Method for calculating section bearing capacity safety coefficient of tunnel crack lining

Abstract

The invention discloses a method for calculating a bearing capacity safety coefficient of a tunnel crack lining section, which comprises the following steps of: calculating two conditions that the total section of the crack lining section is pressed and one side of the crack lining section is pressed and the other side of the crack lining section is pulled; according to the method, the ultimate bearing capacity and axial force of the crack lining section under the two conditions that the total section of the crack lining section is pressed and one side is pressed and the other side is pulled are calculated respectively, the safety coefficients of the ultimate bearing capacity and axial force of the crack lining section under the two conditions are further obtained, and the safety coefficients are compared with standard safety coefficient threshold values to obtain calculation results; and then the safety coefficient calculation method is verified through an on-site monitoring result, so that the method is scientific.

Description

Technical Field The invention belongs to the technical field of tunnel engineering, and in particular relates to a method for calculating the safety factor of the bearing capacity of a tunnel lining section with cracks and damages. Background Art At present, the secondary lining of tunnels at home and abroad mainly adopts reinforced concrete cast-in-place lining. During the long-term service of the tunnel, the tunnel lining will inevitably crack and be in a joint working state, but at this time the reinforced concrete lining still has a certain bearing capacity. The joint work of the reinforced concrete lining of the tunnel has become the normal service state, but there is no unified understanding on how to evaluate the safety of the joint working stage. At present, the safety factor calculation methods for reinforced concrete in the intact and uncracked stage and plain concrete tunnel lining in the cracked stage are relatively mature, but there is still a blank for the safety factor calculation method of reinforced concrete tunnel lining in the cracked stage. Due to the cracking or large degree of cracking of the lining section, the structural bearing capacity and safety factor calculation methods recommended by the specification are no longer applicable to the calculation of the cracked section, and it is difficult to accurately quantify the degree of cracking and safety of the structure. Therefore, constructing a safety factor calculation method suitable for cracked reinforced concrete lining of tunnels is of great value for evaluating the safety and durability of cracked linings in service tunnels, and can provide an important basis for tunnel operation and maintenance decisions. Summary of the invention The present invention proposes a method for calculating the safety factor of the cross-section bearing capacity of a tunnel lining with cracks, which fills the gap in the existing method for calculating the safety factor of a reinforced concrete tunnel lining in the cracking stage of the tunnel lining, and provides important value for evaluating the safety and durability of cracked linings in serving tunnels. The present invention adopts the following technical scheme as follows: A method for calculating the safety factor of the bearing capacity of a tunnel lining section with cracks and damages, comprising the following steps:

[0001] The calculation section is regarded as a rectangular double-reinforced section and a calculation model is established;

[0002] Calculation of axial force N of rectangular double reinforced section:

[0003] Ultimate bearing capacity of rectangular double reinforced section N max calculate:

[0004] Calculate N and N respectively according to the two cases of full section compression and one side compression and the other side tension. max :

