CN106638537A - Method for calculating soil pressure of limited soil - Google Patents

Abstract

A method for calculating the earth pressure of a finite soil body, said method comprising: determining the profile of the foundation pit and the profile parameters of the finite soil body, setting the angle between the fracture surface of the finite soil body and the horizontal direction, and performing force analysis on the fractured sliding body, Calculate the weight of the ruptured sliding body, use the known parameters, establish a system of equations according to the static equilibrium conditions in the horizontal direction and vertical direction, and replace the expression of the limited soil earth pressure with the shear force Derivation of the shear failure angle, set the derivative equation to zero, obtain the value of the shear failure angle, and then reversely substitute into the expression of the earth pressure of the finite soil body, and calculate the value, which is the effect of the finite soil body on the enclosure structure per linear meter earth pressure. The present invention covers different finite soil boundary conditions through the different values of the β angle , fully considers the mechanical characteristics of the finite soil, and deduces the azimuth of the fracture surface of the finite soil, in order to calculate the actual finite soil Body active pressure, has a very good promotion and application value.

Description

A Calculation Method of Earth Pressure in Finite Soil

technical field

The invention relates to a method for calculating the earth pressure of a finite soil mass, which belongs to the technical field of civil engineering.

Background technique

In many foundation pit support projects and slope support projects, the earth pressure acting on the retaining wall is generally calculated by the classical earth pressure theory. The classical Rankine earth pressure theory and the Coulomb earth pressure theory are based on semi-infinite soil derived under the conditions.

With the continuous development of urban engineering construction and the continuous development of engineering construction to underground space, there are existing underground building structures near many retaining works. When the distance between them is called finite soil. The lateral pressure generated by the limited soil on the foundation pit enclosure structure is called the limited soil earth pressure. The calculation of the limited soil earth pressure does not conform to the situation of the infinite soil in the classical earth pressure theory. If the traditional earth pressure calculation is still used There must be some differences between different models, and the calculated earth pressure value is often larger than the actual value. This will cause unnecessary waste in costs.

Therefore, it is a very practical technical problem to conduct reasonable analysis and calculation of the earth pressure of limited soil and find a calculation method that is in line with the actual situation.

Contents of the invention

The object of the present invention is, aiming at the problems existing in the calculation of the above-mentioned finite soil earth pressure, the present invention provides a kind of finite soil earth pressure calculation method, according to local conditions, according to the specific engineering parameters of the finite soil, carry out force analysis, reasonable calculation The earth pressure has been able to rationally design the support structure to achieve the purpose of safe, economical and effective support.

The technical solution of the present invention is a method for calculating the earth pressure of a finite soil body, the steps are as follows:

(1) Determine the profile parameters of the foundation pit enclosure and the limited soil, including the depth H of the foundation pit, the profile shape of the limited soil, the width b of the limited soil, the boundary inclination angle β of the limited soil, and the bulk density γ of the soil, Angle of internal friction The external friction angle δ of the soil;

(2) Take the finite soil mass per unit length for analysis, first set the angle θ between the fracture surface and the horizontal direction, then analyze the force of the fractured sliding body, and use known parameters to obtain the weight W of the fractured sliding body;

When the active earth pressure is required, first determine the direction of the active earth pressure Ea, and set the angle between the oblique upward direction and the horizontal direction as the external friction angle of the soil to be δ, and perform static balance calculations for the horizontal and vertical directions of the limited soil: can be calculated Then the expression of active earth pressure of finite soil is obtained as:

Similarly, when the passive earth pressure is required, the direction of the passive earth pressure Ep is determined, the angle between the oblique downward direction and the horizontal direction is the external friction angle of the soil body is δ, and the static force balance is performed on the horizontal direction and the vertical direction of the limited soil body calculate: can be calculated Then the expression of passive earth pressure of finite soil is obtained as:

(3) The earth pressure Ea or Ep of the finite soil body is derived from the shear failure angle θ respectively,

Let dEa/dθ=0 or dEp/dθ=0, find the value of θ, and then substitute it into the expression of earth pressure of finite soil to calculate the value, which is the earth pressure produced by finite soil on the enclosure structure per linear meter.

The enclosure structure of the foundation pit is vertical, the limited soil is non-cohesive soil, the surface of the soil is horizontal, and there is no overlying load on the surface of the soil.

The beneficial effect of the present invention is that the present invention covers different limited soil boundary conditions through the different values of the β angle, fully considers the mechanical characteristics of the limited soil, uses the limit equilibrium theory to establish an equation, and reasonably derives The azimuth angle of the fracture surface of the finite soil is calculated, and the active pressure of the finite soil is calculated more realistically, which is economical, reasonable and practical, and has a good value for popularization and application.

