Method for calculating stratum deformation caused by space linear tunnel construction

Abstract

The invention belongs to the technical field of stratum settlement, discloses a method for calculating stratum deformation caused by space linear tunnel construction, and relates to a space linear tunnel with a first section, a second section and a third section with different gradients under the same turning radius. The stratum deformation calculation method for the third section comprises the following steps that a space linear shield three-dimensional mathematical model of the third section is constructed, and the space linear shield three-dimensional mathematical model is constructed from the two perspectives of soil mass loss and construction load; and stratum settlement caused by a shield tail integration gap, additional thrust, shield shell axial friction force and rotation friction force and grouting pressure is considered, and cumulative summation is carried out. The method has the advantages that for shield tunnel construction under a space curve, a theoretical solution of stratum settlement caused by shield tunnel tunneling construction composed of multiple tunnel sections with different gradients under the condition that the same turning radius is guaranteed is provided; the theoretical analysis comprises calculation formulas of stratum deformation caused by soil body loss and various construction loads.

Description

Technical Field

[0001] The present invention belongs to the technical field of ground settlement, and particularly relates to a calculation method for ground deformation caused by the construction of a spatial linear tunnel. Background Technique

[0002] With the continuous development of the underground space and the further improvement of the requirements for tunnel selection, more and more spatial linear (including large slopes, horizontal curves, spatial curves, etc.) shield tunnels are designed and constructed.

[0003] Compared with straight shield tunnels, the law of ground settlement caused by the construction of spatial linear shield tunnels with super-large diameter and small turning radius is relatively complex.

[0004] For the spatial circular curve shield tunnel project, many scholars have also carried out relevant research from different perspectives. Sugimoto et al. conducted a comparative analysis of on-site monitoring and numerical simulation on the construction of a circular curve shield tunnel (outer diameter 6.2 m) with a radius of curvature of 400 m, and found that when the shield tail passed through the monitoring section, the soil on the inner and outer sides of the circular curve tunnel had a tendency to horizontally move towards the inner and outer sides of the circular curve tunnel respectively. Alsahly et al. proposed a finite element automatic mesh generation technique and a steering algorithm for simulating the tunneling of a shield along a circular curve trajectory, and applied it to the Barcelona subway tunnel project. By comparing the circular curve trajectory of the tunnel obtained by simulation with the designed route and the eccentricity of the jack thrust, the reliability of the proposed model was verified. Pan Hong et al. conducted a systematic on-site monitoring analysis on a circular curve shield tunnel (outer diameter 4.1 m) with a radius of curvature of 118 m, and pointed out that the ground settlement on the inner side of the circular curve tunnel section should be larger than that of the straight tunnel section; affected by the turning of the shield machine, it is easy to cause asymmetric deformation of the soil strata on the inner and outer sides of the circular curve tunnel. Taking the circular curve shield tunnel project with a radius of curvature of 300 m of Jinan Metro as the background, Wang Guofu et al. considered the asymmetric distribution of the support force on the excavation face of the circular curve shield tunnel, and proposed a theoretical model of the limit equilibrium of a curved surface gradient wedge prism, and then deduced the theoretical formula of the limit support force for active failure of the excavation face; Lu Linhai et al. carried out multi-section surface settlement monitoring on this project, and compared the monitoring results with the numerical simulation results of excavating 6-ring segment widths per step and the calculation results of the Peck formula, and pointed out that the shield construction has a greater disturbance range on the inner side stratum of the circular curve. Fu Helin et al. established a "reverse trapezoid - wedge prism" combined model and deduced the theoretical formula of the limit support force on the excavation face of the circular curve shield tunnel; and carried out a sensitivity analysis on parameters such as the radius of curvature and burial depth of the tunnel. Taking 4 circular curve shield tunnel sections (the minimum radius of curvature is 300 m) of the Kuala Lumpur subway tunnel as the background, Feng Hao and Zhang Yan conducted a statistical analysis on the shield tunneling parameters and the resulting vertical ground deformation, gave the ratio of the jack thrust on the outer side to the inner side of the circular curve tunnel, and pointed out that the peak settlement of each monitoring section has a tendency to shift towards the inner side of the circular curve, and increases with the decrease of the radius of curvature of the tunnel. Li established a tunneling model, and based on the improved Mindlin formula, obtained the theoretical solution of the vertical ground deformation caused by the friction force between the shield shell and the soil, and the results were in good agreement with the finite element simulation results.