[0005] The safety factor K1 of the bearing capacity of the reinforced concrete rectangular section is calculated. In the above method for calculating the safety factor of the bearing capacity of the tunnel lining section with cracks, in step [2], the axial force N of the rectangular double-reinforced section is: N=C+T S ′-T S Where C is the pressure on the concrete; T' s is the pressure at the compressive reinforcement; T s is the tensile force at the tensile reinforcement. In the above-mentioned calculation method of the bearing capacity safety factor of the tunnel cracked lining section, the ultimate bearing capacity N of the rectangular double-reinforced section in step [3] is max for: N max =f cd bx+(f s ' d -f sd )A s Where f cd —Design value of concrete axial compressive strength, f s ' d —Design value of steel bar compressive strength, f sd —Design value of steel bar tensile strength, b—section width (m), x—height of concrete compression zone (m). In the above-mentioned calculation method of the bearing capacity safety factor of the tunnel cracked lining section, when the cracked lining section is under full section compression; Where: R a —Ultimate compressive strength of concrete; R′ s —Standard value of steel bar compressive strength; e—The distance between the axial force application point and the combined force application point of the lower compressive steel bar; A′ s —Cross-sectional area of ​​steel bars in compression zone, m 2 ; a′ s —Rebar A′ s The distance from the center of gravity to the nearest edge of the cross section, m; h—height of the cross section, m; h0—effective height of the cross section, m, h0=ha; Where: c1 —The smaller compressive stress on concrete; σ c2 —The larger compressive stress on concrete; σ s ,σ′ s —compressive stress on the steel bars on both sides; A s —Cross-sectional area of ​​steel bars in compression zone, m 2 . In the above-mentioned calculation method of the safety factor of the bearing capacity of the cracked lining section of the tunnel, when the cracked lining section is under compression on one side and tension on the other side; Where: R l —Ultimate tensile strength of concrete; R s—Standard value of tensile strength of steel bar; l—Concrete height in tensile zone; x n —Concrete height in compression zone; A s —Cross-sectional area of ​​steel bars in compression zone, m 2 ; Where: c1 —tensile stress on concrete; σ c2 —compressive stress on concrete; σ s ,σ′ s —Tensile stress on steel bars, compressive stress on steel bars; A s —Cross-sectional area of ​​steel bars in compression zone, m 2 ; a—crack depth, m. In the above-mentioned calculation method of the bearing capacity safety factor of the tunnel lining section with cracks and damage, the calculation formula of the bearing capacity safety factor K1 of the reinforced concrete rectangular section is: Where K is the safety factor; N is the axial force; N max It is the ultimate bearing capacity of the lining section with cracks. In the above-mentioned calculation method of the safety factor of the bearing capacity of the tunnel lining section with cracks, in step [2], the calculation method of the pressure C on the concrete is: Pressure T at the compression reinforcement s The calculation method of ′ is: In the formula, A s ′ is the cross-sectional area of ​​the compressive reinforcement, a s ′ is the distance from the compression reinforcement to the edge of the section, α Es is the conversion factor of the reinforced concrete member section, α Es =E s / E c ; Tensile force T at the tensile reinforcement s The calculation method is: In the formula, A s is the cross-sectional area of ​​the tensile reinforcement, a s is the distance from the tensile reinforcement to the edge of the section. In the above-mentioned method for calculating the safety factor of the bearing capacity of the cracked lining section of the tunnel, in step [2], the following assumptions are made in calculating the internal force of the cracked lining section: (1) the cross-sectional strain remains flat; (2) the tensile strength of concrete is not considered; and (3) before reaching the ultimate strength, the stress-strain relationship of concrete and steel bars is proportional. In the above method for calculating the safety factor of the bearing capacity of the section of the tunnel with cracks and damage, in step [3], the ultimate bearing capacity N of the section is calculated. max When the concrete stress in the compression zone is equivalent to a rectangular stress diagram, the following conditions are met: (1) the area of ​​the equivalent rectangular diagram is equal to the area of ​​the theoretical stress diagram, that is, the total pressure on the concrete remains unchanged; (2) the centroid of the area of ​​the equivalent rectangular diagram coincides with the centroid of the area of ​​the theoretical stress diagram, that is, the position of action remains