CN111090904B - Soil pressure calculation method based on generalized double-shear stress yield criterion - Google Patents
Soil pressure calculation method based on generalized double-shear stress yield criterion Download PDFInfo
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Abstract
The invention provides a soil pressure calculation method based on a generalized double-shear stress yield criterion, and relates to the technical field of geotechnical engineering. The method is firstly based onEstablishing a balance condition when any point in the soil body is in an extreme balance state according to a generalized double-shear stress criterion, wherein the generalized double-shear stress criterion considers two larger main shear stresses or a middle main stress sigma 2 And stress rod angle theta σ The effect on yield or failure; meanwhile, the influence of hydrostatic pressure on yield or damage and the S-D effect of different tensile and compressive strengths of the material are also considered; then calculating the soil pressure distribution under the active limit state and the passive limit state based on the balance condition in the limit balance state; the method of the invention can provide early warning when the active soil pressure calculation result is larger and the soil body does not reach the active limit state, and can provide early warning when the passive soil pressure calculation result is smaller and the soil body does not reach the passive limit state, so that certain safety reserve can be provided when the method is applied to engineering.
Description
Technical Field
The invention relates to the technical field of geotechnical engineering, in particular to a soil pressure calculation method based on a generalized double-shear stress yield criterion.
Background
In the design of retaining walls of projects such as side slopes, road beds, foundation pits and the like in geotechnical engineering, firstly, the calculation of soil pressure is required. The classical soil pressure calculation theory in the soil mechanics theory mainly includes Rankine (Rankine) and Coulomb (Coulomb) soil pressure theory, wherein the Rankine soil pressure theory is widely applied due to simple formula and clear meaning. The soil pressure theory is established based on the C-M yield criterion. The C-M yield criterion has simple form, easy parameter determination through experiments, convenience and practicability, thus being widely applied to geotechnical engineering. But the criterion fails to reflect the central principal stress (σ) 2 ) The characteristics that yielding and breaking are influenced and simple hydrostatic pressure can cause rock-soil yielding are provided, and other correction and improved yielding criteria are proposed by a plurality of scholars later, such as scholars in China Shu Luo \37584in 1961 and 1982The yield and damage theory of the double shear stress and the generalized double shear stress aiming at the metal materials and the rock-soil materials is provided.
The C-M yield criterion and the generalized double-shear stress criterion both belong to a shear stress yield theory, but the C-M criterion only considers the maximum shear stress during failure, and the generalized double-shear stress criterion considers two larger main shear stresses or middle main stresses sigma 2 And stress Lode angle theta σ The effect on yield or failure. The generalized double-shear stress criterion further considers the influence of hydrostatic pressure on yield or damage and considers the S-D effect of different tensile and compression strengths of the materials. Therefore, compared with a single shear stress criterion and other energy yield criteria, the method has obvious advantages and is more suitable for geotechnical materials.
In summary, it is necessary to provide a soil body extreme state calculation theory more suitable for rock-soil materials based on the generalized double shear stress yield criterion, so as to improve the existing active and passive soil pressure calculation methods.
Disclosure of Invention
The invention aims to solve the technical problem of providing a soil pressure calculation method based on the generalized double-shear stress yield criterion aiming at the defects of the prior art. The influence of two larger main shear stresses and hydrostatic pressure on soil yield damage is considered, a soil ultimate balance state calculation theory is established based on a generalized double-shear stress yield criterion, and soil pressure calculation of rock and soil materials is achieved.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a soil pressure calculation method based on a generalized double-shear stress yield criterion comprises the following steps:
step 1, establishing a balance condition when any point in a soil body is in an extreme balance state based on a generalized double-shear stress yield criterion;
the soil body is an even and continuous semi-infinite space material, the surface of the soil body is horizontal, the microcell bodies at any point in the soil body are under the action of three-dimensional main stress, and the three-dimensional main stress is respectively as follows: the vertical stress being a major principal stress sigma 1 The horizontal stress is the central principal stress sigma 2 And small principal stress σ 3 ；
The generalized double shear yield criterion is then expressed as:
when compressed in a broad sense: namely, it is
The method comprises the following steps: />
When stretched in a broad sense: namely, it is
The method comprises the following steps:
wherein f is the yield function, τ 23 、τ 13 、τ 12 Respectively acting parallel to the principal stress sigma 1 、σ 2 、σ 3 Principal shear stress on the inclined plane of the shaft, σ 12 、σ 23 、σ 13 Respectively, normal stress on a plane which is equal to the plane of the principal axis of the microcell body, beta, k b The material constants are respectively the material constants of the generalized double-shear stress yield criterion and are determined by tests;
the strength of the generalized double-shear stress yield criterion and the C-M yield criterion is the same in uniaxial tension and uniaxial compression, and the material constant beta, k of the generalized double-shear stress yield criterion is established b With the material constant C of the C-M criterion,
the relationship between the two is shown as the following formula:
wherein c is the cohesive force of the soil,
is the internal friction angle of the soil;
write the yield criterion of generalized double shear stress as
In the form of:
when in use
When the method is used:
when the temperature is higher than the set temperature
When the method is used:
wherein, I 1 Is the stress full tensor first invariant of the microcell bodies, J 2 For stress deflection of a second invariant, θ σ Is the stress rod angle (i.e., lode);
large principal stress sigma to the microcell bodies 1 Namely the dead weight stress of the soil at the point, the formula is as follows:
σ 1 ＝γZ (4)
wherein gamma is the weight of the filled soil behind the wall, and Z is the distance between the calculation point and the surface of the filled soil;
assuming that the soil body is in a side limit condition, namely two horizontal stresses acting on the side surface of the microcell body are equal, then:
σ 2 ＝σ 3 ＝K 0 γZ (5)
wherein, K 0 The lateral pressure coefficient of the soil body;
due to the fact that
Therefore->
/>
The compound represented by the formula (3 a) is 1 Written in principal stress form:
order to
Substituting the formulas (5), (8) and (9) into the formula (6) and simplifying the formula:
is obtained by the method shown in the formula (6),
substituting in formula (10) to obtain:
the formulas (11) and (12) are balance conditions when one point in the soil body is in a limit balance state;
firstly, assuming that the soil mass in a wedge-shaped range behind a wall is in an active limit state, and the rest soil mass is in an elastic state; carrying out stress analysis on the wedge-shaped body; when the wall body has displacement in the direction deviating from the soil body, the soil body is gradually changed into an active state from the original static soil pressure state; at the moment, the vertical dead-weight stress borne by the soil body is large main stress and the horizontal stress (sigma) is equal 2 ＝σ 3 ) Is a small principal stress; the small principal stress in the soil body is gradually reduced along with the increase of the displacement of the retaining wall until an active limit balance state is reached, and the large principal stress and the small principal stress meet the limit balance condition of the soil body;
the soil pressure in the soil body under the active limit state is the small principal stress according to the formula (12):
wherein p is a Is the earth pressure in the active limit state, K a Is the soil pressure coefficient under the active limit state,
the earth pressure in the active limit state is composed of two parts, the first part is obtained by the formula (13)
Is generated by the self weight of soil and is in proportion to the depth Z, the part is in triangular distribution, and a second part +>
Generated by cohesive force of cohesive soil, is independent of the depth Z, and is distributed in a rectangular shape; the depth Z of equation (13) is zeroThe cracking depth of soil is shown by the following formula:
in the passive limit state, the earth pressure calculation formula in the passive limit state of the earth body is obtained by the limit balance condition formula (11), and the formula is shown as follows:
wherein p is p For passive earth pressure, K p Is the soil pressure coefficient in the passive limit state,
the soil pressure distribution under the passive limit state also comprises two parts, wherein the first part is
Is in direct proportion to the depth Z and is distributed in a triangular shape; a second part is +>
The cohesive force of the cohesive soil is generated, is irrelevant to the depth and is distributed in a rectangular shape.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: compared with the result of classical Rankine classical theory calculation, the improved soil pressure calculation method provided by the invention has the advantage that the precision is improved. The active soil pressure calculation result is larger, the early warning can be provided when the soil body does not reach the active limit state, the passive soil pressure calculation is smaller, the early warning can be provided when the soil body does not reach the passive limit state, therefore, certain safety reserve can be provided in the engineering application, and the method is relatively more suitable for the early warning of the soil bodyIn a classical calculation formula, there is a great advantage. Meanwhile, the invention applies the generalized double-shear stress criterion to consider two larger main shear stresses or middle main stresses sigma 2 And stress rod angle (Lode) theta σ The effect on yield or failure. The influence of hydrostatic pressure on yielding or damage is further considered according to the generalized double-shear stress criterion, the S-D effect of different tensile and compressive strengths of the materials is considered, and the safety and the applicability of the retaining wall design are guaranteed.
