阅读说明：本技术 一种考虑植物蒸腾作用的挡土墙静止土压力确定方法 (Method for determining static soil pressure of retaining wall by considering plant transpiration ) 是由 张军辉 胡惠仁 秦卫星 于 2021-07-19 设计创作，主要内容包括：本发明公开了一种考虑植物蒸腾作用的挡土墙静止土压力确定方法,包括以下步骤：确定研究区域范围与坐标系；计算研究区域范围内竖向坐标为z的土体基质吸力、土体吸应力和静止土压力；依次计算研究区域范围内各不同竖向坐标处的静止土压力,从而得到考虑植物蒸腾作用的挡土墙静止土压力整体分布。本发明引入考虑植物蒸腾作用的挡土墙背后填土的基质吸力分布解析解,推导出了相应的静止土压力计算解析解,建立了植物-土体-挡土墙结构之间的相互作用关系,直观地揭示了植物蒸腾作用对挡土墙静止土压力的影响机理,提供了一种可考虑植物蒸腾作用的挡土墙静止土压力确定方法,为进一步研究和应用挡土墙结构提供了理论和技术支持。(The invention discloses a method for determining static soil pressure of a retaining wall by considering plant transpiration, which comprises the following steps of: determining a research area range and a coordinate system; calculating soil matrix suction, soil suction stress and static soil pressure with vertical coordinate z in the research area range; and sequentially calculating the static soil pressure at different vertical coordinates in the research area range, thereby obtaining the whole distribution of the static soil pressure of the retaining wall considering the plant transpiration effect. The invention introduces the matrix suction distribution analytic solution of the back filling soil of the retaining wall considering the plant transpiration, deduces the corresponding static soil pressure calculation analytic solution, establishes the interaction relation between the plant-soil body-retaining wall structure, intuitively reveals the influence mechanism of the plant transpiration on the static soil pressure of the retaining wall, provides the retaining wall static soil pressure determination method considering the plant transpiration, and provides theoretical and technical support for further researching and applying the retaining wall structure.)

1. A method for determining the static soil pressure of a retaining wall in consideration of plant transpiration is characterized by comprising the following steps:

step 1: determining a research area range and a coordinate system under the adaptive condition that the underground water level is flush with the bottom surface of the retaining wall, the back of the retaining wall is filled with soil uniformly, the surface is horizontal and plants grow on the retaining wall, and the plant roots are uniformly distributed;

step 2: calculating the soil matrix suction with the vertical coordinate z in the research area range;

and step 3: calculating the soil body absorption stress with the vertical coordinate z in the research area range;

and 4, step 4: calculating static soil pressure with a vertical coordinate z in the research area range;

and 5, repeating the step 2 to the step 4, and sequentially calculating the static soil pressure at different vertical coordinates in the research area range to obtain the overall distribution of the static soil pressure of the retaining wall considering the plant transpiration effect.

2. A method for determining the static soil pressure of a retaining wall in consideration of plant transpiration as claimed in claim 1, wherein in step 1, the study area is a semi-infinite unsaturated soil layer behind the retaining wall, the bottom surface of the study area is flush with the bottom surface of the retaining wall, and the top surface of the study area is flush with the top surface of the retaining wall; the research area range is divided into a rooted area range and an unrooted area range; the rooted area range is a soil layer area with plant roots in the research area range; the region without the root zone is a soil layer region except the region with the root zone in the research region range.

3. A method for determining static soil pressure of a retaining wall considering plant transpiration as claimed in claim 1, wherein the coordinate system is based on an intersection of a bottom surface of the retaining wall and a bottom surface of a fill as an origin and a vertical direction as a z-axis in step 1.

4. A method for determining the static soil pressure of a retaining wall in consideration of plant transpiration as claimed in claim 1, wherein in step 2, the soil matrix suction force with vertical coordinate z in the research area range is calculated as shown in formula (1):

in the formula (1), u_a-u_wThe matrix suction of the soil body is expressed in kPa; u. of_aRepresenting the pore gas pressure of the soil body in kPa; u. of_wThe expression of the pore water pressure of the soil body is kPa; alpha represents the soil desaturation coefficient and has the unit of kPa^-1(ii) a k is the unsaturated permeability coefficient of the soil body, and the unit is m/s; k is a radical of_sThe unit is m/s, and the saturation permeability coefficient of the soil body is shown.

