A method for calculating the overburden pressure on the top of a large-section rectangular tunnel

Abstract

The present invention discloses a method for calculating the overburden pressure on the top of a large-section rectangular tunnel. The method calculates the lower limit of the soil pressure, including the following steps: (1) taking a differential unit for the overburden of the rectangular tunnel under an active stress state, and solving the vertical stress at the slip boundary of the differential unit in combination with the Mohr stress circle; s v s and major principal stress s 1; (2) the combined s v s and s 1, solve s v s The average vertical stress of the soil differential unit s av (3) Combine the calculation results of steps (1) and (2) to solve the normal stress at the slip boundary s s and tangential stress t s (4) According to the vertical force balance of the differential unit, a differential equation is established to solve the average earth pressure at the top of the tunnel. s av Expression; The present invention proposes a method for calculating the upper and lower limits of soil pressure under corresponding conditions, which provides a more complete guiding method for the design of minimum cover thickness of rectangular tunnels.

Description

Technical Field

[0001] The invention relates to the technical field of tunnel engineering technology, and in particular to a method for calculating the overburden pressure on the top of a large-section rectangular tunnel. Background Art

[0002] The calculation of the overburden pressure on the tunnel is crucial to determining the reasonable burial depth of the tunnel. A greater burial depth of the tunnel will significantly increase the factory cost and construction difficulty. On the contrary, a shallow burial depth can easily induce adverse working conditions such as surface collapse and tunnel floating, endangering the normal operation of personnel and production activities.

[0003] At present, the calculation of overburden pressure on tunnels is mainly carried out around circular tunnels. Some researchers have found that the measured results of top soil pressure of rectangular tunnels are significantly different from those of circular tunnels. Since the soil arch effect in the middle part of rectangular tunnels is significantly weakened, the overburden pressure is significantly increased compared with the circular tunnel of the same size. With the large-scale application of rectangular tunnels in underground engineering, it is extremely important to find an effective overburden pressure calculation method to improve the safety and rationality of rectangular tunnel design. Summary of the invention

[0004] Purpose of the invention: The purpose of the invention is to provide a method for calculating the overburden pressure on the top of a large-section rectangular tunnel to solve the problems existing in the background technology.

[0005] The method for calculating the overburden pressure on the top of a large-section rectangular tunnel described in the present invention calculates the lower limit value of the soil pressure, comprising the following steps:

[0006] (1) Take a differential unit for the soil overlying the rectangular tunnel under active stress state, and solve the vertical stress at the slip boundary of the differential unit in combination with the Mohr stress circle. σ v s and major principal stress σ 1; specifically, take the differential unit of the overlying soil of the rectangular tunnel under the active stress state, and obtain the geometric relationship in the Mohr stress circle:

[0007] (1);

[0008] (2);

[0009] (3);

[0010] in, σ v s is the vertical stress along the slip boundary, σ h s is the horizontal stress along the slip boundary, σ1 and σ 3 are the major principal stress and the minor principal stress, θ 1-h for σ h and σ Angle 1, K a is the Rankine active earth pressure coefficient K a = tan 2 (45°- φ / 2), c is the cohesion of soil; φ is the friction angle within the soil;

[0011] Substituting equation (1) into (2), we get equation (4):

[0012] (4);

[0013] Substituting equation (3) into equation (4), we get:

[0014] (5);

[0015] (6);

[0016] (7);

[0017] (2) Joint σ v s and σ 1, solve σ v s The average vertical stress of the soil differential unit σ av The specific relationship is as follows: According to formula (5), solve σ v s The average vertical stress of the soil differential unit σ av The relationship is:

[0018] (8);

[0019] in, σ av is the vertical mean stress, B 1 indicates the loose belt width, x is the position of any differential element, θ x for σ h and σ 3 inx The angle at the point;

[0020] Combined differential unit pairs σ av Integrating, we get:

[0021] (9);

[0022] in,

[0023] (9-1);

[0024] (9-2);

[0025] (3) Combine the calculation results of steps (1) and (2) to solve the normal stress at the slip boundary: σ s and tangential stress τ s The expression is as follows: It is obtained from the geometric relationship in the Mohr stress circle:

[0026] (10);

[0027] (11);

[0028] in, φ is the internal friction angle of the soil;

[0029] Combine equations (4), (6), (7), (9), (10), and (11) to solve the normal stress at the slip boundary. σ s and shear stress τ s：

[0030] (12);

[0031] (13);

[0032] in,

[0033] (12-1);

[0034] (12-2);

[0035] (13-1);

[0036] (13-2);

[0037] (4) Establish a differential equation based on the vertical force balance of the differential unit to solve the average earth pressure at the top of the tunnel σ av Expression; the details are as follows: The vertical force balance of the differential unit is as follows:

[0038] (14);

[0039] Among them, d z is the thickness of the differential unit, γ For the weight of the soil, B 1 is the width of the loose belt. Combining equations (9), (12), and (13), we get:

[0040] (15);

[0041] in, (15-1); the boundary conditions are: z = C 1, σ av = p s； in, C 1 is the distance from the soil surface to the top of the tunnel, p s Indicates the upper load.