[0005] For the spatial linear tunnels of the first section, the second section, and the third section with different slopes under the same turning radius, particularly when the shield machine enters the third section for tunneling construction, the tunneling work of the first two sections has been completed, and the shield machine changes the slope again. How to relate the construction influence of the third section to the first two sections is the difficulty of theoretical analysis. Summary of the Invention

[0006] The object of the present invention is to provide a method for calculating the ground deformation caused by the construction of a spatial linear tunnel according to the deficiencies of the above-mentioned prior art. When calculating the ground settlement in the third section, the method correlates and analyzes the excavation in the first two sections, and further considers the influence of the shield tail integration gap, additional thrust, shield shell axial friction and rotational friction, and grouting pressure on the ground settlement, so as to obtain the ground settlement value of the third section through the three-dimensional mathematical model of the spatial linear shield.

[0007] The object of the present invention is achieved by the following technical solutions: A method for calculating the ground deformation caused by the construction of a spatial linear tunnel, which relates to a spatial linear tunnel with different slopes in the first section, the second section, and the third section under the same turning radius. The first section, the second section, and the third section are successively excavated by a shield machine. The first section and the second section are downhill, and the third section is uphill. The turning radius of the spatial linear tunnel is 800 m. The slope of the first section is 34‰, and the actual excavation length is 200 m; the slope of the second section is 10‰, and the actual excavation length is 100 m; the slope of the third section is -48‰, and the actual excavation length is 150 m. The method for calculating the ground deformation in the third section includes the following steps: (S1) Construct a three-dimensional mathematical model of the spatial linear shield for the third section, and the calculation formula is: S 3 =S 3,int +S 3,at +S 3,af +S 3,gp +S 3,rf ; In the formula: S 3,int is the ground settlement caused by the integration gap between the shield tail and the soil during the excavation of the shield machine, and the unit is m ; S 3,at is the additional thrust during the excavation of the shield machine f 1 The ground settlement caused by the action of each component force on the working face, and the unit is m ; S 3,af is the ground settlement caused by the shield axial friction, and the unit is m ; S 3,gpThe ground settlement caused by the tail shield grouting pressure, unit: m ; S 3,rf The ground settlement caused by the shield rotation friction, unit: m ; (S2) Calculate respectively S 3,int 、S 3,at 、S 3,af 、S 3,gp 、S 3,rf , where S 3,int The calculation formula of is: ; In the formula: θ s1 、θ s2 、θ s3 Are respectively the arc lengths of the first section, the second section and the third section, unit: m ; β 1 、β 2 、β 3 Are respectively the gradients of the first section, the second section and the third section, positive for downhill and negative for uphill, unit: ‰; L 1 、L 2 、L 3 Are respectively the actual lengths of the shield machine tunneling in the first section, the second section and the third section, unit: m ; Q Is the turning radius of the spatial linear tunnel, unit: m ; q Is the turning radius of the shield machine under abnormal tunneling, unit: m ; L Is the longitudinal total length of the shield machine, unit: m ; R Is the outer diameter of the shield machine, unit: m ; h Is of the second section XOZThe buried depth of the shield tunnel on the plane XOZ The plane is located in the second section, with the unit of m ; h’ For the third section extending towards Y the negative axis direction to XOZ the assumed buried depth on the plane, with the unit of m ; θ is the rotation angle around the Z-axis during the tunneling process of the shield machine, with the unit of rad ; G t is the thickness of the shield tail integration gap, with the unit of m ; z is the coordinate value on the Z-axis, with the unit of m ; S z is the vertical displacement at any point in the half-space caused by a spherical void with a radius of 1 in a semi-infinite body obtained by the three-dimensional mirror theory and three-dimensional space integration method proposed by Sagaseta, with the unit of m ; (S3) Input the calculated S 3,int 、S 3,at 、S 3,af 、S 3,gp 、S 3,rf value into the three-dimensional mathematical model of the space-linear shield to calculate the final ground settlement of the third section.

[0008] S 3,at The calculation formula of ; In the formula: ω x is the over-excavation layer thickness in the x-axis direction, ω y is the over-excavation layer thickness in the y-axis direction, ω z is the over-excavation layer thickness in the z-axis direction, with the unit of m ; f 1x , f 1y and f 1z respectively represent the additional thrust during the tunneling of the shield machine f1 The component forces in the x, y, and z directions, in units of KN· m -2 ; ; e = -1·sin(θ s -α) , dimensionless; f = 1·cos(θ s -α) , dimensionless; g = tanβ , dimensionless; θ s is the rotation angle during the tunneling process of the shield machine in the abnormal tunneling section of the third section, in units of rad ; α is the yaw angle of the shield machine, in units of rad ; β is the pitch angle of the shield machine, in units of rad ; r is the distance between the point ( x, y, z ) and the point ( x 0 , y 0 , z 0 ), in units of m ; The point ( x 0 , y 0 , z 0 ) is the modified coordinate of the acting point ( 0, 0, c ) of the concentrated force F, in units of ( m,m,m ); t is the circular arc radian, in units of rad ; , in units of MPa .