5. A method for determining the static soil pressure of a retaining wall considering plant transpiration as set forth in claim 4, wherein the method is characterized in thatThe calculation method of (2) is specifically shown as the following formula (2):

A＝exp[α((u_a-u_w)₀-z)]+q₀[exp(-αz)-1]/k_s； (2)；

in the formula (2), A represents an intermediate variable; t is_pExpressing the plant transpiration rate in mm/d; z represents the vertical coordinate of the area of investigation, in m; l is₁Is the thickness of the rootless zone, and the unit is m; l is₂Is the thickness of the rooted region in m; l is the height of the retaining wall, and the unit is m; (u)_a-u_w)₀Represents the substrate suction at the groundwater level in kPa; q. q.s₀The unit is the stable infiltration rate of the soil body and is m/s;

the formula (3) is satisfied:

6. the method for determining the static soil pressure of the retaining wall in consideration of the plant transpiration as claimed in claim 1, wherein in the step 3, the suction stress of the soil body with the vertical coordinate z in the research area range is calculated as shown in a formula (4);

in formula (4): χ (u)_a-u_w) Representing the suction stress of the soil body, and x representing the effective stress parameter。

7. A method for determining the static soil pressure of a retaining wall in consideration of plant transpiration as claimed in claim 1, wherein in step 4, the static soil pressure with a vertical coordinate z in the research area is calculated as shown in formula (5),

in formula (5), σ_h-u_aRepresenting the static soil pressure in kPa; sigma_hRepresenting the horizontal stress of the soil body with the unit of kPa; sigma_v-u_aIs the overburden pressure, and the unit is kPa; sigma_vThe vertical stress of the soil body is expressed in kPa; mu represents the soil poisson ratio.

Technical Field

The invention belongs to the technical field of retaining wall engineering, and relates to a method for determining static soil pressure of a retaining wall by considering plant transpiration.

Background

The static soil pressure is the pressure of the soil filled behind the wall acting on the wall back when the retaining wall structure does not move or rotate; the method is one of three soil pressures of a retaining wall, and how to determine the soil pressure is always a hot point of concern in the geotechnical engineering field.

At present, the conventional method for calculating the static soil pressure of a retaining wall mainly considers the factors of soil mass gravity and position, and the specific formula is as follows:wherein p is₀Representing the traditional static soil pressure, and mu represents the soil body Poisson ratio; gamma represents the soil mass gravity; z is a radical of₁The vertical distance from the surface of the soil layer to the calculation point is shown. The influence of the unsaturated state of the soil body is considered in the development of the method, but the influence of plants is not considered.

However, in actual engineering, the surface layer of the earth filling behind the retaining wall is often grown with plants. The presence of plants has a significant effect on soil strength: the transpiration of the plants can absorb the moisture of the soil body, change the suction force and the suction stress of the soil body matrix, and further improve the shear strength of the soil body. The change of the shear strength of the soil body can change the static soil pressure acting on the back of the retaining wall, and the traditional determination method cannot accurately evaluate the static soil pressure of the retaining wall.

Therefore, it is necessary to provide a method for determining the static soil pressure of a retaining wall by considering the plant transpiration, improve the accuracy of the determination method, and provide theoretical support for further research and application of the retaining wall.

Disclosure of Invention

In order to achieve the purpose, the invention provides a method for determining the static soil pressure of a retaining wall in consideration of plant transpiration, which introduces a matrix suction distribution analytical solution of the soil filled behind the retaining wall in consideration of the plant transpiration, deduces a corresponding static soil pressure calculation analytical solution, establishes an interaction relation between a plant-soil body-retaining wall structure and solves the problem that the influence of the plant transpiration on the static soil pressure of the retaining wall is not considered in the prior art.

The invention adopts the technical scheme that a method for determining the static soil pressure of a retaining wall in consideration of plant transpiration comprises the following steps:

step 1: determining a research area range and a coordinate system under the adaptive condition that the underground water level is flush with the bottom surface of the retaining wall, the back of the retaining wall is filled with soil uniformly, the surface is horizontal and plants grow on the retaining wall, and the plant roots are uniformly distributed;

step 2: calculating the soil matrix suction with the vertical coordinate z in the research area range;

and step 3: calculating the soil body absorption stress with the vertical coordinate z in the research area range;

and 4, step 4: calculating static soil pressure with a vertical coordinate z in the research area range;

and 5, repeating the step 2 to the step 4, and sequentially calculating the static soil pressure at different vertical coordinates in the research area range to obtain the overall distribution of the static soil pressure of the retaining wall considering the plant transpiration effect.

