A calculation method for passive earth pressure of saturated cohesive finite soil

Abstract

The present application discloses a method for calculating the passive earth pressure of saturated cohesive finite soil, comprising: calculating the passive earth pressure and its resultant force of the saturated cohesive soil in the case of a semi-infinite soil body based on the material parameters of the saturated cohesive finite soil body and the parameters of the retaining member; calculating the correction coefficient of the passive earth pressure resultant force based on the geometric parameters, material parameters and parameters of the retaining member of the saturated cohesive finite soil body, multiplying the correction coefficient by the passive earth pressure resultant force of the saturated cohesive soil in the case of a semi-infinite soil body to obtain the final passive earth pressure resultant force of the saturated cohesive soil finite soil body, and determining the position of the passive earth pressure resultant force action point. The method solves the problem that the classical Rankine theory and Coulomb theory as well as the existing technology cannot calculate the passive earth pressure of saturated cohesive finite soil body by calculating the passive earth pressure of the saturated cohesive soil body in the case of a semi-infinite soil body. The calculation formula provided has been verified by in-depth conceptual analysis and a large number of numerical examples. It is simple and practical and can be used in calculations such as foundation pit support and retaining wall design.

Description

Technical Field

[0001] The present application relates to the field of geotechnical engineering technology, and in particular to a method for calculating the passive earth pressure of saturated viscous finite soil. Background Art

[0002] In geotechnical engineering, the calculation of earth pressure is crucial for the design of foundation pit support and retaining walls. The classic Rankine and Coulomb theories, both based on the assumption of a semi-infinite soil mass, derive the formulas for calculating active and passive earth pressures. However, engineering practice often encounters the problem of calculating earth pressure for finite soil masses. Specifically, when calculating earth pressure for a semi-infinite soil mass, the failure slip surface cannot be fully accommodated by the soil mass but is instead limited by its boundaries. For example, when the excavation pit is narrow, the slip surface of the soil within the pit exerting passive earth pressure on the retaining elements on one side of the excavation pit support is limited by the retaining elements on the opposite side. In this case, the passive earth pressure on the retaining elements is the passive earth pressure of the finite soil mass. For another example, when a building with a large burial depth is located a short distance outside the pit, the exterior walls of its basement may affect the failure slip surface where active earth pressure occurs. In this case, the active earth pressure is that of the finite soil mass. Since the earth pressure problem of finite soil no longer satisfies the assumption of semi-infinite soil in classical earth pressure theory, if the classical earth pressure theory is still used for calculation, the calculation results will inevitably have large errors. Therefore, it is necessary to develop an earth pressure calculation method for finite soil.

[0003] For the strength of saturated clay soil, the domestic geotechnical industry mostly uses the consolidated undrained strength index and the total stress method to calculate it. However, previous studies have shown that this approach will have a large error. A more reasonable and accurate approach is to use the unconsolidated undrained strength, that is, the undrained shear strength c of the original soil sample consolidated under the effective self-weight stress. u , to consider the strength of saturated clay soil. Summary of the Invention

[0004] This application provides a calculation method for the passive earth pressure of saturated cohesive finite soil to solve the problem that cannot be calculated by the classical Rankine theory and Coulomb theory as well as the existing technology.

[0005] An embodiment of the present application provides a method for calculating the passive earth pressure of a saturated cohesive finite soil, comprising the following steps: determining the geometric parameters, material parameters and parameters of a retaining member of the saturated cohesive finite soil, calculating the passive earth pressure of the saturated cohesive soil under the condition of a semi-infinite soil according to the material parameters of the saturated cohesive finite soil, and determining the passive earth pressure resultant of the saturated cohesive soil according to the parameters of the retaining member; calculating a correction coefficient for the passive earth pressure resultant according to the geometric parameters, material parameters and parameters of the saturated cohesive finite soil, wherein the correction coefficient is obtained by A first dimensionless parameter and a second dimensionless parameter are calculated, wherein the first dimensionless parameter represents the relative size of the width of the saturated cohesive finite soil mass and the height of the retaining member, and the second dimensionless parameter represents the relative size of the strength of the saturated cohesive finite soil mass relative to the weight of the saturated cohesive finite soil mass; the correction coefficient is multiplied by the passive earth pressure resultant in the semi-infinite soil mass case to obtain the passive earth pressure resultant of the saturated cohesive finite soil mass, and the position of the passive earth pressure resultant action point of the saturated cohesive finite soil mass is determined according to the position of the resultant action point in the semi-infinite soil mass case.

