Extreme sinking depth calculation method in shaft sinking construction

Abstract

The invention discloses a method for calculating the limit sinking depth in vertical shaft sinking construction, and the method comprises the steps: S1, building a construction mechanical model in a vertical shaft lifting and controlling sinking process, and obtaining an analysis equation; s2, converting the analysis equation according to the value of the blade foot end resistance Rj; s3, calculating a vertical suspension force T; and S4, calculating the limit sinking depth Hmax of the vertical shaft. The method has the advantages that the analysis equation is obtained by building the construction mechanical model in the shaft lifting and controlling sinking process, the limit sinking depth Hmax of the shaft is finally obtained by calculating the vertical suspension force T, and reference is provided for open caisson parameter design.

Description

Technical Field

[0001] The present invention relates to the technical field of shaft sinking construction, and in particular to a method for calculating the ultimate sinking depth in shaft sinking construction. Background Art

[0002] During the construction process of the traditional open caisson method, problems such as sudden sinking, excessive sinking, deviation, and ground settlement control have always been faced. In response to these problems, the traditional open caisson sinking process is to take a series of remedial measures after problems occur during sinking to ensure the continuous sinking of the open caisson. This method does not fundamentally solve the problems faced by the open caisson sinking, and there is a certain irrationality in terms of technology and economy. In addition, during the entire construction process of the traditional open caisson method, the control of the wall attitude is always in a passive state, and the sinking process cannot be directly and accurately controlled, increasing the construction safety risk and reducing the reliability of the open caisson method. The lifting and controlling sinking of the open caisson has unique advantages in solving the problems encountered in the traditional sinking process. This method actively applies an upward suspension force in the vertical direction of the open caisson. When the open caisson encounters special strata, by adjusting the magnitude of the suspension force, the stress state of the open caisson is changed, and the vertical attitude of the open caisson is adjusted, thereby avoiding the occurrence of adverse conditions. Compared with the traditional sinking process, the lifting and controlling sinking process can not only control the vertical stress state of the open caisson, but also control the vertical displacement of the open caisson through the suspension effect, regulate the sinking speed of the open caisson, and reduce the disturbance of the open caisson to the surrounding soil, solving the problem of excessive settlement of the surrounding soil in the traditional sinking process. At present, there is little research on the stress problem of the wall during the lifting and controlling sinking process of the open caisson in China, and the stress stage, stress condition, and stress change law of the open caisson during the lifting and controlling sinking process have not been mastered, with a large gap compared with the foreign research level. Therefore, it is of great significance to study the stress characteristics during the lifting and controlling sinking process of the open caisson. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for calculating the ultimate sinking depth in shaft sinking construction according to the deficiencies of the above-mentioned prior art. This calculation method obtains an analysis equation by establishing a construction mechanics model for the shaft lifting and controlling sinking process, and finally obtains the ultimate sinking depth H of the shaft by calculating the vertical suspension force T max to provide a reference for the design of open caisson parameters.

[0004] The purpose of the present invention is achieved by the following technical solutions:

[0005] A method for calculating the ultimate sinking depth in shaft sinking construction, the calculation method comprising:

[0006] S1: Establish a construction mechanics model for the shaft lifting and controlling sinking process to obtain an analysis equation;

[0007] The analysis equation is:

[0008] G = F w + T + Rf +R j ;

[0009] Wherein, G is the self-weight of the caisson, F w is the buoyancy of the well wall, T is the vertical suspension force, R f is the side friction resistance, R j is the tip resistance of the cutting edge;

[0010] S2: According to the value of the tip resistance R j of the cutting edge, transform the analysis equation;

[0011] When the value of the tip resistance R j is the maximum value Rj max , G = T + R f +R jmax +F w ;

[0012] When the value of the tip resistance R j is the minimum value R jmin , R jmin is equal to 0, G = F w +T+R f ;

[0013] S3: Calculate the vertical suspension force T;

[0014] When the value of the tip resistance R j is Rj max , the calculation formula for the vertical suspension force T is:

[0015]

[0016] When the value of the tip resistance R j is R jmin , the calculation formula for the vertical suspension force T is:

[0017]

[0018] Wherein, a is the thickness of the well wall, r is the inner radius of the well wall, γ c is the unit weight of the caisson well wall, γ w is the unit weight of water, f is the weighted average of the side friction resistance per unit area, H is the actual sinking depth of the caisson, A is the height of the well wall above the ground, and B is the distance from the liquid level in the well to the ground;

[0019] S4: Calculate the ultimate sinking depth H of the shaft max ;

[0020] When the value of the tip resistance R j is R jmin , and the value of the vertical suspension force T is zero, the ultimate sinking depth H of the shaft is obtainedmax The calculation formula is as follows:

[0021]

[0022] In the formula,

[0023] The calculation formula for the self-weight G of the open caisson is:

[0024] G(H) = πa(2r + a)(H + A)γ c .

