A method for calculating the resultant force of active and passive earth pressure of cohesionless soil considering plastic zone

Abstract

The application relates to a method for calculating the resultant force of active and passive earth pressure of incoherent soil considering the plastic zone in the field of geotechnical design, which comprises the following steps: monitoring the displacement of an existing retaining wall to obtain a monitored displacement amount; bringing the monitored displacement amount into a formula for calculating the resultant force of active earth pressure or a formula for calculating the resultant force of passive earth pressure to obtain the resultant force of active earth pressure E a or the resultant force of passive earth pressure E p experienced by the retaining wall under the current displacement amount; and performing stability analysis on the retaining wall based on the obtained resultant force of active earth pressure or the resultant force of passive earth pressure. The application can calculate the E a and E p under any displacement amount of the retaining wall, and the soil pressure resultant force corresponding to the displacement amount of the retaining wall can be calculated by monitoring the displacement of the existing retaining wall, so that stability checking or internal force analysis of the retaining wall can be performed.

Description

Technical Field

[0001] This invention relates to the field of geotechnical design, and specifically to a method for calculating the resultant of active and passive earth pressures on cohesive soil considering the plastic region. Background Technology

[0002] In engineering, the commonly used methods for calculating the resultant earth pressure of retaining walls are Rankine's earth pressure theory and Coulomb's earth pressure theory. However, these two earth pressure theories can only calculate the resultant earth pressure under active or passive limit equilibrium states. In actual engineering, retaining walls or other support structures may not reach active or passive limit equilibrium states. To address this issue, national standards provide corresponding empirical correction coefficients for the resultant earth pressure for different support structures. However, these empirical correction coefficients cannot be used to calculate the resultant earth pressure based on the actual displacement of the support structure, which may lead to significant errors in the calculated resultant earth pressure. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention provides a method for calculating the resultant force of active and passive earth pressures on cohesive soil considering the plastic zone. This method takes into account the development process of the plastic zone behind the wall and can calculate the resultant force of active or passive earth pressures under any displacement of the retaining wall.

[0004] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions:

[0005] This invention provides a method for calculating the resultant of active and passive earth pressures on cohesionless soil considering the plastic region, comprising the following steps:

[0006] Displacement monitoring was conducted on the existing retaining wall to obtain the monitored displacement.

[0007] By substituting the monitored displacement into the calculation formula for the resultant force of active earth pressure or the resultant force of passive earth pressure, the resultant force of active earth pressure or the resultant force of passive earth pressure on the retaining wall under the current displacement is obtained.

[0008] The formula for calculating the resultant force of active earth pressure is as follows:

[0009]

[0010] Δx a ∈[0,1]

[0011] Where, Δx a =x 外 / x a x 外 x represents the outward horizontal displacement of the retaining wall. a γ represents the outward horizontal displacement of the retaining wall when the soil behind it reaches an active limit equilibrium state. K0 is the coefficient of earth pressure at rest, H is the height of the retaining wall, and γ is the weight of the soil behind the wall. The internal friction angle of the soil;

[0012] The formula for calculating the resultant force of passive earth pressure is as follows:

[0013]

[0014] Δx p ∈[0,1]

[0015] Where, Δx p =x 内 / x p x 内 x represents the inward horizontal displacement of the retaining wall. p This refers to the inward horizontal displacement of the retaining wall when the soil behind it reaches a passive limit equilibrium state.

[0016] Stability analysis of the retaining wall is performed based on the obtained resultant force of active or passive earth pressure.

