A method for determining the width of an enlarged arch foot of a soft stratum tunnel

Abstract

The application discloses a method for determining the expanded arch foot width of a tunnel in a soft stratum, which mainly comprises the following steps: (1) determining the vertical surrounding rock pressure of the tunnel; (2) calculating the self weight of the sprayed concrete layer; (3) calculating the vertical counterforce of the arch foot; (4) calculating the allowable bearing capacity of the foundation; (5) calculating the foundation stress at the arch foot; (6) judging whether the foundation is safe; and (7) calculating the expanded arch foot width under the condition of meeting the allowable bearing capacity of the foundation. The application can evaluate the stability of the foundation under the arch feet on both sides of the tunnel, and can calculate the expanded arch foot width according to the allowable bearing capacity of the foundation and the surrounding rock pressure, so that the problem of determining the expanded arch foot width in the tunnel construction is solved, and the design and construction units can optimize the design of the expanded arch foot width in theory.

Description

Technical Field

[0001] This invention relates to the field of tunnel construction, and specifically to a method for determining the width of the arch foot of a tunnel in soft strata. Background Technology

[0002] Tunnels and underground spaces have seen unprecedented development, such as underground energy storage projects, hydropower tunnel construction, high-speed railway tunnels, subway tunnel sections, and urban underground commercial streets. More and more tunnels will be built, such as the Sichuan-Tibet Highway national project under construction, in which tunnels account for a large proportion.

[0003] Construction at the tunnel entrance and in areas with weak and fractured surrounding rock is one of the challenges faced by tunnels, frequently resulting in problems such as arch foot subsidence and large deformation. Enlarging the arch foot is a commonly used remedial measure. Arch foot enlargement can be implemented at each excavation step of the tunnel and can also be combined with other reinforcement measures. However, there is currently very little literature on how to rationally determine the width of the arch foot enlargement. The few existing studies on arch foot enlargement are based on numerical simulations of individual tunnels or describe specific engineering measures. Tunnel stability is a prerequisite for safe construction, and how to rationally determine the width of the arch foot enlargement is a concern for construction and design units. Summary of the Invention

[0004] The purpose of this invention is to address the aforementioned technical problems in the prior art by providing a method for determining the width of the expanded arch foot of a tunnel in soft strata.

[0005] The above-mentioned objective of the present invention is achieved through the following technical solution:

[0006] The method for determining the width of the tunnel arch foot in soft strata includes the following steps:

[0007] (1) Determine the vertical surrounding rock pressure of the tunnel, which is calculated using the following formula:

[0008] ;

[0009] in, p γ represents the vertical surrounding rock pressure of the tunnel; γ represents the unit weight of the surrounding rock. L This refers to the tunnel excavation width; H The tunnel depth is the vertical distance from the ground surface to the tunnel arch. λ This refers to the lateral pressure coefficient; The apparent friction angle of the surrounding rock is determined by the following formula:

[0010] ;

[0011] in, The internal friction angle of the surrounding rock;

[0012] (2) Calculate the self-weight of the shotcrete layer, which includes the following steps:

[0013] (I) Calculate the central angle corresponding to half the tunnel excavation width using the following formula:

[0014] ;

[0015] Where θ is the central angle corresponding to half the tunnel excavation width; R is the radius of the tunnel arch; and arcsin is the arcsine.

[0016] (II) Calculate the self-weight of the shotcrete corresponding to half the tunnel excavation width using the following formula:

[0017] ;

[0018] Where G is the self-weight of the shotcrete corresponding to half the tunnel excavation width; γ 砼 d represents the unit weight of the shotcrete; d represents the thickness of the shotcrete.

[0019] (3) Calculate the vertical reaction force at the arch foot using the following formula:

[0020] ;

[0021] Among them, F y This is the vertical reaction force at the arch foot;

[0022] (4) Calculate the allowable bearing capacity of the foundation using the following formula:

[0023] ;

[0024] Where [σ] represents the allowable bearing capacity of the foundation; R c η is the uniaxial saturated compressive strength of the surrounding rock of the foundation; η is the reduction factor, which can be taken as 0.5 for intact rock mass, 0.2~0.5 for relatively intact rock mass, and 0.1~0.2 for relatively broken rock mass.

[0025] (5) Calculate the foundation stress at the arch foot using the following formula:

[0026] ;

[0027] (6) Determining whether the foundation is safe includes the following steps:

[0028] (I) If If the foundation is safe, no reinforcement measures are needed.

[0029] (II) If If the foundation is unsafe, reinforcement measures are needed, such as using the method of enlarging the arch foot. The method for determining this is shown in step (7).