unchanged. The beneficial technical effects of the present invention are as follows: 1. The present invention calculates the safety factor of reinforced concrete tunnel lining in the cracking stage. Due to the cracking of the lining section or the large degree of cracking, the structural bearing capacity and safety factor calculation method recommended by the specification is no longer applicable to the calculation of the cracked section, and it is difficult to accurately quantify the degree of crack damage and safety of the structure. Therefore, constructing a safety factor calculation method applicable to cracked reinforced concrete lining of tunnels is of great value for evaluating the safety and durability of cracked linings in service tunnels, and can provide an important basis for tunnel operation and maintenance decisions. 2. The present invention divides the stress conditions of the lining cross section into two conditions: full cross section compression and outer side compression and inner side tension, and calculates the safety factor of the reinforced concrete tunnel lining separately in the two conditions, which is more scientific and reasonable. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 This is a schematic diagram of a cracked lining according to the present invention; Figure 2 It is a schematic diagram of the cracked lining of the present invention under full cross-section compression; Figure 3 It is a schematic diagram of the cracked lining of the present invention with one side under compression and the other side under tension; Figure 4 (a) is a schematic diagram of the stress-strain relationship of reinforced concrete structural materials under concrete compression; Figure 4 (b) is a schematic diagram of the stress-strain relationship of reinforced concrete structure materials under tension of steel bars; Figure 5 (a) is a schematic diagram of the cross-sectional dimensions of the reinforced concrete structure of the present invention; Figure 5 (b) is a schematic diagram of strain distribution of reinforced concrete structure of the present invention; Figure 5 (c) is a schematic diagram of stress distribution of the reinforced concrete structure of the present invention; Figure 6 (a) is a schematic diagram of concrete stress distribution in the compression zone of the present invention; Figure 6 (b) is a schematic diagram of stress distribution of equivalent rectangular concrete according to the present invention; Figure 7 This is an observation diagram of the on-site situation when the entire cross section is under pressure; Figure 8 This is an observation diagram of the on-site situation when one side is under pressure and the other side is under tension; DETAILED DESCRIPTION Figure 1 A structural schematic diagram of tunnel lining cracks is given. It can be seen from the figure that the steel bars on both sides of the concrete are symmetrically distributed. When the tunnel is under pressure all around, the concrete with lining cracks will experience two different stress conditions: compression on both sides and compression on one side and tension on the other side. The Code for Design of Concrete Structures (GB50010-2010) adopts Figure 4 (a) and (b) express the stress-strain relationship between concrete and steel bars. The concrete stress-strain relationship curve consists of a parabola with an ascending segment and a horizontal segment, and the expression is: Where: c —Concrete compressive strain is ε c The concrete compressive stress at f cd —Design value of concrete axial compressive strength; ε c0 —Concrete compressive stress reaches f cd The concrete compressive strain, ε c0 =0.002+0.5(f cu,k -50)×10 -5 When the calculated value is less than 0.002, it is taken as 0.002, f cu,k is the standard value of concrete cube compressive strength; ε cu —ultimate compressive strain of concrete; n—index, n=2-(f cu,k -50) / 60, when the n value is greater than 2.0, take n=2.0. The stress-strain relationship of the steel bar has an obvious yield step, and a simplified ideal elastic-plastic stress-strain relationship can be used, which is expressed as follows: Where: s —The steel bar strain is ε c Steel bar stress at ; f sd —Design value of steel bar tensile strength; ε y —The steel bar stress reaches f sd The steel strain E s —Elastic modulus of steel bars To calculate the internal forces of the cracked lining structure section, the following assumptions are made: (1) The cross-sectional strain remains flat; (2) The tensile strength of concrete is not considered; (3) Before reaching the ultimate strength, the stress-strain relationship of concrete and steel bars is proportional. According to the assumption, the compressive strain of concrete at the horizontal position of the compressed steel bar is proportional to the stress, that is: σ c ′=ε c ′E c (3) At the same time, the tensile strain of concrete at the horizontal position