[0009] S 3,af The calculation formula of is: ; In the formula: θ s is the rotation angle during the tunneling process of the shield machine in the abnormal tunneling section of the third section, in units of rad ; αis the yaw angle of the shield machine, with the unit of rad ; θ L The calculation formula of θ L = L / Q yaw is rad ; where Q yaw is the turning radius during the abnormal tunneling section of the shield machine in the third section, with the unit of m ; f 2 is the actual friction force between the shield shell of the shield machine and the soil mass, with the unit of KN·m -2 ; f 2，head,x , f 2，head,y , f 2，head,z are respectively f 2 decomposed according to the shield head direction vector of the shield machine, with the unit of KN·m -2 ; f 2，tail,x , f 2，tail,y , f 2，tail,z are respectively f 2 decomposed according to the shield tail direction vector of the shield machine, with the unit of KN·m -2 ; ; ; e 1 = -1·sin(θ s1 -α 1 ) , dimensionless; f 11 = 1·cos(θ s1 -α 1 ) , dimensionless; g 1 = tanβ 1 , dimensionless; θ s1 is the rotation angle of the shield tail of the shield machine during the tunneling process in the abnormal tunneling section in the third section, with the unit of rad ; α 1 is the yaw angle of the shield tail of the shield machine, with the unit of rad ; β 1 is the pitch angle of the shield tail of the shield machine, with the unit of rad ; , with the unit of MPa ; φ is the included angle between the vertical connection line between any point on the shield shell of the shield machine and the central axis of the shield machine and the x-axis, with the unit of rad ; ∅ is the angle range to which the shield machine belongs in the spatial linear tunnel, with the unit of rad .

[0010] S 3,gp The calculation formula of ; In the formula: B is the width of the shield segment, with the unit of m ; f 3 is the grouting pressure of the shield tail of the shield machine, f 3x , f 3y , f 3z are respectively f 3 the component forces in the x, y, and z directions, with the unit of KN·m -2 ; ; e 3 = -1·sin(θ s1 -α 1 ) , dimensionless; f 33 = 1·cos(θ s1 -α 1 ) , dimensionless; g 3 = tanβ 1 , dimensionless; θ s1 is the rotation angle of the shield tail of the shield machine during the abnormal tunneling section in the third section, with the unit of rad ; α 1 is the yaw angle of the shield tail of the shield machine, with the unit of rad ; β 1 is the pitch angle of the shield tail of the shield machine, with the unit of rad ; , with the unit of MPa .

[0011] S 3,rf The calculation formula of is: ; In the formula: , with the unit of KN·m -2 ; , with the unit of KN·m -2 ; a 1 、b 1 、c 1 are the vector modulus lengths on the x-axis, y-axis, and z-axis respectively; a 2 、b 2 、c 2 are the vector modulus lengths on the x-axis, y-axis, and z-axis respectively; ; M 盾 is the distributed bending moment, M 盾 = k 2 · ( M 刀 - M 管片 ), with the unit of KN·m ; k 2The reduction coefficient proposed for the additional influence of the shield machine's movement around the tunneling axis has a value between 0.75 and 0.95 and is dimensionless; M 刀 When the cutterhead of the shield machine cuts the soil mass, it is the output torque of the shield machine for the cutterhead to cut the soil mass, with the unit of KN·m ; M 管片 It is the circumferential friction force generated by multiple groups of jacks on the shield machine acting on the shield segment and using the huge thrust on the contact surface, with the unit of KN·m , and the calculation formula is: M 管片 = k 1 · μ · F n，千斤顶，标准 / 平均 · n·R ´ In the formula: k 1 It is the reduction within the limited range of the jack thrust considering the non-vertical contact state, with a value between 0.95 and 1 and is dimensionless; F n，千斤顶 is the propulsion force of a single jack; F n，千斤顶，标准 / 平均 is the average propulsion force of each jack, with the unit of KN ; n is the number of groups of jacks and is dimensionless; μ is the friction coefficient and is dimensionless; R ´ is the average thickness of the shield segment, taking the average of the outer diameter and inner diameter of the segment, with the unit of m ; , with the unit of MPa .