Further, in the step 1, the research area range is a semi-infinite unsaturated soil layer behind the retaining wall, the bottom surface of the research area range is flush with the bottom surface of the retaining wall, and the top surface of the research area range is flush with the top surface of the retaining wall; the research area range is divided into a rooted area range and an unrooted area range; the rooted area range is a soil layer area with plant roots in the research area range; the region without the root zone is a soil layer region except the region with the root zone in the research region range.

Further, in the step 1, the coordinate system takes the intersection point of the bottom surface of the retaining wall and the bottom surface of the filling layer as an origin and takes the vertical direction as the z axis.

Further, in step 2, the calculation of the soil matrix suction force with the vertical coordinate z in the research area range is shown as formula (1):

in the formula (1), u_a-u_wThe matrix suction of the soil body is expressed in kPa; u. of_aIndicating pore pressure of soilIn kPa; u. of_wThe expression of the pore water pressure of the soil body is kPa; alpha represents the soil desaturation coefficient and has the unit of kPa^-1(ii) a k is the unsaturated permeability coefficient of the soil body, and the unit is m/s; k is a radical of_sThe unit is m/s, and the saturation permeability coefficient of the soil body is shown.

Further, in the present invention,the calculation method of (2) is specifically shown as the following formula (2):

A＝exp[α((u_a-u_w)₀-z)]+q₀[exp(-αz)-1]/k_s； (2)；

in the formula (2), A represents an intermediate variable; t is_pExpressing the plant transpiration rate in mm/d; z represents the vertical coordinate of the area of investigation, in m; l is₁Is the thickness of the rootless zone, and the unit is m; l is₂Is the thickness of the rooted region in m; l is the height of the retaining wall, and the unit is m; (u)_a-u_w)₀Represents the substrate suction at the groundwater level in kPa; q. q.s₀The unit is the stable infiltration rate of the soil body and is m/s;

the formula (3) is satisfied:

further, in the step 3, calculating the soil body suction stress with the vertical coordinate z in the research area range, as shown in the formula (4);

in formula (4): χ (u)_a-u_w) The absorption stress of the soil body is shown, and x represents an effective stress parameter.

Further, in step 4, the calculation of the static soil pressure with the vertical coordinate z in the research area range is carried out, as shown in formula (5),

in formula (5), σ_h-u_aRepresenting the static soil pressure in kPa; sigma_hRepresenting the horizontal stress of the soil body with the unit of kPa; sigma_v-u_aIs the overburden pressure, and the unit is kPa; sigma_vThe vertical stress of the soil body is expressed in kPa; mu represents the soil poisson ratio.

The invention has the beneficial effects that: the invention introduces the matrix suction distribution analytic solution of the back filling soil of the retaining wall considering the plant transpiration, deduces the corresponding static soil pressure calculation analytic solution, establishes the interaction relation between the plant-soil body-retaining wall structure, and intuitively reveals the influence mechanism of the plant transpiration on the static soil pressure of the retaining wall, thereby providing a method for determining the static soil pressure of the retaining wall considering the plant transpiration and providing theoretical and technical support for further researching and applying the retaining wall.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a schematic diagram of the invention study area range and coordinate system establishment.

Figure 2 is a schematic view of the stressed and deformed state of the soil mass unit of the invention.

FIG. 3 shows the matrix suction distribution of the stationary soil of the retaining wall at different transpiration rates according to the example of the present invention.

