Servo support axial force regulation and control method based on earth pressure behind retaining structure wall

Abstract

According to the servo support axial force regulation and control method based on the soil pressure behind the enclosure wall, in the calculation process, based on the magnitude of the static soil pressure behind the wall, the axial force threshold value of the servo support is set to be the sum of the static soil pressure in the matched range to serve as the reference value, and therefore the soil pressure borne by an enclosure structure is better balanced, and the stability of the enclosure structure is improved. The method comprises the following steps: step 1, determining geometric and physical mechanical parameters of a soil layer, a diaphragm wall, a support and the like according to actual working conditions, and simplifying the parameters into an elastic foundation beam model; 2, according to the elastic foundation beam model and the excavation working condition, a control balance equation of the elastic foundation beam of the servo system is established and solved; 3, according to the soil layer parameters, determining the static soil pressure behind the wall, and according to the static soil pressure distribution and the support arrangement depth, determining the axial force threshold value of each support; and 4, solving the deformation of the enclosure structure.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of foundation pit support adjustment, in particular to a servo support axial force regulation method based on soil pressure behind the retaining structure wall. BACKGROUND

[0002] With the further development of the city, the land resources in the city, especially in the central city, are increasingly scarce, and the rational use of urban underground space is increasingly valued. As the main way of urban underground space development, the newly built foundation pit is often adjacent to existing buildings under the current background of tight urban land resources. Since the excavation of the foundation pit will cause deformation of the surrounding environment, thereby threatening the safety of the surrounding existing buildings, it is necessary to take measures to control the deformation caused by the excavation of the foundation pit.

[0003] For deep foundation pit engineering in the city, the form of setting up internal support inside the retaining structure is often used for support. The internal support usually adopts reinforced concrete support, steel support or prestressed steel support. Reinforced concrete support and steel support are passive support, which can only play a supporting role after the wall produces horizontal displacement and compression deformation, which will cause excessive deformation of the retaining structure. For prestressed steel support, the axial force loss is accompanied by the construction process, which cannot be applied to the foundation pit excavation with strict deformation control. In order to overcome the axial force loss in the construction process, the servo support system as an active support technology can effectively control the wall deformation.

[0004] However, at present, the determination of the axial force threshold of the servo support in the application process lacks theoretical guidance, and is usually determined according to the experience of engineering personnel. In engineering practice, the confirmation method of the axial force threshold of the servo support is that, under the same conditions, the support axial force value calculated by the traditional support is taken as the reference value, and 75% of the reference value is taken as the actual axial force threshold. Using this confirmation method of the axial force threshold, the calculation working condition in the design process is different from the stress condition in the actual construction process, which will lead to the difference between the stress condition of the wall and the actual situation. Since the calculated bending moment value will be used for the reinforcement of the retaining structure, this difference will cause potential construction risks. Therefore, using this axial force control criterion usually cannot obtain satisfactory control effect. SUMMARY

[0005] The present application proposes a servo support axial force regulation method based on the soil pressure behind the retaining wall. In the calculation process, based on the size of the static soil pressure behind the wall (such as Figure 1 ), the axial force threshold of the servo support is set to the sum of the matching range of the static soil pressure as the reference value, so as to better balance the soil pressure of the retaining structure and control the stress and deformation of the retaining structure. The servo support axial force threshold obtained by using this method is more matched between the stress of the retaining structure in the calculation process and in the actual excavation process, and can better ensure the safety of the foundation pit excavation.

[0006] The application provides a servo support axial force regulation method based on a building envelope wall back earth pressure.

[0007] Step one, according to the actual working condition, the geometric and physical mechanical parameters of the soil layer, the diaphragm wall, the support and the like are determined, and are simplified into an elastic foundation beam model;

[0008] Wherein, the building envelope is simplified into an elastic beam, the pit soil is simplified into a soil spring unit, the servo steel support is simplified into a model combined with a spring and a pre-axial force, and the wall stiffness matrix [K], the soil spring stiffness matrix [K m ], the support stiffness matrix [K s ] and the earth pressure matrix [F e ] are solved;

[0009] The elastic foundation beam model is solved by using the finite element method, and the equivalent elastic beam of the building envelope is divided into n units;

[0010] For the wall stiffness matrix [K], the vertical deformation is ignored, each unit is a rod unit, and the stiffness matrix of each rod unit is:

[0011]

[0012] In the formula, [K i ] is the stiffness matrix of the i-th rod unit, the stiffness matrixes of all units are combined to obtain the wall stiffness matrix [K]; E is the elastic modulus of the building envelope; I is the inertia matrix of the wall; and l is the length of each unit;