[0012] The advantages of the present invention are as follows: For the construction of shield tunnels under spatial curves, a theoretical solution for ground settlement caused by the tunneling construction of shield tunnels composed of multiple tunnel sections with different slopes under the condition of ensuring the same turning radius is proposed; the theoretical analysis includes calculation formulas for ground deformation caused by soil loss and various construction loads respectively. This set of formulas improves the content of the research direction of the influence of spatial linear shield construction on the ground and has wide applicability and compatibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is the overall side view of the spatial linear tunnel in the present invention; Figure 2 It is the plan view of the spatial linear tunnel in the present invention; Figure 3 It is the side view of the transition between the third section and the second section of the spatial linear tunnel in the present invention; Figure 4 It is the schematic diagram of the axial friction force in the present invention; Figure 5 It is the schematic diagram of the load distribution and action mode in the present invention; Figure 6 It is the table of ground settlement caused by various influencing factors in the present invention; Figure 7 It is the schematic diagram of the comparison value between the theoretical and simulated ground settlement under the un-reinforced condition in the present invention. Detailed implementation manners

[0014] The features of the present invention and other related features are further described in detail below with reference to the accompanying drawings through embodiments, so as to facilitate the understanding of those skilled in the same industry: Embodiment: As shown in Figure 1 , 2 , 3, 4, 5, 6, 7, this embodiment specifically relates to a method for calculating the ground deformation caused by the construction of a spatial linear tunnel. The spatial linear tunnel has a first section, a second section, and a third section with different slopes under the same turning radius. The turning radius of the spatial linear tunnel is 800 m, and the three sections are successively excavated by a shield machine. The first section and the second section are downhill, and the third section is uphill; the slope of the first section is 34‰, and the actual excavation length is 200 m; the slope of the second section is 10‰, and the actual excavation length is 100 m; the slope of the third section is -48‰, and the actual excavation length is 150 m.

[0015] As shown in Figure 1 , 2 , 3, 4, 5, the method for calculating the ground deformation in the third section of the spatial linear tunnel includes the following steps: (S1) As shown in Figure 1 , 2 , 3, construct a three-dimensional mathematical model of the spatial linear shield in the third section. The calculation formula of the three-dimensional mathematical model of the spatial linear shield is: S 3 =S 3,int +S 3,at +S 3,af +S 3,gp +S 3,rf ; In the formula: S 3,int The ground settlement caused by the integration gap between the shield tail and the soil during the tunneling of the shield machine, with the unit of m ; S 3,at The additional thrust during the tunneling of the shield machine f 1 The ground settlement caused by the action of each component force of m on the heading face, with the unit of f 1 ; To ensure the stability of the shield excavation face, a certain amount of additional thrust will be applied to the front heading face during shield construction, and this additional thrust is the additional thrust during the tunneling of the shield machine S 3,af The ground settlement caused by the axial frictional force of the shield, with the unit of m ; S 3,gp The ground settlement caused by the shield tail grouting pressure, with the unit of m ; S 3,rf The ground settlement caused by the rotational frictional force of the shield, with the unit of m .

[0016] (S2) Calculate the values of S 3,int 、S 3,at 、S 3,af 、S 3,gp 、S 3,rf respectively through the three-dimensional mathematical model of the shield machine with spatial alignment.

[0017] (S2.1) The ground settlement caused by the integration gap between the shield tail and the soil during the tunneling of the shield machine is S 3,int , and the calculation formula is: ; In the formula: θ s1 、θ s2 、θ s3 are the arc lengths of the first section, the second section, and the third section respectively, with the unit of m ; β 1 、β2 、β 3 They are the gradients of the first section, the second section, and the third section respectively. The downhill direction is positive and the uphill direction is negative, with the unit of ‰; L 1 、L 2 、L 3 They are the actual lengths of the shield machine tunneling in the first section, the second section, and the third section respectively, with the unit of m ; Q is the theoretical turning radius of the spatial linear tunnel, with the unit of m ; q is the actual turning radius of the spatial linear shield machine under abnormal tunneling, with the unit of m ; L is the total longitudinal length of the shield machine, with the unit of m ; R is the outer diameter of the shield machine, with the unit of m ; h is the XOZ burial depth of the shield tunnel in the plane of the second section, XOZ the plane is located within the second section, with the unit of m ; h’ is the Y assumed burial depth on the plane where the third section extends to the XOZ negative axis direction, with the unit of m ; θ is the rotation angle of the shield machine around the Z-axis during tunneling, with the unit of rad ; G t is the thickness of the shield tail integration gap, with the unit of m ; z is the coordinate value on the Z-axis, with the unit of m ; S z is the vertical displacement of any point in the half-space caused by a spherical void with a radius of 1 in a semi-infinite body obtained by the three-dimensional mirror theory and the three-dimensional space integration method proposed by Sagaseta, with the unit of m ; S z The calculation formula of Sz =(3 / 4π)·( S z1 +S z2 +S z3 ); ; ; ; In the formula, s is the function variable, in units of m ; t is the function variable, in units of rad ; b and c are the integral upper and lower limit variables, in units of m; μ is Poisson's ratio, dimensionless.