[0025] The buoyancy force F of the shaft wall w The calculation formula is as follows:

[0026] Fw = πa(2r + a)(H - B)γ w .

[0027] The tip resistance Rj of the cutting edge max The calculation method is:

[0028] When shear failure occurs in the soil at the bottom of the cutting edge, assuming the soil area is B'C'D'E'A'A”F' and the sliding surface arc is a logarithmic spiral, the interaction between the straight lines A'B' and the combination of the straight line C'D' and the logarithmic spiral B'C' form the sliding surface; assuming the angle between A'B' and the horizontal plane is The angle between C'D' and A'D' is Among them, is the internal friction angle of the soil;

[0029] The influence of the soil weight above the A'D' plane and the interaction between the soil and the shaft wall side A'A” are represented by the equivalent stresses σ0 and τ0 on the A'D' plane;

[0030] The normal stress on the shaft wall side is distributed according to the at-rest earth pressure, so the average normal stress σ a and the shear stress τ a are:

[0031]

[0032] In the formula, k0 is the at-rest earth pressure coefficient of the soil, γ h is the unit weight of the soil, ΔH is the height of the soil in the caisson at the end of each sinking cycle, and δ is the friction angle between the shaft wall and the soil;

[0033] Assuming that the bearing layer under the cutting edge is a weightless medium, based on the geometric relationship of the slip surface, calculate the distance l from the inner side of the shaft wall to the end point of the slip surface:

[0034]

[0035] From the balance of all forces in the normal and tangential directions of the A'D' plane, we can obtain:

[0036]

[0037] In the formula, γ s is the unit weight of soil and water in the well;

[0038] The calculation formulas for the initial normal stress σ0 and tangential stress τ0 on the blade foot surface are as follows:

[0039]

[0040] According to the geometric relationship, we can get:

[0041]

[0042] Calculate through the following formula the value of:

[0043]

[0044] In the formula, c is the cohesion of the unit soil mass;

[0045] Since the A'C' plane is in the limit equilibrium state, the relationship between the tangential stress and the normal stress is as follows:

[0046]

[0047] Using the geometric properties of the logarithmic spiral, solve the stress σ c and τ c on the A'B' plane:

[0048]

[0049] Taking A'B'F' as the reference object, through the balance of vertical forces, we can obtain:

[0050] p m = cN c + σ0N q ;

[0051]

[0052] The ultimate bearing capacity of the self-weight of the soil mass and the passive earth pressure within the slip surface is:

[0053]

[0054] Then the ultimate bearing capacity of the soil mass below the blade foot surface is:

[0055]

[0056] The tip resistance of the blade foot R jmaxis as follows:

[0057]

[0058] The sidewall friction resistance R f has the following calculation formula:

[0059]

[0060] In the formula, f(h) is the distribution function of the unit friction resistance value of the soil mass varying with depth;

[0061] If the friction coefficient of the formation with the same mean value is the same, then the sidewall friction resistance is the sum of the friction resistances of each layer. The calculation formula for the sidewall friction resistance R f is as follows:

[0062]

[0063] In the formula, f i is the standard value of the side friction resistance per unit area, and H i is the thickness of the formation with the same mean value;

[0064] When H < 5m,

[0065] When H ≥ 5m, R f = 2π(r + a)(H - 2.5)f;

[0066] In the formula,

[0067] The advantages of the present invention are as follows: By establishing a construction mechanics model for the process of sinking a shaft by lifting and controlling, an analysis equation is obtained, and by calculating the vertical suspension force T, the ultimate sinking depth H of the shaft is finally obtained max , providing a reference for the design of the caisson parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 is the load diagram during the sinking process of the caisson of the present invention;

[0069] Figure 2 is the geometric schematic diagram of the caisson wall of the present invention;

[0070] Figure 3 is the schematic diagram of the interaction between the soil mass inside the well and the well wall of the present invention;

[0071] Figure 4 is the schematic diagram of the stress state of the soil mass A'B'C' of the present invention;

[0072] Figure 5 is the schematic diagram of the stress state of the soil mass A'B'F' of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0073] The features of the present invention and other related features will be further described in detail below in conjunction with the accompanying drawings through embodiments for the understanding of those skilled in the same industry:

[0074] Embodiment: As Figures 1 to 5 shown, this embodiment relates to a method for calculating the ultimate sinking depth in the construction of a shaft sinking, and the calculation method mainly includes the following steps:

[0075] S1: Establish a construction mechanics model for the process of lifting and sinking the shaft to obtain an analysis equation.

