function of the ultra-deep adjacent ratio, the internal friction angle, and the reduction coefficient of the pile-soil external friction angle.

[0022] Furthermore, the formula for obtaining the ultra-deep proximity ratio is:

[0023] ,

[0024] , ,

[0025] In the formula, h b is the depth of the retaining piles embedded in the soil, and b is the width of the foundation pit. , The dip angle of the sliding surface is the boundary angle. It is an ultra-deep adjacent ratio.

[0026] Furthermore, when the soil is determined to be cohesive-free based on soil cohesion, the fitting formula for the spatial effect amplification factor is:

[0027] ,

[0028] In the formula, the coefficients , , , Both B and φ are reduction coefficients for the internal friction angle φ and the external friction angle of the pile and soil. The function, It is an ultra-deep adjacent ratio.

[0029] Furthermore, when the soil is determined to be cohesive based on soil cohesion, the spatial effect amplification factor includes the φ term. and option C ,in:

[0030] ,

[0031] ,

[0032] In the formula, the coefficients , , , , Both B and φ are reduction coefficients for the internal friction angle φ and the external friction angle of the pile and soil. The function, , The critical depth at which a slip surface is generated.

[0033] Furthermore, the passive earth pressure intensity of the soil calculated based on the spatial effect amplification factor and the improved Rankine method is specifically as follows:

[0034] The passive earth pressure strength of the soil that takes into account spatial effects is obtained by multiplying the aforementioned spatial effect amplification factor in the passive earth pressure strength formula of the improved Rankine method.

[0035] The present invention also provides a computer-readable storage medium including one or more programs executable by one or more processors of an electronic device, the one or more programs including instructions for performing the method for calculating passive earth pressure on finite soil considering the spatial effects of narrow foundation pits as described above.

[0036] Furthermore, an application of a finite soil passive earth pressure calculation method based on the narrow foundation pit space effect, as described above, in the optimization of retaining pile penetration depth, is proposed. Based on the calculated passive earth pressure, the overturning stability safety factor corresponding to different retaining pile penetration depths is determined, thereby obtaining the optimal retaining pile penetration depth.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1. This invention proposes a spatial effect amplification factor. Based on the spatial effect amplification factor and the improved Rankine method, the passive earth pressure of the soil is obtained by simplifying the calculation, which effectively avoids the complexity of high-order iteration and solving cubic equations, significantly improves the calculation efficiency, and lays a reliable foundation for the subsequent engineering application of the spatial effect amplification factor.

[0039] 2. This invention can more accurately and quantitatively assess the spatial effect of narrow foundation pits by increasing the spatial effect coefficient, thereby obtaining more accurate passive earth pressure. It can be used to optimize the penetration depth of retaining piles and has significant engineering application value. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the process of the present invention;

[0041] Figure 2This is a schematic diagram of the passive earth pressure calculation model for narrow foundation pit finite soil constructed in an embodiment of the present invention, wherein (a) is a single slip surface model, (b) is a double slip surface model, and (c) is a multi-slip surface model;

[0042] Figure 3 This is a schematic diagram of a typical passive soil wedge equilibrium force system;

[0043] Figure 4 Comparison of multi-width foundation pit enlargement coefficients (R) in embodiments of the present invention slb (where y is the vertical axis)

[0044] Figure 5 This is a scatter plot of coefficient A1 in an embodiment of the present invention;

[0045] Figure 6 This is a scatter plot of coefficient A2 in an embodiment of the present invention;

[0046] Figure 7 This is a scatter plot of coefficient A3 in an embodiment of the present invention;

[0047] Figure 8 This is a scatter plot of coefficient A4 in an embodiment of the present invention;

[0048] Figure 9 This is a scatter plot of coefficient B in an embodiment of the present invention;

[0049] Figure 10 This is a comparison of the fitting of the spatial effect amplification coefficient when φ=5︒ in the embodiments of the present invention;

[0050] Figure 11 This is a comparison of the fitting of the spatial effect amplification coefficient when φ=17︒ in the embodiments of the present invention;

[0051] Figure 12 This is a comparison of the fitting of the spatial effect amplification coefficient when φ=30︒ in the embodiments of the present invention;

