Bayesian theory-based tubular pile vertical bearing capacity estimation method

Abstract

The invention belongs to the field of tubular pile bearing capacity evaluation, provides a Bayesian theory-based tubular pile vertical bearing capacity estimation method, and aims to improve the accuracy and reliability of tubular pile bearing capacity prediction. The method comprises the following steps: firstly, collecting related characteristic information of the tubular pile through field test and experimental data, wherein the related characteristic information comprises a pile body material, a pile length, soil layer properties and the like; then, constructing a prior distribution model of the tubular pile bearing capacity by utilizing the Bayesian theory, and forming posterior distribution by combining the model with the actually measured data updating model; and the vertical ultimate bearing capacity of the pipe pile is evaluated by analyzing the posterior distribution. According to the method, uncertainty factors are fully considered, errors possibly existing in a traditional method can be effectively reduced, and scientificity and practicability of bearing capacity evaluation are improved.

Description

Technical Field

[0001] The invention belongs to the field of pipe pile bearing capacity assessment, and in particular relates to a method for estimating the vertical bearing capacity of pipe piles based on Bayesian theory. Background Art

[0002] In engineering construction, pipe piles are an important form of foundation, and accurate assessment of their vertical ultimate bearing capacity is of great significance to ensure the safety and stability of the project. Traditional methods for assessing the vertical bearing capacity of pipe piles often rely on empirical formulas or single test data. They are easily affected by a variety of uncertain factors, such as the limited number of test piles, large discreteness of test data, irregular operations of on-site pile testers, reading errors of test equipment, etc., which lead to inaccurate assessment results. Bayesian statistics links the prior information, sample information, and overall information of statistical parameters, and its statistical results are closer to the actual values. In order to improve the scientificity and practicality of pipe pile bearing capacity assessment, a new assessment method is urgently needed. Summary of the invention

[0003] In order to solve the above technical problems, the present invention provides a method for estimating the vertical bearing capacity of pipe piles based on Bayesian theory to solve the problems in the prior art. The technical solution adopted by the present invention is:

[0004] A method for estimating the vertical bearing capacity of pipe piles based on Bayesian theory includes the following steps:

[0005] Step 1: Estimate the vertical bearing capacity of the pile based on experimental data and geological information;

[0006] Step 2: Use the Bayesian principle to construct a prior distribution model of the vertical bearing capacity of pipe piles;

[0007] Step 3: Combined with the estimated vertical bearing capacity of the pile, the Bayesian formula is used to update the model and form the posterior distribution;

[0008] Step 4: Conduct a posteriori probability evaluation on the model parameters in the Bayesian formula to assess the ultimate vertical bearing capacity of the pile.

[0009] Furthermore, the following formula is used to estimate the vertical bearing capacity of the pile:

[0010]

[0011] Where Q is the vertical bearing capacity of a single pile; i is the thickness of the i-th soil layer; d1 is the outer diameter of the pile; d2 is the inner diameter of the pile; q si is the average lateral friction of each soil layer at a certain site; q p is the average end resistance of the soil layer at the site end.

[0012] Furthermore, in step 2, let the ultimate bearing capacity Q be a random variable with a mean of Probability density function of the population sample The uncertain factor parameters are the average side friction, the average end resistance and the soil thickness R = {q si ,q p ,l i}, denoted as random parameters R1~R3, and its probability density function is assumed The prior probability distribution density function of is Its probability density function is:

[0013]

[0014] Among them, σ1, σ2 are standard deviations;

[0015] The mean and variance of the vertical bearing capacity of pipe piles are expressed as:

[0016]

[0017]

[0018] In the formula, and D(l i ) is the average soil layer l i The mean and variance of D(q si )and D(q p ) are the mean and variance of the average side friction of each soil layer and the average end resistance of the soil layer at the pile end, respectively.

[0019] Furthermore, in step 3, the Bayesian theory formula is:

[0020]

[0021] Among them, Q represents the data for estimating the vertical bearing capacity of the pile, R is the model parameter, P(Q) is the probability of the prior model distribution, P(Q|R) is the likelihood function, and P(R) is the marginal function;

[0022] Combined with the prior probability distribution, the Bayesian formula posterior probability density distribution formula is constructed:

[0023]

[0024] Furthermore, step 4 includes: selecting the model with the largest probability of posterior random variables as the final vertical bearing capacity model of the pile; calculating the average value of the model parameters as the inversion result of the random variable parameters; determining the three random parameters of the model {q si ,q p,l i}.