[0076] Specifically, as Figures 1 to 2 shown, the analysis equation is:

[0077] G = F w + T + R f + R j ;

[0078] In the formula, G is the self-weight of the caisson, F w is the buoyancy of the shaft wall, T is the vertical suspension force, R f is the side wall friction resistance, R j is the end resistance of the cutting edge.

[0079] The self-weight G of the caisson is the driving force for the sinking of the shaft wall, which is mainly composed of the self-weight of the shaft wall, the self-weight of the cutting edge, and the weight of the excavation machinery attached to the shaft wall. The ground load can also be included. For the convenience of calculation and analysis, only the self-weight of the shaft wall and the cutting edge is considered, and it is calculated according to the diameter, wall thickness, material specific weight, and sinking depth of the shaft wall. The cutting edge part is simplified as the shaft wall for calculation. The calculation formula for the self-weight G of the caisson is:

[0080] G(H) = πa(2r + a)(H + A)γ c ;

[0081] In the formula, a is the wall thickness of the shaft wall, r is the inner radius of the shaft wall, γ c is the specific weight of the caisson shaft wall, H is the actual sinking depth of the caisson, and A is the height of the shaft wall above the ground.

[0082] During the sinking process of the shaft wall, the liquid level in the shaft should always be higher than the surrounding water level to balance the water and soil pressure outside the shaft. Therefore, the buoyancy of the shaft wall is calculated based on the height of the liquid level in the shaft. The calculation formula for the buoyancy F w of the shaft wall is:

[0083] Fw = πa(2r + a)(H - B)γ w ;

[0084] In the formula, γ w is the specific weight of water, and B is the distance from the liquid level in the shaft to the ground.

[0085] The calculation formula for the side wall friction resistance R f is:

[0086]

[0087] In the formula, f(h) is the distribution function of the unit skin friction value of the soil mass varying with depth;

[0088] If the formation friction coefficient is the same according to the same mean value, the sidewall skin friction is the sum of the skin frictions of each layer, and the sidewall skin friction R f has the following calculation formula:

[0089]

[0090] In the formula, f i is the standard value of the side skin friction per unit area, and H i is the thickness of the formation with the same mean value;

[0091] It is assumed that the sidewall skin friction per unit area within 5 m below the ground surface is distributed in a linear pattern, increasing from zero until it reaches the maximum value when the depth is equal to 5 m, and then remaining constant; the friction coefficient evolves into the standard value of the friction per unit area and is calculated as the weighted average by thickness. Therefore, the distribution of the sidewall skin friction is simplified to a trapezoidal distribution.

[0092] When H < 5 m,

[0093] When H ≥ 5 m, R f = 2π(r + a)(H - 2.5)f;

[0094] In the formula, f is the weighted average of the side skin friction per unit area,

[0095] S2: According to the value of the toe resistance R j of the cutting edge, transform the analysis equation.

[0096] Specifically, due to the sinking displacement of the shaft wall of the sunk shaft, the suspension force restricts the sinking displacement. During the excavation and soil-breaking operation, the force balance of the shaft wall is not broken, but the vertical balance force is redistributed between the toe resistance and the suspension force. When the shaft wall is stationary, the toe resistance gradually decreases from the maximum value to zero. When the shaft wall sinks, the toe resistance gradually increases from zero to the maximum value again.