[0042] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: 1. The overburden pressure calculation method provided by the present invention addresses the shortcomings of the circular tunnel soil pressure calculation method, and fully considers the weakening characteristics of the soil arch effect in the middle part of the rectangular tunnel. Compared with the existing calculation method, its calculation result is closer to the actual monitoring result; 2. The overburden pressure calculation method provided by the present invention takes into account the active and passive instability characteristics of the overburden soil, and proposes a calculation method for the upper and lower limits of the soil pressure under corresponding conditions, which provides a more complete guidance method for the design of the minimum cover thickness of the rectangular tunnel, and has great engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is the principle diagram of the present invention;

[0044] Figure 2 The figure is a theoretical model diagram for calculating the lower limit earth pressure of the present invention;

[0045] Figure 3 The upper limit earth pressure calculation theoretical model diagram of the present invention;

[0046] Figure 4 is the minimum principal stress trajectory under the active earth pressure of the present invention;

[0047] Figure 5is the Mohr circle of the sliding surface under the active earth pressure of the present invention;

[0048] Figure 6 is the minimum principal stress trajectory under the passive earth pressure of the present invention;

[0049] Figure 7 is the Mohr circle of the sliding surface under the passive earth pressure of the present invention;

[0050] Figure 8 The following is a simplified calculation diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0051] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0052] like Figure 1 As shown, an embodiment of the present invention provides a method for calculating the overburden pressure on the top of a large-section rectangular tunnel, comprising the following steps:

[0053] (1) Specific calculation steps for the lower limit of earth pressure:

[0054] Step 1: Take the differential unit of the overlying soil of the rectangular tunnel under the active stress state, analyze the force, and obtain the calculation model diagram of the overlying soil pressure, such as Figure 2 As shown in , it is assumed that the minimum principal stress trajectory of the differential element under the active limit state is a downward arc, as shown in Figure 4 shown.

[0055] according to Figure 5 The geometric relationship in the Mohr stress circle under the active earth pressure is obtained:

[0056] (1);

[0057] (2);

[0058] (3);

[0059] in, σ v s is the vertical stress along the slip boundary, σ h s is the horizontal stress along the slip boundary, σ 1 and σ 3 are the major principal stress and the minor principal stress, θ 1-h for σ h and σ Angle 1, K a is the Rankine active earth pressure coefficient (K a = tan 2 (45°- φ / 2))、 c is the cohesion of soil; is the friction angle within the soil;

[0060] Substituting equation (1) into (2), we get equation (4):

[0061] (4);

[0062] Substituting equation (3) into equation (4), we get:

[0063] (5);

[0064] (6);

[0065] (7).

[0066] Step 2: According to Figure 4 And equation (5), solve σ v s The average vertical stress of the soil differential unit σ av The relationship is:

[0067] (8);

[0068] in, σ av is the vertical mean stress, B 1 indicates the loose belt width, x is the position of any differential element, θ x for σ h and σ 3 in x The angle at the point;

[0069] Combined differential unit pairs σ av Integrating, we get:

[0070] (9);

[0071] in,

[0072] (9-1);

[0073] (9-2).

[0074] Step 3: According toσ s , τ s and σ 1. σ 3 and the calculation results of steps 1 and 2, find σ s , τ s and σ av The relationship between:

[0075] Depend on Figure 5 The geometric relationship in the Mohr stress circle under active earth pressure is obtained:

[0076] (10);

[0077] (11);

[0078] in, φ is the internal friction angle of the soil;

[0079] Combine equations (4), (6), (7), (9), (10), and (11) to solve the normal stress at the slip boundary. σ s and shear stress τ s：

[0080] (12);

[0081] (13);

[0082] in,

[0083] (12-1);

[0084] (12-2);

[0085] (13-1);

[0086] (13-2).

[0087] Step 4: According to Figure 2 The vertical force balance of the differential unit is as follows:

[0088] (14);

[0089] Among them, d z is the thickness of the differential unit, γ For the weight of the soil, B1 is the width of the loose belt. Combining equations (9), (12), and (13), we get:

[0090] (15);

[0091] in, (15-1); the boundary conditions are: z = C 1, σ av = p s； in, C 1 is the distance from the soil surface to the top of the tunnel, p s Indicates the upper load.