[0017] The formula for calculating the resultant force of active earth pressure is obtained through the following process:

[0018] Step S1: Establish the outward horizontal displacement x of the retaining wall 外 The functional relationship between the penetration amount y of the plastic zone of the soil behind the wall and the wall is as follows:

[0019]

[0020] x 外 ∈[0,x a ]

[0021]

[0022] Step S2: Displace the retaining wall horizontally outward by a distance of x. 外 The resultant force of active earth pressure E at that time a The soil behind the wall is divided into two parts: the horizontal sliding force T of the right-angled trapezoidal plastic body corresponding to the penetration volume y of the plastic zone behind the wall, and the static earth pressure E0 of the right-angled triangular elastic body at the rear edge of the plastic body. a The calculation formula is as follows:

[0023] E a =T+E0

[0024] Step S3: Calculate T in step S2 based on Coulomb's active earth pressure theory, and calculate E0 in step S2 based on the at-rest earth pressure theory. Summate the calculated T and E0 to establish E. a With Δx a The functional relationship between them is as follows:

[0025]

[0026] Δx a ∈[0,1].

[0027] Wherein, the outward horizontal displacement x of the retaining wall 外 The functional relationship between the penetration amount y of the plastic zone of the soil behind the wall and the wall was obtained through the following process:

[0028] Assume the outward horizontal displacement of the retaining wall is x 外 The functional relationship between the penetration amount y of the plastic zone in the soil behind the wall and the plastic zone is linear, and the penetrated plastic zone is consistent with the slip surface l of Rankine's active earth pressure theory for cohesionless soil. The plastic zone is an angle with the horizontal plane. The plane is as follows:

[0029]

[0030] By x 外 The linear functional relationship between y and y can be expressed by the following formula.

[0031]

[0032] Combining the two equations, we can obtain the outward horizontal displacement x of the retaining wall. 外 The functional relationship between the penetration amount y of the plastic zone of the soil behind the wall and the wall.

[0033] Where, when Δx a When Δx = 0, the formula for calculating the resultant force of active earth pressure is transformed into the formula for calculating the resultant force of static earth pressure. a When the value is 1, the formula for calculating the resultant force of active earth pressure is transformed into the Rankine formula for calculating the resultant force of active earth pressure when the soil behind the wall reaches the active limit equilibrium state.

[0034] Where, when Δx p When Δx = 0, the formula for calculating the resultant passive earth pressure is transformed into the formula for calculating the resultant static earth pressure. p When the value is 1, the formula for calculating the resultant passive earth pressure is transformed into the Rankine formula for calculating the resultant passive earth pressure when the soil behind the wall reaches the passive limit equilibrium state.

[0035] The method for calculating the resultant of active and passive earth pressures on cohesionless soil considering the plastic region, as described in this embodiment of the invention, yields E... a and E p A functional relationship was established with the displacement of the retaining wall, allowing the calculation of E under any retaining wall displacement. a and E p By monitoring the displacement of an existing retaining wall, the resultant earth pressure corresponding to the displacement of the retaining wall can be calculated, and then operations such as stability verification or internal force analysis of the retaining wall can be performed.

[0036] Of course, implementing any product or method of the present invention does not necessarily require achieving all of the advantages described above at the same time. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart of a method for calculating the resultant of active and passive earth pressures on cohesive soil considering the plastic region, according to the present invention.

[0039] Figure 2 This is a flowchart of the active earth pressure resultant force calculation method according to an embodiment of the present invention;

[0040] Figure 3 The present invention comprises a right-angled trapezoidal plastic body of the soil behind the retaining wall and a right-angled triangular elastic body at its rear edge. Detailed Implementation

[0041] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. It should be noted that, without conflict, the embodiments and features in the embodiments of the present invention can also be combined with each other.

[0042] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In the description of the invention, the terms "first," "second," "third," "fourth," etc., are used only to distinguish descriptions and should not be construed as merely or implying relative importance.

[0043] This invention provides a method for calculating the resultant force of active and passive earth pressures on cohesive soil considering the plastic region. As the retaining wall moves outward horizontally, the penetration of the plastic region of the soil behind the wall gradually develops from "no occurrence" to "penetrating the soil surface." A functional relationship is established between the outward horizontal displacement of the retaining wall and the penetration of the plastic region of the soil behind the wall. The horizontal sliding force of the right-angled trapezoidal plastic body of the soil behind the wall and the static earth pressure of the right-angled triangular elastic body at its rear edge are solved separately. The resultant force of the active earth pressure of the retaining wall is obtained by summing them. The resultant force of the passive earth pressure can also be obtained using the same principle. Therefore, the stability analysis of the retaining wall can be performed based on the resultant force of the active or passive earth pressure, such as stability verification or internal force analysis.