of the tensile reinforcement is proportional to the stress, that is: σ c =ε c E c (4) Calculate the cross-sectional dimensions, strain and stress distribution as follows Figure 5 As shown in the figure, h is the section height, b is the section width, A s is the cross-sectional area of ​​the tensile reinforcement, A s ′ is the cross-sectional area of ​​the compressive reinforcement, a s is the distance from the tensile reinforcement to the edge of the section, a s ′ is the distance from the compression reinforcement to the edge of the section, h0 is the effective height of the section, x n is the height of the concrete compression zone. According to the principle of similar triangles, Figure 5 (b) The cross-sectional strain distribution can be obtained by calculating the compressive reinforcement strain: Similarly, the strain of the tensile reinforcement can be obtained: Tensile force T at the tensile reinforcement s for: T s =σ s A s (7) Substituting equation (4) and equation (6) into the above equation, we can obtain: In the formula, α Es is the conversion factor of the reinforced concrete member section, α Es =E s / E c . Similarly, the pressure T at the compressive reinforcement is s 'for: The pressure C on concrete is: For a rectangular double-reinforced section, according to the force equilibrium condition, the sum of the internal and external forces along the longitudinal direction of the member is taken as 0, and the axial force N is obtained as: N=C+T S ′-T S (11) For the secondary lining structure, the steel bars are generally arranged symmetrically, so: Substituting equations (8), (9), (10) and (12) into equation (11), we can obtain: Under the limit state, the concrete stress in the compression zone reaches the design value of the axial compressive strength, and the stress of the tensile steel bar also reaches the design value of the tensile strength. According to the relevant provisions of the "Concrete Structure Design Code" (GB50010-2010) and the "Highway Tunnel Design Code" (JTG3370.1-2018) on the strength verification of rectangular reinforced concrete components, the concrete material cannot be regarded as an elastic material at this time. The true stress distribution of the cross section is as follows Figure 6 (a) shows the concrete stress in the compression zone being equivalent to a rectangular stress diagram, and the following conditions are met: (1) the area of ​​the equivalent rectangular diagram is equal to the area of ​​the theoretical stress diagram, that is, the total pressure of the concrete remains unchanged; (2) the centroid of the area of ​​the equivalent rectangular diagram coincides with the centroid of the area of ​​the theoretical stress diagram, that is, the position of action remains unchanged. The distribution of the rectangular stress in the compression zone concrete after equivalent is shown in Figure 6 (b) The equivalent rectangular stress diagram can be determined by two dimensionless eigenvalues ​​α and β. The equivalent concrete pressure C is: C=αf cd bx(14) Calculation of equivalent rectangular stress diagram The height x of the compression zone is calculated as follows: x=βx n (15) According to the Code for Design of Concrete Structures (GB50010-2010), for concrete with strength grade lower than or equal to C50, α=1.0 and β=0.8. Substituting equations (12), (14) and (15) into equation (11), we can obtain the ultimate bearing capacity N of the section: max for: N max =f cd bx+(f s ' d -f sd )A s (16) Where: f s ' d —Design value of steel bar compressive strength. Pass-through The safety factor K1 of the section bearing capacity can be obtained. When K1 is greater than the safety threshold given in the specification, the lining structure is considered safe; otherwise, it is considered that the bearing capacity has reached the limit state and the structure is prone to destruction. When the lining cracks, the height of the cross-section compression zone is smaller, and the bearing capacity of the lining section is bound to decrease. Therefore, it is necessary to calculate the ultimate bearing capacity of the cracked lining. When calculating the stress of the secondary lining section of the tunnel, according to the stress characteristics of the secondary lining, the lining structure of limited length is usually selected to be approximately regarded as a rectangular double-reinforced eccentric compression member for calculation. For rectangular eccentric compression members, whether it is material damage caused by large eccentric compression failure or small eccentric compression failure, the concrete in the compression zone reaches the ultimate compressive strain, and the compression steel bar A on the same side s ′ can generally reach the design value of compressive strength f s ' d , while the steel bars on the other side may be in tension or compression. Therefore, the stress conditions of the section