[0052] Figure 13 In this embodiment of the invention, φ = 17︒. =2 / 3 space increase coefficient curve;

[0053] Figure 14 This is a comparison of the expansion coefficient curves for foundation pits of different widths in embodiments of the present invention;

[0054] Figure 15 This is a scatter plot of coefficient A5 in an embodiment of the present invention;

[0055] Figure 16 This is a cross-sectional view of the foundation pit in an embodiment of the present invention. Detailed Implementation

[0056] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0057] This embodiment provides a method for calculating passive earth pressure on finite soil considering the spatial effects of narrow foundation pits, including the following steps:

[0058] S1. Obtain the calculation parameters for the narrow foundation pit, and determine the spatial effect amplification factor based on the calculation parameters for the narrow foundation pit. Specifically, the calculation parameters for the narrow foundation pit include soil cohesion, foundation pit width, depth of retaining piles into the soil, internal friction angle, and reduction factor of pile-soil external friction angle, etc.

[0059] S2. The passive earth pressure intensity of the soil is calculated based on the spatial effect amplification factor and the improved Rankine method, and then the passive earth pressure of the soil is obtained. The spatial effect amplification factor is calculated based on the fitting formula.

[0060] The above method proposes using the spatial effect amplification coefficient as the core parameter for quantifying the spatial effect of narrow foundation pits, which can more accurately and quantitatively assess the spatial effect of narrow foundation pits.

[0061] Specifically, the spatial effect amplification factor is defined as the ratio of the passive earth pressure intensity in a finite space to the improved Rankine passive earth pressure intensity. That is, the modified passive earth pressure intensity of the soil is obtained by multiplying the spatial effect amplification factor in the passive earth pressure intensity formula of the improved Rankine method.

[0062] like Figure 1 As shown, the process of obtaining the fitting formula for the narrow foundation pit space effect amplification factor in this embodiment includes:

[0063] A mechanical model of passive soil wedges in finite soil is established. A calculation program is developed based on the mechanical model to calculate the passive earth pressure at each depth of the finite soil. The passive earth pressure intensity of the finite soil is calculated based on the passive earth pressure.

[0064] The spatial effect amplification factor is determined based on the ratio of the passive earth pressure intensity to the improved Rankine passive earth pressure intensity.

[0065] Plot the spatial effect amplification coefficient curves for different foundation pit widths, compare the spatial effect amplification coefficient curves for different widths, introduce the ultra-deep adjacency ratio as the independent variable, merge the spatial effect amplification coefficient curves for different widths into one, and fit to obtain a simplified calculation formula for the spatial effect amplification coefficient applicable to cohesive and non-cohesive soils.

[0066] Furthermore, different fitting formulas for the spatial effect amplification factor can be obtained for different soil layers.

[0067] In practical applications, the passive earth pressure intensity considering the narrow pit space effect can be obtained by multiplying the improved Rankine earth pressure intensity formula by the space effect amplification factor. The safety factor for overturning stability of the foundation, the safety factor for heave at the bottom of the pit, and the internal force calculation program of the foundation pit can be calculated according to the passive earth pressure intensity, so as to quantitatively calculate the beneficial effect of the narrow pit space effect on the foundation pit.

[0068] Furthermore, the fitting formula for the spatial effect amplification factor in this embodiment is determined through the following derivation process:

[0069] I. Establishment of a Calculation Model for Passive Earth Pressure on Limited Soil in Narrow Foundation Pit

[0070] 1. Basic Assumptions:

[0071] a) The retaining piles are rigid retaining walls, and the retaining piles undergo translational displacement into the foundation pit;

[0072] b) The passive zone soil produces associated broken-line slip surfaces;

[0073] c) All slip surfaces simultaneously reach the passive limit state;

[0074] d) Consider the external friction angle between the pile and the soil, and ignore the cohesion between the pile and the soil.

[0075] 2. Calculation Model

[0076] Based on Coulomb's plane soil wedge theory, a theoretical calculation model for passive earth pressure on finite soil in narrow foundation pits is established, such as... Figure 2 As shown, it includes single-slip surface model, double-slip surface model and multi-slip surface model.

[0077] 1) Single slip surface model

[0078] When the depth of the retaining piles into the soil ( When the critical depth for generating the second slip surface is reached, only a single slip surface is generated in the passive zone. The slip surface intersects with the pit bottom within the pit area, forming a triangle ΔABC, where the height of AB is... .