[0018] (S2.2) Additional thrust of shield machine excavation f 1 The ground settlement caused by the various components of the force acting on the tunnel face is S 3,at The calculation formula is; ; Where: ω x is the thickness of the over-excavation layer in the x-axis direction, ω y is the thickness of the over-excavation layer in the y-axis direction, ω z is the thickness of the over-excavation layer in the z-axis direction, in units of m ; ω x , ω y and ω z This is a rewrite of the classic Mindlin displacement solution, that is, the point of action of the concentrated force F (0, 0, c) is changed to an arbitrary point ( x 0 , y 0 , z 0 ), we can get the value acting on any point in the semi-infinite elastic body ( x 0 , y 0 , z 0 ), the unit is ( m,m,m ), along the positive direction of the X, Y and Z axes, causing a point in the soil (x, y, z The vertical displacement calculation formula of (

[0019] f 1x ), f 1y and f 1z respectively represent the component forces of the additional thrust during the tunneling of the shield machine f 1 in the x, y, and z directions, with the unit of KN· m -2 ; ; e = -1·sin(θ s -α) , dimensionless; f = 1·cos(θ s -α) , dimensionless; g = tanβ , dimensionless; θ s is the rotation angle during the tunneling of the shield machine in the abnormal tunneling section of the third section, with the unit of rad ; α is the yaw angle of the shield machine, with the unit of rad ; β is the pitch angle of the shield machine, with the unit of rad ; r is the distance between the point ( x, y, z ) and the point ( x 0 , y 0 , z 0 ), with the unit of m ; The point ( x 0 , y 0 , z 0 ) is the modified coordinate of the acting point ( 0, 0, c ) of the concentrated force F, with the unit of ( m,m,m ); t is the circular arc radian, with the unit of rad ; , with the unit of MPa .

[0020] (S2.3) As Figure 4As shown, the ground settlement caused by the axial friction of the shield is S 3,af , and the calculation formula is: ; In the formula: θ s is the rotation angle during the abnormal tunneling section of the shield machine in the third section, with the unit of rad ; The shield machine is divided into the shield head and the shield tail, with equal lengths, and both sections are straight cylinders. Due to the existence of the articulation device, there is a certain angular deviation between the shield head and the shield tail during the curved shield process, and the process of angular deviation is the abnormal tunneling section; α is the yaw angle of the shield machine, with the unit of rad ; θ L is the angle converted from the length occupied by the shield machine, and the calculation formula is θ L = L / Q yaw , with the unit of rad ; Among them, Q yaw is the turning radius during the abnormal tunneling section of the shield machine in the third section, with the unit of m ; f 2 is the actual friction force between the shield shell of the shield machine and the soil mass, with the unit of KN·m -2 ; f 2，head,x , f 2，head,y , f 2，head,z are respectively the decomposition of f 2 according to the direction vector of the shield head of the shield machine, with the unit of KN·m -2 ; f 2，tail,x , f 2，tail,y , f 2，tail,z are respectively the decomposition of f 2 according to the direction vector of the shield tail of the shield machine, with the unit of KN·m -2 ; ; ; e 1 = -1·sin(θ s1 -α 1 ) , dimensionless; f 11 = 1·cos(θ s1 -α 1 ) , dimensionless; g 1 = tanβ 1 , dimensionless; θ s1 is the rotation angle of the shield tail of the shield machine during the abnormal tunneling section in the third section, with the unit of rad ; α 1 is the yaw angle of the shield tail of the shield machine, with the unit of rad ; β 1 is the pitch angle of the shield tail of the shield machine, with the unit of rad ; , with the unit of MPa ; φ is the angle between the vertical connection line from any point on the shield shell of the shield machine to the central axis of the shield machine and the x-axis, with the unit of rad ; ∅ is the angular range to which the shield machine belongs in the spatial linear tunnel, with the unit of rad .