can be divided into full section compression and one side compression and the other side tension. Refer to the specification. Strength calculation method of rectangular section eccentric compression member. When e≤0.2h, the full section is in compression, otherwise, there is a tension zone in the section. The stress distribution of the two forms of rectangular sections is as follows Figure 2 and Figure 3 shown. (1) Full section under compression After the lining concrete cracks, the cracks tend to close under pressure, and the cracks can still withstand axial pressure under compression. Therefore, the full section can still be calculated under compression. The ultimate bearing capacity of the section can be calculated according to the formula given in the tunnel design specification: Where: N—axial force of lining section, MN; R a — Ultimate compressive strength of concrete; R′ s — compressive strength of steel bars; e—the distance from the center of gravity of the compressed steel bar to the point of action of the axial force, m; A′ s —Cross-sectional area of ​​steel bars in tension zone, m 2 ; a′ s —Rebar A′ s The distance from the center of gravity to the nearest edge of the cross section, m; h—section height, m; h0—effective height of the cross section in m, h0=ha; b—section width, m; The stress distribution of the rectangular double-reinforced section of the lining under full section compression is shown in Figure 2 As shown, the height of the concrete compression zone is xn =h, compressive stress on concrete σ c =σ c1 +σ c2 , because the strains of the steel bar and concrete are equal, the compressive stress on the steel bar is Substituting the above equation into equation (13) we can obtain: Where: c1 - Smaller compressive stress on concrete; σ c2 —Higher compressive stress on concrete; σ s ,σ′ s —Compressive stress on the steel bars on both sides; A s —Cross-sectional area of ​​steel bars in compression zone, m 2 . (2) One side is under compression and the other side is under tension When one side is under compression and the other side is under tension, it is unreasonable to ignore the tensile strength of concrete. After the lining cracks, the concrete at the crack is withdrawn from the work, and the concrete height l in the tensile zone is changed from hx n becomes hx n -a, a is the crack depth. Substituting the above equation into equation (16), we can obtain the ultimate bearing capacity of the section: Where: R l —Ultimate tensile strength of concrete; R s —Standard value of tensile strength of steel bars; The stress distribution of the rectangular double-reinforced section of the lining under compression on one side and tension on the other side is shown in Figure 3 As shown, the compressive stress on concrete Compressive stress on steel bars Substituting the above equation into equation (13) we can obtain: Where: c1 —tensile stress on concrete; σ c2 —compressive stress on concrete; σ s ,σ′ s —Tensile stress on steel bars, compressive stress on steel bars; A s —Cross-sectional area of ​​steel bars in compression zone, m 2 ; a—crack depth, m; xn —Concrete height in compression zone. Taking the Lianchengshan Tunnel of the Baoji-Hanzhong Expressway in Shaanxi Province as the engineering support, the correctness of the safety factor calculation method for the bearing capacity of the tunnel lining section with cracks and damage proposed in the present invention is verified and explained. The surrounding rock of the Hanzhong section of the Lianchengshan Tunnel is mainly chlorite schist, which has strong water-softening and extrusion deformation characteristics. It encountered serious extrusion and large deformation disasters during construction, and many cracks appeared in the lining during operation. In order to ensure the safety of tunnel construction and operation, a complete health monitoring system has been built for the tunnel. Taking the ZK197+129 section as an example, it can be seen from the long-term measured data of the monitoring section that the secondary lining steel bars and concrete are under pressure inside and outside. In the sixth year of service (December 2023), the secondary lining cracks appear as oblique cracks extending from the side wall to the foot of the wall ( Figure 7 ), the section bearing capacity safety factor K1 at the side wall is calculated according to the compression condition of the entire section. When the entire section is under compression, after the lining concrete cracks, the cracks tend to close under the action of pressure, and the cracks can still withstand axial pressure under compression. Therefore, when the entire section is under compression, it can still be calculated as a complete section. The ultimate bearing capacity of the section is calculated according to formula (17). The steel bars on both sides are arranged symmetrically, e is 0.16m, the section width b is 1m, the height of