[0097] When the value of the toe resistance R j is the maximum value Rj max at this time, G = T + R f + R jmax + F w ;

[0098] When the value of the toe resistance R j is the minimum value R jmin at this time, R jmin is equal to 0, G = Fw +T+R f 。

[0099] As Figures 3 to 5 shown, the calculation method of the tip resistance Rj of the cutting edge is as follows: max When shear failure occurs in the soil at the bottom of the cutting edge, assuming the soil area is B'C'D'E'A'A”F', the sliding surface arc is a logarithmic spiral, and the interaction between the straight lines A'B', and the straight lines C'D' and the logarithmic spiral B'C' together form the sliding surface; assuming the angle between A'B' and the horizontal plane is

[0100] and the angle between C'D' and A'D' is where is the internal friction angle of the soil; The influence of the soil weight above the A'D' plane and the interaction between the soil and the side wall A'A” of the shaft are represented by the equivalent stresses σ0 and τ0 on the A'D' plane;

[0101] The normal stress on the side wall of the shaft is distributed according to the at-rest earth pressure, so the average normal stress σ

[0102] and the shear stress τ a and a are as follows:

[0103]

[0104] In the formula, k0 is the at-rest earth pressure coefficient of the soil, γ h is the unit weight of the soil, ΔH is the height of the soil in the shaft at the end of each cycle of the caisson sinking, and δ is the friction angle between the shaft wall and the soil;

[0105] Assuming that the bearing stratum under the cutting edge is a weightless medium, based on the geometric relationship of the slip surface, calculate the distance l from the inner side of the shaft wall to the end point of the slip surface:

[0106]

[0107] From the equilibrium of all normal and shear forces on the A'D' plane, we can obtain:

[0108]

[0109] In the formula, γ s is the unit weight of the water and soil in the shaft;

[0110] The calculation formulas for the initial normal stress σ0 and shear stress τ0 on the cutting edge foot surface are as follows:

[0111]

[0112] According to the geometric relationship, we can get:

[0113]

[0114] Calculate the value of 2η + φ by the following formula:

[0115]

[0116] Where c is the cohesion of the unit soil mass;

[0117] Since the A'C' plane is in the limit equilibrium state, the relationship between the tangential stress and the normal stress is as follows:

[0118]

[0119] Utilize the geometric properties of the logarithmic spiral to solve the stresses σ c and τ c acting on the A'B' plane:

[0120]

[0121] Taking A'B'F' as the reference object, the following can be obtained through the balance of vertical forces:

[0122] p m = cN c + σ0N q ;

[0123]

[0124] The ultimate bearing capacity of the self-weight of the soil mass and the passive earth pressure within the slip surface is:

[0125]

[0126] Then the ultimate bearing capacity of the soil mass under the blade foot tread is:

[0127]

[0128] The blade tip resistance R jmax is:

[0129]

[0130] S3: Calculate the vertical suspension force T.

[0131] Specifically, the vertical suspension force T is an important feature that differentiates the shaft wall lifting and sinking method from the traditional sinking method. The suspension force changes the vertical force balance system of the shaft wall and theoretically can make the blade tip resistance zero, which solves problems such as sudden sinking and excessive sinking of the traditional caisson shaft wall.

[0132] When the value of the blade tip resistance R j is Rj maxWhen the vertical suspension force T, the calculation formula is:

[0133]

[0134] When the tip resistance R of the cutting edge j takes the value of R jmin When, the calculation formula of the vertical suspension force T is:

[0135]

[0136] S4: Calculate the ultimate sinking depth H of the shaft max .

[0137] Specifically, when the tip resistance R of the cutting edge j takes the value of R jmin , and when the value of the vertical suspension force T is zero, the calculation formula for the ultimate sinking depth H of the shaft max is:

[0138]

[0139] In the formula,

[0140] The beneficial technical effect of this embodiment is that by establishing a construction mechanics model for the controlled sinking process of the shaft, an analysis equation is obtained, and by calculating the vertical suspension force T, the ultimate sinking depth H of the shaft is finally obtained max , providing a reference for the design of the caisson parameters.

[0141] Although the above embodiments have detailed the concept and implementation of the present invention with reference to the accompanying drawings, those of ordinary skill in the art can recognize that various improvements and transformations can still be made to the present invention without departing from the scope defined by the claims, so they will not be elaborated here one by one.