[0021] (S2.4) The ground settlement caused by the shield tail grouting pressure is S 3,gp , and the calculation formula is: ; In the formula: B is the width of the shield segment, with the unit of m ; f 3 is the shield tail grouting pressure of the shield machine, f 3x , f 3y , f 3z are respectively f 3The component forces in the x, y, and z directions, in units of KN·m -2 ; ; e 3 = -1·sin(θ s1 -α 1 ) , dimensionless; f 33 = 1·cos(θ s1 -α 1 ) , dimensionless; g 3 = tanβ 1 , dimensionless; θ s1 is the rotation angle of the shield tail of the shield machine during the abnormal tunneling section in the third section, in units of rad ; α 1 is the yaw angle of the shield tail of the shield machine, in units of rad ; β 1 is the pitch angle of the shield tail of the shield machine, in units of rad ; , in units of MPa .

[0022] The ground settlement caused by the shield rotation friction is S 3,rf , and the calculation formula is: ; In the formula: , in units of KN·m -2 ; , in units of KN·m -2 ; a 1 、b 1 、c 1 are the vector moduli on the x-axis, y-axis, and z-axis respectively; a2 、b 2 、c 2 The vector modulus lengths on the x-axis, y-axis, and z-axis respectively; ; M 盾 is the distributed bending moment, M 盾 = k 2 · ( M 刀 - M 管片 ) with the unit of KN·m ; k 2 is the reduction coefficient proposed for the additional influence of the movement of the shield machine around the tunneling axis, with a value between 0.75 and 0.95, dimensionless; M 刀 is the output torque of the shield machine for the cutterhead to cut the soil when the cutterhead of the shield machine cuts the soil, with the unit of KN·m ; M 管片 is the circumferential friction force generated by multiple groups of jacks on the shield machine acting on the shield segment and using the huge thrust on the contact surface, with the unit of KN·m , and the calculation formula is: M 管片 = k 1 · μ · F n，千斤顶，标准 / 平均 · n·R ´ In the formula: k 1 is the reduction considering the reduction within the limited range of the jack thrust in the non-vertical contact state, with a value between 0.95 and 1, dimensionless; F n，千斤顶 is the propulsion force of a single jack; F n，千斤顶，标准 / 平均 is the average propulsion force of each jack, with the unit of KN ; n is the number of groups of jacks, dimensionless; μ is the friction coefficient, dimensionless; R´ is the average thickness of the shield segment, which is the average of the outer diameter and inner diameter of the segment, with the unit of m ; , with the unit of MPa .

[0023] (S3) Input the S 3,int 、S 3,at 、S 3,af 、S 3,gp 、S 3,rf values obtained from the calculation into the three-dimensional mathematical model of the spatial linear shield to calculate the final ground settlement of the third section.

[0024] As Figure 5 , 6 , as shown in Figure 7, perform theoretical calculations and numerical simulations on the three-dimensional mathematical model of the spatial linear shield in this embodiment: The parameters that need to be additionally confirmed before the calculation are: the shield tail integration gap G t , the additional thrust f 1 , the axial friction force of the shield shell f 2 、 the grouting pressure f 3 and the rotational friction force of the shield shell f r . According to the actual situation of this project, take G t to be 0.11m; the specific values of the construction loads are: f 1 = 50 kN·m -2 , f 2 = 57.5 kN·m -2 , f 3 = 200 kN·m -2 , f r = 1.01 kN·m -2 , and the distribution and action mode of each load are as Figure 5 shown. Input the above shield construction parameters into the three-dimensional mathematical model of the spatial linear shield for calculation, and the results are as Figure 6As shown in the figure. Entering the third section, the shield machine moves uphill, and the influence of the axial friction force of the shield shell on the uplift of the front soil mass is more obvious, and the effect of the individual influence even reaches the level of 30 mm. Compared with the downhill sections of the first and second sections, the influence of the axial friction force of the shield shell is more obvious in the uphill section, which should be particularly noted in shield tunneling construction.

[0025] After the above model is solved, numerical simulation is carried out. The comparison diagram of the theoretical calculation results and the numerical simulation results is as Figure 7 shown in the figure. It can be seen from the figure that the soil settlement behind the excavation face is larger than the theoretical result, which may be caused by more plastic behavior of the soil in the simulation. Generally, it proves that the theoretical method of the present invention is reasonable, and it also reflects that the stratum settlement under un-reinforced conditions is large, and appropriate and safe stratum reinforcement measures are required to ensure shield tunneling construction.