the concrete compression zone x = h0, the thickness of the concrete protective layer d is 6cm, the section height h is 80cm, the ultimate compressive strength of C35 concrete is 26.3MPa, the ultimate bending compressive strength is 32.9MPa, the ultimate compressive strength of HPB400 steel bars is 540MPa, and the steel bar diameter is 28mm. Substituting the above parameters into formula (17) to calculate N max =31250.03KN. When the entire section is under compression, the axial force of the lining rectangular double-reinforced section of the side wall is calculated according to formula (18). c1 =5.303MPa,σ c2 =5.076MPa,σ s =56.419MPa,σ′ s =56.936MPa, substituting the above parameters into formula (18), we can calculate N=4221.4KN. The calculated result of the cross-sectional bearing capacity safety factor K1 of the side wall is 7.40, which is higher than the safety factor threshold of 2.0 given in the code, indicating that the tunnel structure is safe. The long-term observation results of the tunnel health monitoring system show that after the sixth year of service, the width of the oblique crack extending from the side wall to the foot of the wall in the monitoring section remains unchanged, and the cracks do not develop. At the same time, the stress monitoring results of the secondary lining show that the concrete stress and the steel stress remain basically stable and have no growth trend. The comprehensive monitoring results of the secondary lining crack width and the secondary lining stress monitoring results show that the secondary lining structure is stable and safe, which is consistent with the results obtained by the calculation method of the present invention. The safety factor of the secondary lining is still within the safe allowable value range. The existing lining cracks do not affect the structural safety, and the tunnel lining can still serve normally. Taking the ZK196+758 section as an example, the long-term measured data of this monitoring section show that the secondary lining steel bars and concrete are under compression on the inside and tension on the outside. In the sixth year of service (August 2023), the secondary lining cracks appear as oblique cracks extending from the side wall to the foot of the wall ( Figure 8 ), the safety factor K1 of the section bearing capacity at the foot of the wall is calculated according to the condition that one side is under compression and the other side is under tension. When one side is under compression and the other side is under tension, the ultimate bearing capacity of the section is calculated according to formula (19). The steel bars on both sides are arranged symmetrically, the section width b is 1m, and the height of the concrete compression zone is x n =56cm, concrete tensile zone height l = 56cm, concrete cover thickness d is 6cm, section height h is 80cm, C35 concrete compressive strength limit value is 26.3MPa, C35 concrete tensile strength limit value is 2.47MPa, HPB400 steel bar compressive strength limit value is 540MPa, HPB400 steel bar tensile strength limit value is 540MPa, steel bar diameter is 28mm. Substituting the above parameters into formula (19) to calculate N max =7191.1KN. The axial force of the rectangular double-reinforced section of the lining at the corner of the wall under compression on one side and tension on the other side is calculated according to formula (20). c1 =1.623MPa,σ c2 =6.6083MPa,σ s =1.4454MPa,σ′ s =3.784MPa, substituting the above parameters into formula (20), we can calculate N=1738.154KN. The calculated result of the cross-sectional bearing capacity safety factor K1 of the wall corner is 4.14, which is higher than the safety factor threshold of 2.0 given in the specification, indicating that the tunnel structure is safe. Through the long-term observation results of the tunnel health monitoring system, it can be known that after the sixth year of service, the width of the oblique crack extending from the side wall to the foot of the wall in the monitoring section remains unchanged, and the cracks do not develop. At the same time, the stress monitoring results of the secondary lining show that the concrete stress and the steel stress remain basically stable, and there is no growth trend. The comprehensive monitoring results of the secondary lining crack width and the secondary lining stress monitoring results show that the secondary lining structure is stable and safe, which is consistent with the results obtained by the calculation method of the present invention. The safety factor of the secondary lining is still within the safe allowable value range. The existing lining cracks do not affect the structural safety, and the tunnel lining can still serve normally. Therefore, it is shown that the method for calculating the bearing capacity safety factor of a cracked lining section proposed by the present invention is correct and reliable.

