US-12618668-B2 - Method for calculating diameter of annular non-full formwork support for circular shaft

Abstract

The present invention relates to the technical field of tunnel shield construction, specifically to a method for calculating diameter of an annular non-full formwork support for a circular shaft. By calculating and designing an inner diameter of a formwork support, sufficient space left inside a shaft can be ensured, and the thickness of secondary lining can be ensured at the same time, thereby preventing from affecting the structural stability of the shaft.

Inventors

• Jian Hu
• Xuejian Yang
• Fei ZHANG
• Zilong Zhang
• Zhengwei Fu
• Sihong Zhu
• Quansheng Ran
• Zeyu Wang
• Malin Dong
• Yue Lin

Assignees

• CHINA RAILWAY NO. 8 ENGINEERING GROUP CO., LTD.

Dates

Publication Date

20260505

Application Date

20231208

Priority Date

20231114

Claims (5)

1. 1 . A method for calculating diameter of an annular non-full formwork support for a circular shaft, characterized in that the annular non-full formwork support for a circular shaft comprises a shaft, primary lining concrete, secondary lining concrete, and an annular formwork support, wherein the shaft is excavated in surrounding rock, the annular formwork support is fixedly mounted in the shaft, the primary lining concrete is poured on an inner wall of the shaft, the secondary lining concrete is poured between the annular formwork support and the primary lining concrete, a sliding surface is located in the surrounding rock, the primary lining concrete is uniformly distributed on the inner wall of the shaft, and the diameter of the annular formwork support is calculated by the following formula: R = 2 ⁢ ( a - d r ⁢ a ⁢ l - U ) , ( Formula ⁢ 1 ) in Formula 1, R is the diameter of the annular formwork support, U is a thickness of the secondary lining concrete, a is a radius of the shaft, and d ral is a radial deformation of the primary lining concrete; a formula for the radial deformation d ral of the primary lining concrete is as follows: { d r ⁢ a ⁢ l = 1 E [ N ⁡ ( a - t ) ⁢ ( 1 - μ ) - ( 1 + μ ) ⁢ M a - t ] M = ( a - t ) 2 ⁢ a 2 ⁢ q t ⁡ ( 2 ⁢ a - t ) , N = - a 2 ⁢ q t ⁡ ( 2 ⁢ a - t ) , ( Formula ⁢ 2 ) in Formula 2, d ral is the radial deformation of the primary lining concrete, t is a thickness of the primary lining concrete, E is an elasticity modulus of the shaft, μ is a Poisson's ratio of the shaft, a is the radius of the shaft, q is a surrounding rock pressure on the shaft wall, M is an intermediate process quantity; and N is an intermediate process quantity.
2. 2 . A method for calculating diameter of an annular non-full formwork support for a circular shaft according to claim 1 , characterized in that after excavation of the shaft, rock and soil on the surrounding rock slide towards the shaft through the sliding surface, a distance from any point in the rock and soil in the sliding surface to the ground is s, and a formula for the pressure q of the surrounding rock on the shaft wall at any depth can be found as follows: { q = γ ⁢ a ⁡ ( b - a b ) λ - 1 ⁢ tan ⁡ ( 45 ⁢ ° - φ / 2 ) λ - 1 b = a + ( h 0 - s ) ⁢ tan ⁡ ( 45 ⁢ ° - φ / 2 ) , λ = 2 ⁢ tan ⁢ φ ⁢ tan ⁡ ( 45 ⁢ ° + φ / 2 ) , ( Formula ⁢ 3 ) in Formula 3, h 0 is a depth of the shaft, a is the radius of the shaft, b is a length from a center of the shaft to the sliding surface, γ is a bulk density of the rock and soil, φ is an internal friction angle of the rock and soil, 45 ⁢ ° + φ 2 is an angle between the sliding surface and a horizontal plane that can be determined by the internal friction angle of the rock and soil, and s is a distance from any point in the rock and soil to the ground.
3. 3 . A method for calculating diameter of an annular non-full formwork support for a circular shaft according to claim 1 , characterized in that the annular formwork support is composed of support trusses, uprights and crossbars, and the annular formwork support is fixed to the inner wall of the shaft by means of anchors.
4. 4 . A method for calculating diameter of an annular non-full formwork support for a circular shaft according to claim 1 , characterized in that a maximum value of the radial deformation of the primary lining concrete is taken for calculation.
5. 5 . A method for calculating diameter of an annular non-full formwork support for a circular shaft according to claim 3 , characterized in that the support trusses are fixedly connected to the crossbars by means of bolts, and the crossbars are fixedly connected to the uprights by means of bolts.