Description of drawings

Figure 1 is a simplified active earth pressure model diagram of finite soil;

Fig. 2 is a schematic diagram of active earth pressure analysis of finite soil;

Fig. 3 is a simplified passive earth pressure model diagram of finite soil;

Fig. 4 is a schematic diagram of passive earth pressure analysis of finite soil;

In the figure: 1 is the retaining structure of the foundation pit, 2 is the boundary of the limited soil body, and 3 is the bottom of the foundation pit.

detailed description

A method for calculating the earth pressure of a finite soil body proposed by the present invention will be further described in detail in conjunction with the accompanying drawings and specific embodiments. In a river-crossing tunnel project in a certain province and city, there is a large height difference between the foundation pit on the east bank of a ramp and the foundation pit below the bank, and the piled soil around the foundation pit on the bank is treated by grading, forming a limited state of the soil. According to the relevant information of the project, the vertical height H between the bottom of the slope and the top of the slope is 10.5m, the slope angle of the limited soil boundary 2 is β is 45°, and the internal friction angle between the soil is 17°, the experimentally measured friction angle between the soil and the outer wall is generally 2/3 of the internal friction angle between the soil, so the external friction angle δ is taken as 11°, regardless of the uniform load q, the limited soil The body width is 5m, and the parameters of each layer of soil are shown in Table 1:

Table 1 List of design values of soil layer parameters

Soil layer number Soil layer name Soil thickness r(KN/m3) C(KPa) φ(°) ① plain fill 11 18.0 / 17 ② Middle sand 4 19.0 / 30 ③ coarse sand 3 19.9 / 32 ④ Gravel 6.5 20.1 / 35 ⑤ argillaceous silty rock 0.75 23.5 100 /

Taking the finite soil mass per unit length into consideration, the gravity W of the sliding body can be obtained from Fig. 1 as:

In the formula: γ is the weight of the soil (18kN/m3); b is the width of the limited soil (5m); H is the vertical distance from the top of the slope to the bottom of the slope (10.5m); β is the slope angle of the slope (45° ).

According to the set relationship:

EF=(H-AE)cotθ=b+AEcotβ (2)

So you can get:

When the overlying load of the limited soil is not considered, according to the relationship of each force shown in Figure 1, a plane Cartesian coordinate system (Figure 2) is established, and according to the static force balance formula in the horizontal direction and the vertical direction:

For active earth pressure there are:

Available:

From the formula (5), the active earth pressure formula of the limited soil on the enclosure structure 1 can be deduced as:

Substitute (1) and (3) into (6) to get:

Derivation of formula (7):

Let dEa/dθ=0 and related parameters b, H, β, γ, Substituting the value of δ, the value of θ is calculated to be 55.8°. At this time, the value of θ is the value of θ corresponding to the maximum value of Ea. Substituting the value of θ into Ea, the active earth pressure Ea of the finite soil mass can be obtained It is 420KN/m. Using the traditional Coulomb earth pressure theory, the active earth pressure is 500KN/m.

For passive earth pressure there are:

Available:

From the formula (5), the passive earth pressure formula of the limited soil on the enclosure structure 1 can be deduced as:

Substitute (1) and (3) into (6) to get:

Derivation of formula (7):

Let dEp/dθ=0 and related parameters b, H, β, γ, Substituting the value of δ, the value of θ is calculated to be 62.8°. At this time, the value of θ is the value of θ corresponding to the maximum value of Ep. Substituting the value of θ into Ep, the passive earth pressure Ea of the finite soil mass can be obtained It is 601KN/m. Using the traditional Coulomb earth pressure theory, the passive earth pressure is 615KN/m.

Compared with the traditional calculation method of earth pressure, the earth pressure calculation method of finite soil provided by this embodiment can more accurately calculate the magnitude of the earth pressure of finite soil, which is economical and practical, and has good application value.

Claims (2)

1. a kind of finite soil Calculating method of earth pressure, it is characterised in that methods described step is as follows：

(1) sectional parameter of foundation pit enclosure section and finite soil, including foundation depth H are determined, the section shape of finite soil, The width b of finite soil, the border angle of inclination beta of finite soil, the unit weight γ of soil, internal friction angleAngle of external friction δ of the soil body；

(2) finite soil for taking unit length is analyzed, and first sets the angle theta of the plane of fracture and horizontal direction, and then rupture is slided Kinetoplast carries out force analysis, using known parameters, obtains weight W of rupture slide mass；

According to horizontal direction and the static balance condition of vertical directionSet up active earth pressure equation group and broken ground Pressure equation group：

I) active earth pressure equation group：

The expression formula of the finite soil active earth pressure that replaced out according to equation group：

Ii) passive earth pressure equation group：

Replace out the expression formula of finite soil passive earth pressure according to equation group：

(3) respectively finite soil soil pressure Ea or Ep carried out into derivation to failure by shear angle θ,

DEa/d θ=0 or dEp/d θ=0 are made, θ values are obtained, then inverse iteration enters finite soil soil pressure expression formula, calculates numerical value, i.e., It is soil pressure that every linear meter(lin.m.) finite soil is produced to building enclosure.

2. a kind of finite soil Calculating method of earth pressure according to claim, it is characterised in that the foundation pit enclosure knot Vertically, finite soil is non-cohesive soil to structure, soil body surface level, and soil body surface is without overlying burden.