Patent ID: 11946831
Assignee: SHANDONG JIANZHU UNIVERSITY
Field: Measurement (Instruments)
Classification: CPC G  B | IPC B  G

Claim 0:
1. A method for determining and applying an active jacking force of a tunneling closely undercrossing existing station, comprising:
acquiring design parameters of existing and new stations, and acquiring geological parameters of a construction site;
obtaining a stress solution expression of the active jacking force on the existing station according to the design parameters, the geological parameters and a Mindlin's solution calculation model to obtain a vertical stress solution σz of any point in a semi-infinite space under the action of a vertical load P, replacing the vertical load β with a vertical load acting on the existing station, and performing integration in an excavation region to obtain a vertical stress solution σz′ of the existing station;
obtaining a relational expression between a deflection and the vertical stress solution σz′ of the existing station according to a differential equation of a beam-on-elastic-foundation model, wherein
the relational expression between the deflection and the vertical stress solution σz′ of the existing station is:, EI
     ⁢
     
      
       
        d
        4
       
       ⁢
       w
      
      
       dx
       4
      
     
    
    +
    
     k
     ⁢
     w
    
   
   =
   
    σ
    y
   
  
  ,
 

E is the elastic modulus of the existing station, I is the inertia moment of the existing station, w is the deflection of the existing station, k=k0f, k0 is a foundation coefficient that reflects the interaction between soil and the existing station, and f represents the width of the existing station,
the relational expression between the deflection and the vertical stress solution σz′ of the existing station is converted into a fourth-order non-homogeneous linear equation with constant coefficients after simplification, and a general solution thereof is:, w
   =
   
    
     
      e
      
       β
       ⁢
       x
      
     
     (
     
      
       A
       ⁢
        
       cos
       ⁢
         
       β
       ⁢
       x
      
      +
      
       B
       ⁢
         
       sin
       ⁢
         
       β
       ⁢
       x
      
     
     )
    
    +
    
     
      e
      
       
        -
        β
       
       ⁢
       x
      
     
     (
     
      
       C
       ⁢
         
       cos
       ⁢
         
       β
       ⁢
       x
      
      +
      
       D
       ⁢
         
       sin
       ⁢
         
       β
       ⁢
       x
      
     
     )
    
    +
    
     
      σ
      y
     
     k
    
   
  
  ,
     
  and
 

β is a characteristic coefficient, with a dimension of m−1; A, B, C and D are four unknown coefficients in the general solution, which are obtained by the boundary conditions at both ends of the beam on elastic foundation; and x is a horizontal coordinate in the beam-on-elastic-foundation model, and e is a natural constant;
substituting the stress solution expression of the active jacking force on the existing station into the relational expression between the deflection and the vertical stress solution σz′ of the existing station according to required parameters obtained according to boundary conditions at both ends of a beam on elastic foundation to obtain the active jacking force that controls the deflection of the existing station; and
applying the active jacking force by with a plurality of jacks, each of the plurality of jacks applying a respective portion of the active jacking force,
an expression of the vertical stress solution σz of any point in the semi-infinite space under the action of a certain vertical load β is:, σ
       z
      
      =
      
       
        P
        
         8
         ⁢
         
          π
          ⁡
          (
          
           1
           -
           
            μ
            0
           
          
          )
         
        
       
       [
       
        
         
          
           (
           
            1
            -
            
             2
             ⁢
             μ
            
           
           )
          
          ⁢
          
           (
           
            z
            -
            d
           
           )
          
         
         
          R
          1
          3
         
        
        -
        
         
          
           (
           
            1
            -
            
             2
             ⁢
             μ
            
           
           )
          
          ⁢
          
           (
           
            z
            -
            d
           
           )
          
         
         
          R
          2
          3
         
        
        +
        
         
          3
          ⁢
          
           
            (
            
             z
             -
             d
            
            )
           
           3
          
         
         
          R
          1
          5
         
        
       
      
     
    
   
   
    
     
             
      
       
        +
        
         
          3
          ⁢
          0
          ⁢
          d
          ⁢
          
           
            z
            ⁡
            (
            
             z
             +
             d
            
            )
           
           3
          
         
         
          R
          2
          7
         
        
       
       +
       
        
         
          3
          ⁢
          
           (
           
            3
            -
            
             4
             ⁢
             μ
            
           
           )
          
          ⁢
          
           
            z
            ⁡
            (
            
             z
             +
             d
            
            )
           
           2
          
         
         -
         
          3
          ⁢
          
           d
           ⁡
           (
           
            z
            +
            d
           
           )
          
          ⁢
          
           (
           
            
             5
             ⁢
             z
            
            -
            d
           
           )
          
         
        
        
         R
         2
         5
        
       
      
      ]
     
    
   
  
  ,
 

wherein μ is Poisson's ratio of the existing station, μ0 is Poisson's ratio of a soil mass, d is the depth of load action, R1 and R2 are distances from a load action point (0, 0, d) and a symmetrical point (0, 0, −d) relative to the ground to any point (x, y, z), respectively;
the expression of the vertical stress solution σz of any point in the semi-infinite space under the action of the certain vertical load β is processed simultaneously with a relational expression between the vertical load β and unloading stress P1 and an active jacking force P2 of the new station, and integration is performed in the excavation region to obtain the stress solution expression of the active jacking force on the existing station; and
the expression of the vertical stress solution of the existing station is obtained after the vertical stress solution σz′ of the existing station expression of the active jacking force on the existing station is simplified.