[0044] like Figure 1 As shown, the method for calculating the resultant of active and passive earth pressures on cohesive soil considering the plastic zone includes the following steps:

[0045] S110, Displacement monitoring is performed on the existing retaining wall to obtain the monitored displacement;

[0046] The monitored displacement can be the outward horizontal displacement of the retaining wall, x. 外 or the inward horizontal displacement x of the retaining wall 内 .

[0047] S120, the monitored displacement is substituted into the active earth pressure resultant force calculation formula or the passive earth pressure resultant force calculation formula to obtain the active earth pressure resultant force or passive earth pressure resultant force on the retaining wall under the current displacement.

[0048] The formula for calculating the resultant force of active earth pressure is as follows:

[0049]

[0050] Δx a ∈[0,1]

[0051] Where, Δx a =x 外 / x a x 外 x represents the outward horizontal displacement of the retaining wall. a γ represents the outward horizontal displacement of the retaining wall when the soil behind it reaches an active limit equilibrium state. K0 is the coefficient of earth pressure at rest, H is the height of the retaining wall, and γ is the weight of the soil behind the wall. The internal friction angle of the soil;

[0052] The above method for calculating the resultant force of active earth pressure is as follows: Figure 2 The steps shown are as follows:

[0053] Step S1: Establish the outward horizontal displacement x of the retaining wall 外 The functional relationship between the penetration amount y of the plastic zone of the soil behind the wall and the wall is as follows:

[0054]

[0055] x 外 ∈[0,x a ]

[0056]

[0057] The derivation process of the above functional relationship is as follows:

[0058] Assume the outward horizontal displacement of the retaining wall is x外 The functional relationship between the penetration amount y of the plastic zone in the soil behind the wall and the penetration amount is linear, and the plastic zone is consistent with the slip surface l of Rankine's active earth pressure theory for cohesionless soil, that is, the plastic zone is a slip surface perpendicular to the horizontal plane. The plane is shown in equation (3).

[0059]

[0060] By x 外 The linear functional relationship between y and y can be expressed as equation (4).

[0061]

[0062] Substituting equation (3) into equation (4) yields the above functional relationship (2).

[0063] Step S2: Displace the retaining wall horizontally outward by a distance of x. 外 The resultant force of active earth pressure E at that time a It is divided into two parts: the penetration amount y of the plastic zone of the soil behind the wall, corresponding to the horizontal sliding force T of the right trapezoidal plastic body, and the static earth pressure E0 of the right-angled triangular elastic body at the rear edge of the plastic body.

[0064] Where the outward horizontal displacement of the retaining wall is x 外 When considering the amount of penetration in the plastic zone, the resultant active earth pressure E of the cohesive soil is... a The soil pressure consists of two parts: the horizontal sliding force T of the right-angled trapezoidal plastic body corresponding to the penetration volume y of the plastic region behind the wall, and the at-rest earth pressure E0 of the right-angled triangular elastic body at the rear edge of the plastic body. Figure 3 As shown, E a The calculation formula is shown in equation (5).

[0065] E a =T+E0 (5)

[0066] Step S3: Calculate T in step S2 based on Coulomb's active earth pressure theory, and calculate E0 in step S2 based on the at-rest earth pressure theory. Summate the calculated T and E0 to establish E. a With Δx a The functional relationship between them is shown in equation (1).

[0067] According to Coulomb's active earth pressure theory, the formula for calculating the horizontal sliding force T of the right trapezoidal plastic body is shown in equation (6), and the formula for calculating the static earth pressure E0 of the right-angled triangular elastic body at the rear edge of the plastic body is shown in equation (7).

[0068]

[0069]

[0070] Where G is the weight of the right trapezoidal plastic body, and G is a function of y as shown in equation (8).