[0079] Soil wedge parameters: height h, unit weight γ internal friction angle φ Cohesion C, pile-soil external friction angle δ Slip surface dip angle θ Given the passive earth pressure E, the resultant force of cohesion at the slip surface T, and the resultant force of the normal force and frictional force R, and considering that the soil wedge is in a passive limit equilibrium state, the static equilibrium equations for the sliding soil wedge are established as follows:

[0080] Horizontal direction: (1)

[0081] Vertical horizontal:

[0082] (2)

[0083] Joint (1) (2) elimination R 1 The expression for passive earth pressure is:

[0084] (3)

[0085] Through extreme value conditions Solve for the dip angle of the slip surface E1 corresponds to passive earth pressure. Let:

[0086] ,

[0087] ,

[0088] ,

[0089] (4)

[0090] For non-cohesive soil ( C= 0), degenerates into Coulomb passive slip surface dip angle.

[0091] 2) Double-slip surface model

[0092] As the depth of the retaining piles continues to increase, the first slip surface extends to the opposite retaining pile, and then the slip surface turns to form the second slip surface CE. The passive soil wedge evolves from a triangle into a trapezoid ABCD, where the height of CD is h1.

[0093] The mechanical equilibrium equations of the trapezoidal soil wedge ABCD are as follows:

[0094] Horizontal equilibrium: (5)

[0095] Vertical balance: (6)

[0096] Solving the equations simultaneously yields the expression for passive earth pressure (7):

[0097] (7)

[0098] in E 1 The improved Rankine earth pressure formula (8) is adopted.

[0099] (8)

[0100] In the formula , , .

[0101] After trigonometric expansion and simplification, we obtain E2 with respect to... The rational function expression (9):

[0102] (9)

[0103] ,

[0104] ,

[0105] ,

[0106] ,

[0107] ,

[0108] ,

[0109] Through extreme value conditions The cubic equation (10) is obtained, and the dip angle of the slip surface is solved. This allows us to determine the passive earth pressure E2.

[0110] (10)

[0111] In the formula: , , , .

[0112] 3) Multi-slip surface model

[0113] As the depth of the retaining piles continues to increase, the second slip surface extends to the opposite retaining pile and then turns, forming the third slip surface. Similarly, as the depth of penetration further increases, the fourth to nth slip surfaces will be generated in sequence.

[0114] The general calculation formula uses a top-down numbering method for the slip surfaces to establish a recursive equilibrium equation:

[0115] (11)

[0116] Through extreme value conditions The optimal slip surface dip angle is determined, and then the exact solution of passive earth pressure is obtained. This recursive formula establishes a general method for calculating passive earth pressure in the case of multiple slip surfaces.

[0117] The dip angle of the slip surface of cohesionless soil was established by regression analysis. Approximate calculation formula:

[0118] (12)

[0119] In the formula, the fitting coefficients , The reduction factor for the external friction angle of the pile and soil The function, with values ​​taken according to Shanghai standards: steel sheet piles =2 / 3, concrete pile =3 / 4, No water dewatering condition inside the pit =0.

[0120] The expressions for each coefficient are as follows:

[0121] ,

[0122] ,

[0123] .

[0124] In this embodiment, to simplify the calculation, an approximation is taken. After comparison and verification, the passive earth pressure value calculated by this approximation method has a very small error with the exact solution. For specific comparison data, please refer to Table 1.

[0125] Table 1. Comparison of Calculation Results of Approximate Method, Numerical Solution, and Improved Rankine Earth Pressure

[0126]

[0127] The data in Table 1 show that, considering spatial effects, the passive earth pressure values ​​are all significantly greater than the improved Rankine theory solution, the approximate solution is slightly greater than the numerically exact solution, and the relative errors are all controlled within 3‰. This meets the engineering accuracy requirements.

[0128] 3. Parameter sensitivity analysis

[0129] Passive earth pressure is influenced by a combination of factors, including the depth of penetration, the width of the foundation pit, soil mechanical parameters, and the external friction angle of the wall and soil. In addition, the dynamic changes in the number and inclination of slip surfaces make it difficult to derive accurate analytical solutions, which limits its engineering applications.