[0013] The calculation of the soil spring stiffness matrix [K m ] is as follows:

[0014] K m,i =k h bd (2)

[0015] k h =mz (3)

[0016] In the formula, K m,i is the stiffness of the i-th soil spring, the stiffnesses of all soil springs are combined to obtain the soil spring stiffness matrix [K m ]; k h is a horizontal base coefficient of the soil; d is the height of the soil spring, and the value is equal to l; m is a depth coefficient of the horizontal base coefficient; and z is the depth of the soil;

[0017] The calculation of the support stiffness matrix [K s ] is as follows:

[0018]

[0019] In the formula, Ks,i The stiffness of the i-th support is combined with all support stiffnesses to obtain the support stiffness matrix [K s ] ; E s is the support elastic modulus; L s is the support equivalent length; S s is the support equivalent spacing;

[0020] For the soil pressure matrix [F e ], the static soil pressure is used, and is calculated as follows:

[0021] F e,i = K0σ z bl (5)

[0022]

[0023] σ z = γz (7)

[0024] In the formula, F e,i is the soil pressure load on the i-th node, and all node soil pressures are combined to obtain the soil pressure matrix [F e ]; K0 is the static soil pressure coefficient; σ z is the overburden soil weight at depth z; γ is the unit weight of the soil; is the internal friction angle of the soil.

[0025] Step two, according to the elastic foundation beam model and the excavation working condition, the control balance equation of the servo system elastic foundation beam is established, and is solved;

[0026] Equations (1), (3), (5) and (6) are substituted into the control balance equation of the servo system elastic foundation beam to solve:

[0027]

[0028] In the formula:

[0029] [△] is the deformation matrix of the enclosure structure to be solved; [F s ] is the additional force matrix caused by the installation hysteresis of the support, F s,i = K s,i △ s,i , F s,i is the hysteresis additional force of the i-th support, and all support additional forces are combined to obtain the support additional force matrix [F s ], K s,i is the stiffness of the i-th support, and △ s,i is the hysteresis displacement of the i-th support;

[0030] [F axial ] is the servo support axial force matrix, F axial,iThe axial force threshold of the i-th support is calculated according to the following formula: axial ]。

[0031] Step three, according to the soil parameters, the static earth pressure behind the wall is determined, and the axial force threshold of each support is determined according to the static earth pressure distribution and the support arrangement depth;

[0032] The calculation formula of the axial force threshold of the i-th support is as follows:

[0033] F axial,i =1.2×(P i +P i+1 )×(H i+1 -H i ) / 2 (9)

[0034] In the formula, F axial,i is the axial force threshold of the i-th support; P i and P i+1 are the static earth pressures behind the wall at the depths of the i-th support and the i+1-th support; H i and H i+1 are the depths at the depths of the i-th support and the i+1-th support; when the i-th support is the last support, the depth at the i+1-th support is the depth of the pit bottom.

[0035] Step four, the axial force threshold calculated in step three is brought into the control balance equation of the elastic foundation beam of the servo system in step two to solve the deformation of the enclosure structure; formula (9) is substituted into formula (8); and the solving formula of the deformation of the enclosure structure is as follows:

[0036] [△]=([K]+[K m ]+[K s ]) -1 ([F e ]+[F s ]-[F axial ]) (10)

[0037] Step five, it is judged whether the excavation is to the last working condition, if the excavation is still continued, the calculation of the second step to the fourth step is repeated.

[0038] The essential feature of the present application is that the absolute values of the maximum negative bending moment and the maximum positive bending moment of the enclosure structure calculated and regulated by the method are more similar, and the stress is more balanced. The servo support axial force threshold obtained by the method is more matched with the stress of the enclosure structure in the calculation process and the actual excavation process, and can better ensure the safety of the foundation pit excavation. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 The mechanical calculation model of the servo support;

[0040] Figure 2 for the flow chart of the present application;

[0041] Figure 3 for the comparison chart of the horizontal displacement of the enclosure in Example 1 of the present application;

[0042] Figure 4 for the comparison chart of the bending moment of the enclosure in Example 1 of the present application. DETAILED DESCRIPTION

[0043] The technical solutions of the present application will be further specifically described below by means of specific examples and in combination with the drawings.

[0044] The present application proposes a servo support axial force regulation method based on the soil pressure behind the enclosure wall, which provides a theoretical reference for determining the axial force threshold of the actual deep foundation servo support.