[0025] The present invention has the following beneficial effects: the present invention fully considers various uncertain factors that affect the bearing capacity of pipe piles, can effectively reduce the errors that may exist in traditional methods, and improve the scientificity and practicality of bearing capacity evaluation. Through the application of Bayesian theory, dynamic updating of bearing capacity and more accurate evaluation results can be achieved, providing a reliable basis for engineering design and construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a schematic diagram of the overall process of the present invention;

[0027] Figure 2 Schematic diagram of the process of estimating the bearing capacity of pipe piles based on Bayesian theory. DETAILED DESCRIPTION

[0028] The following will be combined with the embodiments of the present invention Figure 1-Figure 2 , the technical solutions in the embodiments of the present invention are described clearly and completely. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0029] The present invention aims to improve the accuracy and reliability of the prediction of pipe pile bearing capacity. The method first collects relevant characteristic information of pipe piles through field tests and experimental data, including pile body material, pile length, soil layer properties, etc. Then, the prior distribution model of pipe pile bearing capacity is constructed using Bayesian theory, and the model is updated in combination with the actual measured data to form a posterior distribution. By analyzing the posterior distribution, the vertical ultimate bearing capacity of the pipe pile is evaluated. This method fully considers the uncertainty factors, can effectively reduce the errors that may exist in traditional methods, and improve the scientificity and practicality of bearing capacity evaluation.

[0030] The present invention provides the following solutions:

[0031] Data collection, through field tests and experimental data to collect relevant characteristic information of pipe piles, including: the physical and mechanical properties of the pile body material, the length, diameter and wall thickness of the pipe pile, and the properties of the soil layer (such as soil type, density, moisture content, etc.).

[0032] Estimate the vertical bearing capacity of the pipe piles and calculate the estimated value of the ultimate bearing capacity of the pipe piles based on the empirical parameter method.

[0033] Construct a prior distribution model and use Bayesian theory to construct a prior distribution model of the vertical bearing capacity of pipe piles. Assume that the vertical ultimate bearing capacity of pipe piles can be represented by a probability density function. For example, the probability density function can select uniform distribution, normal distribution, gamma distribution, etc. as the prior distribution model.

[0034] Data updating and posterior distribution, combining the actual measured data (such as static load test results) and the ultimate bearing capacity of the piles obtained by experience, apply the Bayesian formula to update the model and construct the posterior distribution.

[0035] Evaluate the vertical bearing capacity and evaluate the ultimate vertical bearing capacity of the pile by analyzing the posterior distribution. The evaluation process includes calculating the expected value, variance and other statistical indicators of the posterior distribution to provide a scientific basis for the vertical bearing capacity of the pile.

[0036] The present invention fully considers the various uncertain factors that affect the bearing capacity of pipe piles, can effectively reduce the errors that may exist in traditional methods, and improve the scientificity and practicality of bearing capacity assessment. Through the application of Bayesian theory, dynamic updating of bearing capacity and more accurate assessment results can be achieved, providing a reliable basis for engineering design and construction.

[0037] Specifically, a method for estimating the vertical bearing capacity of pipe piles based on Bayesian theory includes the following steps:

[0038] Step 1: Based on experimental data and geological data, the vertical bearing capacity of the pipe pile is estimated by empirical calculation method. Specifically, the ultimate lateral friction resistance and pile end resistance of the pipe pile passing through each layer of soil are estimated according to the above preset data according to the empirical parameter method. Specifically, the empirical method finally obtains the estimated value of the theoretical vertical bearing capacity of the pipe pile, and the empirical formula is as follows:

[0039]

[0040] Where Q is the vertical bearing capacity of a single pile; i is the thickness of the i-th soil layer; d1 is the outer diameter of the pile; d2 is the inner diameter of the pile; q si is the average lateral friction of each soil layer at a certain site; q p is the average end resistance of the soil layer at the site end.

[0041] Step 2: Use the Bayesian principle to construct a prior distribution model of the vertical bearing capacity of pipe piles. The specific steps include:

[0042] In the empirical estimation formula in step 1, the average lateral friction resistance of the soil layer q si , the average end resistance of the end soil layer q p and soil layer thickness l i , the three factors can be considered independent of each other; assuming that the geometric dimensions of the piles vary very little, that is, the variability of the inner diameter and the outer diameter is small, they are not considered as random variables. The vertical bearing capacity of the pile is determined by the three random parameters {q si ,q p ,l i}Sure.

[0043] Due to many uncertain factors, the ultimate bearing capacity of the pile varies randomly. Let the ultimate bearing capacity (Q) be a random variable, and its mean is Probability density function of the population sample According to the calculation formula above, the uncertain factor parameters can be the average side friction resistance, the average end resistance and the soil layer thickness R = {q si ,q p ,l i}. The random parameters are R1~R3. Their probability density functions are assumed The prior probability distribution density function of is Its probability density function is:

[0044]

[0045] Among them, σ1, σ2 are standard deviations.

[0046] Suppose the mean of the random variable R is Probability density function of the population sample The probability density function with random parameters R1 to R3 is It can be uniformly distributed or Gaussian distributed. Here, it is assumed that it approximately obeys the normal distribution. The prior probability distribution density function of is According to the central limit theorem, it also approximately obeys the normal distribution, and its probability density function is:

[0047]

[0048] Among them, σ1, σ2 are standard deviations.