[0130] To intuitively analyze the influence of various parameters on passive earth pressure, a equilibrium force diagram of a passive soil wedge was drawn based on a typical engineering case. Basic parameters: pit width 5m, retaining pile depth 5m, soil cohesion C=17kPa, internal friction angle φ=17°, and external friction angle between the wall and soil. Balanced force system such as Figure 3 As shown.

[0131] Depend on Figure 3As shown in equation (7), when the soil wedge height is determined, the internal friction angle φ controls the direction of the normal force R on the slip surface, and the external friction angle δ of the pile and soil determines the direction of the resultant passive earth pressure. Both play a dominant role in the passive earth pressure. The cohesion C generates a very small resistance component on the slip surface (shown as a barely visible triangular area in the figure), and calculations by equation (10) show that its influence on the slip surface inclination angle θ2 is negligible. The influence of the pit width b on the passive earth pressure is linear, and its influence is significantly lower than that of the parameters φ and δ.

[0132] II. Calculation of Space Effect Magnification Factor for Cohesion-Free Soil

[0133] 1) Determination of the fitting formula

[0134] Based on the analysis of influencing factors, the internal friction angle φ and external friction angle δ were identified as controlling parameters, while the pit width b and embedment depth h were the main variables. Numerical analysis was used to calculate the passive earth pressure values ​​at different embedment depths for the same pit width, and the passive earth pressure intensity distribution was obtained based on the differential principle. A spatial effect amplification factor was defined. The ratio of passive earth pressure strength to improved Rankine earth pressure strength, taking into account spatial effects.

[0135] In actual calculations, the passive earth pressure strength formula in the specification is multiplied by... It can effectively take into account the effects of spatial effects on earth pressure distribution, foundation pit stability and structural stress while maintaining the original calculation method.

[0136] In this embodiment, to unify the amplification factor curves for foundation pits of different widths, an ultra-deep proximity parameter is introduced. :

[0137] (13)

[0138] , ,

[0139] In the formula, h b is the depth of the retaining piles embedded in the soil, and b is the width of the foundation pit. , The dip angle of the sliding surface is the boundary angle. It is an ultra-deep adjacent ratio.

[0140] Plot a curve with the ultra-deep proximity ratio as the ordinate, such as... Figure 4 As shown, the amplification factor curves for foundation pits of different widths completely overlap, verifying the normalization of this parameter. This method significantly simplifies the derivation of the calculation formula and enhances the universality and engineering applicability of the method.

[0141] In this embodiment, an exponential function is used as the basic fitting term for calculating the spatial effect amplification coefficient, which can be used to fit the same... The fitting equations for different angle φ values ​​are expressed in a unified manner, which significantly simplifies the mathematical expressions and facilitates engineering applications.

[0142] Specifically, in this embodiment, the fitting formula for the spatial effect amplification coefficient curve of cohesive-free soil is ultimately determined to be a piecewise function, composed of a combination of exponential functions:

[0143] (14)

[0144] coefficients in the formula , , , Both B and φ are reduction coefficients for the internal friction angle φ and the external friction angle of the pile and soil. The function.

[0145] In the fitting formula for the spatial effect amplification factor curve of the above cohesionless soil, the fitting expressions for each coefficient are as follows:

[0146] Fitting coefficients A1

[0147] like Figure 5 As shown, A1 varies with φ and Increases and grows. Same. Under the given conditions, A1 can be fitted as a cubic polynomial of φ (radians):

[0148] (15)

[0149] coefficient A2 fitting

[0150] like Figure 6 As shown, system A2 varies with φ and Increases and grows. Same. Under the given conditions, A2 can be fitted as a fourth-order polynomial of φ:

[0151] (16)

[0152] Coefficient A3 Fitting

[0153] like Figure 7 As shown, the coefficient A3 varies with φ and Increases and grows. Same. Under the given conditions, A3 can be fitted as a fourth-order polynomial of φ:

[0154] (17)

[0155] A4 coefficient fitting

[0156] like Figure 8 As shown, the coefficient A4 varies with φ and Increases and grows. Same. Under the given conditions, A4 can be fitted as a quadratic polynomial of φ:

[0157] (18)