[0092] (2) Calculation steps for the upper limit of earth pressure:

[0093] The calculation method of this part is similar to the lower limit value. The passive limit state differential unit stress state is as follows Figure 3 Assume that the minimum principal stress trajectory is an upward arc according to the direction of soil movement, as shown in Figure 6 As shown in the figure, the Mohr circle of the sliding surface under passive earth pressure is as follows: Figure 7 shown.

[0094] Repeat steps one And two, solve σ v s The average vertical stress of the soil differential unit σ av The relationship is:

[0095] Repeat step 3 above to calculate the normal stress at the slip boundary σ s and shear stress τ s :

[0096] Repeat step 4 above, according to Figure 3 In the vertical force balance of the differential unit, list the vertical force balance equation and solve it. Specific embodiment:

[0098] (1) Project overview and calculation parameters:

[0099] Next, I will verify the above calculation results in conjunction with a rectangular pipe jacking project under the Beijing-Hangzhou Grand Canal in Suzhou City.

[0100] There are two lines in this project: N line and S line. The minimum coverage depth of N line and S line is 4.45 m and 4.39 m respectively. The prefabricated reinforced concrete pipe section is 9.8 m wide, 5.9 m high, 1.5 m long and 0.7 m thick. The mechanical properties of different strata obtained through indoor tests and field measurements are shown in Table 1. The calculation diagram of the two lines is shown in the attached figure. Figure 8 As shown. When calculating multi-layer soil, the soil pressure on the top of the rectangular tunnel is calculated by layer-by-layer calculation and stacking layer by layer. The additional load of the upper river is 20kPa. T1, T2, and T3 are the locations of the three monitoring points.

[0101] Table 1 Mechanical characteristics of soil in different strata

[0102] ;

[0103] (2) Calculation results:

[0104] Table 2 Comparison of N-line results

[0105] ;

[0106] Table 3 Comparison of S-line results

[0107] .

Claims

1. A method for calculating the overburden pressure on the top of a large-section rectangular tunnel, characterized in that: Calculating the lower limit value of earth pressure, including the following steps: (1) Take a differential unit for the soil overlying the rectangular tunnel under active stress state, and solve the vertical stress at the slip boundary of the differential unit in combination with the Mohr stress circle. σ v s and major principal stress σ 1; specifically, take the differential unit of the overlying soil of the rectangular tunnel under the active stress state, and obtain the geometric relationship in the Mohr stress circle: （1）； （2）； （3）； in, σ v s is the vertical stress along the slip boundary, σ h s is the horizontal stress along the slip boundary, σ 1 and σ 3 are the major principal stress and the minor principal stress, θ 1-h for σ h and σ Angle 1, K a is the Rankine active earth pressure coefficient K a = tan 2 (45°- φ / 2), c is the cohesion of soil; φ is the friction angle within the soil; Substitute Equation (1) into (2) to obtain Equation (4): （4）； Substitute Equation (3) into Equation (4) to obtain: （5）； （6）； （7）； (2) Joint σ v s and σ 1, solve σ v s The average vertical stress of the soil differential unit σ av The specific relationship is as follows: According to formula (5), solve σ v s The average vertical stress of the soil differential unit σ av The relationship is: （8）； in, σ av is the vertical mean stress, B 1 indicates the loose belt width, x is the position of any differential element, θ x for σ h and σ 3 in x The angle at the point; Combined differential unit pairs σ av Integrating, we get: （9）； Wherein, （9-1）； （9-2）； (3) Combine the calculation results of steps (1) and (2) to solve the normal stress at the slip boundary: σ s and tangential stress τ s The expression is as follows: It is obtained from the geometric relationship in the Mohr stress circle: （10）； （11）； in, φ is the internal friction angle of the soil; Combine equations (4), (6), (7), (9), (10), and (11) to solve the normal stress at the slip boundary. σ s and shear stress τ s： （12）； （13）； Wherein, （12-1）； （12-2）； （13-1）； （13-2）； (4) Establish a differential equation based on the vertical force balance of the differential unit to solve the average earth pressure at the top of the tunnel σ av Expression; the details are as follows: The vertical force balance of the differential unit is as follows: （14）； Among them, d z is the thickness of the differential unit, γ For the weight of the soil, B 1 is the width of the loose belt. Combining equations (9), (12), and (13), we get: （15）； in, (15-1); the boundary conditions are: z = C 1, σ av = p s； in, C 1 is the distance from the soil surface to the top of the tunnel, p s Indicates the upper load.

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