[0030] (7) Calculate the width of the arch foot to meet the allowable bearing capacity of the foundation, using the following formula:

[0031] ;

[0032] Where B represents the increased arch foot width;

[0033] This allows for the assessment of the stability of the foundation at the arch feet on both sides of the tunnel; and the widening of the arch feet can be calculated based on the allowable bearing capacity of the foundation and the surrounding rock pressure.

[0034] The advantage of this invention compared to existing research methods lies in the fact that there is very little literature available on how to reasonably determine the width of the arch foot. The few existing studies on arch foot widening are based on numerical simulations of individual tunnels or descriptions of specific engineering measures; theoretical analysis and research are rarely reported.

[0035] This invention provides a quantitative theoretical method for determining the width of the enlarged arch foot in tunnels located in weak strata. This method can assess the stability of the foundation beneath the arch feet on both sides of the tunnel; and can calculate the width of the enlarged arch foot based on the allowable bearing capacity of the foundation and the surrounding rock pressure. This solves the problem of determining the width of the enlarged arch foot during tunnel construction, and is beneficial for design and construction units to theoretically optimize the design of the enlarged arch foot width. The method of this invention can be applied to the stability analysis of the arch foot in tunnels and underground engineering projects such as mining roadways, hydraulic tunnels, and subways during construction in weak strata, and provides a theoretical reference for determining the width of the enlarged arch foot. Attached Figure Description

[0036] Figure 1 This is a calculation diagram illustrating the method for determining the width of the arch foot of a tunnel in soft strata according to the present invention.

[0037] Figure 1 In the middle: 1 is the tunnel; 2 is the surrounding rock; 3 is the shotcrete layer; 4 is the enlarged arch foot; H For tunnel burial depth; h This refers to the tunnel excavation height; L R is the tunnel excavation width; R is the radius of the tunnel arch; θ is the central angle corresponding to half the tunnel excavation width. p d represents the vertical surrounding rock pressure of the tunnel; d represents the thickness of the shotcrete; B represents the width of the arch foot; F represents the vertical surrounding rock pressure of the tunnel. y To increase the vertical reaction force at the arch foot.

[0038] Figure 2 Diagram showing the increased arch foot width at different tunnel excavation heights.

[0039] Figure 3 Diagram showing the increased arch foot width at different tunnel depths. Detailed Implementation

[0040] The present invention will now be further described with reference to the accompanying drawings and embodiments.

[0041] The method of this invention is applied to an engineering example. Specific data for this example project are as follows: the unit weight γ of the surrounding rock in a tunnel is 20 kN / m³. 3 Cohesion of surrounding rock c The internal friction angle of the surrounding rock is 100 kPa. The angle is 22°, and the tunnel depth is [missing information]. H The tunnel has a length of 20m, an arch radius R of 6m, an excavation height h of 1.5m, an excavation width L of 7.94m, a shotcrete thickness d of 0.25m, and a shotcrete unit weight γ. 砼 23kN / m 3 The lateral pressure coefficient λ is 0.5, and the uniaxial saturated compressive strength R of the foundation surrounding rock is... c The pressure is 3000 kPa, and the reduction factor η is 0.1.

[0042] See Figure 1 The method for determining the width of the arch foot of a tunnel in soft strata according to the present invention is as follows:

[0043] Step 1: Determine the vertical surrounding rock pressure of the tunnel, which is calculated using the following formula:

[0044] ;

[0045] in, p γ represents the vertical surrounding rock pressure of the tunnel; γ represents the unit weight of the surrounding rock. L This refers to the tunnel excavation width; H The tunnel depth is the vertical distance from the ground surface to the tunnel arch. λ This refers to the lateral pressure coefficient; The apparent friction angle of the surrounding rock is determined by the following formula:

[0046] ;

[0047] in, The internal friction angle of the surrounding rock;

[0048] Step 2: Calculate the self-weight of the shotcrete layer, which includes the following steps:

[0049] (I) Calculate the central angle corresponding to half the tunnel excavation width using the following formula:

[0050] ;

[0051] Where θ is the central angle corresponding to half the tunnel excavation width; R is the radius of the tunnel arch; and arcsin is the arcsine.

[0052] (II) Calculate the self-weight of the shotcrete corresponding to half the tunnel excavation width using the following formula:

[0053] ;

[0054] Where G is the self-weight of the shotcrete corresponding to half the tunnel excavation width; γ 砼 d represents the unit weight of the shotcrete; d represents the thickness of the shotcrete.