[0006] Optionally, in one embodiment of the present application, the formula for calculating the passive earth pressure of the saturated clayey soil in the case of a semi-infinite soil body according to the material parameters of the saturated clayey finite soil body is:

[0007] p p0 =γ′z+2c u +p st =σ v +2c u

[0008] Where, γ′ is the effective density of saturated clay, z is the depth from the soil surface, and c u is the undrained strength of saturated clay, p st is the hydrostatic pressure at depth z, σ v =γ′z+p st is the sum of the vertical pressures of soil and water at depth z;

[0009] The passive earth pressure resultant force E of the saturated clay body is determined based on the passive earth pressure of the saturated clay body in the semi-infinite soil case and the parameters of the retaining structure. p0 The calculation formula is:

[0010]

[0011] Where D is the height of the retaining member.

[0012] Optionally, in one embodiment of the present application, the undrained strength c of the saturated clay is uObtained by an unconsolidated undrained test after consolidation under deadweight stress or an undrained test in situ test, where

[0013] c u =c0+c inc z

[0014] Where c0 is the value of undrained shear strength at the top surface of the soil layer, c inc is the rate of increase of undrained shear strength with depth;

[0015] When there is only the undrained consolidation strength index in the geological survey report, c0 and c inc The calculation method is:

[0016]

[0017]

[0018] Where K0 is the static earth pressure coefficient, c cu For cohesion, is the internal friction angle, and γ′ is the effective density of saturated clay.

[0019] Optionally, in one embodiment of the present application, the calculation formula of the correction coefficient α is:

[0020]

[0021] Wherein, k1 is the first dimensionless parameter, B is the width of the saturated clay finite soil, D is the height of the retaining member, k2 is the second dimensionless parameter, c0 is the value of undrained shear strength at the top surface of the finite soil mass, c inc is the rate of increase of undrained shear strength with depth, and γ is the saturated density of saturated clay.

[0022] Optionally, in one embodiment of the present application, determining the position of the resultant force action point of the passive earth pressure of the saturated cohesive finite soil according to the position of the resultant force action point in the case of a semi-infinite soil comprises:

[0023] Calculate the distance between the passive earth pressure resultant action point and the top of the passive earth pressure action area of ​​the retaining member, and determine the position of the passive earth pressure resultant action point of the saturated cohesive finite soil based on the distance, wherein the distance from the resultant action point to the top of the soil in the case of semi-infinite soil is used to represent the distance from the passive earth pressure resultant action point to the top of the finite soil in the case of finite soil, and the distance d from the passive earth pressure resultant action point to the top of the passive earth pressure action area of ​​the retaining member is p The calculation formula is:

[0024]

[0025] Where D is the height of the retaining member, z is the depth from the soil surface, P p0 is the passive earth pressure of saturated clay soil in the semi-infinite soil case.

[0026] A method for calculating the passive earth pressure of saturated viscous finite soil in an embodiment of the present application has the following beneficial effects:

[0027] 1) This paper addresses the calculation of passive earth pressure in saturated cohesive finite soils, solving problems that are beyond the reach of classical Rankine and Coulomb theories, as well as existing technologies. The proposed formula, validated through in-depth conceptual analysis and extensive numerical examples, is both simple and practical, and can be used in calculations such as foundation pit support and retaining wall design.

[0028] 2) A correction coefficient for the earth pressure on semi-infinite soil masses is proposed, which is related to two dimensionless parameters. This reduces the number of independent factors affecting the earth pressure to two. This not only facilitates the calculation of the formula, but also reveals the underlying influence of each parameter on earth pressure. The calculation of both dimensionless parameters and earth pressure in this invention is very simple, avoiding the tedious iterative solution process of existing methods and making it easier for designers to master.

[0029] 3) The proposed method for calculating passive earth pressure on finite soils can be used to verify the anti-uplift of saturated soft soil foundation pit bottoms. Numerous numerical examples have demonstrated that the magnitude and point of action of the earth pressure calculated by this method are more accurate than those of existing solutions, ensuring the safety and cost-effectiveness of related engineering designs.

[0030] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0032] Figure 1 A flow chart of a method for calculating the passive earth pressure of saturated cohesive finite soil provided in an embodiment of the present application;

[0033] Figure 2 A schematic diagram of passive earth pressure of a finite soil mass provided according to an embodiment of the present application;

[0034] Figure 3 Schematic diagram of passive earth pressure of retaining components in a narrow foundation pit according to an embodiment of the present application. DETAILED DESCRIPTION

[0035] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to be used to explain the present application, but should not be understood as limiting the present application.