Claims

1. A method for calculating the safety factor of the bearing capacity of a tunnel lining section with cracks and damage, characterized in that: The following steps are involved: 【1】Consider the calculation section as a rectangular double-reinforced section and establish a calculation model; 【2】Calculation of axial force N of rectangular double-reinforced section: 【3】Ultimate bearing capacity of rectangular double reinforced section N max calculate: 【4】 Calculate N and N separately according to the two cases where the whole section is in compression and one side is in compression and the other side is in tension. max : 【5】Calculate the bearing capacity safety factor K1 of the reinforced concrete rectangular section.

2. A method for calculating the safety factor of the cross-section bearing capacity of a tunnel lining with cracks and damage according to claim 1, characterized in that: In step [2], the axial force N of the rectangular double-reinforced section is: N=C+T S ′-T S Where C is the pressure on the concrete; T' s is the pressure at the compressive reinforcement; T s is the tensile force at the tensile reinforcement.

3. The method for calculating the safety factor of the cross-section bearing capacity of a tunnel lining with cracks and damage according to claim 1 is characterized by: The ultimate bearing capacity of the rectangular double-reinforced section in step [3] is N max for: N max =f cd bx+(f s ′ d -f sd )A s Where f cd —Design value of concrete axial compressive strength, f′sd—Design value of steel bar compressive strength, f sd —Design value of steel bar tensile strength, b—section width (m), x—height of concrete compression zone (m).

4. A method for calculating the safety factor of the cross-section bearing capacity of a tunnel lining with cracks and damage according to claim 1, characterized in that: When the cracked lining section is under full section compression; Where: R a —Ultimate compressive strength of concrete; R′ s —Standard value of steel bar compressive strength; e—The distance between the axial force application point and the combined force application point of the lower compressive steel bar; A′ s —Cross-sectional area of ​​steel bars in compression zone, m 2 ; a′ s —Rebar A′ s The distance from the center of gravity to the nearest edge of the cross section, m; h—height of the cross section, m; h0—effective height of the cross section, m, h0=ha; Where: c1 —The smaller compressive stress on concrete; σ c2 —The larger compressive stress on concrete; σ s ,σ′ s —compressive stress on the steel bars on both sides; A s —Cross-sectional area of ​​steel bars in compression zone, m 2 .

5. The method for calculating the safety factor of the cross-section bearing capacity of a tunnel lining with cracks and damage according to claim 1 is characterized in that: When the cracked lining section is under compression on one side and tension on the other side; Where: R l —Ultimate tensile strength of concrete; R s —Standard value of steel bar tensile strength; l—Concrete height in tensile zone; x n —Concrete height in compression zone; A s —Cross-sectional area of ​​steel bars in compression zone, m 2 ; Where: c1 —tensile stress on concrete; σ c2 —compressive stress on concrete; σ s ,σ′ s —Tensile stress on steel bars, compressive stress on steel bars; A s —Cross-sectional area of ​​steel bars in compression zone, m 2 ; a—crack depth, m.

6. A method for calculating the safety factor of the cross-section bearing capacity of a tunnel lining with cracks and damage according to claim 1, characterized in that: The calculation formula for the safety factor K1 of the reinforced concrete rectangular section bearing capacity is: Where K is the safety factor; N is the axial force; N max It is the ultimate bearing capacity of the lining section with cracks.

7. A method for calculating the safety factor of the cross-section bearing capacity of a tunnel lining with cracks and damage according to claim 1, characterized in that: In step [2], the calculation method of the pressure C on the concrete is: Pressure T at the compression reinforcement s The calculation method of ′ is: In the formula, A s ′ is the cross-sectional area of ​​the compressive reinforcement, a s ′ is the distance from the compression reinforcement to the edge of the section, α Es is the conversion factor of the reinforced concrete member section, α Es =E s / E c ; Tensile force T at the tensile reinforcement s The calculation method is: In the formula, A s is the cross-sectional area of ​​the tensile reinforcement, a s is the distance from the tensile reinforcement to the edge of the section.

8. A method for calculating the safety factor of the cross-section bearing capacity of a tunnel lining with cracks and damage according to claim 1, characterized in that: In step [2], the following assumptions are made in calculating the internal forces of the cracked lining structure section: (1) the cross-sectional strain remains flat; (2) the tensile strength of concrete is not considered; and (3) before reaching the ultimate strength, the stress-strain relationship of concrete and steel bars is proportional.

9. A method for calculating the safety factor of the cross-section bearing capacity of a tunnel lining with cracks and damage according to claim 1, characterized in that: In step [3], calculate the ultimate bearing capacity of the section N max When the concrete stress in the compression zone is equivalent to a rectangular stress diagram, the following conditions are met: (1) the area of ​​the equivalent rectangular diagram is equal to the area of ​​the theoretical stress diagram, that is, the total pressure on the concrete remains unchanged; (2) the centroid of the area of ​​the equivalent rectangular diagram coincides with the centroid of the area of ​​the theoretical stress diagram, that is, the position of action remains unchanged.

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