A system for reducing uncertainties in the analysis of the bearing pressure-settlement relationship of spread footings on clay

Abstract

A system for reducing uncertainty in the analysis of the bearing pressure-settlement relationship of shallow foundations on clay, consisting of: a global probabilistic model database configured to store normalized bearing pressure-settlement data from a variety of plate load tests (PLTs) conducted at multiple geographical locations; a hyperbolic model fitting module configured to fit bearing pressure-settlement data to a hyperbolic model with parameters; a Monte Carlo simulation module configured to generate a variety of normalized pressure-settlement curves based on statistical distributions of the hyperbolic model parameters; a local data acquisition module configured to receive site-specific plate load test data from a construction site; a Bayesian inference module configured to update global model parameters using the site-specific plate pressure plate test data as a likelihood function; an observation module configured to predict foundation behavior at higher loads based on initial load-settlement data from foundation load tests (FLTs); a data processing unit configured to normalize bearing pressure and settlement values ​​to dimensionless pressure ratio and settlement ratio quantities; and an uncertainty quantification module configured to calculate posterior distributions with reduced uncertainties; The system is configured to combine Bayesian inference with observational methods to enable accurate prediction of stance behavior and reduce uncertainties in model parameters.

Description

FIELD OF THE INVENTION

[0001] The present disclosure relates to a system for reducing uncertainty in the analysis of the bearing pressure-settlement relationship of shallow foundations on clay. More specifically, the present invention relates to a system for reducing uncertainty in the bearing pressure-settlement relationship of shallow foundations on clay by applying Bayesian inference and observation techniques. BACKGROUND OF THE INVENTION

[0002] Shallow foundations are often preferred over pile foundations for low-rise buildings, retaining walls, abutments, and other structures on clayey soils due to their economic advantages and rapid construction. However, the design of these foundations is typically based on serviceability limit state (SLS) rather than ultimate limit state (ULS), as settlement control often dictates foundation dimensions. Traditional design approaches rely on plate load tests (PLTs) to determine bearing pressure-settlement relationships. However, significant uncertainties arise from the difference in scale between small test plates and the actual foundation size, as well as widely varying soil properties, which can lead to significant deviations in predicted loads at different sites.

[0003] Current design methods address these uncertainties through conservative safety factors applied to the maximum bearing capacity. However, this approach does not account for the undetected site-specific variability and equipment limitations that arise during the construction phase. The combination of limited reliable data and significant epistemic uncertainties in geomaterial properties requires more sophisticated probabilistic approaches. While Bayesian inference has shown promise in geotechnical applications for updating model parameters from field data, and observational methods have proven effective for design changes during staged construction, there is no comprehensive system that integrates these approaches specifically for the design of shallow foundations on clay soils.

[0004] In view of the previous discussion, it is clear that there is a need for a system to reduce the uncertainty in the analysis of the bearing pressure-settlement relationship of shallow foundations on clay by using Bayesian inference and the observational method. Summary of the invention

[0005] The present disclosure relates to a system for uncertainty reduction in the analysis of the bearing pressure-settlement relationship of shallow foundations on clay soils. The invention presents a comprehensive system that combines Bayesian inference with observational methods to reduce uncertainties in predicting the bearing pressure-settlement behavior of shallow foundations on clay soils. The system integrates a global database of plate load tests with site-specific data, utilizes Monte Carlo simulations for probabilistic modeling, and uses real-time construction monitoring to continuously refine predictions and optimize foundation design.

[0006] The present disclosure aims to provide a system for uncertainty reduction in the analysis of the bearing pressure-settlement relationship of shallow foundations on clay. The system includes: a global probabilistic model database configured to store normalized bearing pressure-settlement data from a plurality of plate load tests (PLTs) conducted at multiple geographical locations; a hyperbolic model fitting module configured to fit bearing pressure-settlement data to a hyperbolic model with parameters; a Monte Carlo simulation module configured to generate a plurality of normalized pressure-settlement curves based on statistical distributions of the hyperbolic model parameters; and a local data acquisition module configured to receive site-specific plate load test data from a construction site.a Bayesian inference module configured to update global model parameters using the site-specific data from plate load tests as a likelihood function; an observation module configured to predict foundation behavior at higher loads based on initial load-settlement data from foundation load tests (FLTs); a data processing unit configured to normalize bearing pressure and settlement values ​​to dimensionless pressure and settlement ratio quantities; and an uncertainty quantification module configured to calculate posterior distributions with reduced uncertainties, the system configured to combine Bayesian inference with observational methods to enable accurate prediction of footing behavior and reduce the uncertainties of the model parameters.