[0026] The beneficial effects of this embodiment are as follows: For the shield tunneling construction under a spatial curve, a theoretical solution for the stratum settlement caused by the shield tunneling construction composed of multiple tunnel sections with different slopes under the condition of ensuring the same turning radius is proposed. The theoretical analysis includes the calculation formulas for the stratum deformation caused by soil loss and various construction loads respectively; this set of three-dimensional mathematical models for spatial linear shield tunneling improves the research content of the influence of spatial linear shield tunneling on the stratum, and has wide applicability and compatibility.

Claims

1. A method for calculating stratum deformation caused by construction of a spatial linear tunnel, involving a spatial linear tunnel with a first section, a second section, and a third section having different slopes at the same turning radius, wherein the first section, the second section, and the third section are excavated sequentially by a shield machine, the first section and the second section are downslopes, and the third section is upslope, the turning radius of the spatial linear tunnel is 800m, the slope of the first section is 34‰, and the actual excavation length is 200m; the slope of the second section is 10‰, and the actual excavation length is 100m; the slope of the third section is -48‰, and the actual excavation length is 150m, characterized in that The method for calculating the stratum deformation of the third section comprises the following steps: (S1) constructing a three-dimensional mathematical model of the spatial linear shield in the third section, and the calculation formula is: S 3 =S 3,int +S 3,at +S 3,af +S 3,gp +S 3,rf ； Where: S 3,int It is the ground settlement caused by the integrated gap between the shield tail and the soil during the tunneling process of the shield machine, in units of m ; S 3,at Adding thrust to shield machine excavation f 1 The ground settlement caused by the various components of the force acting on the tunnel face is in units of m ; S 3,af is the ground settlement caused by the axial friction of the shield, in units of m ; S 3,gp is the ground settlement caused by the shield tail grouting pressure, in units of m ; S 3,rf is the ground settlement caused by the friction of shield rotation, in units of m ; (S2) are calculated separately S 3,int 、S 3,at 、S 3,af 、S 3,gp 、S 3,rf ,in S 3,int The calculation formula is: ； Where: θ s1 ,θ s2 ,θ s3 are the arc lengths of the first, second and third segments respectively, in units of m ; β 1 、β 2 、β 3 The slopes of the first, second and third sections are respectively, with downslope being positive and upslope being negative, and the unit is ‰; L 1 、L 2 、L 3 They are the actual lengths of tunneling by the shield machine in the first, second and third sections, respectively, in units of m ; Q is the turning radius of the space linear tunnel, in units of m ; q is the turning radius of the shield machine under abnormal excavation, in units of m ; L is the total longitudinal length of the shield machine, in units of m ; R is the outer diameter of the shield machine, in units of m ; h For the second section XOZ The depth of shield tunnel on the plane, XOZ The plane is located in the second section, and the unit is m ; h’ For the third section Y The negative axis extends to XOZ Assumed burial depth on the plane, in units m ; θ is the rotation angle of the shield machine around the Z axis during tunneling, in units of rad ; G t is the shield tail integrated gap thickness, in units of m ; z is the coordinate value on the Z axis, in units of m ; S z is the vertical displacement of any point in the half space caused by a spherical void with a radius of 1 in a semi-infinite body, obtained by the three-dimensional mirror theory proposed by Sagaseta and the three-dimensional space integration method, in units of m ; (S3) The calculated S 3,int 、S 3,at 、S 3,af 、S 3,gp 、S 3,rf The values ​​are input into the three-dimensional mathematical model of the spatial linear shield to calculate the final ground settlement of the third section.

2. The method for calculating ground deformation caused by construction of a spatial linear tunnel according to claim 1, characterized in that S 3,at The calculation formula is: ； Where: ω x is the thickness of the over-excavation layer in the x-axis direction, ω y is the thickness of the over-excavation layer in the y-axis direction, ω z is the thickness of the over-excavation layer in the z-axis direction, in units of m ; f 1x , f 1y and f 1z Respectively represent the additional thrust of shield machine excavation f 1 Component forces in the x, y, and z directions, in units of KN·m -2 ; ； e=-1·sin(θ s -α) , dimensionless; f=1·cos(θ s -α) , dimensionless; g = tanβ , dimensionless; θ s is the rotation angle of the shield machine during the excavation process of the abnormal excavation section in the third section, in units of rad ; α is the yaw angle of the shield machine, in units of rad ; β is the pitch angle of the shield machine, in units of rad ; r For point ( x, y, z ) and point ( x 0 , y 0 , z 0 ) in units of m ;point( x 0 , y 0 , z 0 ) is the point of action of the concentrated force F ( 0, 0, c )'s modified coordinates, in units of ( m, m, m ); t is the arc of the circular surface, in units of rad ; , the unit is MPa .