[0158] coefficient B fitting

[0159] like Figure 9 As shown, the coefficient B varies with φ and Increases and grows. Same. Under the given conditions, B can be fitted as a fourth-order polynomial of φ:

[0160] (19)

[0161] 2) Fitting accuracy verification

[0162] Based on formulas (15) to (19), the values ​​of each coefficient are determined and substituted into formula (14) to obtain the fitting equation for the spatial effect amplification coefficient. The solution of the fitting equation and the numerical solution are plotted on [the graph]. Figures 10-12 A comparative analysis was conducted. The verification results show that the fitted equation curve and the numerical solution curve are in high agreement.

[0163] when At that time, the two curves completely overlapped;

[0164] when At that time, the deviation was controlled within within;

[0165] when At that time, most of the curve deviations were within The deviations are mostly negative (the fitted curve lies below the numerical solution), which conforms to the principle of biased safety design. A few curves have slightly larger deviations, but all still meet the requirements. It meets the engineering precision requirements.

[0166] Comparison with the same The three curves under the given conditions show that the internal friction angle φ affects... Significant impact: The larger the φ value, The faster the curve grows, the better. The calculation formulas for coefficients A1 to A4 also show that φ is a high-power function.

[0167] Pile-soil external friction angle reduction factor right The impact is equally significant: The larger, The faster the growth rate, the slightly lower its impact. In a logarithmic coordinate system, this is represented by a slope product relationship, indicating... right The effect is a product of powers.

[0168] III. Calculation of Space Effect Increment Coefficient for Cohesive Soil

[0169] In this embodiment, when the soil is cohesive, the spatial effect amplification factor is divided into φ terms. and option C .

[0170] This embodiment calculates the passive earth pressure under different cohesion and depth conditions using a calculation program, and then obtains the passive earth pressure value and strength corresponding to the ultra-deep proximity ratio of cohesive soil through linear interpolation. Finally, it systematically analyzes the distribution law of passive earth pressure, strength and spatial amplification factor of cohesive soil taking into account spatial effects.

[0171] In this embodiment, when φ=17︒, The total spatial effect amplification coefficient and the spatial effect amplification coefficient of C corresponding to different cohesive C values ​​under the condition of 2 / 3 are plotted on Figure 13 .

[0172] from Figure 13 visible:

[0173] The space magnification factor corresponding to cohesion C is significantly greater than that of cohesionless soil;

[0174] The total space expansion coefficient of cohesive soil increases with the increase of cohesion C value.

[0175] Further analysis of the spatial effect amplification coefficient curves for different C values ​​revealed:

[0176] The curve for the increase factor in option C shows a typical wave shape, with the trough appearing near an integer multiple of the ultra-deep critical ratio.

[0177] By fitting the lower envelope of each curve, the lower bounds of the spatial amplification coefficient curves with different C values ​​all coincide with the same curve.

[0178] This indicates that the curve of the space increase factor in item C is not significantly correlated with the cohesive force C value.

[0179] At the same time, φ=17︒, The curves of spatial amplification coefficients for foundation pits of different widths under the condition of C=2 / 3 and C=20kPa were plotted on [the following text is incomplete and likely refers to a separate plot]. Figure 14 .

[0180] Depend on Figure 14 The analysis results show that:

[0181] Space magnification factor of cohesive soil (C item) Always greater than the space gain factor of cohesionless soil ;

[0182] Total space magnification factor of cohesive soil It is negatively correlated with the width of the foundation pit, that is, the smaller the width of the foundation pit, the greater the increase in the total space.

[0183] C. Space Increase Coefficient The curve exhibits a wavy shape; except for slight differences in the positions of the crests and troughs, the lower bound of the curve can be fitted to the same exponential function curve under different width conditions. This characteristic is similar to that of cohesionless soils. The consistent curves indicate that they are independent of the width of the foundation pit.

