CN108446413B - Method for optimally measuring pile diameter of grouting-formed club-footed pile - Google Patents
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Abstract
The invention relates to a method for optimally measuring the pile diameter of a grouting forming club-footed pile, which comprises the following steps: the method comprises the following steps: determining main factors influencing the uplift bearing capacity of the club-footed pile; step two: determining the optimal diameter expansion ratio of the grouting-formed club-footed pile; step three: determining a grouting forming pedestal pile bearing capacity BP neural network model; step four: determining parameters of a grouting forming pedestal pile bearing capacity BP neural network model; step five: determining a relation curve between the uplift bearing capacity and the pile diameter of the grouting-formed club-footed pile; step six: and (5) determining the pile diameter of the club-footed pile formed by grouting. The method can exactly simulate the loading mechanism of the pile, the obtained bearing capacity and the measured value have small error, scientific rationality basis is provided for pile diameter design, and then accurate pile diameter design can be carried out.
Description
Technical Field
The invention belongs to the field of optimization determination of the pile diameter of a grouting forming pedestal pile, and particularly relates to a determination method for optimizing the pile diameter based on a grouting forming pedestal pile uplift bearing capacity BP neural network prediction model.
Background
With the development of economic construction in China, land resources are increasingly tense, urban high-rise buildings are rapidly increased, in recent years, competition for land resources gradually shifts from the ground to the underground, development and utilization of underground spaces become important contents of current engineering design, particularly in the field of municipal engineering, and development and utilization of various underground facilities (urban rail transit, river-crossing tunnels, sunken squares, various water pool purification facilities and the like) become effective means for relieving the contradiction of land scarcity due to the fact that the difficulty of land acquisition and removal is continuously increased. However, in the coastal and river regions in the south of China, because the groundwater level is generally higher, the underground buildings are always subjected to larger groundwater buoyancy force in the construction or use stage, so that the anti-floating design becomes a problem which must be frequently considered in the development and design of the underground space. In general, anti-floating piles are often used to help anti-floating in anti-floating due to waterproof, geological and anchor durability considerations. The uplift pile is widely adopted due to high stability, easy construction and wide application range, so the uplift problem of the pile foundation becomes a new focus of the engineering field. The grouting forming club-footed pile is a pile type with high bearing efficiency, increases effective bearing area through the pile bottom enlarged head, improves pile foundation bearing capacity, and further obviously improves material utilization efficiency, so that the improvement of the uplift resistance through the grouting forming club-footed pile becomes one of effective schemes for solving the problem of pile foundation uplift resistance, and how to accurately design the pile diameter of the grouting forming club-footed pile has important engineering application value.
However, because the factors influencing the bearing capacity of the grouting forming pedestal pile are many and unstable, how to reasonably design the pile diameter and accurately determine the bearing capacity of the pile and give full play to the technical and economic benefits of the pile foundation is always a very concerned problem for engineering design constructors. The bearing capacity problem of the pile is not well solved all the time due to the influence of various factors such as engineering geological conditions, complexity of interaction mechanism between the pile and soil around the pile and the like, so that the design of the pile diameter is lack of rationality. Design calculation of the uplift pile has no clear regulation in each specification, and designers often calculate according to experience and understanding, so that the design results of different personnel are very different.
The design and calculation of the current uplift pile mainly depends on the design experience of designers, and numerical calculation methods such as a limit balance theory, a slip field theory, a pile-soil combined action theory, a finite element and the like are adopted to calculate the bearing capacity of a single pile, but the methods have limitations and cannot accurately simulate the loading mechanism of the pile, so that the obtained bearing capacity has a certain error with actual measurement, and the design of the pile diameter lacks a scientific rationality basis. How to establish a corresponding correlation between the pile diameter and the bearing capacity and further accurately design the pile diameter becomes a great problem faced by designers at present.
Disclosure of Invention
Aiming at the problems that the traditional design method cannot exactly simulate the pile loading mechanism, the obtained bearing capacity has a certain error with the actual measurement, and the accurate pile diameter design cannot be carried out, the patent provides a new method for optimizing and measuring the pile diameter of the slip casting club-footed pile, namely a method for predicting the bearing capacity of the slip casting club-footed pile and optimizing the pile diameter design by using BP neural network modeling.
A method for optimizing and measuring the pile diameter of a slip casting pedestal pile specifically comprises the following steps:
the method comprises the following steps: determining main factors influencing the uplift bearing capacity of the club-footed pile;
step two: determining the optimal diameter expansion ratio of the grouting-formed club-footed pile;
step three: determining a grouting forming pedestal pile bearing capacity BP neural network model;
step four: determining parameters of a grouting forming pedestal pile bearing capacity BP neural network model;
step five: determining a relation curve between the uplift bearing capacity and the pile diameter of the grouting-formed club-footed pile;
step six: and (5) determining the pile diameter of the club-footed pile formed by grouting.