Description

CROSS REFERENCE TO RELATED APPLICATIONS The present application claims the benefit of Chinese Patent Application No. 202311512309.4 filed on Nov. 14, 2023, the contents of which are incorporated herein by reference in their entirety. TECHNICAL FIELD The present invention relates to the technical field of tunnel shield construction, specifically to a method for calculating diameter of an annular non-full formwork support for a circular shaft. BACKGROUND During tunnel shield construction, a shaft needs to be excavated so that a shield machine can enter to carry out construction work. A circular shaft is usually used. When the circular shaft is relatively deep, a formwork support is needed to carry out secondary lining concrete from bottom to top of the shaft. However, as subjected to the pressure of surrounding rock, the shaft will be constantly deformed, and it is difficult to determine the dimension of the inner diameter of the annular formwork support. Thus a method for calculating diameter of an annular non-full formwork support for a circular shaft is proposed. SUMMARY The purpose of the present invention is to provide a method for calculating diameter of an annular non-full formwork support for a circular shaft. By calculating and designing an inner diameter of a formwork support, sufficient space left inside a shaft can be ensured, and the thickness of secondary lining concrete can be ensured at the same time, thereby preventing from affecting the structural stability of the shaft. The purpose of the present invention is to provide a method for calculating diameter of an annular non-full formwork support for a circular shaft. The annular non-full formwork support for a circular shaft includes a shaft, primary lining concrete, secondary lining concrete, and an annular formwork support, where the shaft is excavated in surrounding rock, the annular formwork support is fixedly mounted in the shaft, the primary lining concrete is poured on an inner wall of the shaft, the secondary lining concrete is poured between the annular formwork support and the primary lining concrete, a sliding surface is located in the surrounding rock, the primary lining concrete is uniformly distributed on the inner wall of the shaft, and the diameter of the annular formwork support is calculated by the following formula: R=2⁢ (a-dral-U),(Formula⁢ 1)in Formula 1, R is the diameter of the annular formwork support,U is a thickness of the secondary lining concrete,a is a radius of the shaft, anddral is a radial deformation of the primary lining concrete;the formula of the radial deformation dral of the primary lining concrete is as follows: {dr⁢a⁢l=1E[N⁡(a-t)⁢(1-μ)-(1+μ)⁢Ma-t]M=(a-t)2⁢a2⁢qt⁡(2⁢a-t),N=-a2⁢qt⁡(2⁢a-t),(Formula⁢ 2)in Formula 2, dral is the radial deformation of the primary lining concrete,t is a thickness of the primary lining concrete,E is an elasticity modulus of the shaft,μ is a Poisson's ratio of the shaft,a is the radius of the shaft,q is a surrounding rock pressure on the shaft wall,M is an intermediate process quantity; andN is an intermediate process quantity. Optionally, after excavation of the shaft, rock and soil on the surrounding rock slide towards the shaft through the sliding surface, a distance from any point in the rock and soil in the sliding surface to the ground is s, and a formula for the pressure q of the surrounding rock on the shaft wall at any depth can be found as follows: {q=γ⁢a⁡(b-ab)λ-1⁢tan⁡(45⁢°-φ/2)λ-1b=a+(h0-s)⁢tan⁡(45⁢°-φ/2),λ=2⁢tan⁢φ⁢tan⁡(45⁢°+φ/2),(Formula⁢ 3)in Formula 3, h0 is a depth of the shaft,a is the radius of the shaft,b is a length from a center of the shaft to the sliding surface,γ is a bulk density of the rock and soil,φ is an internal friction angle of the rock and soil, 45⁢°+φ2 is an angle between the sliding surface and the horizontal plane that can be determined by the internal friction angle of the rock and soil, and s is a distance from any point in the rock and soil to the ground. Optionally, the annular formwork support is composed of support trusses, uprights and crossbars, and the annular formwork support is fixed to the inner wall of the shaft by means of anchors. Optionally, a maximum value of the radial deformation of the primary lining concrete is taken for calculation. Optionally, the support trusses are fixedly connected to the crossbars by means of bolts, and the crossbars are fixedly connected to the uprights by means of bolts. The present invention provides a method for calculating diameter of an annular non-full formwork support for a circular shaft. The annular non-full formwork support for a circular shaft includes a shaft, primary lining concrete, secondary lining concrete, and an annular formwork support. The shaft is excavated in surrounding rock, the annular formwork support is fixedly mounted in the shaft, the primary lining concrete is poured on an inner wall of the shaft, the secondary lining concrete is poured between the annular formwork