[0184] Furthermore, the φ term of the spatial effect amplification factor for cohesive soil The fitting formula is the same as the space effect amplification factor for cohesive soil. The expression for the space amplification factor in option C is:

[0185] (20)

[0186] Perform a scatter plot analysis on the statistical data of coefficient A5, such as... Figure 15 As shown, the results indicate that:

[0187] Coefficient A5 is a reduction factor for the internal friction angle φ and the external friction angle of the pile and soil. It increases monotonically with increasing magnitude. The same... Under the given conditions, A5 can be fitted as a quadratic polynomial of φ (radians):

[0188] (twenty one)

[0189] IV. Engineering Application Methods of Space Effect Amplification Coefficient

[0190] In this embodiment, the space effect amplification factor is used as follows:

[0191] Coefficient decomposition principle: The coefficient for increasing the spatial effect of passive earth pressure on cohesive soil is decomposed into a φ term corresponding to the improved Rankine earth pressure strength formula. and option C Both amplification factors are the ultra-deep proximity ratio R. slb Internal friction angle φ and reduction coefficient The function is independent of the pit width b and cohesion C in form, which significantly improves the universality of the simplified formula and the convenience of engineering applications.

[0192] Calculation process:

[0193] a. Parameter determination: Determined based on the type of retaining piles and the drainage conditions of the foundation pit. The values ​​are determined based on the soil mechanical parameter φ and the ultra-deep ratio. R slb Sure and The approximate calculation formula.

[0194] b. Earth pressure strength correction: Multiply each of the two terms in the improved Rankine method passive earth pressure strength formula by... and The coefficient allows for the accurate accounting of the beneficial effects of spatial effects in the calculation of passive earth pressure intensity. The modified formula for passive earth pressure intensity is expressed as follows:

[0195] (twenty two)

[0196] in,

[0197]

[0198] c. Assumptions for layered soil calculation: Considering that the spatial effect amplification factor of the m-th soil layer is affected by the mechanical properties of the overlying soil layer, to ensure the reliability of the overturning stability calculation results, the internal friction angle of the m-th layer is calculated when calculating the spatial effect amplification factor. To be on the safe side, we take the minimum value of the friction angle in each soil layer above this layer in the pit.

[0199] d. Optimization of anti-overturning stability calculation: The product of the passive earth pressure intensity determined by equation (22) and the distance of the lowest support is integrated along the depth to obtain the anti-overturning bending moment of each soil layer. The anti-overturning stability safety factor calculated by this anti-overturning bending moment takes into account the beneficial effect of the narrow foundation pit space effect.

[0200] (twenty three)

[0201]

[0202] In the formula, the subscript m represents the corresponding parameters of the m-th soil layer.

[0203] Furthermore, the depth of the retaining piles can be optimized based on the anti-overturning stability safety factor obtained above.

[0204] The innovative aspects of the above method include:

[0205] 1) Using the depth of retaining piles into the soil as the core variable, systematically analyze its impact on spatial effects;

[0206] 2) By comparing the passive earth pressure intensity under spatial effects with the improved Rankine earth pressure intensity, a passive earth pressure spatial amplification factor is proposed;

[0207] 3) Introducing ultra-deep proximity ratio As a key parameter, its functional relationship with the spatial effect amplification factor was established, and a universally applicable simplified calculation method for the spatial effect amplification factor was developed.

[0208] 4) Multiply the standard formula by an amplification factor. and This allows for the quantitative accounting of spatial effects.

[0209] This method presents a clear mechanical concept and derives a general calculation formula for the spatial effect amplification factor applicable to both cohesive and non-cohesive soils. Numerical examples demonstrate that this method can effectively quantify the beneficial influence of spatial effects on overturning stability, providing a theoretical basis for the optimized design of retaining piles and possessing significant engineering application value.

[0210] If the above methods are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0211] This embodiment uses a DN800 sewage main pipe trench excavation pit as the research object. The pit width is 2.2m, the excavation depth is 6.0m, and the safety and environmental protection levels are both Level III. The retaining structure uses 15m long Larssen steel sheet piles. The specific pit cross-section is shown below. Figure 16 As shown. The soil layers in the foundation pit, from top to bottom, are distributed as follows:

[0212] Backfill: Heavy γ =17.5kN / m 3 Cohesion C = 10 kPa, internal friction angle φ =10.0;

[0213] Silty clay: Heavy γ =18.4kN / m 3 Cohesion C = 18 kPa, internal friction angle φ =19.5;

[0214] Silty clay: Severe γ =17.4kN / m 3 Cohesion C = 13 kPa, internal friction angle φ =17.0;

[0215] Silty clay: Severe γ =16.9kN / 3 Cohesion C = 13 kPa, internal friction angle φ =13.5.