[0036] The following describes a method for calculating the passive earth pressure of saturated viscous finite soil according to an embodiment of the present invention with reference to the accompanying drawings. This method can be used in calculations such as the design of narrow foundation pit support structures, and can achieve convenient and accurate calculation of the passive earth pressure under corresponding conditions.

[0037] Specifically, Figure 1 The present invention provides a flowchart of a method for calculating the passive earth pressure of saturated clay finite soil according to an embodiment of the present application.

[0038] like Figure 1 As shown in Figure 1, a method for calculating the passive earth pressure of the saturated cohesive finite soil includes the following steps:

[0039] In step S101 , the geometric parameters, material parameters and parameters of the retaining element of the saturated clay finite soil are determined.

[0040] In calculating the passive earth pressure of soil, the geometric parameters of retaining elements and finite soil as well as the material parameters of soil are needed. Figure 2 As shown, the geometric parameters of the finite soil include the width B of the finite soil, the height D of the retaining wall, the soil density γ, and the undrained strength c of the soil. u The c can be directly obtained by unconsolidated undrained test or in-situ undrained test after consolidation of undisturbed soil sample under self-weight stress. u In natural soil, c u Generally, it increases approximately linearly with depth.

[0041] c u =c0+c inc z (1)

[0042] Where c0 is the value of undrained shear strength at the top surface of the soil layer; c inc is the rate of increase of undrained shear strength with depth; z is the depth;

[0043] The more common indicator in geological survey reports is the soil consolidation undrained strength index c. cu and If only the consolidated undrained strength index can be obtained in the geological survey report, the c0 and c1 in the unconsolidated undrained shear strength calculation formula should be calculated as follows: inc :

[0044]

[0045]

[0046] Where K0 is the static earth pressure coefficient. If K0 is not clearly given in the local survey report, it can also be obtained from Make an estimate; γ′ is the effective density of saturated clay.

[0047] In step S102, the passive earth pressure of the saturated cohesive soil is calculated in the case of a semi-infinite soil according to the material parameters of the saturated cohesive finite soil, and the resultant passive earth pressure of the saturated cohesive soil is determined according to the parameters of the retaining member.

[0048] In the embodiment of the present application, the passive earth pressure of saturated clay soil in the case of semi-infinite soil is calculated according to the following formula:

[0049] p p0 =γ′z+2c u +p st =σ v +2c u (4)

[0050] Where γ′ is the effective density of saturated cohesive finite soil, z is the depth from the surface of saturated cohesive finite soil, c u =c0+c inc z is the unconsolidated undrained strength of the soil at depth z. When the soil surface is not the original ground surface, such as the bottom of an excavated foundation pit, c0 needs to be calculated based on the value of the undrained strength of the soil at the ground surface, the depth growth rate of the undrained strength, and the pit depth. st =γ w z is the hydrostatic pressure at depth z, γ w =10kN / m 3 is the bulk density of water. v =γ′z+p st The sum of the vertical pressures of soil and water at depth z. The resultant force of the passive earth pressure calculated above is E p0 It can be calculated by the following formula:

[0051]

[0052] In step S103, a correction coefficient of the passive earth pressure is calculated based on the geometric parameters, material parameters, and parameters of the retaining element of the saturated cohesive finite soil. The correction coefficient is calculated using a first dimensionless parameter and a second dimensionless parameter. The first dimensionless parameter represents the relative size of the width of the saturated cohesive finite soil and the height of the retaining element, and the second dimensionless parameter represents the relative size of the strength of the saturated cohesive finite soil relative to the weight of the saturated cohesive finite soil.

[0053] In the embodiments of this application, after in-depth conceptual analysis combined with extensive numerical calculations, it was discovered that the correction coefficient α can be determined by two dimensionless parameters, k1 and k2. The dimensionless parameter k1 reflects the relative size of the finite soil width and the height of the retaining structure, while the dimensionless parameter k2 comprehensively reflects the size of the soil strength relative to the soil density. The definitions of the two dimensionless parameters and the calculation formula for the correction coefficient α are as follows:

[0054]

[0055]

[0056]

[0057] Among them, k1 is the first dimensionless parameter, B is the width of saturated clay finite soil, D is the height of retaining structure, k2 is the second dimensionless parameter, c0 is the value of undrained shear strength at the top surface of the soil layer, c inc is the rate of increase of undrained shear strength with depth, and γ is the saturated density of saturated cohesive finite soil.