[0049] The mean and variance of the vertical bearing capacity of pipe piles can be expressed as

[0050]

[0051]

[0052] In the formula, and D(l i ) is the average soil layer l i The mean and variance of can be found by definition; D(q si )and D(q p ) are the mean and variance of the average side friction resistance of each soil layer and the average end resistance of the pile end soil layer, respectively. According to the classification of each soil layer and the main physical and mechanical indicators, linear interpolation is performed to further calculate the mean and variance.

[0053] Step 3: Combined with the vertical bearing capacity model of the pipe pile measured in practice or estimated by the empirical formula method, the Bayesian formula is used to update the model and form the posterior distribution.

[0054] The Bayesian theory formula is

[0055]

[0056] Among them, Q represents the data for estimating the vertical bearing capacity of the pipe pile, and R is the model parameter, which refers to the factors that affect the calculation of the vertical bearing capacity, such as soil thickness, soil side friction, and soil end friction. P(Q) is the prior model distribution probability, P(Q|R) is the likelihood function, which represents the probability of observing R under a given bearing capacity Q, and P(R) is the marginal function, which is usually a normalized constant. According to the above formula, combined with the prior probability distribution, the Bayesian formula posterior probability density distribution formula can be constructed. The posterior distribution density function can be expressed as

[0057]

[0058] Step 4: Evaluate the posterior probability of the model parameters in the Bayesian formula.

[0059] The specific process includes: selecting the model with the largest probability of posterior random variables as the final vertical bearing capacity model of pipe piles; calculating the average value of model parameters as the inversion result of random variable parameters.

[0060] Using the above steps, we can finally determine the three random parameters of the model {q si ,q p ,l i}.

[0061] From the above derivation process, it can be seen that the prior distribution of the mean value of the bearing capacity of the pile foundation fully utilizes the classification of each soil layer in the survey data, the statistical parameters of the main physical and mechanical indicators, the statistical parameters of the depth of the stratified soil in each survey hole, and the statistical information of the value range of the pile side friction and pile end resistance, etc., and has considerable credibility. Combined with the results of the static load test, the Bayesian method is used to estimate its mean value, and the value range is between the prior value and the test value, which achieves the purpose of safety and reliability without losing economy.

[0062] The embodiments described above are only descriptions of the preferred modes of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations, modifications, and substitutions made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for estimating the vertical bearing capacity of pipe piles based on Bayesian theory, characterized in that: The following steps are involved: Step 1: Estimate the vertical bearing capacity of the pile based on experimental data and geological information; Step 2: Use the Bayesian principle to construct a prior distribution model of the vertical bearing capacity of pipe piles; Step 3: Combined with the estimated vertical bearing capacity of the pile, the Bayesian formula is used to update the model and form the posterior distribution; Step 4: Conduct a posteriori probability evaluation on the model parameters in the Bayesian formula to assess the ultimate vertical bearing capacity of the pile.

2. The method for estimating the vertical bearing capacity of a pipe pile based on Bayesian theory according to claim 1 is characterized in that: In step 1, the vertical bearing capacity of the pile is estimated using the following formula: Where Q is the vertical bearing capacity of a single pile; i is the thickness of the i-th soil layer; d1 is the outer diameter of the pile; d2 is the inner diameter of the pile; q si is the average lateral friction of each soil layer at a certain site; q p is the average end resistance of the soil layer at the site end.

3. The method for estimating the vertical bearing capacity of pipe piles based on Bayesian theory according to claim 2 is characterized in that: In step 2, let the ultimate bearing capacity Q be a random variable with a mean of Probability density function of the population sample The uncertain factor parameters are the average side friction, the average end resistance and the soil thickness R = {q si ,q p ,l i }, denoted as random parameters R1~R3, and its probability density function is assumed The prior probability distribution density function of is Its probability density function is: Among them, σ1, σ2 are standard deviations; The mean and variance of the vertical bearing capacity of pipe piles are expressed as: In the formula, and D(l i ) is the average soil layer l i The mean and variance of D(q si )and D(q p ) are the mean and variance of the average side friction of each soil layer and the average end resistance of the soil layer at the pile end, respectively.

4. The method for estimating the vertical bearing capacity of pipe piles based on Bayesian theory according to claim 1 is characterized in that: In step 3, the Bayesian theory formula is: Among them, Q represents the data for estimating the vertical bearing capacity of the pile, R is the model parameter, P(Q) is the probability of the prior model distribution, P(Q|R) is the likelihood function, and P(R) is the marginal function; Combined with the prior probability distribution, the Bayesian formula posterior probability density distribution formula is constructed: [0034] 5. The method for estimating the vertical bearing capacity of pipe piles based on Bayesian theory according to claim 3 is characterized in that: Step 4 includes: selecting the model with the largest probability of posterior random variables as the final vertical bearing capacity model of the pile; calculating the average value of the model parameters as the inversion result of the random variable parameters; determining the three random parameters of the model {q si ,q p ,l i }.

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