[0216] Based on the above trench foundation pit with b=2.2m, the analysis was further extended to foundation pits with widths of 3.65m, 5.0m, and 10.0m, and overturning stability calculations were carried out. The overturning stability safety factors under each working condition are summarized in Table 2.

[0217] Table 2 Comparison of Overturning Stability Safety Factors for Foundation Pits of Different Widths

[0218]

[0219] Table 2 shows that, without considering the beneficial effects of the excavation pit space effect, when using 12m long Larssen sheet piles, with an insertion depth of 6.0m and an insertion ratio of 1:1.0, the overturning stability safety factor is [not specified]. The value is 0.992, lower than the standard requirement of 1.05, and therefore does not meet the stability requirements. However, when using 15m long Larssen sheet piles, with an insertion depth of 9.0m and an insertion ratio of 1:1.5, The value is 1.153, which meets the specification requirements. Furthermore, when the retaining piles are driven 7.1m into the ground and the insertion ratio is 1:1.183, The value is 1.054, which also meets the specification requirements.

[0220] If the beneficial effects of the excavation pit space effect are taken into account, when using 12m long Larssen steel sheet piles for retaining walls, the overturning stability safety factor for pipeline trench excavations with widths of 2.2m, 3.65m, and 5.0m is [not specified]. The values ​​are 1.641, 1.216, and 1.093 respectively, all greater than the standard requirement of 1.05. This indicates that the smaller the width of the foundation pit, the higher the overturning stability safety factor and the more significant the spatial effect. For a subway entrance foundation pit with a width of 10.0m, the overturning stability safety factor is 0.992, which is basically consistent with the result of wide foundation pits without considering spatial effects, indicating that the spatial effect of wider foundation pits can be ignored.

[0221] Table 2 lists the required penetration depths and corresponding insertion ratios of retaining piles to meet the overturning stability safety factor requirements: 2.2m wide pit (penetration depth 3.55m, insertion ratio 0.592), 3.65m wide pit (penetration depth 4.9m, insertion ratio 0.817), 5.0m wide pit (penetration depth 5.65m, insertion ratio 0.942), and 10.0m wide pit (penetration depth 7.0m, insertion ratio 1.167). These data indicate that as the pit width decreases, the required penetration depth of the retaining piles decreases accordingly, increasing the optimization design space. For example, a 2.2m wide trench requires 3.45m less penetration depth than a wider pit, demonstrating significant optimization potential. Specifically, for a pipe trench with a width of B=2.2m, if a 0.6m slope is set at the top of the pit, the length of Larssen sheet piles can be optimized from 15m to 9m, reducing the amount of retaining pile work by 40%; for trenches with a width of B=3.65m and 5.0m, Larssen sheet piles can be optimized from 15m to 12m, reducing the amount of work by 20%; while for a subway entrance pit with a width of 10.0m, the space effect is not obvious, and there is basically no room for optimization.

[0222] The overturning stability calculation results in this embodiment demonstrate that the empirical provision in Article 10.2.3.3 of the original Shanghai Municipal Code for Design of Foundation Pit Engineering (DBJ08-61-97) regarding "the insertion ratio of the pipeline trench into the foundation pit can be taken as 0.5~0.8" was reasonable to some extent when pipe diameters were generally small in the early stages. However, with the significant increase in the diameter of rainwater pipes, continuing to apply this empirical provision lacks theoretical basis and may lead to unsafe designs. The overturning stability safety factor obtained by the method of this invention can reasonably reflect the spatial effect of foundation pits of different widths, providing theoretical support for the optimized design of narrow foundation pits.