[0045] In order to achieve the above-mentioned purpose, the method comprises the following steps as shown in Figure 2

[0046] First, according to the actual working condition, the geometric and physical and mechanical parameters of the soil layer, the diaphragm wall, the support and the like are determined, which are simplified as an elastic foundation beam model. Among them, the enclosure is simplified as an elastic beam placed vertically, the soil body in the pit is simplified as a soil spring unit, the servo steel support is simplified as a model combined with a spring and a pre-axial force, and the wall stiffness matrix [K], the soil spring stiffness matrix [K m ], the support stiffness matrix [K s ] and the soil pressure matrix [F e ] are solved.

[0047] The elastic foundation beam model is solved by using the finite element method, and the equivalent elastic beam of the enclosure is divided into n units. For the wall stiffness matrix [K], the vertical deformation is ignored, each unit is a rod unit, and the stiffness matrix of each rod unit is:

[0048]

[0049] In the formula:

[0050] [K i ] - the stiffness matrix of the i-th rod unit, and the stiffness matrix of all units is combined to obtain the wall stiffness matrix [K]; E - the elastic modulus of the enclosure (kPa), the case of the present patent takes E = 3 × 10 7 kPa;

[0051] I - the moment of inertia of the wall (m 4 ), the case of the present patent takes the underground continuous wall b is the calculated width of the diaphragm wall, which is 1m, and h is the thickness of the diaphragm wall, which is 1m;

[0052] ​l——Length of each unit (m), l=L / n, L is the length of the diaphragm wall, which is taken as 30m, and n is the number of units, which is taken as 200;

[0053] The force balance equations for each rod element are as follows:

[0054]

[0055] In the formula:

[0056] F j F k —Horizontal nodal loads (kN) at nodes j and k;

[0057] M j M k —Nodal bending moments (kN·m) at nodes j and k;

[0058] v j v k —Horizontal deformation (m) at nodes j and k;

[0059] v j v k — Horizontal deformation (rad) at nodes j and k.

[0060] The direction of action of the soil spring is horizontal. For the soil spring stiffness matrix [K] m ]:

[0061] K m,i =k h bd (13)

[0062] k h =mz (14)

[0063] In the formula:

[0064] K m,i —The horizontal equivalent stiffness (kN / m) of the i-th soil spring, combined with the stiffness of all soil springs to obtain the soil spring stiffness matrix [K m ];

[0065] k h — Soil horizontal subgrade coefficient (kN / m) 3 );

[0066] d—Height of the soil spring (m), its value is equal to l;

[0067] m — Depth coefficient of horizontal subgrade (kN / m) 4 In this patent case, m = 500 kN / m 4 ;

[0068] z — Soil depth (m).

[0069] Support spring action direction along the horizontal direction, for support stiffness matrix [K s ]:

[0070]

[0071] In the formula:

[0072] K s,i - The horizontal equivalent stiffness of the i-th support (kN / m), and the support stiffness matrix [K s ] is obtained by combining all support stiffnesses;

[0073] E s - Support elastic modulus (kN / m 2 ), the servo steel support in this patent case takes E s = 2 × 10 8 kN / m 2 , and the concrete support takes E s = 3 × 10 7 kN / m 2 ;

[0074] L s - Support equivalent length (m), which is half of the width of the foundation pit in this patent case;

[0075] S s - Support equivalent spacing (m), which takes S s = 3m for the servo steel support in this patent case, and S s = 10m for the concrete support.

[0076] For the soil pressure matrix [F e ], the static soil pressure is used:

[0077] F e,i = K0σ z bl (16)

[0078]

[0079] σ z = γz (18)

[0080] In the formula:

[0081] F e,i - The horizontal soil pressure load on the i-th node, and the soil pressure matrix [F e ] is obtained by combining the soil pressures of all nodes;

[0082] K0 - Static soil pressure coefficient;

[0083] σ z— the overlying soil weight (kN / m 2 ) at depth z;

[0084] — the unit weight of soil (kN / m 3 ), in this patent case, γ = 18 kN / m 3 ;

[0085] — the internal friction angle of soil, in this patent case, φ = 30°;

[0086] Second step, according to the elastic foundation beam model and the excavation working condition, the formula (1), (3), (5) and (6) are substituted into the control balance equation of the elastic foundation beam of the servo system to solve:

[0087] [F e ] = ([K] + [K m ] + [K s ]) · [△] - [F s ] + [F axial ] (19)

[0088] In the formula:

[0089] [△] — the deformation matrix of the enclosure structure to be solved;

[0090] [F s ] — the additional force matrix caused by the support installation hysteresis, F s,i = K s,i △ s,i , F s,i is the hysteresis additional force of the i-th support, and the additional force matrix [F s ] of all supports is obtained by combining the additional forces of all supports, K s,i is the stiffness of the i-th support, and △ s,i is the hysteresis displacement (m) of the i-th support;

[0091] [F axial ] — the axial force matrix of the servo support, F axial,i is the axial force threshold value of the i-th servo support, and the axial force matrix [F axial ] of all servo supports is obtained by combining the axial force threshold values of all servo supports, and the axial force threshold value of the servo support in this patent case is obtained through the third step.