Claims

1. A method for calculating the ultimate sinking depth in the construction of shaft sinking, characterized in that The calculation method includes: S1: Establish a construction mechanics model for the sinking process of the shaft hoisting and obtain the analysis equation; The analysis equation is: G = F w + T + R f + R j ; Wherein, G is the self-weight of the open caisson, F w is the buoyancy force of the shaft wall, T is the vertical suspension force, R f is the side friction resistance, R j is the tip resistance of the cutting edge; S2: Transform the analysis equation according to the value of the tip resistance R of the cutter foot j of the cutter foot When the tip resistance of the cutting edge R j takes the maximum value Rj max , G = T + R f + R jmax + F w ; When the tip resistance of the cutting edge R j takes the minimum value R jmin , R jmin equals 0, and G = F w + T + R f ; S3: Calculate the vertical suspension force T; When the tip resistance of the cutting edge R j takes the value of Rj max the calculation formula for the vertical suspension force T is: When the tip resistance of the cutting edge is R j and its value is R jmin the calculation formula for the vertical suspension force T is as follows: Wherein, a is the thickness of the well wall, r is the inner radius of the well wall, γ c is the unit weight of the open caisson well wall, γ w is the unit weight of water, f is the weighted average of the lateral friction resistance per unit area, H is the actual sinking depth of the open caisson, A is the height of the well wall above the ground, and B is the distance from the liquid level in the well to the ground; S4: Calculate the ultimate sinking depth H of the shaft max ; When the tip resistance of the cutting edge R j takes the value of R jmin , and when the value of the vertical suspension force T is zero, the calculation formula for the ultimate sinking depth H max of the shaft is: Wherein, 2. The method for calculating the ultimate sinking depth in the shaft sinking construction according to claim 1, characterized in that The calculation formula for the self-weight G of the open caisson is: G(H) = πa(2r + a)(H + A)γ c 。 3. The method for calculating the ultimate sinking depth in the shaft sinking construction according to claim 2, wherein Buoyancy force F of the wellbore wall w The calculation formula is as follows: Fw = πa(2r + a)(H - B)γ w 。 4. The method for calculating the ultimate sinking depth in the shaft sinking construction according to claim 3, characterized in that The toe resistance Rj max is calculated as follows: When shear failure occurs in the soil at the bottom of the cutting edge, assume that the soil area is B'C'D'E'A'A”F', the sliding surface arc is a logarithmic spiral, and the interaction between the straight lines A'B' and the combination of the straight line C'D' and the logarithmic spiral B'C' form the sliding surface; assume that the angle between A'B' and the horizontal plane is The angle between C'D' and A'D' is Among them, is the internal friction angle of the soil; The influence of the soil weight above the A'D' plane and the interaction between the soil mass and the side surface A'A” of the shaft wall are represented by the equivalent stresses σ0 and τ0 on the A'D' plane; If the normal stress on the side wall of the wellbore is distributed according to the static earth pressure, the average normal stress σ a and tangential stress τ a are as follows: wherein, \(k_0\) is the coefficient of earth pressure at rest of soil; \(\gamma\) h is the unit weight of soil, \(\Delta H\) is the height of soil inside the caisson at the end of each sinking cycle, and \(\delta\) is the friction angle between the caisson wall and the soil; Assume that the bearing layer under the blade foot is a weightless medium, and based on the geometric relationship of the slip surface, calculate the distance l from the inner side of the shaft wall to the end point of the slip surface: From the balance of all normal and tangential forces on the A'D' plane, it can be obtained that: where γ s is the unit weight of soil and water in the well; The calculation formulas for the initial normal stress σ0 and tangential stress τ0 on the blade foot surface are as follows: According to the geometric relationship, it can be obtained that: Calculate by the following formula The value of: In the formula, c is the cohesion of the unit soil mass; Since the A'C' plane is in a state of limiting equilibrium, the relationship between the tangential stress and the normal stress is as follows: Solve for the stresses σ c and τ c acting on the plane A'B' by making use of the geometric properties of the logarithmic spiral Taking A'B'F' as the reference object, through the balance of vertical forces, it can be obtained that: p m = cN c + σ0N q ; The ultimate bearing capacity of the self-weight and passive earth pressure of the soil mass within the slip surface is: Then the ultimate bearing capacity of the soil mass under the blade foot surface is: The tip resistance of the cutting edge R jmax is as follows:

5. The calculation method for the ultimate sinking depth in the shaft sinking construction according to claim 4, characterized in that Sidewall frictional resistance R f The calculation formula is as follows: In the formula, f(h) is the distribution function of the unit frictional resistance value of the soil mass varying with depth; If the formation friction coefficient of the same mean value is the same, the sidewall frictional resistance is the sum of the frictional resistances of each layer, and the sidewall frictional resistance R f The calculation formula of is as follows: where f i is the standard value of the lateral frictional resistance per unit area, and H i is the thickness of the same homogeneous formation; When H < 5m, When H ≥ 5m, R f = 2π(r + a)(H - 2.5)f; In the formula,

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