Further, the main factor influencing the uplift bearing capacity of the club-footed pile in the first step is soil layer liquidity index ILWeighted average of effective internal friction angles of pile side soil
Deformation modulus E of soil layer of diameter-expanded partSThe pile length l, the pile diameter D of the non-expanded bottom part, the expanded bottom height h, the ratio D/D of the pile diameter of the expanded bottom part to the pile diameter of the non-expanded bottom part and the expansion angle beta of the diameter gradual change section at the upper part of the expanded head; D/D is represented by λ.
Further, the optimal diameter ratio of the club-footed pile formed by grouting in the second step is determined by the following formula,
where ρ istFor the diameter expansion ratio lambdaThe increase rate of the single pile limit uplift bearing capacity corresponding to t is larger than the increase rate of the single pile limit uplift bearing capacity corresponding to the expansion ratio lambda being t-0.2; t istThe expansion ratio lambda is equal to t and corresponds to the ultimate uplift bearing capacity of the single pile; t ist-0.2The expansion ratio lambda is t-0.2 corresponding to the ultimate uplift bearing capacity of the single pile; when the improvement efficiency of the ultimate uplift bearing capacity of the single pile reaches the maximum value, the corresponding expansion ratio is the optimal expansion ratio lambda'.
Further, the step three BP neural network structure model is composed of an input layer, a hidden layer and an output layer.
Further, the input layer comprises 8 nodes and is formed by pile length vectors [ l1,l2,Λ,ln]Pile diameter vector group [ d ] of non-expanded bottom part1,d2,Λ,dn]The set of height vectors [ h ] of the bottom extension1,h2,Λ,hn]The ratio vector group [ lambda ] of the pile diameter of the expanded bottom part and the pile diameter of the non-expanded bottom part1,λ2,Λ,λn]Soil layer liquidity index vector group [ I ]L1,IL2,Λ,ILn]Pile side soil effective internal friction angle weighted average value vector group
Deformation modulus vector group [ E ] of soil layer of diameter-expanding parts1,Es2,Λ,Esn]And an expansion angle vector group [ beta ] of the diameter gradual change section at the upper part of the expansion head1,β2,Λ,βn]Eight factors represent; the hidden layer is a single hidden layer; the number of output layer units is 1, and the uplift bearing capacity vector group of the club-footed pile is formed by grouting
Represents; the weight and threshold from the input layer to the hidden layer are wjkAnd thetajkThe weight and threshold from the hidden layer to the output layer are vkjAnd gammakt。
Further, the method for determining parameters of the step four BP neural network model specifically includes:
(1) trial algorithm for determining hidden layer neuron node number
Firstly, determining a hidden layer neuron node number range [12, 22] according to [2n-4, 2n +6] (n is the number of influencing factors); inputting the sample data into a trial algorithm training program compiled in Matlab, and performing trial calculation on the node number [12, 22] of the neuron in the hidden layer; selecting the hidden layer neuron node number corresponding to the minimum mean square error and convergence step number as the hidden layer neuron node number of the final network;
(2) determination of weight and threshold of BP artificial neural network
1) The number of samples is determined according to N ≧ 2N, and the numbers of training samples and test samples are determined by formulas (2) and (3):
n-is the total number of samples; t is1-the number of training samples; t is2-the number of samples examined; []Representing a rounding operation;
2) initializing a weight value and a threshold value by a random value in a (0,1) interval, then carrying out normalization processing on training sample data, transmitting the training sample data to a hidden layer neuron through a formula (4), and outputting the hidden layer neuron according to a formula (5):
bk＝f(S(k))＝1/(1+e-S(k))(k＝1,2,Λ,p) (5)
wherein, PjIs an input vector group, j is the number of elements in the input vector group, and k is the number of hidden layer units;
3) the hidden layer neuron output value is transmitted to the output layer neuron through a formula (6), and the output layer neuron outputs according to a formula (7):
4) calculating the network error e according to equation (8):
wherein t is the number of elements in the output vector group;
when the global error e of the network is less than 0.0006, the accuracy requirement is met, and the network training is terminated; when the network error e is more than or equal to 0.0006, the accuracy requirement is not met, and the weight and the threshold of the network need to be corrected according to the following steps 5) and 6);
5) according to the desired output TUKtAnd network real output
Calculating the correction error d of the neurons of the output layer using equation (9)t：
The corrected error ek for the hidden layer neurons is calculated according to equation (10):
6) correcting the connection weight v from the hidden layer to the output layer according to the formulas (11) and (12)ktAnd threshold gamma of neurons in the output layerktWherein alpha is learning rate, 0 < alpha < 1
vkt(i+1)＝vkt(i)+α·dt·bk(k＝1,2,Λ,p；t＝1,2,Λ,n) (11)
γkt(i+1)＝γkt(i)+α·dt(t＝1,2,Λ,n) (12)
Correcting the connection weight W from the input layer to the hidden layer according to the formulas (13) and (14)jkAnd threshold θ for hidden layer neuronsjkWherein beta is learning rate, beta is more than 0 and less than 1
wjk(i+1)＝wjk(i)+β·ek·Pj(j＝1,2,Λ,n；k＝1,2,Λ,p) (13)
θjk(i+1)＝θjk(i)+β·ek(k＝1,2,Λ,p) (14)
7) Randomly selecting the next learning mode, returning to the step 3) and continuing training until the network error e meets the precision requirement, terminating the network training, and determining the weight and the threshold of the neural network;
(3) programming of neural network programs
And determining a BP neural network model according to the above, and compiling a grouting forming pedestal pile pulling-resistant bearing capacity neural network prediction program by using a Matlab neural network tool box.