[0007] An object of the present disclosure is to provide a system for reducing uncertainty in the analysis of the bearing pressure-settlement relationship of strip foundations on clay.

[0008] Another objective of the present disclosure is to develop an advanced probabilistic framework that significantly reduces uncertainties in foundation design by integrating global geotechnical data with local, site-specific information through Bayesian inference, enabling more accurate prediction of bearing pressure-settlement relationships for shallow foundations on clay.

[0009] Another objective of the present disclosure is to develop a real-time adaptive system that utilizes observational methods during construction phases to continuously update and refine foundation behavior predictions, enabling dynamic design optimization and risk mitigation based on actual on-site performance data.

[0010] Another objective of the present disclosure is to combine theoretical probabilistic modeling with practical field observations, thus providing engineers with a reliable tool for quantifying uncertainties and reliability-based design approaches in geotechnical foundation engineering.

[0011] To further clarify the advantages and features of the present disclosure, the invention will be explained in more detail with reference to specific embodiments illustrated in the accompanying drawings. These drawings illustrate only typical embodiments of the invention and are therefore not to be considered as limiting its scope. The invention will be described and explained in more detail with reference to the accompanying drawings. SHORT DESCRIPTION OF THE FIGURE

[0012] These and other features, aspects, and advantages of the present disclosure will be better understood when the following detailed description is read with reference to the accompanying drawings, in which like characters represent like parts throughout. Fig. 1 shows a block diagram of a system for reducing uncertainty in analyzing the bearing pressure-settlement relationship of shallow foundations on clay according to an embodiment of the present disclosure.

[0013] Those skilled in the art will also appreciate that the elements in the drawings are shown for convenience and are not necessarily to scale. For example, the flowcharts illustrate the method by key steps to enhance understanding of aspects of the present disclosure. Furthermore, with respect to device construction, one or more components of the device may be represented in the drawings by conventional symbols. The drawing may show only the specific details relevant to understanding embodiments of the present disclosure in order not to clutter the drawing with details that would be readily apparent to those skilled in the art from the present description. DETAILED DESCRIPTION:

[0014] To facilitate understanding of the principles of the invention, reference will now be made to the embodiment illustrated in the drawings and a clear description will be given. However, the scope of the invention is not limited thereby. Changes and further modifications to the illustrated system, as well as further applications of the principles of the invention, are possible, as would normally occur to one skilled in the art to which the invention pertains.

[0015] It will be understood by those skilled in the art that the foregoing general description and the following detailed description are exemplary and explanatory of the invention and are not intended to be limiting thereof.

[0016] References in this specification to "one aspect," "another aspect," or similar language mean that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present disclosure. Therefore, the language "in one embodiment," "in another embodiment," and similar language throughout this specification may or may not refer to the same embodiment.

[0017] The terms "comprises," "comprising," or other variations thereof are intended to cover non-exclusive inclusion, such that a process or method comprising a list of steps may include not only those steps, but also additional steps not expressly listed or inherent in that process or method. Likewise, the statement "comprises" for one or more devices, subsystems, elements, structures, or components does not exclude, without further limitation, the existence of other devices, subsystems, elements, structures, components, or additional devices, subsystems, elements, structures, or components.

[0018] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the invention pertains. The systems, methods, and examples provided herein are for illustrative purposes only and should not be considered limiting.

[0019] Embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings.

