A design method for horizontally loaded cast-in-place piles to eliminate the influence of necking defects

Abstract

The present invention discloses a method for designing a horizontally loaded cast-in-place pile for eliminating the influence of necking defects, comprising the following steps: selecting the diameter and length of the cast-in-place pile as design parameters to obtain M design combinations; using a spreadsheet calculation model to quantitatively characterize and quantitatively calculate the randomness of the necking location, necking amount, and saturated sand parameters; obtaining a design combination that meets the safety index and evaluating the robustness to obtain the optimal design combination. The present invention utilizes a spreadsheet efficient calculation method and a random simulation method, and utilizes a spreadsheet efficient calculation method and a random simulation method, and comprehensively considers the optimization objectives of cost, safety, and robustness, to achieve multi-objective optimization of the design parameters of cast-in-place piles under uncertain conditions.

Description

Technical Field

[0001] The invention belongs to the technical field of cast-in-place piles, and in particular relates to a design method for horizontally loaded cast-in-place piles that eliminates the influence of necking defects. Background Art

[0002] Pile foundation is a common foundation form in poor foundation and plays a vital role in the field of engineering construction. In saturated sandy soil, cast-in-place piles are a common form of pile foundation. However, the boreholes in saturated sandy soil are prone to collapse, resulting in local necking of concrete cast-in-place piles. The cross-sectional size, bending stiffness and bearing capacity of the cast-in-place piles are reduced at the necking point. Under the horizontal load on the top of the pile, the cast-in-place piles with necking defects are difficult to meet the requirements of bearing capacity and deformation control. In saturated sandy soil, the location and amount of necking of cast-in-place piles are highly random and difficult to predict. Only through testing after pile construction can the specific parameters of necking be determined, and then the influence of necking defects can be quantitatively evaluated to provide a reference for engineering treatment. This method is not only time-consuming and labor-intensive, but also seriously affects the progress of the project. Therefore, it is necessary to consider the influence of the randomness of necking defects in the design stage and establish an effective design method to eliminate the influence of necking defects on the bearing capacity and deformation of cast-in-place piles. Summary of the invention

[0003] In view of the problem that the shrinkage position and shrinkage amount of bored piles in saturated sandy soil are highly random and difficult to predict, the present invention proposes a multi-objective design method considering the safety, economy and robustness of bored piles under horizontal load based on a random simulation method.

[0004] To achieve the above purpose, the technical solution provided by the present invention is:

[0005] A method for designing horizontally loaded cast-in-place piles to eliminate the influence of necking defects comprises the following steps:

[0006] Step 1: According to the specification requirements and design experience, the diameter and length of the cast-in-place pile are selected as design parameters, and different combinations of the two form M alternative design schemes;

[0007] Step 2: For each design scheme, a calculation model of cast-in-place piles under horizontal loads is established using a spreadsheet. The model uses a differential method to discretize the pile body. The cross-sectional dimensions, bending stiffness, and bearing capacity of the pile unit after discretization are input in the corresponding cells. Combined with the mechanical parameters of saturated sand, this method can efficiently calculate the deformation, bending moment, and shear force of cast-in-place piles under horizontal loads.

[0008] Step 3: The location where the necking occurs, the amount of necking and the saturated sand parameters are taken as three random variables, and N groups of necking locations, necking amounts (by reducing the pile cross-sectional area) and saturated sand mechanical parameters are generated through Monte-Carlo simulation, and the values ​​are assigned to the corresponding cells. The deformation, bending moment and shear force of the N groups of cast-in-place piles corresponding to the design scheme are calculated using the spreadsheet method;

[0009] Step 4: Calculate the average value and standard deviation of deformation, bending moment and shear force of N groups of cast-in-place piles. When the average value of deformation, bending moment and shear force is less than the limit value specified in the specification, the design scheme meets the safety requirements;

[0010] Step 5. For the design scheme that meets the safety requirements, the statistically obtained standard deviations of deformation, global and shear force are used to evaluate the sensitivity of the stress response of the bored pile to the uncertain factors (neck position, neck amount and saturated sand parameters). If the standard deviation is smaller, it means that the stress response of the bored pile is less sensitive to the change of the uncertain factors, that is, the corresponding design scheme is more robust.