Further, the method for determining the relation curve between the uplift bearing capacity and the pile diameter of the club-footed pile formed by grouting in the fifth step specifically comprises the following steps:
determining soil layer property parameters through on-site geological condition investigation; according to research results of bearing characteristics of the pedestal pile and design regulations of a pile foundation in building foundation design Specifications (GB50007-2011), determining the length l of the pile, the height h of the pedestal pile which is 0.6D is 1.2D, the ratio lambda' of the diameter of the pedestal part to the diameter of the non-pedestal part and the expansion angle beta of a diameter transition section at the upper part of the expansion head which is 90 degrees; preliminarily designing the pile diameter d' of the non-expanded bottom part according to building foundation basic design specifications (GB50007-2011), inputting a trained neural network prediction model to predict the uplift bearing capacity, and selecting a reasonable interval according to the error between the predicted value and the design value of the uplift bearing capacity
Taking values (d ' -10 mu, lambda, d ' -mu, d ') in the d ' neighborhood of the preliminary design value of the pile diameter of the non-expanded bottom part '+ mu, Λ, d' +10 mu), inputting the trained neural network prediction model to predict the uplift bearing capacity, and drawing a relation curve between the uplift bearing capacity and the uplift bearing capacity of the grouting-formed pedestal pile according to the relation between the uplift bearing capacity output by the neural network prediction model and the pile diameter of the non-pedestal part.
Further, determining a non-expanded-base part pile diameter D corresponding to the designed value of the uplift bearing capacity of the grouting-formed club-footed pile by using a linear interpolation method, and determining a club-footed part pile diameter D according to the non-expanded-base part pile diameter D and the optimal expansion ratio lambda' of the grouting-formed club-footed pile:
D＝λ′d (16)。
further, the linear interpolation method comprises the following specific steps:
(1) according to the design value of the pulling-resistant bearing capacity of the grouting-formed club-footed pile determined by the curve chart drawn in the step five, determining an interval [ d '+ k mu, d' + (k +1) mu ] (k is 0,1,2,3,4,5,6,7,8 and 9) where the corresponding pile diameter d of the non-club-footed part is located;
(2) determining a linear equation of the pulling resistance bearing capacity corresponding to the curve in the interval [ d '+ k mu, d' + (k +1) mu ] (k is 0,1,2,3,4,5,6,7,8,9) according to the formula (15),
(3) designed value T of uplift bearing capacity of grouting-formed club-footed pileUKSubstituting into formula (15) to calculate corresponding non-bottom-expanding part pile diameter d, inputting the non-bottom-expanding part pile diameter d into neural network prediction model to obtain its predicted value of uplift bearing capacity, and using formula
Calculating the relative error between the pile diameter d and the design value, and if the error is within 5 percent, the pile diameter d of the non-expanded bottom part is consistent with the design valueMeasuring the requirement; and if the error is less than 0 or more than 5 percent, the pile diameter d of the non-expanded-base part does not meet the design requirement, properly adjusting the pile diameter d, repeatedly inputting the error into the neural network prediction model for error detection until the error meets the requirement, and determining the pile diameter d of the non-expanded-base part of the grouting forming expanded-base pile.
The principle of the invention is as follows:
principle one is as follows:
the MATLAB training program based on the trial algorithm was as follows:
principle two:
input data normalization pre-processing and output data post-processing
The input data is normalized using equation (17) and distributed over the interval [0,1 ].
Wherein,
the normalized data is obtained; x is original data; xmax is the maximum value of x; x is the number ofminIs the minimum value of x.
And (4) adopting a scaling reduction mode for pile diameter data with high similarity, and dividing all the pile diameter data by 1000 to ensure that all the pile diameter data are distributed between [0,1 ].
And (3) performing inverse normalization processing on the output data of the neural network by adopting a formula (18):
x＝x′×(xmax-xmin)+xmin (18)
principle three:
BP neural network prediction program
Defining an input sample as
Defining a target vector as
Compared with the prior art, the invention establishes the grouting forming pedestal pile uplift bearing capacity BP neural network prediction model, trains the BP neural network prediction model by utilizing field test actual measurement data, combines the advantages of self-adaption, high precision, strong practicability and the like of the BP neural network, establishes the prediction model with a prediction result more consistent with the actual bearing capacity, finally draws a relation curve of the grouting forming pedestal pile diameter and the uplift bearing capacity through the BP neural network prediction model, and further determines the pile diameter d of the non-pedestal part of the grouting forming pedestal pile by utilizing a function approximation method, realizes the optimal design of the pile diameter of the grouting forming pedestal pile, and provides a practical grouting forming pedestal pile design method for designers. The method can exactly simulate the loading mechanism of the pile, the obtained bearing capacity and the measured value have small error, scientific rationality basis is provided for pile diameter design, and then accurate pile diameter design can be carried out.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph showing the relationship between the increase rate of the ultimate uplift bearing capacity and the diameter expansion ratio of a single pile in example 1;
FIG. 3 is a diagram of a BP neural network model according to example 1;
FIG. 4 is a calculation flowchart of the BP neural network according to embodiment 1;
FIG. 5 is a graph showing the relationship between the pullout resistance and the diameter of a pile under non-expanded base in example 1;
FIG. 6 is a graph showing the relationship between the pullout resistance and the diameter of a non-pedestal pile in example 2.