[0055] Step 3: Calculate the vertical reaction force at the arch foot using the following formula:

[0056] ;

[0057] Among them, F y This is the vertical reaction force at the arch foot;

[0058] Step 4: Calculate the allowable bearing capacity of the foundation using the following formula:

[0059] ;

[0060] Where [σ] represents the allowable bearing capacity of the foundation; R c η is the uniaxial saturated compressive strength of the surrounding rock of the foundation; η is the reduction factor, which can be taken as 0.5 for intact rock mass, 0.2~0.5 for relatively intact rock mass, and 0.1~0.2 for relatively broken rock mass.

[0061] Step 5: Calculate the foundation stress at the arch foot using the following formula:

[0062] ;

[0063] Step 6: Determine if the foundation is safe, which includes the following steps:

[0064] (I) If If the foundation is safe, no reinforcement measures are needed.

[0065] (II) If If the foundation is unsafe, reinforcement measures are needed, such as using the method of enlarging the arch foot. The method for determining this is shown in step seven.

[0066] Step 7: Calculate the width of the arch foot to meet the allowable bearing capacity of the foundation, using the following formula:

[0067] ;

[0068] Where B represents the width of the arch foot.

[0069] Based on the above method and steps, the stress of the arch foot foundation can be obtained. Foundation bearing capacity According to step six, This indicates that the foundation is unsafe and requires reinforcement measures.

[0070] Furthermore, it is proposed to adopt reinforcement measures by expanding the arch foot. According to step seven, the minimum width B of the expanded arch foot can be obtained as 1.48m.

[0071] Furthermore, with other parameters remaining constant, the tunnel excavation height is changed. h Then the corresponding enlarged arch foot curve diagram can be obtained as follows: Figure 2 As shown, with the tunnel excavation height h As the arch length increases, the minimum width B of the enlarged arch foot also increases. When the width B exceeds 2m, on-site construction becomes difficult, and it is recommended to take other reinforcement measures in conjunction with other methods.

[0072] Furthermore, with other parameters remaining constant, the tunnel burial depth is changed. H Then the corresponding enlarged arch foot curve diagram can be obtained as follows: Figure 3 As shown, with the tunnel depth H As the value increases, the minimum width of the expanded arch foot, B, also increases.

Claims

1. A method for determining the width of the arch foot of a tunnel in soft strata, characterized in that... Includes the following steps: (1) Determine the vertical surrounding rock pressure of the tunnel, which is calculated using the following formula: ； in, p γ represents the vertical surrounding rock pressure of the tunnel; γ represents the unit weight of the surrounding rock. L This refers to the tunnel excavation width; H The tunnel depth is the vertical distance from the ground surface to the tunnel arch. λ This refers to the lateral pressure coefficient; The apparent friction angle of the surrounding rock is determined by the following formula: ； in, The internal friction angle of the surrounding rock; (2) Calculate the self-weight of the shotcrete layer, which includes the following steps: (I) Calculate the central angle corresponding to half the tunnel excavation width using the following formula: ； Where θ is the central angle corresponding to half the tunnel excavation width; R is the radius of the tunnel arch; and arcsin is the arcsine. (II) Calculate the self-weight of the shotcrete corresponding to half the tunnel excavation width using the following formula: ； Where G is the self-weight of the shotcrete corresponding to half the tunnel excavation width; γ 砼 d represents the unit weight of the shotcrete; d represents the thickness of the shotcrete. (3) Calculate the vertical reaction force at the arch foot using the following formula: ； Among them, F y This is the vertical reaction force at the arch foot; (4) Calculate the allowable bearing capacity of the foundation using the following formula: ； Where [σ] represents the allowable bearing capacity of the foundation; R c η is the uniaxial saturated compressive strength of the surrounding rock of the foundation; η is the reduction factor, which can be taken as 0.5 for intact rock mass, 0.2~0.5 for relatively intact rock mass, and 0.1~0.2 for relatively broken rock mass. (5) Calculate the foundation stress at the arch foot using the following formula: ； (6) Determining whether the foundation is safe includes the following steps: (I) If If the foundation is safe, no reinforcement measures are needed. (II) If If the foundation is unsafe, reinforcement measures are needed, such as using the method of enlarging the arch foot. The method for determining this is shown in step (7). (7) Calculate the width of the arch foot to meet the allowable bearing capacity of the foundation, using the following formula: ； Where B represents the increased arch foot width; This allows for the assessment of the stability of the foundation at the arch feet on both sides of the tunnel; and the widening of the arch feet can be calculated based on the allowable bearing capacity of the foundation and the surrounding rock pressure.

Images