[0071]

[0072] Substituting equations (6), (7), and (8) into formula (5), we can obtain the resultant active earth pressure E of cohesive soil considering the penetration of the plastic zone. a The calculation formula is shown in equation (9).

[0073]

[0074] Substituting equation (2) into equation (9) and rearranging, we can obtain E. a With x 外 The functional relationship between them is shown in equation (10).

[0075]

[0076] Let Δx a =x 外 / x a Substituting into equation (10), we get equation (1).

[0077] Where, when Δx a When Δx = 0, equation (1) is transformed into the formula for calculating the resultant force of earth pressure at rest. a When =1, formula (1) is transformed into the Rankine active earth pressure resultant force calculation formula when the soil behind the wall reaches the active limit equilibrium state.

[0078] In addition, the resultant passive earth pressure E, considering the penetration of the plastic zone, is also considered. p The same calculation method can be used, assuming the inward displacement of the retaining wall is x. 内 The functional relationship between the penetration amount y of the plastic zone behind the wall and the penetration amount remains linear, and the penetrated plastic zone is consistent with the slip surface in Rankine's passive earth pressure theory, that is, the plastic zone is an area perpendicular to the horizontal plane. If the plane is E, then E p The calculation formula is shown in (11).

[0079]

[0080] Δx p ∈[0,1]

[0081] Where, Δx p =x 内 / x p x 内 x represents the inward horizontal displacement of the retaining wall. pThis is the inward horizontal displacement of the retaining wall when the soil behind it reaches a passive limit equilibrium state; its derivation principle is the same as the calculation formula for the resultant force of active earth pressure, which will not be repeated here.

[0082] Where, when Δx p When Δx = 0, equation (11) is transformed into the formula for calculating the resultant force of earth pressure at rest. p =1, Equation (11) is transformed into the formula for calculating the resultant passive earth pressure of Rankine when the soil behind the wall reaches the passive limit equilibrium state.

[0083] S130, stability analysis of the retaining wall is performed based on the obtained resultant force of active earth pressure or passive earth pressure.

[0084] The E obtained by the above process a and E p A functional relationship was established with the displacement of the retaining wall, allowing the calculation of E under any retaining wall displacement. a and E p By monitoring the displacement of an existing retaining wall, the resultant earth pressure corresponding to the displacement of the retaining wall can be calculated, and then the stability of the retaining wall or internal force analysis can be performed.

[0085] To facilitate understanding of this solution and to demonstrate its technical advantages, the following specific embodiments will be used to describe the solution of this invention.

[0086] A retaining wall has a height H = 6m and a soil weight γ = 18kN / m². 3 internal friction angle The coefficient of earth pressure at rest, K0 = 0.5, is the outward horizontal displacement x of the retaining wall when the soil behind the retaining wall reaches the active limit equilibrium state. a =0.012m, based on the actual outward horizontal displacement x of the retaining wall monitored on site. 外 =0.007m, then Δx a =0.007 / 0.012 = 0.583, E is calculated from equation (1). a =117.3kN / m.

[0087]

[0088] The inward horizontal displacement x of the retaining wall when the soil behind the retaining wall reaches the passive limit equilibrium state. p =0.12m, based on the actual inward horizontal displacement x of the retaining wall monitored on site. 内 =0.05m, then Δx p =0.05 / 0.12 = 0.417, E is calculated from equation (11). p = 696.69 kN / m.