[0092] Third step, according to the soil layer parameters, the static soil pressure behind the wall is determined, and the axial force threshold value of each support is determined according to the static soil pressure distribution and the support arrangement depth.

[0093] F axial,i = 1.2 × (P i + P i+1 ) × (H i+1 - Hi ) / 2 (20)

[0094] wherein:

[0095] F axial,i — the threshold value of the axial force of the i-th support (kN / m);

[0096] P i , P i+1 — the post-construction earth pressure at the depth of the i-th support and the i+1-th support;

[0097] H i , H i+1 — the depth at the depth of the i-th support and the i+1-th support; when the i-th support is the last support, the depth at the i+1-th support is the depth of the pit bottom.

[0098] Fourthly, substituting equation (10) into equation (9) and solving the deformation of the enclosure;

[0099] [△]=([K]+[K m ]+[K s ]) -1 ([F e ]+[F s ]-[F axial ]) (21)

[0100] Fifthly, determining whether the excavation is to the last working condition, if the excavation continues, repeating the calculation of the second step to the fourth step.

[0101] Example 1

[0102] In this patent calculation case, the excavation depth is 15m, the excavation width is 20m, and the diaphragm wall depth is 30m. The cross section of the foundation pit is that the first support is a reinforced concrete support, and the second to fifth supports are servo steel supports. The buried depths of the supports are 0.5m, 3.5m, 6.5m, 9.5m and 12.5m respectively. The cross section of the reinforced concrete support is

[0103] 800×700mm rectangular section, and the cross section of the servo steel support is φ609×16 circular ring section.

[0104] The traditional servo support axial force threshold confirmation method takes the axial force of the traditional support equivalent to the servo support at the last working condition as the reference value, and takes 75% of the axial force. The traditional axial force thresholds of the second to fifth servo supports are 163kN / m, 245kN / m, 342kN / m and 261kN / m respectively.

[0105] The servo support shaft force threshold confirmation method of the present application adopts the support shaft force threshold corresponding to the static soil pressure behind the wall in formula (10), and the shaft force thresholds of the second to fifth servo supports are 197 kN / m, 314 kN / m, 430 kN / m and 628 kN / m respectively.

[0106] As shown in Figure 3 and Figure 4 Compared with the traditional shaft force threshold and the shaft force threshold of the servo support of the present application, the stress deformation of the enclosure structure, the wall deformation values of working condition five and working condition six are reduced from 32 mm and 51 mm to 21 mm and 30 mm respectively based on the servo support shaft force regulation method based on the soil pressure behind the enclosure structure wall compared with the traditional shaft force threshold confirmation method. The difference of the maximum positive bending moment is not big, and the traditional method is similar to the method of the present application. However, by using the method of the present application, the absolute values of the maximum negative bending moment and the maximum positive bending moment are more similar, and the stress is more balanced.

Claims

1. A servo-driven support axial force control method based on earth pressure behind retaining wall, characterized in that, Includes the following steps: Step 1: Based on the actual working conditions, determine the geometric and physical mechanical parameters of the soil layers, diaphragm walls, supports, etc., and simplify them into an elastic foundation beam model; The retaining structure is simplified to a vertically placed elastic beam, the soil in the pit is simplified to a soil spring element, and the servo steel support is simplified to a model of springs combined with pre-applied axial force. The wall stiffness matrix [K] and the soil spring stiffness matrix [K] are then solved. m ], Support stiffness matrix [K s and earth pressure matrix [F e ]; The finite element method is used to solve the elastic foundation beam model, and the equivalent elastic beam of the retaining structure is divided into n elements; Step 2: Based on the elastic foundation beam model and excavation conditions, establish and solve the control equilibrium equations for the servo system's elastic foundation beam. Step 3: Determine the at-rest earth pressure behind the wall based on the soil layer parameters, and determine the axial force threshold of each support based on the distribution of at-rest earth pressure and the depth of the support arrangement. Step 4: Substitute the axial force threshold calculated in Step 3 into the control equilibrium equation of the elastic foundation beam of the servo system in Step 2 to solve for the deformation of the retaining structure. Step 5: Determine whether the excavation has reached the final working condition. If excavation continues, repeat the calculations from Step 2 to Step 4.