Detailed Description
The present invention will be described in further detail with reference to the following embodiments and the accompanying drawings.
Example 1
A certain pile foundation is located in a certain area A, and the anti-pulling engineering pile is designed into a slip casting club-footed pile.
The method comprises the following steps: determining main factors influencing uplift bearing capacity of club-footed pile
According to the technical Specifications of building pile foundations (JGJ94-2008), the technical Specifications of building pile foundations (JGJ106-2014) and the practical engineering experience of the slip casting type club-footed pile, on the basis of researching the uplift bearing capacity characteristics and the load transfer mechanism of the slip casting type club-footed pile, determining the influence factor of the uplift bearing capacity of the slip casting type club-footed pile, namely the soil layer liquidity index ILWeighted average of effective internal friction angles of pile side soil
Deformation modulus E of soil layer of diameter-expanded partSEight factors, namely the pile length l, the pile diameter D of the non-expanded bottom part, the expanded bottom height h, the ratio D/D (represented by lambda) of the pile diameter of the expanded bottom part to the pile diameter of the non-expanded bottom part and the expansion angle beta of the diameter gradual change section at the upper part of the expanded head, are main factors influencing the pulling-resistant bearing capacity of the grouting-formed expanded bottom pile.
Step two: determination of optimal expanding ratio of grouting-formed club-footed pile
According to the single-pile vertical pulling-resistant static load test regulation in the building foundation pile detection technical specification (JGJ106-2014), the single-pile ultimate pulling-resistant bearing capacity of the grouting pedestal pile in the same geological condition area is measured, the pile length l is 37m, the pile diameter d of a non-pedestal part is 300mm, the pedestal height h is 360mm, the diameter expansion ratios are 1, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8 and 3.0 respectively, and the increase rate rho of the single-pile ultimate pulling-resistant bearing capacity of the grouting pedestal pile is calculated according to the formula (1)tThe results are shown in Table 1.
TABLE 1 growth rate of ultimate uplift bearing capacity of single pile
A large number of test results show that the increase rate of the ultimate uplift bearing capacity of the single pile and the diameter ratio of the ultimate uplift bearing capacity of the single pile tend to increase first and then decrease (see fig. 2), so that when the improvement efficiency of the ultimate uplift bearing capacity of the single pile reaches the maximum value, the corresponding diameter expansion ratio is the optimal diameter expansion ratio λ ', and the optimal diameter expansion ratio λ' is 2 as can be known from table 1.
Step three: determination of grouting forming pedestal pile bearing capacity BP neural network structure model
According to the modeling principle of the BP neural network prediction method, the BP neural network model is determined to be composed of 3 parts including an input layer, a hidden layer and an output layer, the input layer is finally determined to be 8 nodes, and the nodes are formed by pile length vectors [ l ]1,l2,Λ,ln]Pile diameter vector group [ d ] of non-expanded bottom part1,d2,Λ,dn]The set of height vectors [ h ] of the bottom extension1,h2,Λ,hn]The ratio vector group [ lambda ] of the pile diameter of the expanded bottom part and the pile diameter of the non-expanded bottom part1,λ2,Λ,λn]Soil layer liquidity index vector group [ I ]L1,IL2,Λ,ILn]Pile side soil effective internal friction angle weighted average value vector group
Deformation modulus vector group [ E ] of soil layer of diameter-expanding parts1,Es2,Λ,Esn]And an expansion angle vector group [ beta ] of the diameter gradual change section at the upper part of the expansion head1,β2,Λ,βn]Eight factors represent; the hidden layer is a single hidden layer; the number of output layer units is 1, and the uplift bearing capacity vector group of the club-footed pile is formed by grouting
Represents; the weight and threshold from the input layer to the hidden layer are wjkAnd thetajkThe weight and threshold from the hidden layer to the output layer are vkjAnd gammakt. The established BP neural network model is shown in figure 3.
Step four: determination of grouting forming pedestal pile bearing capacity BP neural network model parameters
And determining the number of samples to be 26 according to N ≧ 2N, determining the number of training samples to be 15 and the number of test samples to be 11 according to formulas (2) and (3). The sample data is shown in Table 2.
TABLE 2 sample data
The principle is utilized to carry out normalization processing on two pairs of training sample data, a trial algorithm training program is input to train the node numbers of different hidden layer neurons in the range of [12, 22], and the network outputs the corresponding network mean square error and convergence step number, and the specific values are listed in Table 3.
TABLE 3 error and Convergence step counts for different hidden layer nodes
By analyzing two factors of mean square error and convergence step number, the number of the nodes of the optimal hidden layer of the BP neural network model of the pile foundation engineering is 19.