[0058] In step S104, the correction coefficient is multiplied by the passive earth pressure resultant in the semi-infinite soil case to obtain the passive earth pressure resultant of the saturated cohesive finite soil, and the position of the passive earth pressure resultant action point of the saturated cohesive finite soil is determined according to the position of the action point of the resultant force in the semi-infinite soil case.

[0059] The embodiment of the present application calculates a correction coefficient for the resultant earth pressure. By multiplying the correction coefficient by the calculated resultant passive earth pressure of the semi-infinite soil, the final resultant passive earth pressure of the finite saturated clay soil can be obtained:

[0060] E p =αE p0 (9)

[0061] Here, α is greater than 1.

[0062] Numerous numerical examples show that the dimensionless parameters defined above are correct, and the correction coefficient α calculated above can be substituted into Eq. (9) to give a sufficiently accurate resultant of the passive earth pressure E of saturated cohesive finite soil. p .

[0063] Optionally, in one embodiment of the present application, determining the position of the resultant force action point of the passive earth pressure of the saturated cohesive finite soil according to the position of the resultant force action point in the case of a semi-infinite soil includes:

[0064] Calculate the distance between the passive soil resultant force action point and the top of the passive earth pressure action area of ​​the retaining structure, and determine the position of the passive earth pressure resultant force action point of the saturated cohesive finite soil based on the distance. The distance from the resultant force action point to the top of the soil in the case of semi-infinite soil is used to represent the distance from the passive earth pressure resultant force action point to the top of the finite soil in the case of finite soil. The distance d from the passive earth pressure resultant force action point to the top of the passive earth pressure action area of ​​the retaining structure is p The calculation formula is:

[0065]

[0066] Where D is the height of the retaining structure, z is the depth from the soil surface, and p p0 is the passive earth pressure of saturated clay soil in the semi-infinite soil case.

[0067] The position of the passive earth pressure resultant action point is determined. After a large number of numerical calculations, it is verified that the resultant action point calculated by semi-infinite soil theory can be used to approximate the passive earth pressure resultant action point in the finite soil case, and the error does not exceed 10%.

[0068] like Figure 3 As shown, taking the calculation of the passive earth pressure of the soil in a foundation pit on the embedded section of the retaining member as an example, the method for calculating the passive earth pressure of saturated clay finite soil in the embodiment of the present application is explained in detail.

[0069] Table 1 and Table 2 show the site soil parameters and basic parameters of the foundation pit respectively.

[0070] Table 1 Site land parameters

[0071]

[0072] Table 2 Basic parameters of foundation pit

[0073] <![CDATA[Depth of pit z0 / m]]> Pit width B / m Depth of retaining elements embedded in the pit bottom D / m 10 5 10

[0074] First, the consolidation undrained strength parameters of the saturated soft clay were obtained from the geological survey report: cohesion c cu =25kPa, internal friction angle and saturation density γ=19kN / m 3 The unconsolidated undrained shear strength parameters are calculated according to the formula:

[0075]

[0076]

[0077] Secondly, the passive earth pressure of the embedded section of the retaining member can be calculated according to formulas (4) and (5), and we can know that:

[0078] p p0=σ v +2c u =19z+2×(32.58+2.59×(10+z))=116.96+24.18z(kPa)

[0079]

[0080] Again, find the correction coefficient α:

[0081]

[0082]

[0083]

[0084] Therefore, the resultant of the passive earth pressure of the finite soil is E p =αE p0 =3226.96kN / m.

[0085] Finally, find the position of the resultant force action point, that is, the distance d between the earth pressure resultant action point and the top of the passive earth pressure action area of ​​the retaining structure. p It can be calculated as follows:

[0086]

[0087] In this way, the resultant force and the position of the action point of the passive earth pressure of the finite soil can be obtained, which can be used in the design of foundation pit support and retaining wall.

[0088] The above description is merely an illustration of preferred embodiments of the present invention and the technical principles employed, and is not intended to limit the scope of the invention as claimed, but merely represents a preferred embodiment of the present invention.

[0089] According to the embodiment of the present application, a calculation method for the passive earth pressure of saturated cohesive finite soil is proposed. The calculation method solves the problem that the classical Rankine theory and Coulomb theory as well as the existing technology cannot calculate for the passive earth pressure of saturated cohesive finite soil. The calculation formula given has been verified by in-depth conceptual analysis and a large number of numerical examples. It is simple and practical and can be used in calculations such as foundation pit support and retaining wall design. It is also proposed that the correction coefficient affecting the earth pressure of finite soil and semi-infinite soil is related to two dimensionless parameters, thereby reducing the independent influencing factors affecting the change of earth pressure to two. It is convenient to fit the calculation formula and reveals the influence of each parameter on earth pressure at a deep level. The calculation of dimensionless parameters and earth pressure is very simple, avoiding the tedious iterative solution process of existing methods, which is easy for designers to master. It can be used for anti-uplift calculation of saturated soft soil foundation pits. After verification by a large number of numerical examples, it is known that the calculated earth pressure size and action point are more accurate than the existing technical solutions, ensuring the safety and economy of related engineering designs.