[0020] The functional units described in this specification are referred to as devices. A device may be implemented in programmable hardware devices such as processors, digital signal processors, central processing units, field-programmable gate arrays, programmable array logic systems, programmable logic devices, cloud processing systems, or the like. The devices may also be implemented in software for execution by various types of processors. An identified device may contain executable code and may consist, for example, of one or more physical or logical blocks of computer instructions, which may be organized, for example, as an object, procedure, function, or other construct.However, the executable file of an identified device does not have to be physically stored in the same location, but may consist of different instructions stored in different locations which, logically linked, form the device and fulfill its purpose.

[0021] The executable code of a device or module can consist of one or more instructions and can even be distributed across multiple code segments, different applications, and multiple storage devices. Likewise, operational data can be identified and represented within the device and presented in any form and data structure. The operational data can be captured as a single data set or distributed across different storage devices and can be represented, at least in part, as electronic signals in a system or network.

[0022] References in this specification to "a selected embodiment," "an embodiment," or "an embodiment" mean that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the disclosed subject matter. Therefore, the phrases "a selected embodiment," "in an embodiment," or "in an embodiment" in various places in this specification do not necessarily refer to the same embodiment.

[0023] Furthermore, the described features, structures, or characteristics may be combined in any manner in one or more embodiments. The following description contains numerous specific details to provide a thorough understanding of embodiments of the disclosed subject matter. However, those skilled in the art will recognize that the disclosed subject matter may be practiced without one or more of the specific details, or with different methods, components, materials, etc. In other instances, well-known structures, materials, or operations are not shown or described in detail in order not to obscure aspects of the disclosed subject matter.

[0024] According to the exemplary embodiments, the disclosed computer programs or modules may be executed in a variety of ways, for example, as an application in the memory of a device or as a hosted application on a server that communicates with the device application or browser using various standard protocols such as TCP / IP, HTTP, XML, SOAP, REST, JSON, and other suitable protocols. The disclosed computer programs may be written in exemplary programming languages ​​that execute from the memory of the device or from a hosted server, such as BASIC, COBOL, C, C++, Java, Pascal, or scripting languages ​​such as JavaScript, Python, Ruby, PHP, Perl, or other suitable programming languages.

[0025] Some of the disclosed embodiments involve or otherwise involve the transmission of data over a network, for example, the delivery of various inputs or files over the network. The network may include, for example, the Internet, wide area networks (WANs), local area networks (LANs), analog or digital wired and wireless telephone networks (e.g., PSTN, Integrated Services Digital Network (ISDN), cellular networks, and Digital Subscriber Line (xDSL)), radio, television, cable, satellite, and / or other transmission or tunneling mechanisms for transmitting data. The network may include multiple networks or subnetworks, each containing, for example, a wired or wireless data path. The network may include a circuit-switched voice network, a packet-switched data network, or another network for transmitting electronic communications.For example, the network may include Internet Protocol (IP) or Asynchronous Transfer Mode (ATM) networks that support voice, such as VoIP, Voice over ATM, or other comparable protocols for voice data communication. In one implementation, the network includes a cellular network configured for the exchange of text or SMS messages.

[0026] Examples of the network include a Personal Area Network (PAN), a Storage Area Network (SAN), a Home Area Network (HAN), a Campus Area Network (CAN), a Local Area Network (LAN), a Wide Area Network (WAN), a Metropolitan Area Network (MAN), a Virtual Private Network (VPN), an Enterprise Private Network (EPN), the Internet, a Global Area Network (GAN), etc.

[0027] Fig. 1 shows a block diagram of a system (100) for reducing uncertainty in analyzing the bearing pressure-settlement relationship of shallow foundations on clay according to an embodiment of the present disclosure.

[0028] According to Fig.1, the system (100) comprises: a global probabilistic model database (102) configured to store normalized bearing pressure-settlement data from multiple plate load tests (PLTs) conducted at multiple geographical locations; a hyperbolic model fitting module (104) configured to fit bearing pressure-settlement data to a hyperbolic model with parameters; a Monte Carlo simulation module (106) configured to generate multiple normalized pressure-settlement curves based on statistical distributions of the hyperbolic model parameters; a local data acquisition module (108) configured to receive site-specific plate load test data from a construction site; a Bayesian inference module (110) configured to update global model parameters using the site-specific plate load test data as a probability function;an observation module (112) configured to predict foundation behavior at higher loads based on initial load-settlement data from foundation compression tests (FLTs); a data processing unit (114) configured to normalize bearing pressure and settlement values ​​to dimensionless pressure ratio and settlement ratio quantities; and an uncertainty quantification module (116) configured to calculate posterior distributions with reduced uncertainties; wherein the system (100) is configured to combine Bayesian inference with observational methods to provide an accurate prediction of foundation behavior and reduce uncertainties in model parameters.