Drawings
FIG. 1 is a schematic view of stress distribution at any point in a soil mass according to an embodiment of the present invention;
fig. 2 is a schematic view of a limit state of a soil pressure in a limit state according to an embodiment of the present invention, in which (a) is a schematic view of an active limit state, and (b) is a schematic view of a passive limit state;
fig. 3 is a soil pressure distribution diagram in a passive limit state according to an embodiment of the present invention, in which (a) is the soil pressure distribution diagram in an active limit state, and (b) is the soil pressure distribution diagram in a passive limit state.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
A soil pressure calculation method based on a generalized double-shear stress yield criterion comprises the following steps:
step 1, establishing a balance condition when any point in a soil body is in a limit balance state based on a generalized double-shear stress yield criterion;
for the soil body which is a uniform and continuous semi-infinite space material, the surface of the soil body is horizontal, the microcell bodies at any point in the soil body are acted by three-dimensional main stress, as shown in figure 1, the three-dimensional main stress is respectively as follows: the vertical stress being a major principal stress sigma 1 The horizontal stress is the central principal stress sigma 2 And small principal stress σ 3 ；
The generalized double shear yield criterion is then expressed as:
when compressed in a broad sense: namely that
When the method is used:
when stretched in a broad sense: namely that
When the method is used:
wherein f is the yield function, τ 23 、τ 13 、τ 12 Respectively acting parallel to the principal stress sigma 1 、σ 2 、σ 3 Principal shear stress on the inclined plane of the shaft, σ 12 、σ 23 、σ 13 Respectively, normal stress on a plane which is equal to the plane of the principal axis of the microcell body, beta, k b The material constants are respectively the material constants of the generalized double-shear stress yield criterion and are determined by tests;
the strength of the generalized double-shear stress yield criterion and the C-M yield criterion is the same in uniaxial tension and uniaxial compression, and the material constant beta, k of the generalized double-shear stress yield criterion is established b With the material constant C of the C-M criterion,
the relationship between them is shown by the following formula:
wherein c is the cohesive force of the soil,
is the internal friction angle of the soil;
write the yield criterion of generalized double shear stress as
In the form of:
when in use
The method comprises the following steps:
when the temperature is higher than the set temperature
When the method is used:
wherein, I 1 Is the stress full tensor first invariant of the microcell bodies, J 2 For stress deflection of a second invariant, θ σ Is the stress rod angle (i.e., lode);
as can be seen from FIG. 1, the microcell bodies are subjected to a large principal stress σ 1 Namely the dead weight stress of the soil at the point, the formula is as follows:
σ 1 ＝γZ (4)
wherein gamma is the weight of the filling soil behind the wall, and the unit is kN/m 3 Z is the distance (i.e., depth) of the calculated point from the surface of the fill in m;
assuming that the soil body is in a lateral limit condition, namely two horizontal stresses acting on the side surface of the microcell body are equal, then:
σ 2 ＝σ 3 ＝K 0 γZ (5)
wherein, K 0 The lateral pressure coefficient of the soil body;
due to the fact that
Therefore->
I in the formula (3 a) 1 Written in principal stress form:
order to
Substituting the formulas (5), (8) and (9) into the formula (6) and simplifying the formula:
is obtained by the formula (6),
substituted into formula (10) to obtain:
the formulas (11) and (12) are balance conditions when one point in the soil body is in a limit balance state;
first, assume that the soil mass in the wedge-shaped range behind the wall is in an active limit state, and the rest of the soil mass is in an elastic state, as shown in fig. 2 (a). And carrying out stress analysis on the wedge body. When the wall body has displacement in the direction deviating from the soil body, the soil body is gradually changed into an active state from the original static soil pressure state. At the moment, the vertical dead-weight stress borne by the soil body is large main stress and the horizontal stress (sigma) is equal 2 ＝σ 3 ) Is a small principal stress. The small principal stress in the soil body is gradually reduced along with the increase of the displacement of the retaining wall until an active ultimate balance state is reached, and the large principal stress and the small principal stress meet the ultimate balance condition of the soil body.