And substituting the sample data subjected to normalization processing into the grouting forming pedestal pile pulling resistance bearing capacity neural network prediction program of the principle III for training and checking, and continuously optimizing the weight and the threshold value through cyclic learning training to establish the high-precision grouting forming pedestal pile pulling resistance bearing capacity neural network prediction program.
Step five: determination of relation curve of uplift bearing capacity and pile diameter of grouting forming pedestal pile
Through the investigation of the site geological conditions, the soil layer liquidity index I is determinedL0.97, weighted average of effective internal friction angle of pile side soil
Deformation modulus E of soil layer of diameter-expanded partS68 MPa; according to research results of bearing characteristics of a large number of pedestal piles and design regulations of pile foundations in building foundation design specifications (GB50007-2011), reasonable pile length l is 37m, pedestal height h is 0.6D is 1.2D, the ratio lambda' of the pile diameter of a pedestal part to the pile diameter of a non-pedestal part is 2, and an expansion angle beta of an upper diameter transition section of an expansion head is 90 degrees.
According to basic design specifications of building foundations (GB50007-2011), the diameter d 'of a non-bottom-expanding part pile is preliminarily designed to be 600mm, a trained neural network prediction model is input to obtain a predicted value of the uplift bearing capacity to be 1900kN, the error of the predicted value is calculated to be-8% according to the designed value of the uplift bearing capacity to be-8%, values are taken in the right neighborhood of the preliminary value d' of the diameter of the non-bottom-expanding part pile at the interval of 30mm (630, 660,690,720,750,780,810,840,870,900), and the trained neural network prediction model is input to predict the uplift bearing capacity, and the result is shown in a table 4.
TABLE 4 predicted values of plucking resistance
And drawing a relation curve of the non-expanded-base pile diameter and the anti-pulling bearing capacity of the slip casting expanded-base pile according to the relation of the anti-pulling bearing capacity output by the neural network prediction model and the non-expanded-base pile diameter, and the figure is 5.
Step six: determination of pile diameter of grouting forming club-footed pile
(1) And determining an interval [690,720] where the corresponding non-expanded-base part pile diameter d is located according to the design value of the uplift bearing capacity of the grouting-formed expanded-base pile determined by the curve chart drawn in the step five.
(2) Determining a linear equation of the pullout resistance bearing capacity corresponding to the curve in the interval (690,720) (k is 0,1,2,3,4,5,6,7,8,9) according to equation (15):
y＝6.743x-2124.2
(3) designed value T of uplift bearing capacity of grouting-formed club-footed pileUKSubstituting the formula into the formula to calculate the corresponding pile diameter d of the non-expanded bottom part which is 715mm, inputting the pile diameter d of the non-expanded bottom part which is 715mm into a neural network prediction model to obtain the predicted value of the pulling resistance bearing capacity of the neural network prediction model which is 2714.2kN, and utilizing the formula
The relative error of the pile diameter d of the non-expanded-base part and the design value is calculated to be 0.53 percent and less than 5 percent, and the pile diameter d of the non-expanded-base part is 715mm and meets the design requirement.
(4) According to the non-expanded-base part pile diameter D and the optimal expansion ratio lambda' of the grouting-formed expanded-base pile, the pile diameter D of the expanded-base part is determined to be 1430mm by using the formula (16).
Example 2
A pile foundation is located in a certain area B, and a grouting forming club-footed pile is adopted for the design of the uplift engineering pile.
The method comprises the following steps: determining main factors influencing uplift bearing capacity of club-footed pile
According to the technical Specifications of building pile foundations (JGJ94-2008), the technical Specifications of building pile foundations (JGJ106-2014) and the practical engineering experience of the slip casting type club-footed pile, on the basis of researching the uplift bearing capacity characteristics and the load transfer mechanism of the slip casting type club-footed pile, determining the influence factor of the uplift bearing capacity of the slip casting type club-footed pile, namely the soil layer liquidity index ILWeighted average of effective internal friction angles of pile side soil
Deformation modulus E of soil layer of diameter-expanded partSEight factors, namely the pile length l, the pile diameter D of the non-expanded bottom part, the expanded bottom height h, the ratio D/D (represented by lambda) of the pile diameter of the expanded bottom part to the pile diameter of the non-expanded bottom part and the expansion angle beta of the diameter gradual change section at the upper part of the expanded head, are main factors influencing the pulling-resistant bearing capacity of the grouting-formed expanded bottom pile.
Step two: determination of optimal expanding ratio of grouting-formed club-footed pile
According to construction foundation pile detectionThe vertical pulling-resistant static load test procedure of single pile in technical specification (JGJ106-2014) measures the ultimate pulling-resistant bearing capacity of single pile of the grouting pedestal pile in the same geological condition area, wherein the length l of the pile is 25m, the diameter d of the part without pedestal is 300mm, the height h of pedestal is 360mm, the diameters of the pedestal piles are respectively 1, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8 and 3.0, and the growth rate rho of the ultimate pulling-resistant bearing capacity of the grouting pedestal pile is calculated according to the formula (1)tThe results are shown in Table 5.