FIG. 4 shows the distribution of the static soil pressure of the retaining wall at different transpiration rates according to the example of the invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

A method for determining the static soil pressure of a retaining wall in consideration of plant transpiration specifically comprises the following steps:

step 1: flush with the retaining wall bottom surface at ground water level, the retaining wall is filled out the homogeneity behind one's back, surface level and has the plant for a long time, under plant roots evenly distributed's the adaptation condition, confirms research area scope and coordinate system:

as shown in fig. 1, the research area range is a semi-infinite unsaturated soil layer behind the retaining wall, the bottom surface of the research area range is flush with the bottom surface of the retaining wall, and the top surface of the research area range is flush with the top surface of the retaining wall; the research area range is divided into a rooted area range and an unrooted area range; the rooted area range is a soil layer area with plant roots in the research area range; the region without the root zone is a soil layer region except the region with the root zone in the research region range;

considering that the filling soil behind the retaining wall is a homogeneous semi-infinite unsaturated soil layer, a coordinate system is established by taking the intersection point of the bottom surface of the retaining wall and the bottom surface of the filling soil layer as an original point and taking the vertical direction as a z-axis.

Step 2: calculating the matrix suction of a soil body with a vertical coordinate z in the research area range, wherein the formula is shown as (1):

in the formula (1), u_a-u_wThe matrix suction of the soil body is expressed in kPa; u. of_aRepresenting the pore gas pressure of the soil body in kPa; u. of_wThe expression of the pore water pressure of the soil body is kPa; alpha represents the soil desaturation coefficient and has the unit of kPa^-1(ii) a k is the unsaturated permeability coefficient of the soil body, and the unit is m/s; k is a radical of_sThe unit is m/s, and the saturation permeability coefficient of the soil body is shown.

Wherein the content of the first and second substances,the calculation of (2) has different calculation methods in the range of the rooted region and the range of the non-rooted region, and is specifically shown in formula (2):

A＝exp[α((u_a-u_w)₀-z)]+q₀[exp(-αz)-1]/k_s； (2)；

wherein A represents an intermediate variable; t is_pExpressing the plant transpiration rate in mm/d, d expressing day; z represents the vertical coordinate of the study area range, the unit is m, and the coordinate of z is 0-L in the rootless area₁In the rooted region, z has a coordinate L₁～L；L₁Is the thickness of the rootless zone, and the unit is m; l is₂Is the thickness of the rooted region in m; l is the height of the retaining wall, and the unit is m; (u)_a-u_w)₀Representing the substrate suction at the underground water level, and taking 0 kPa; q. q.s₀The unit is the stable infiltration rate of the soil body and is m/s.

According to a mathematical definition, in the above formula (2)Need to be greater than 0; meanwhile, from the physical point of view, the unsaturated permeability coefficient k of the soil body is less than or equal to the saturated permeability coefficient k of the soil body_sThus, therefore, it isLess than or equal to 1, then:

the ratio of the unsaturated permeability coefficient of the soil body to the saturated permeability coefficient of the soil bodyThe influence of the plant transpiration on the suction of the soil matrix is considered in the calculation, and compared with the prior art that the influence of the plant transpiration on the soil filling behind the retaining wall is not considered, the static soil pressure is determined to be closer to the actual condition, so that the rationality of the design of the retaining wall is facilitated.

And step 3: determining the soil mass suction stress chi (u) at the vertical coordinate position according to the soil mass matrix suction force with the vertical coordinate z in the research area range obtained in the step 1_a-u_w) As shown in formula (4);

in formula (4): χ represents an effective stress parameter.

And 4, step 4: determining the static soil pressure sigma of the vertical coordinate position according to the soil body suction stress with the vertical coordinate z in the research area range obtained in the step 2_h-u_aAs shown in the formula (5),

in the formula, σ_hRepresenting the horizontal stress of the soil body with the unit of kPa; sigma_v-u_aIs the overburden pressure, and the unit is kPa; mu represents the soil poisson ratio; sigma_vThe vertical stress of the soil body is expressed in kPa, and the expression is sigma_v-u_aγ (L-z), γ represents the bulk density of the soil and has the unit kN/m³。

The specific derivation process of equation (5) is as follows:

based on the theory of elastic mechanics, the stressed and deformed states of the soil body units are shown in fig. 2, the strain response of one soil body unit is equivalent to the main strain components of the three directions x ', y ' and z ' in the horizontal direction and the vertical direction, and according to Hooke's law, the strain components of the soil body unit in the three directions x ', y ' and z ' are respectively shown as the formula (6a), the formula (6b) and the formula (6 c):

in the formula: epsilon_x′、ε_y′、ε_z′The strain components in the three directions of x ', y ' and z ' respectively; sigma'_x′、σ'_y′、σ'_z′Effective stress components in the three directions of x ', y ' and z ' respectively; e is Young's modulus.