The soil pressure in the active limit state in the soil body is the small principal stress, which is obtained by the formula (12), and the following formula is shown:
wherein p is a The soil pressure in the active limit state is expressed in kPa, K a Is the soil pressure coefficient under the active limit state,
/>
the earth pressure in the active limit state is composed of two parts, the first part is obtained by the formula (13)
Is generated by the self weight of soil and is in proportion to the depth Z, the part is in triangular distribution, and a second part +>
The portion generated by cohesive force of cohesive soil is rectangular regardless of the depth Z, as shown in fig. 3 (a); two-part stress stackAfter addition, a tension zone and a compression zone appear. In fact, the tensile strength of the soil body material is very small, and the soil body is separated from the wall body under the action of very small tensile force, so that the retaining wall is considered not to bear the tensile force, namely the actual soil pressure is only a triangular part; the depth Z of the equation (13) is zero, namely the cracking depth of the soil, and the following equation is shown:
in the passive limit state, this is shown in fig. 2 (b). And (3) obtaining a soil pressure calculation formula under the soil passive limit state by the limit balance condition formula (11), wherein the formula is as follows:
wherein p is p Is passive earth pressure in kPa, K p Is the soil pressure coefficient in the passive limit state,
the soil pressure distribution under the passive limit state also comprises two parts, wherein the first part is
Is in direct proportion to the depth Z and is distributed in a triangular shape; a second part is +>
The cohesive force of the cohesive soil is generated, the cohesive force is independent of the depth Z and is distributed in a rectangular shape, and as shown in fig. 3 (b), the two parts of stress are superposed to obtain the soil pressure in a passive limit state, and the soil pressure is distributed in a trapezoidal shape.
Example 1:
in this example, the active earth pressure separation of retaining wall using Nanjing mica sand as test materialTaking the heart model as an example, testing and calculating the soil pressure in an active limit state; wherein the height of the model wall is H =190mm, the centrifugal acceleration is 50g, and the geometric similarity ratio of the model is lambda = 1: 100. Measuring the internal friction angle of the soil body according to the drainage shear test
γ＝12.6kN/m 3 The soil pressure at the active limit of the measuring point was 45.26kPa at a burial depth of 130mm (calculated depth Z =13m in accordance with the model similarity ratio λ) measured by the test. P can be obtained by adopting the classical Rankine soil pressure calculation theory a ＝tan 2 (45 ° - Φ/2) γ z =35.25kPa, obtainable with the improved soil pressure calculation method of the present invention: />
Compared with the classical soil pressure theory, the calculation result is closer to the test result.
Example 2:
in this embodiment, taking a retaining wall active earth pressure geotechnical centrifugal model with a model wall height H of 25cm as an example, the earth pressure under an active limit state is tested and calculated; the test soil body is cohesive soil, and the geometric similarity ratio of the model is lambda = 1: 100. The shear strength index c =38.2kPa of the soil mass is measured according to a large-scale direct shear test,
γ＝18.6kN/m 3 the active soil pressure at the measuring point was measured to be 237.44kPa with a burial depth of 240mm (calculated depth Z =24m in accordance with the model similarity ratio λ) by the test. P can be obtained by adopting the classical Rankine soil pressure calculation theory a ＝tan 2 (45-phi/2) gammaz-2 c tan (45-phi/2) =146.94kPa, and the improved soil pressure calculation method can be adopted to obtain the following results: />
Compared with the classical soil pressure theory, the calculation result is closer to the test result.
Example 3: in this embodiment, a large-scale retaining wall with a wall height H =1.68m is taken as an example, and the test material is sandy soilAnd (4) carrying out test and calculation on the soil pressure under the passive limit state. The strength index c =14kPa corresponding to the test soil body,
γ＝18.6kN/m 3 the soil pressure under the passive limit state of a measuring point with the burial depth of 1.2m is 171.63kPa through test, and p can be obtained by adopting the classical Rankine soil pressure calculation theory p ＝tan 2 (45 ° + Φ/2) γ z +2c tan (45 ° + Φ/2) =199.17kPa, which can be obtained by the improved soil pressure calculation method of the present invention: />
Compared with the classical soil pressure theory, the calculation result is closer to the test result.
Examples 1-3 the results of comparing the soil pressures obtained by the test and calculation and the calculation errors are shown in table 1:
TABLE 1 soil pressure comparison results and calculation errors obtained by test and calculation
As can be seen from Table 1, compared with the result of the classical Rankine theory calculation, the improved soil pressure calculation method provided by the invention has the advantage that the precision is improved. The soil pressure under the active limit state is calculated to be larger, early warning can be provided when the soil body does not reach the active limit state, the soil pressure under the passive limit state is calculated to be smaller, and early warning can be provided when the soil body does not reach the passive limit state, so that certain safety reserve can be provided in engineering application, and the soil pressure early warning method has a larger advantage compared with a classical calculation formula.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, and not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.