[0011] Step 6: Repeat the above process for each alternative design scheme, screen out all the design schemes that meet the safety requirements, and calculate the corresponding cost;

[0012] Step 7. Engineering practice shows that the higher the cost of bored piles (the larger the diameter and the longer the pile length), the better the robustness of the design scheme. It is impossible to achieve the best robustness at the lowest cost. In order to balance the cost and robustness, the optimal bored pile design parameters (pile length and diameter) are determined. In the four-dimensional space of cost-deformation standard deviation-bending moment standard deviation-shear standard deviation, each indicator is normalized, and the distance of each design scheme from the coordinate origin is calculated. The design corresponding to the point with the smallest distance is the optimal design that balances the cost and the robustness of each indicator.

[0013] Beneficial effects of the present invention:

[0014] 1. The present invention utilizes an efficient spreadsheet calculation method and a random simulation method to achieve quantitative characterization and quantitative calculation of the randomness of the necking location, necking amount, and saturated sand parameters, thus solving the problem of the difficulty in predicting necking defects.

[0015] 2. The present invention takes into account the optimization objectives of cost, safety and robustness, and realizes multi-objective optimization of the design parameters of cast-in-place piles under uncertain conditions.

[0016] 3. The design method of the present invention has a wide application range, and is particularly suitable for situations where cost and other factors are comprehensively considered. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of the design method of the present invention;

[0018] Figure 2 It is the electronic table Sheet1 in the specific implementation mode of the present invention;

[0019] Figure 3 It is the electronic table Sheet2 in the specific implementation mode of the present invention;

[0020] Figure 4 It is the electronic table Sheet3 in the specific implementation mode of the present invention;

[0021] Figure 5 It is a design combination that meets safety requirements in a specific embodiment of the present invention;

[0022] Figure 6 It is a three-dimensional graph of deflection standard deviation-bending moment standard deviation-Cost in a specific embodiment of the present invention; DETAILED DESCRIPTION

[0023] In order to further understand the content of the present invention, the present invention is described in detail in conjunction with examples. The following examples are used to illustrate the present invention but are not used to limit the scope of the present invention.

[0024] refer to Figure 1 As shown, this embodiment relates to a method for optimizing the robustness of landslides in anti-slide pile-reinforced accumulation layers, comprising the following steps:

[0025] First, we need to select the parameter combination of the cast-in-place pile, namely the pile length and radius. The range of the pile length is [13, 27], the increment is 1.0, and the unit is m. The range of the radius is [0.40, 0.85], the increment is 0.05, and the unit is m. There are 15*10=150 design combinations in total.

[0026] Using a spreadsheet, establish a calculation model for the bending moment and deflection of cast-in-place piles in Sheet 1, such as Figure 2 As shown, the details are as follows:

[0027] First, the buried depth L of the pile body is discretized by the difference method and can be divided into 30 segments Δz of unequal length. The node coordinates of Δz can be expressed as:

[0028] z1=z0+Δz1 (1)

[0029] Where Δz1 is the initial segment length, which is set to 0.3m;

[0030] z i =z i-1 +r Δz (z i-1 -z i-2 ),i>2 (2)

[0031] In the formula, r Δz is the common ratio;

[0032] In a spreadsheet, the GoalSeek function can be used to calculate r Δz is the variable term, the last node z=L is the target term, and the length of each segment and the node coordinate value after discretization are obtained;

[0033] The third column is the bending stiffness of the cast-in-place pile at the node position:

[0034] E p I P =E*π*d 4 / 64 (3)

[0035] Where E is the elastic modulus of concrete, and d is the diameter of the cast-in-place pile;

[0036] The E of C30 concrete is 3.0*10 4 mm 2 ;

[0037] The fourth column is the pile side deflection under horizontal load:

[0038] y i =y i+1 +(Δz i+1 / Δz i+2 ) 2 *(y i+2 -y i+1 )-Δz i+1 *(1+Δz i+1 / Δz i+2 )*y' i+1 (4)

[0039] In the formula, Δz i+1 =Δz i+1 -Δz i , Δz i+2 =Δz i+2 -Δz i+1 , the last two nodes y at the pile end i The initial value is 0;