[0090] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0091] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of technical features indicated. Thus, a feature specified as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of this application, "N" means at least two, for example, two, three, etc., unless otherwise specifically defined.

[0092] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or more executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may be performed out of the order shown or discussed, including performing functions in a substantially simultaneous manner or in reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present application belong.

Claims

1. A method for calculating the passive earth pressure of saturated cohesive finite soil, characterized in that: The following steps are involved: Determine the geometric parameters, material parameters and retaining element parameters of saturated cohesive finite soil; Determining the passive earth pressure resultant of the saturated clay body according to the passive earth pressure of the saturated clay body in the case of a semi-infinite soil body and the parameters of the retaining member; The correction coefficient of the passive earth pressure resultant force is calculated based on the geometric parameters, material parameters and parameters of the saturated cohesive finite soil and the parameters of the retaining member; wherein the correction coefficient is calculated using a first dimensionless parameter and a second dimensionless parameter, wherein the first dimensionless parameter represents the relative size of the width of the saturated cohesive finite soil and the height of the retaining member, and the second dimensionless parameter represents the relative size of the strength of the saturated cohesive finite soil relative to the weight of the saturated cohesive finite soil, wherein: The calculation formula of the correction coefficient α is: Wherein, k1 is the first dimensionless parameter, B is the width of the saturated clay finite soil, D is the height of the retaining member; k2 is the second dimensionless parameter, c0 is the value of undrained shear strength at the top surface of the finite soil mass, c inc is the rate of increase of undrained shear strength with depth, γ is the saturated density of saturated clay; The correction coefficient is multiplied by the passive earth pressure resultant in the semi-infinite soil case to obtain the passive earth pressure resultant of the saturated cohesive finite soil, and the position of the passive earth pressure resultant action point of the saturated cohesive finite soil is determined according to the position of the resultant action point in the semi-infinite soil case.

2. The method according to claim 1, characterized in that The formula for calculating the passive earth pressure of saturated clayey soil in the case of semi-infinite soil based on the material parameters of the saturated clayey finite soil is: p p0 =γ′z+2c u +p st =σ v +2c u Where, γ′ is the effective density of saturated clay, z is the depth from the soil surface, and c u is the undrained strength of saturated clay, p st is the hydrostatic pressure at depth z, σ v =γ′z+p st is the sum of the vertical pressures of soil and water at depth z; The passive earth pressure resultant force E of the saturated clay body is determined based on the passive earth pressure of the saturated clay body in the semi-infinite soil case and the parameters of the retaining structure. p0 The calculation formula is: Where D is the height of the retaining member.

3. The method according to claim 2, characterized in that The undrained strength c of the saturated clay soil u Obtained by an unconsolidated undrained test after consolidation under deadweight stress or an undrained test in situ test, where c u =c0+c inc z Where c0 is the value of undrained shear strength at the top surface of the soil layer, c inc is the rate of increase of undrained shear strength with depth; When there is only the undrained consolidation strength index in the geological survey report, c0 and c inc The calculation formula is: Where K0 is the static earth pressure coefficient, c cu For cohesion, is the internal friction angle, and γ′ is the effective density of saturated clay.

4. The method according to claim 1, wherein The method of determining the position of the resultant force action point of the passive earth pressure of the saturated viscous finite soil according to the position of the resultant force action point in the semi-infinite soil case includes: Calculate the distance between the passive earth pressure resultant action point and the top of the passive earth pressure action area of ​​the retaining member, and determine the position of the passive earth pressure resultant action point of the saturated cohesive finite soil based on the distance, wherein the distance from the resultant action point to the top of the soil in the case of semi-infinite soil is used to represent the distance from the passive earth pressure resultant action point to the top of the finite soil in the case of finite soil, and the distance d from the passive earth pressure resultant action point to the top of the passive earth pressure action area of ​​the retaining member is p The calculation formula is: Where D is the height of the retaining member, z is the depth from the soil surface, p p0 is the passive earth pressure of saturated clay soil in the semi-infinite soil case.

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