[0223] The above method addresses the issue that current foundation pit codes do not consider the spatial effect of narrow foundation pits. Based on classical soil mechanics theory, it proposes a simplified calculation method for passive earth pressure under the spatial effect of narrow foundation pits by comparing the differences in passive earth pressure distribution between finite soil masses and classical methods. By introducing the ultra-deep contiguous ratio as a key parameter, a method for calculating the amplification factor of the passive earth pressure spatial effect applicable to different working conditions is established. Studies using examples show that introducing an amplification factor into the standard earth pressure formula demonstrates that… and This method can effectively quantify the beneficial impact of spatial effects on overturning stability. The amplification factor is positively correlated with the ultra-deep contiguous ratio, the internal friction angle φ, and the pile-soil external friction angle δ. When φ and δ are determined, it is an exponential function of the ultra-deep contiguous ratio. Numerical examples demonstrate that this method can quantitatively assess spatial effects, optimize the insertion depth of retaining piles, and has significant engineering application value.

[0224] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for calculating passive earth pressure in finite soil considering the spatial effects of narrow foundation pits, characterized in that, Includes the following steps: Obtain the calculation parameters for narrow foundation pits, and determine the spatial effect amplification factor based on the calculation parameters for narrow foundation pits. The calculation parameters for narrow foundation pits include soil cohesion, foundation pit width, depth of retaining piles into the soil, internal friction angle, and reduction factor of pile-soil external friction angle. Multiply the aforementioned spatial effect amplification factor in the passive earth pressure intensity formula of the improved Rankine method to obtain the passive earth pressure intensity of the soil taking into account the spatial effect, and then obtain the passive earth pressure of the soil. The spatial effect amplification coefficient is calculated based on a fitting formula, which is specifically obtained by: A finite soil passive earth wedge mechanical model is established. Based on the mechanical model, the passive earth pressure of the finite soil at different depths is simulated and calculated. Based on the passive earth pressure, the passive earth pressure intensity of the finite soil is calculated. The ratio of the simulated passive earth pressure intensity of the finite soil to the improved Rankine passive earth pressure intensity is defined as the spatial effect amplification factor. Plot the spatial effect amplification coefficient curves for different foundation pit widths, introduce the ultra-deep adjacency ratio as the independent variable, merge the spatial effect amplification coefficient curves for different foundation pit widths into one, and establish a fitting formula for the spatial effect amplification coefficient. When constructing the fitting formula for the spatial effect amplification coefficient, the width of the foundation pit and the depth of the retaining piles are parameterized as the ultra-deep criterion ratio, and the fitting formula for the spatial effect amplification coefficient is constructed as a function of the ultra-deep criterion ratio, the internal friction angle and the pile-soil external friction angle reduction coefficient. The formula for obtaining the ultra-deep proximity ratio is: ， In the formula, h b is the depth of the retaining piles embedded in the soil, and b is the width of the foundation pit. , The dip angle of the sliding surface is the boundary angle. It is an ultra-deep proximity; When the soil is determined to be cohesive-free based on soil cohesion, the fitting formula for the spatial effect amplification factor is: In the formula, the coefficients , , , Both B and φ are reduction coefficients for the internal friction angle φ and the external friction angle of the pile and soil. The function, It is an ultra-deep proximity; When the soil is determined to be cohesive based on soil cohesion, the spatial effect amplification factor includes the φ term. and option C ,in: In the formula, the coefficients , , , , Both B and φ are reduction coefficients for the internal friction angle φ and the external friction angle of the pile and soil. The function, , The critical depth at which a slip surface is generated; The expression for the passive earth pressure intensity of soil taking into account spatial effects is: 。 2. The method for calculating passive earth pressure on finite soil considering the spatial effect of narrow foundation pits according to claim 1, characterized in that, This calculation method satisfies the following assumptions: a) The retaining piles are rigid retaining walls, and the retaining piles undergo translational displacement into the foundation pit; b) The passive zone soil produces associated broken-line slip surfaces; c) All slip surfaces simultaneously reach the passive limit state; d) Consider the external friction angle between the pile and the soil, and ignore the cohesion between the pile and the soil.

3. A computer-readable storage medium, characterized in that, Includes one or more programs executable by one or more processors of an electronic device, the one or more programs including instructions for performing the finite soil passive earth pressure calculation method considering the narrow foundation pit space effect as described in any one of claims 1-2.

4. An application of the finite soil passive earth pressure calculation method considering the spatial effect of narrow foundation pits as described in claim 1 in the optimization of the penetration depth of retaining piles, characterized in that, Based on the calculated passive earth pressure, the overturning stability safety factor corresponding to different pile penetration depths is determined, thereby obtaining the optimal pile penetration depth.

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