Wherein, the expression of the effective stress sigma' aiming at the unsaturated soil is shown as the formula (7):

σ'＝(σ-u_a)+χ(u_a-u_w) (7)

in the formula (7), σ' represents the effective stress of unsaturated soil in kPa, and σ represents the total soil stress in kPa.

Formula (7) is respectively substituted into formula (6a), formula (6b) and formula (6c), Hooke's law is expanded, and strain components of soil body units of unsaturated soil in three directions of x', y 'and z' are obtained, wherein the expressions are shown as formula (8a), formula (8b) and formula (8 c):

in the formula, σ_x′、σ_y'、σ_z′Representing the total stress in the three directions x ', y ', z ', respectively.

Because the earth is filled behind the retaining wall to be a homogeneous semi-infinite unsaturated soil layer, the following conditions exist:

condition 1: the horizontal stress of the soil body is equal by adopting sigma_hMeans that there is σ_x′＝σ_y′＝σ_h；

Condition 2: the horizontal strain of soil body is equal, and epsilon is adopted_hThis means that there are: epsilon_x′＝ε_y′＝ε_h＝0。

For matching expression, the stress and strain in the vertical direction are expressed in the following way: sigma_z′＝σ_v，ε_z′＝ε_v。

By substituting the following formulae (8a), (8b) and (8c) under conditions 1 to 2:

substituting formula (4) for formula (9) to obtain the static soil pressure at the vertical coordinate z in the research area range:

and 5, repeating the step 2 to the step 4, and calculating the static soil pressure at different vertical coordinates in the research area range, so as to obtain the overall distribution of the static soil pressure of the retaining wall considering the plant transpiration effect.

Examples

Back filling of retaining wallThe soil is homogeneous silt, the total thickness of the soil layer is 5m, plants grow on the surface layer, the roots of the plants are uniformly distributed, the thickness of a rooted area is 0.5m, the thickness of a non-rooted area is 4.5m, and the underground water level is positioned at the bottom of the soil layer; the physical parameters of the soil body are as follows: saturated permeability coefficient k_s＝1×10^-7m/s, desaturation factor α ═ 0.01kPa^-1，μ＝0.35，γ＝18kN/m³Transpiration rate T_pIs 0mm/d, 2mm/d, 4mm/d and 6mm/d, and has stable infiltration rate q of earth surface₀Is 0 m/s. According to the determination method of the application, the matrix suction distribution (calculated according to the formula 1) and the static soil pressure distribution (calculated according to the formula 5) of the static soil of the retaining wall at different transpiration rates are obtained, and the results are respectively shown in fig. 3 and fig. 4.

As can be seen from FIG. 3, no plant influence, i.e., T, was taken into account_pWhen the thickness is 0mm/d, the substrate suction is linearly distributed; after considering the influence of plants, the suction force of the matrix is obviously increased under the action of transpiration, because the water in soil is absorbed by the root system of the plants under the action of transpiration; with the enhancement of transpiration, the water absorption capacity of the plants is increased, the suction force of the matrix shows an increasing trend, and the suction force is increased more close to the surface of the soil layer.

As can be seen from fig. 4, the calculated soil pressure has positive and negative values, positive values indicating compression, negative values indicating tension, and the tension area is not considered when evaluating the static soil pressure of the retaining wall. When plant transpiration is not taken into account, i.e. T_pWhen the soil pressure is 0mm/d, the vertical coordinate of the static soil pressure of 0kPa is about z to 3.8 m; after considering plant transpiration, the vertical coordinate position with the static soil pressure of 0kPa continuously moves downwards at T_pWhen the thickness is 6mm/d, the thickness is decreased to 3.4 m. Meanwhile, the static soil pressure is reduced along with the enhancement of the transpiration. The plant transpiration is shown to reduce the area and size of the retaining wall subjected to static soil pressure, which is beneficial to the stabilization of the retaining wall.

It is noted that, in the present application, relational terms such as first, second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.

All the embodiments in the present specification are described in a related manner, and the same and similar parts among the embodiments may be referred to each other, and each embodiment focuses on the differences from the other embodiments.

The above description is only for the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.