TABLE 5 growth rate of ultimate uplift bearing capacity of single pile
A large number of test results show that the increase rate of the ultimate uplift bearing capacity of the single pile and the diameter ratio of the ultimate uplift bearing capacity of the single pile tend to increase first and then decrease (see fig. 2), so that when the improvement efficiency of the ultimate uplift bearing capacity of the single pile reaches the maximum value, the corresponding diameter expansion ratio is the optimal diameter expansion ratio λ ', and the optimal diameter expansion ratio λ' is 2 as can be known from table 1.
Step three: determination of grouting forming pedestal pile bearing capacity BP neural network structure model
According to the modeling principle of the BP neural network prediction method, the BP neural network model is determined to be composed of 3 parts including an input layer, a hidden layer and an output layer, the input layer is finally determined to be 8 nodes, and the nodes are formed by pile length vectors [ l ]1,l2,Λ,ln]Pile diameter vector group [ d ] of non-expanded bottom part1,d2,Λ,dn]The set of height vectors [ h ] of the bottom extension1,h2,Λ,hn]The ratio vector group [ lambda ] of the pile diameter of the expanded bottom part and the pile diameter of the non-expanded bottom part1,λ2,Λ,λn]Soil layer liquidity index vector group [ I ]L1,IL2,Λ,ILn]Pile side soil effective internal friction angle weighted average value vector group
Deformation modulus vector group [ E ] of soil layer of diameter-expanding parts1,Es2,Λ,Esn]And an expansion angle vector group [ beta ] of the diameter gradual change section at the upper part of the expansion head1,β2,Λ,βn]Eight factors represent; the hidden layer is a single hidden layer; the number of output layer units is 1, and the uplift bearing capacity vector group of the club-footed pile is formed by grouting
Represents; the weight and threshold from the input layer to the hidden layer are wjkAnd thetajkThe weight and threshold from the hidden layer to the output layer are vkjAnd gammakt. The established BP neural network model is shown in figure 3.
Step four: determination of grouting forming pedestal pile bearing capacity BP neural network model parameters
And determining the number of samples to be 26 according to N ≧ 2N, determining the number of training samples to be 15 and the number of test samples to be 11 according to formulas (2) and (3). The sample data is shown in Table 6.
TABLE 6 sample data
The principle is utilized to carry out normalization processing on two pairs of training sample data, a trial algorithm training program is input to train the node numbers of different hidden layer neurons in the range of [12, 22], and the network outputs the corresponding network mean square error and convergence step number, and the specific values are listed in Table 7.
TABLE 7 error and Convergence step counts for different hidden layer nodes
By analyzing two factors of mean square error and convergence step number, the number of the nodes of the optimal hidden layer of the BP neural network model of the pile foundation engineering is 19.
And substituting the sample data subjected to normalization processing into the grouting forming pedestal pile pulling resistance bearing capacity neural network prediction program of the principle III for training and checking, and continuously optimizing the weight and the threshold value through cyclic learning training to establish the high-precision grouting forming pedestal pile pulling resistance bearing capacity neural network prediction program.
Step five: determination of relation curve of uplift bearing capacity and pile diameter of grouting forming pedestal pile
Through the investigation of the site geological conditions, the soil layer liquidity index I is determinedL0.97, weighted average of effective internal friction angle of pile side soil
Deformation modulus E of soil layer of diameter-expanded partS68 MPa; according to research results of bearing characteristics of a large number of pedestal piles and design regulations of pile foundations in building foundation design specifications (GB50007-2011), reasonable pile length l is 20m, pedestal height h is 0.6D is 1.2D, the ratio lambda' of the pile diameter of a pedestal part to the pile diameter of a non-pedestal part is 2, and an expansion angle beta of an upper diameter transition section of an expansion head is 90 degrees.
According to the basic design specification of building foundation (GB50007-2011), the pile diameter d 'of the non-expanded bottom part is preliminarily designed to be 300mm, a trained neural network prediction model is input to obtain the predicted value of the uplift bearing capacity to be 2040kN, the error of the predicted value is-7.3% according to the designed value of the uplift bearing capacity 2200kN, the value is taken in the right neighborhood of the preliminary designed value d' of the pile diameter of the non-expanded bottom part at the interval of 30mm (330, 360,390,420,450,480,510,540,570 and 600), and the trained neural network prediction model is input to predict the uplift bearing capacity, and the result is shown in a table 8.
TABLE 8 predicted values of plucking resistance
And drawing a relation curve of the non-expanded-base pile diameter and the anti-pulling bearing capacity of the slip casting expanded-base pile according to the relation of the anti-pulling bearing capacity output by the neural network prediction model and the non-expanded-base pile diameter, and the figure is 6.
Step six: determination of pile diameter of grouting forming club-footed pile
(1) And determining an interval [390,420] where the corresponding non-expanded-base part pile diameter d is located according to the design value of the uplift bearing capacity of the grouting-formed expanded-base pile determined by the curve chart drawn in the step five.