[0089]

[0090] The above description is merely a preferred embodiment of the present invention and an explanation of the technical principles employed, and is not intended to limit the scope of the claimed invention, but merely to illustrate preferred embodiments of the invention. Those skilled in the art should understand that the scope of the invention is not limited to the specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

Claims

1. A method for calculating the resultant of active and passive earth pressures on cohesionless soil considering the plastic region, characterized in that, Includes the following steps: Displacement monitoring was conducted on the existing retaining wall to obtain the monitored displacement. Substitute the monitored displacement into the active earth pressure resultant force calculation formula or the passive earth pressure resultant force calculation formula to obtain the active earth pressure resultant force or passive earth pressure resultant force on the retaining wall under the current displacement. Resultant force of active earth pressure E a The calculation formula is as follows: Δx a ∈[0,1] Where, Δx a =x 外 / x a x 外 x represents the outward horizontal displacement of the retaining wall. a γ represents the outward horizontal displacement of the retaining wall when the soil behind it reaches an active limit equilibrium state. K0 is the coefficient of earth pressure at rest, H is the height of the retaining wall, and γ is the weight of the soil behind the wall. The internal friction angle of the soil; Resultant passive earth pressure E p The calculation formula is as follows: Δx p ∈[0,1] Where, Δx p =x 内 / x p x 内 x represents the inward horizontal displacement of the retaining wall. p This refers to the inward horizontal displacement of the retaining wall when the soil behind it reaches a passive limit equilibrium state. Stability analysis of the retaining wall is performed based on the obtained resultant force of active or passive earth pressure.

2. The method for calculating the resultant of active and passive earth pressures on cohesive soil considering the plastic region, as described in claim 1, is characterized in that... The formula for calculating the resultant force of active earth pressure is obtained through the following process: Step S1: Establish the outward horizontal displacement x of the retaining wall 外 The functional relationship between the penetration amount y of the plastic zone of the soil behind the wall and the wall is as follows: x 外 ∈[0,x a ] Step S2: Displace the retaining wall horizontally outward by a distance of x. 外 The resultant force of active earth pressure E at that time a The soil behind the wall is divided into two parts: the horizontal sliding force T of the right-angled trapezoidal plastic body corresponding to the penetration volume y of the plastic zone behind the wall, and the static earth pressure E0 of the right-angled triangular elastic body at the rear edge of the plastic body. a The calculation formula is as follows: E a <T+E0 Step S3: Calculate T in step S2 based on Coulomb's active earth pressure theory, and calculate E0 in step S2 based on the at-rest earth pressure theory. Summate the calculated T and E0 to establish E. a With Δx a The functional relationship between them is as follows: Δx a ∈[0,1]。 3. The method for calculating the resultant of active and passive earth pressures on cohesive soil considering the plastic zone, as described in claim 2, is characterized in that... The outward horizontal displacement of the retaining wall is x 外 The functional relationship between the penetration amount y of the plastic zone of the soil behind the wall and the wall was obtained through the following process: Assume the outward horizontal displacement of the retaining wall is x 外 The functional relationship between the penetration amount y of the plastic zone in the soil behind the wall and the plastic zone is linear, and the penetrated plastic zone is consistent with the slip surface l of Rankine's active earth pressure theory for cohesionless soil. The plastic zone is an angle with the horizontal plane. The plane is as follows: By x 外 The linear functional relationship between y and y can be expressed by the following formula. Combining the two equations, we can obtain the outward horizontal displacement x of the retaining wall. 外 The functional relationship between the penetration amount y of the plastic zone of the soil behind the wall and the wall.

4. The method for calculating the resultant of active and passive earth pressures on cohesive soil considering the plastic region, as described in claim 1, is characterized in that... When Δx a When Δx = 0, the formula for calculating the resultant force of active earth pressure is transformed into the formula for calculating the resultant force of static earth pressure. a When the value is 1, the formula for calculating the resultant force of active earth pressure is transformed into the Rankine formula for calculating the resultant force of active earth pressure when the soil behind the wall reaches the active limit equilibrium state.

5. The method for calculating the resultant of active and passive earth pressures on cohesive soil considering the plastic zone, as described in claim 1, is characterized in that... When Δx p When Δx = 0, the formula for calculating the resultant passive earth pressure is transformed into the formula for calculating the resultant static earth pressure. p When the value is 1, the formula for calculating the resultant passive earth pressure is transformed into the Rankine formula for calculating the resultant passive earth pressure when the soil behind the wall reaches the passive limit equilibrium state.

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