2. The servo-support axial force control method based on the earth pressure behind the retaining structure wall according to claim 1, characterized in that, In step one: For the wall stiffness matrix [K], neglecting vertical deformation, each element is a bar element, and the stiffness matrix of each bar element is: In the formula: [K i [] is the stiffness matrix of the i-th rod element. The stiffness matrices of all elements are combined to obtain the wall stiffness matrix [K]; E is the elastic modulus of the enclosure structure; I is the moment of inertia of the wall; l is the length of each element; The force balance equations for each rod element are as follows: In the formula: F j F k M represents the horizontal nodal loads (kN) at nodes j and k; j M k v represents the nodal bending moments (kN·m) at nodes j and k; j v k v represents the horizontal deformation (m) at nodes j and k; j v k Let be the horizontal deformation (rad) at nodes j and k; Soil spring stiffness matrix [K] m The calculation is as follows: K m,i =k h bd (3) k h =mz (4) Where: K m,i For the horizontal equivalent stiffness of the i-th soil spring, the stiffness of all soil springs is combined to obtain the soil spring stiffness matrix [K]. m ];k h is the horizontal subgrade coefficient; d is the soil spring height, which is equal to l; m is the depth coefficient of the horizontal subgrade coefficient; z is the soil depth; Support stiffness matrix [K s The calculation is as follows: Where: K s,i To obtain the horizontal equivalent stiffness of the i-th support, the stiffness of all supports is combined to obtain the support stiffness matrix [K]. s ]; E s To support the elastic modulus; L s To support the equivalent length; S s To support the equivalent spacing; For the earth pressure matrix [F e Using at-rest earth pressure, the calculation is as follows: F e,i =K0σ z with (6) s z =γz (8) In the formula: F e,i For the earth pressure load on the i-th node, the earth pressure matrix [F] is obtained by combining the earth pressures of all nodes. e K0 is the coefficient of earth pressure at rest; σ z γ is the weight of the overlying soil at depth z; γ is the unit weight of the soil. The friction angle within the soil.

3. The servo-support axial force control method based on the earth pressure behind the retaining structure wall according to claim 2, characterized in that, Elastic modulus of the building envelope E = 3 × 10 7 kPa; diaphragm wall b is the calculated width of the diaphragm wall, taken as 1m; h is the thickness of the diaphragm wall, taken as 1m; l = L / n, where L is the length of the diaphragm wall, taken as 30m; and n is the number of units, taken as 200. The depth coefficient of the horizontal subgrade is m = 500 kN / m 4 ; Example: Servo steel support, take E s =2×10 8 kN / m 2 Concrete support is taken as E s =3×10 7 kN / m 2 ; Support equivalent length L s The width of the foundation pit is half; the servo steel support is S. s =3m, concrete support taken S s =10m; The unit weight of soil γ = 18 kN / m 3 ; soil internal friction angle 4. The servo-support axial force control method based on the earth pressure behind the retaining structure wall according to claim 2, characterized in that, Substituting equations (1), (3), (5), and (6) into the control equilibrium equations for the elastic foundation beam of the servo system, we can solve for the following: [F e ]=([K]+[K m ]+[K s ])·[△]-[F s ]+[F axial (9) Where: [△] is the deformation matrix of the enclosure structure to be determined; [F s [F] represents the matrix of additional forces caused by installation lag. s,i =K s,i △ s,i F s,i The hysteresis additional force of the i-th support is obtained by combining all support additional forces to obtain the support additional force matrix [F]. s ], K s,i Let Δ be the stiffness of the i-th support. s,i Let be the hysteresis displacement of the i-th support; [F axial [F] represents the servo support axial force matrix. axial,i Let be the axial force threshold of the i-th servo support. Combine all servo support axial force thresholds to obtain the servo support axial force matrix [F]. axial ].

5. The servo-support axial force control method based on the earth pressure behind the retaining structure wall according to claim 4, characterized in that, The formula for calculating the axial force threshold of the i-th support is as follows: F axial,i =1.2×(P i +P i+1 )×(H i+1 -H i ) / 2 (10) In the formula: F axial,i P is the axial force threshold of the i-th support; i P i+1 H represents the at-rest earth pressure behind the wall at the depths of the i-th and (i+1)-th supports; i H i+1 The depth at the support depth of the i-th and i+1-th supports; when the i-th support is the last support, the depth at the i+1-th support is the depth of the pit bottom.

6. The servo-support axial force control method based on the earth pressure behind the retaining structure wall according to claim 4, characterized in that, Step four involves substituting equation (10) into equation (9); The formula for solving the deformation of the enclosure structure is: [△]=([K]+[K m ]+[K s ]) -1 ([F e ]+[F s ]-[F axial ]) (11)。

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