(2) Determining a linear equation of the pullout resistance bearing capacity corresponding to the curve in the interval (390,420) (k is 0,1,2,3,4,5,6,7,8,9) according to equation (15):
y＝2.67x+1098.6
(4) designed value T of uplift bearing capacity of grouting-formed club-footed pileUKSubstituting the formula into the formula to calculate the corresponding pile diameter d of the non-expanded bottom part which is 413mm, inputting the pile diameter d of the non-expanded bottom part which is 413mm into a neural network prediction model to obtain the predicted value of the pulling resistance bearing capacity of the neural network prediction model which is 2281kN, and utilizing the formula
The relative error of the pile diameter d of the non-expanded bottom part and the design value is calculated to be 3.68 percent and less than 5 percent, and the pile diameter d of the non-expanded bottom part meets the design requirement when being 413 mm.
(5) According to the non-enlarged-base part pile diameter D and the optimal diameter ratio lambda' of the grouting-formed enlarged-base pile, the diameter D of the enlarged-base part is determined to be 2 x 413 x 826mm by using the formula (16).
Claims (1)
1. An optimal measurement method for the pile diameter of a grouting forming club-footed pile is characterized by comprising the following steps:
the method comprises the following steps: determining main factors influencing the uplift bearing capacity of the club-footed pile;
step two: determining the optimal diameter expansion ratio of the grouting-formed club-footed pile;
step three: determining a grouting forming pedestal pile bearing capacity BP neural network model;
step four: determining parameters of a grouting forming pedestal pile bearing capacity BP neural network model;
step five: determining a relation curve between the uplift bearing capacity and the pile diameter of the grouting-formed club-footed pile;
step six: determining the pile diameter of the grouting forming club-footed pile;
the main factor influencing the uplift bearing capacity of the club-footed pile in the first step is soil layer liquidity index ILWeighted average of effective internal friction angles of pile side soil
Deformation modulus E of soil layer of diameter-expanded partSThe pile length l, the pile diameter D of the non-expanded bottom part, the expanded bottom height h, the ratio D/D of the pile diameter of the expanded bottom part to the pile diameter of the non-expanded bottom part and the expansion angle beta of the diameter gradual change section at the upper part of the expanded head; D/D is represented by lambda;
the optimal diameter ratio of the club-footed pile formed by grouting in the second step is determined by the following formula,
where ρ istThe expansion ratio lambda is t, the corresponding single-pile ultimate uplift bearing capacity is compared with the expansion ratio lambda is t-0.2, and the corresponding single-pile ultimate uplift bearing capacity is increased; t istThe expansion ratio lambda is equal to t and corresponds to the ultimate uplift bearing capacity of the single pile; t ist-0.2The expansion ratio lambda is t-0.2 corresponding to the ultimate uplift bearing capacity of the single pile; when the single-pile ultimate uplift bearing capacity improvement efficiency reaches the maximum value, the corresponding expansion ratio is the optimal expansion ratio lambda';
the step three BP neural network model consists of an input layer, a hidden layer and an output layer;
the input layer is 8 nodes and is formed by a pile length vector group [ l1,l2,…,ln]Pile diameter vector group [ d ] of non-expanded bottom part1,d2,…,dn]The set of height vectors [ h ] of the bottom extension1,h2,…,hn]The ratio vector group [ lambda ] of the pile diameter of the expanded bottom part and the pile diameter of the non-expanded bottom part1,λ2,…,λn]Soil layer liquidity index vector group [ I ]L1,IL2,…,ILn]Pile side soil effective internal friction angle weighted average value vector group
Deformation modulus vector group [ E ] of soil layer of diameter-expanding parts1,Es2,…,Esn]And an expansion angle vector group [ beta ] of the diameter gradual change section at the upper part of the expansion head1,β2,…,βn]Eight factors represent; the hidden layer is a single hidden layer; the number of output layer units is 1, and the uplift bearing capacity vector group of the club-footed pile is formed by grouting
Represents; the weight and threshold from the input layer to the hidden layer are wjkAnd thetajkThe weight and threshold from the hidden layer to the output layer are vkjAnd gammakt；
The method for determining the model parameters of the BP neural network in the fourth step specifically comprises the following steps:
(1) trial algorithm for determining hidden layer neuron node number
Firstly, determining the node number range [12, 22] of the hidden layer neurons; inputting the sample data into a trial algorithm training program compiled in Matlab, and performing trial calculation on the node number [12, 22] of the neuron in the hidden layer; selecting the hidden layer neuron node number corresponding to the minimum mean square error and convergence step number as the hidden layer neuron node number of the final network;
(2) determination of weight and threshold of BP artificial neural network
1) The number of samples is determined according to N ≧ 2n, and the numbers of training samples and test samples are determined by formulas (2) and (3):
n isA total number of samples; t is1The number of training samples; t is2The number of samples tested; []Representing a rounding operation;
2) initializing a weight value and a threshold value by a random value in a (0,1) interval, then carrying out normalization processing on training sample data, transmitting the training sample data to a hidden layer neuron through a formula (4), and outputting the hidden layer neuron according to a formula (5):
