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

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
• dral is a radial deformation of the primary lining concrete;
• a formula for the radial deformation dral 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, 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;
• and
• N is an intermediate process quantity.