3. The method for calculating stratum deformation caused by construction of a spatial linear tunnel according to claim 2, characterized in that S 3,af The calculation formula is: ； Where: θ s is the rotation angle of the shield machine during the excavation process of the abnormal excavation section in the third section, in units of rad ; α is the yaw angle of the shield machine, in units of rad ; θ L The calculation formula is θ L =L / Q yaw , the unit is rad ;in, Q yaw is the turning radius of the shield machine during the excavation process of the abnormal excavation section in the third section, in units of m ; f 2 is the actual friction between the shield shell of the shield machine and the soil, in units of KN·m -2 ; f 2，head,x , f 2，head,y , f 2，head,z Respectively f 2 According to the decomposition of the shield head direction vector of the shield machine, the unit is KN·m -2 ; f 2，tail,x , f 2，tail,y , f 2，tail,z Respectively f 2 According to the decomposition of the shield tail direction vector of the shield machine, the unit is KN·m -2 ; ； ； e 1 = -1·sin(θ s1 -α 1 ) , dimensionless; f 11 =1·cos(θ s1 -α 1 ) , dimensionless; g 1 =tanβ 1 , dimensionless; θ s1 is the rotation angle of the shield tail of the shield machine during the excavation process in the abnormal excavation section of the third section, in units of rad ; α 1 is the yaw angle of the shield tail of the shield machine, in units of rad ; β 1 is the pitch angle of the shield tail of the shield machine, in units of rad ; , the unit is MPa ; φ It is the angle between any point on the shield shell of the shield machine and the vertical line connecting the central axis of the shield machine and the x-axis, in units of rad ; ∅ is the angle interval of the shield machine in the spatial linear tunnel, in units of rad .

4. The method for calculating stratum deformation caused by construction of a spatial linear tunnel according to claim 3 is characterized in that S 3,gp The calculation formula is: ； Where: B is the width of the shield segment, in units of m ; f 3 is the grouting pressure at the tail of the shield machine, f 3x , f 3y , f 3z They are f 3 The components of force in the x, y, and z directions are in KN· m -2 ; ； e 3 = -1·sin(θ s1 -α 1 ) , dimensionless; f 33 =1·cos(θ s1 -α 1 ) , dimensionless; g 3 =tanβ 1 , dimensionless; θ s1 is the rotation angle of the shield tail of the shield machine during the excavation process in the abnormal excavation section of the third section, in units of rad ; α 1 is the yaw angle of the shield tail of the shield machine, in units of rad ; β 1 is the pitch angle of the shield tail of the shield machine, in units of rad ; , the unit is MPa .

5. The method for calculating ground deformation caused by construction of a space linear tunnel according to claim 4, characterized in that S 3,rf The calculation formula is: ； Where: , the unit is KN·m -2 ; , the unit is KN·m -2 ; a 1 、b 1 、c 1 are the vector modulus lengths on the x-axis, y-axis, and z-axis respectively; a 2 、b 2 、c 2 are the vector modulus lengths on the x-axis, y-axis, and z-axis respectively; ； M 盾 is the distributed bending moment, M 盾 = k 2 ·( M 刀 - M 管片 ), the unit is KN·m ; k 2 The reduction factor proposed for the additional effect of the shield machine's movement around the tunneling axis is between 0.75 and 0.95 and is dimensionless; M 刀 The output torque of the shield machine for the cutterhead to cut the soil when the shield machine cutterhead is cutting the soil, in units of KN·m ; M 管片 It is the annular friction force generated by the multiple sets of jacks on the shield machine acting on the shield segments and using the huge thrust on the contact surface, and the unit is KN·m , the calculation formula is: M 管片 = k 1 · μ · F n，千斤顶，标准 / 平均 · n·R ´ Where: k 1 In order to take into account the reduction of the jack thrust within a limited range in the non-vertical contact state, the value is between 0.95 and 1 and is dimensionless; F n，千斤顶 is the propulsion force of a single jack; F n，千斤顶，标准 / 平均 is the average thrust of each jack, in units of KN ; n is the number of jack groups, dimensionless; μ is the friction coefficient, dimensionless; R ´ is the average thickness of the shield segment, which is the average of the outer and inner diameters of the segment, in units of m ; , the unit is MPa .

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