Claims (3)
1. A soil pressure calculation method based on a generalized double-shear stress yield criterion is characterized by comprising the following steps: the method comprises the following steps:
step 1, establishing a balance condition when any point in a soil body is in a limit balance state based on a generalized double-shear stress yield criterion;
step 2, calculating the soil pressure distribution in the active limit state according to the balance condition in the limit balance state;
firstly, assuming that the soil mass in the range of a wedge behind a wall is in an active limit state, and the rest soil mass is in an elastic state; carrying out stress analysis on the soil body within the wedge-shaped range; when the wall body has displacement in the direction deviating from the soil body, the soil body is gradually changed into an active state from the original static soil pressure state; at the moment, the vertical dead-weight stress borne by the soil body is a large main stress, and the horizontal equal stress is a small main stress; the small principal stress in the soil body is gradually reduced along with the increase of the displacement of the retaining wall until an active limit balance state is reached, and the large principal stress and the small principal stress meet the limit balance condition of the soil body;
step 3, calculating the soil pressure distribution in the passive limit state according to the balance condition in the limit balance state;
the specific method of the step 1 comprises the following steps:
the soil body is an even and continuous semi-infinite space material, the surface of the soil body is horizontal, the microcell bodies at any point in the soil body are under the action of three-dimensional main stress, and the three-dimensional main stress is respectively as follows: vertical stress being large principal stress sigma 1 The horizontal stress is the central principal stress sigma 2 And small principal stress σ 3 ；
The generalized double shear yield criterion is then expressed as:
when compressed in a broad sense: namely, it is
The method comprises the following steps:
when stretched in a broad sense: namely, it is
The method comprises the following steps:
wherein f is the yield function, τ 23 、τ 13 、τ 12 Respectively acting parallel to the principal stress sigma 1 、σ 2 、σ 3 Principal shear stress on the inclined plane of the shaft, σ 12 、σ 23 、σ 13 Respectively, normal stress on a plane which is equal to the plane of the principal axis of the microcell body, beta, k b The material constants are respectively the material constants of the generalized double-shear stress yield criterion and are determined by tests;
the strength of the generalized double-shear stress yield criterion and the C-M yield criterion is the same in uniaxial tension and uniaxial compression, and the material constant beta, k of the generalized double-shear stress yield criterion is established b With the material constant C of the C-M criterion,
the relationship between them is shown by the following formula:
wherein c is the cohesive force of the soil,
is the internal friction angle of the soil;
write the yield criterion of generalized double shear stress as
In the form of:
when in use
The method comprises the following steps:
when the temperature is higher than the set temperature
The method comprises the following steps:
wherein, I 1 Is the stress full tensor first invariant of the microcell body, J 2 For stress deflection of a second invariant, θ σ Is the stress rod angle;
large principal stress sigma to the microcell bodies 1 Namely the dead weight stress of the soil at the point, the following formula is shown:
σ 1 ＝γZ(4)
wherein gamma is the weight of the filling behind the wall, and Z is the distance between the calculation point and the surface of the filling;
assuming that the soil body is in a lateral limit condition, namely two horizontal stresses acting on the side surface of the microcell body are equal, then:
σ 2 ＝σ 3 ＝K 0 γZ(5)
wherein, K 0 Lateral pressure coefficient of soil body；
Due to the fact that
Therefore->
The compound represented by the formula (3 a) is 1 Written in principal stress form:
order to
Substituting the formulas (5), (8) and (9) into the formula (6) for arrangement and simplification to obtain:
is obtained by the formula (6),
substituted into formula (10) to obtain:
the equations (11) and (12) are the equilibrium conditions when one point in the soil body is in the limit equilibrium state.
2. The soil pressure calculation method based on the generalized double-shear stress yield criterion as claimed in claim 1, wherein: according to the equilibrium condition formula (12) in the extreme equilibrium state, the soil pressure in the active extreme state in the soil mass calculated in the step 2 is the small principal stress, and the following formula is shown:
wherein p is a Is the soil pressure in the active limit state, K a Is the soil pressure coefficient under the active limit state,
the earth pressure in the active limit state is composed of two parts, the first part, as obtained by the formula (13)
Is generated by the self weight of soil and is in proportion to the depth Z, the part is in triangular distribution, and a second part +>
Generated by cohesive force of cohesive soil, is independent of the depth Z, and is distributed in a rectangular shape; let the depth Z of equation (13) be zero, which is the cracking depth of the soil, as shown in the following equation:
3. the soil pressure calculation method based on the generalized double-shear stress yield criterion as recited in claim 2, wherein: according to the equilibrium condition formula (11) in the limit equilibrium state, the soil pressure in the passive limit state of the soil body calculated in the step 3 is shown as the following formula:
wherein p is p For passive earth pressure, K p Is the soil pressure coefficient in the passive limit state,
the soil pressure distribution under the passive limit state also comprises two parts, wherein the first part is
Is in direct proportion to the depth Z and is distributed in a triangular shape; a second part is->
Generated by cohesive force of cohesive soil, is independent of depth and is distributed in a rectangular shape. />
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