[0040] The fifth column is the slope of the pile at each node:

[0041]

[0042] In the formula, when i is the last node, y' i =(y i -y i-1 ) / (z i -z i-1 );

[0043] The sixth column is ksec d, that is, (secant k)*d. According to Matlock's py curve model, VBA program can be used to write about k sec The formula for d is:

[0044] ksecd(gammaz,cu,J,z,b,gammaB,epsilon,y,) (6)

[0045] Where gammaz = γ'*z i , where γ'=11.8kN / m 3 Undrained shear strength cu=150kN / m 2 , J=0.25, b=1.3m, gammaB=15.34kN / m 3 , epsilon = 0.01;

[0046] Column 7 is the reaction force of soil on piles:

[0047] p i =-k h d*y i (7)

[0048] In the formula, the negative sign represents that the reaction force of the soil on the pile is in the opposite direction to the deflection of the pile, k h d represents the secant modulus at the node;

[0049] Column 8 is the shear force on the cast-in-place pile at the node:

[0050] Q=Q i+1 -0.5*(p i+1 +p i )*(z i+1 -z i ) (8)

[0051] In the formula, when i is the last node, Q = 0;

[0052] Column 9 is the bending moment borne by the cast-in-place pile at the node:

[0053] M i =M i+1 -Q i+1 Δz i+1 +1 / 6*Δz i+1 2 (2p i+1 +p i ) (9)

[0054] In the formula, when i is the last node, M = 0;

[0055] According to the equilibrium condition, at z0, the following conditions must be met:

[0056] Q0-P h =0 (10)

[0057] M0-M z0 =0 (11)

[0058] Where P h =35kN, M z0 =910kN*m. Formula (10), (11) need to be determined recursively based on formula (4) to formula (11);

[0059] The 10th column is yprev. Use VBA program to repeatedly call Solver: Formula (10) is equal to 0, and the change term is the last two nodes y in the 4th column. i , the constraint condition is that formula (11) is equal to 0, and the iteration accuracy is 0.000001.

[0060] Using a spreadsheet, establish a calculation model for the cast-in-place pile after necking in Sheet2, such as Figure 3 As shown, the details are as follows:

[0061] For cast-in-place piles that have experienced shrinkage, their position is random relative to the entire pile length before the location where the shrinkage occurs is detected; for the location where the shrinkage occurs, its pile diameter is also random relative to the original pile diameter before the pile diameter is detected.

[0062] According to the parameter range of the design combination, it is assumed that the nodes where necking occurs are uniformly distributed, and it is assumed that the radius after necking occurs is also uniformly distributed.

[0063] The first column is the sample number. Write a VBA program to generate 100 groups of samples through Monte-Carlo simulation;

[0064] The second column is the node position. The position where the necking occurs is uncertain and has a random range of [0,30], taking an integer.

[0065] The third column is the radius at the necking position. The degree of necking is uncertain and the random range is [0.7*r, 0.9*r].

[0066] The fourth column is the cross-sectional area after necking occurs at the node:

[0067] A=πr 2 (12)

[0068] The fifth column is the moment bearing capacity after necking occurs at the node:

[0069]

[0070] Where, α1 = 1.0, f c =14.3*103 kN / m 2 , the ratio of the central angle of the concrete compression zone to 2π is α=1 / 3.

[0071] The sixth column is the bending stiffness after necking occurs at the node, which is calculated using formula (3).

[0072] The 7th column is the deflection of the pile top after necking occurs at the node. Write a VBA program to replace the value of the 6th column in Sheet2 with the corresponding cell in Sheet1, call the Sub in Sheet1, and get the new deflection of the pile top after necking occurs.

[0073] Through the VBA program, the above operations are executed cyclically to obtain 100 groups of samples generated by Monte-Carlo simulation, as well as the average value, standard deviation of the bending moment (the maximum bending moment of the internal force exerted on the cast-in-place pile) and the average value, standard deviation of the deflection (the deflection at the top of the cast-in-place pile) of these 100 groups of samples.