bk＝f(S(k))＝1/(1+e-S(k))(k＝1,2,…,p) (5)
wherein, PjIs an input vector group, j is the number of elements in the input vector group, and k is the number of hidden layer units;
3) the hidden layer neuron output value is transmitted to the output layer neuron through a formula (6), and the output layer neuron outputs according to a formula (7):
4) calculating the network error e according to equation (8):
wherein t is the number of elements in the output vector group;
when the network error e is less than 0.0006, meeting the precision requirement and terminating the network training; when the network error e is more than or equal to 0.0006, the accuracy requirement is not met, and the weight and the threshold of the network need to be corrected according to the following steps 5) and 6);
5) according to the desired output TUKtAnd network real output
Calculating the correction error d of the neurons of the output layer using equation (9)t：
Computing the corrected error e for hidden layer neurons from equation (10)k：
6) Correcting the connection weight v from the hidden layer to the output layer according to the formulas (11) and (12)ktAnd threshold gamma of neurons in the output layerktWherein alpha is learning rate, 0 < alpha < 1
vkt(i+1)＝vkt(i)+α·dt·bk(k＝1,2,…,p；t＝1,2,…,n) (11)
γkt(i+1)＝γkt(i)+α·dt(t＝1,2,…,n) (12)
Correcting the connection weight W from the input layer to the hidden layer according to the formulas (13) and (14)jkAnd threshold θ for hidden layer neuronsjkWherein beta is learning rate, beta is more than 0 and less than 1
wjk(i+1)＝wjk(i)+β·ek·Pj(j＝1,2,…,n；k＝1,2,…,p) (13)
θjk(i+1)＝θjk(i)+β·ek(k＝1,2,…,p) (14)
7) Randomly selecting the next learning mode, returning to the step 3) and continuing training until the network error e meets the precision requirement, terminating the network training, and determining the weight and the threshold of the neural network;
(3) programming of neural network programs
According to the determined BP neural network model, compiling a grouting forming pedestal pile pulling-resistant bearing capacity neural network prediction program by using a Matlab neural network tool kit;
the method for determining the relation curve between the uplift bearing capacity and the pile diameter of the club-footed pile formed by grouting in the step five specifically comprises the following steps:
determining soil layer property parameters through on-site geological condition investigation; according to research results of bearing characteristics of the pedestal pile and design regulations of a pile foundation in building foundation design Specifications (GB50007-2011), determining the length l of the pile, the height h of the pedestal pile which is 0.6D is 1.2D, the ratio lambda' of the diameter of the pedestal part to the diameter of the non-pedestal part and the expansion angle beta of a diameter transition section at the upper part of the expansion head which is 90 degrees; preliminarily designing the pile diameter d' of the non-expanded bottom part according to building foundation basic design specifications (GB50007-2011), inputting a trained neural network prediction model to predict the uplift bearing capacity, and selecting a reasonable interval according to the error between the predicted value and the design value of the uplift bearing capacity
Taking values (d '-10 mu, …, d' -mu, d ', d' + mu, …, d '+ 10 mu) in the neighborhood of the preliminary design value d' of the pile diameter of the non-expanded bottom part, inputting a trained neural network prediction model to predict the uplift bearing capacity, and drawing a relation curve between the non-expanded bottom pile diameter and the uplift bearing capacity of the slip casting expanded bottom pile according to the relation between the uplift bearing capacity output by the neural network prediction model and the pile diameter of the non-expanded bottom part;
determining the pile diameter D of the non-expanded bottom part corresponding to the design value of the uplift bearing capacity of the grouting-formed expanded-bottom pile by using a linear interpolation method, and determining the pile diameter D of the expanded-bottom part according to the pile diameter D of the non-expanded-bottom part of the grouting-formed expanded-bottom pile and the optimal expansion ratio lambda':
D＝λ′d (16)；
the linear interpolation method comprises the following specific steps:
(1) according to the design value of the pulling-resistant bearing capacity of the grouting-formed club-footed pile determined by the curve chart drawn in the step five, determining an interval [ d '+ k mu, d' + (k +1) mu ] (k is 0,1,2,3,4,5,6,7,8 and 9) where the corresponding pile diameter d of the non-club-footed part is located;
(2) determining a linear equation of the pulling resistance bearing capacity corresponding to the curve in the interval [ d '+ k mu, d' + (k +1) mu ] (k is 0,1,2,3,4,5,6,7,8,9) according to the formula (15),
(3) designed value T of uplift bearing capacity of grouting-formed club-footed pileUKSubstituting into formula (15) to calculate corresponding non-bottom-expanding part pile diameter d, inputting the non-bottom-expanding part pile diameter d into neural network prediction model to obtain its predicted value of uplift bearing capacity, and using formula
Calculating the relative error between the pile diameter d and the design value, wherein if the error is within 5 percent, the pile diameter d of the non-expanded bottom part meets the design requirement; and if the error is less than 0 or more than 5 percent, the pile diameter d of the non-expanded-base part does not meet the design requirement, properly adjusting the pile diameter d, repeatedly inputting the error into the neural network prediction model for error detection until the error meets the requirement, and determining the pile diameter d of the non-expanded-base part of the grouting forming expanded-base pile.
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