[0074] Using a spreadsheet, establish a calculation model for all design combinations of cast-in-place piles in Sheet3, such as Figure 3 As shown, the details are as follows:

[0075] The first column is the pile length, the range of the pile length is [13,27], the increment is 1.0, and the unit is m;

[0076] The second column is the radius, the radius range is [0.40, 0.85], the increment is 0.05, the unit is m;

[0077] The third column is the standard deviation of the bending moment, and the fourth column is the standard deviation of the deflection. Write a VBA program and input the results in Sheet2 to obtain;

[0078] The fifth column is the cost of the cast-in-place pile, which is directly related to the pile length and pile diameter:

[0079] Cost = L * D (14)

[0080] In the formula, the pile length is L and the pile diameter is D;

[0081] Write a VBA program to call the Sub in Sheet2 to obtain the standard deviation of the bending moment and the standard deviation of the deflection of the design combination under Monte-Carlo simulation;

[0082] By using the VBA program, the above operations are executed repeatedly to obtain the standard deviation of the bending moment and the standard deviation of the deflection for 150 design combinations, as shown in Figure 4 As shown;

[0083] Set safety requirements, the average bending moment is less than 200, and the average deflection is less than 0.0015;

[0084] Finally, a design combination that meets safety requirements is obtained, such as Figure 5 shown.

[0085] like Figure 6 As shown in the figure, in the three-dimensional space of deflection standard deviation-bending moment standard deviation-Cost, each indicator is normalized, the distance of each design scheme from the coordinate origin is calculated, the standard deviation is used to evaluate the robustness of each indicator, and the design corresponding to the point with the smallest distance is the optimal design that balances the cost and the robustness of each indicator.

[0086] By calculating and comparing the distance between each design combination that meets the safety requirements and the coordinate origin in a spreadsheet, the optimal design combination can be obtained, eliminating the influence of necking defects on the bearing capacity and deformation of cast-in-place piles.

[0087] Although the preferred embodiments of the present invention are described above in conjunction with the embodiments, the present invention is not limited to the above specific implementations, which are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, for example, considering the randomness of soil parameters, considering the randomness of the length of the necking section, and considering different or more safety parameters. All of these belong to the protection scope of the present invention.

[0088] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for designing horizontally loaded cast-in-place piles to eliminate the influence of necking defects, characterized in that: It includes the following steps: Step 1: According to the specification requirements and design experience, the diameter and length of the cast-in-place pile are selected as design parameters, and different combinations of the two form M alternative design schemes; Step 2: For each design scheme, a calculation model of cast-in-place piles under horizontal load is established using a spreadsheet. The model uses a differential method to discretize the pile body. The cross-sectional dimensions, bending stiffness, and bearing capacity of the pile unit after discretization are input in the corresponding cells, combined with the mechanical parameters of saturated sand; Step 3: The location of necking, the amount of necking and the saturated sand parameters are taken as three random variables, and N groups of necking locations, necking amounts and saturated sand mechanical parameters are generated through Monte-Carlo simulation, and the values ​​are assigned to the corresponding cells. The deformation, bending moment and shear force of the N groups of cast-in-place piles corresponding to the design scheme are calculated using the spreadsheet method; Step 4: Calculate the average value and standard deviation of deformation, bending moment and shear force of N groups of cast-in-place piles. When the average value of deformation, bending moment and shear force is less than the limit value specified in the specification, the design scheme meets the safety requirements; Step 5: For the design scheme that meets the safety requirements, the sensitivity of the force response of the bored pile to the uncertainty factors is evaluated by using the statistically obtained standard deviations of deformation, global and shear force. If the standard deviation is smaller, it means that the force response of the bored pile is less sensitive to the change of the uncertainty factors, that is, the corresponding design scheme is more robust; Step 6: Repeat steps 1 to 5 for each alternative design scheme, select all the design schemes that meet the safety requirements, and calculate the corresponding cost; Step 7: In the four-dimensional space of cost, deformation standard deviation, bending moment standard deviation and shear force standard deviation, normalize each indicator and calculate the distance of each design scheme from the coordinate origin. The design corresponding to the point with the smallest distance is the optimal design that balances the cost and the robustness of each indicator.

2. The method for designing horizontally loaded bored piles to eliminate the influence of necking defects according to claim 1 is characterized in that: The uncertainties include the necking position, necking amount and saturated sand parameters.

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