[0029] In one embodiment, the global probabilistic model database (102) comprises: data from 61 plate load tests compiled from 19 literature sources; 22 small-scale laboratory tests and 39 full-scale field tests; normalized bearing pressure and settlement data to reduce economies of scale; and hyperbolic curve fitting parameters for each test data set.

[0030] In one embodiment, the Monte Carlo simulation module (106) is configured to: assume hyperbolic model parameters to be statistically independent based on low correlation coefficients; generate 10,000 pairs of said parameter values ​​with prescribed log-normal distribution; simulate normalized pressure-settlement curves for probabilistic analysis; and define serviceability limit state (SLS) criteria based on settlement ratio values.

[0031] In one embodiment, the Bayesian inference module (110) is configured to: use global data as prior knowledge for parameter estimation, incorporate local PLT data as a likelihood function, update the parameter to be updated (λ) with the normal distribution as the conjugate prior distribution, maintain the known population parameter (ξ), and generate posterior distributions with reduced variability compared to prior distributions.

[0032] In one embodiment, the observation module (112) is configured to monitor initial load increments and corresponding settlements during the construction phases; use the first data points from the foundation load tests to estimate the parameter with the highest uncertainty; retain low uncertainty parameters as uncertain random variables; predict future foundation behavior at higher loads based on initial observations; and generate pressure ratio distributions at different limit states.

[0033] In one embodiment, the data processing unit (114) is configured to fit site-specific bearing pressure-settlement data to a hyperbolic model, calculate dimensionless pressure ratios and settlement ratios to reduce economies of scale, determine statistical parameters of lognormal distributions under multiple SLS conditions, and process field measurement data for real-time analysis.

[0034] In one embodiment, the uncertainty quantification module (116) is configured to: calculate the posterior mean and standard deviation of the parameter λ using Bayesian equations, compare prior, likelihood and posterior distributions, quantify the uncertainty reduction by reduced standard deviation in posterior distributions, and generate probability density functions (PDFs) for reliability analysis at corresponding limit states.

[0035] In one embodiment, the system (100) further comprises a validation module (118) configured to compare the predicted behavior with the actual foundation load test results, to verify the accuracy of the Bayesian update through field observations, to validate the predictions of the observation method using measured settlements, and to confirm the effectiveness of the combined method through actual foundation performance data.

[0036] In one embodiment, the system (100) is further configured to: perform sequential Bayesian updating by using posterior parameters from the PLT analysis as prior parameters for observation updating; combine global database knowledge with local, site-specific information; integrate real-time construction monitoring data for continuous model refinement; and provide probabilistic design parameters for foundation engineering applications.

[0037] In one embodiment, the system (100) further comprises a design optimization module (120) configured to: apply final probability density functions for probabilistic foundation analysis; enable design revision and modification based on observational principles; support reliability-based design approaches using updated model parameters; and provide uncertainty-quantified bearing capacity and settlement predictions for the design of strip foundations on clayey soils.

[0038] The present invention relates to a system configured to reduce the uncertainty in the bearing pressure-settlement relationship of shallow foundations on clay by implementing Bayesian inference and observation techniques.

[0039] The present invention addresses the critical challenge of uncertainty in geotechnical foundation design. It introduces a sophisticated framework that combines Bayesian statistical methods with observational techniques to improve the accuracy of bearing pressure settlement predictions for shallow foundations on clayey soils. Conventional foundation design approaches are often based on limited site-specific data or overly conservative assumptions, resulting in either insufficient safety margins or uneconomical overdesign. This invention overcomes these limitations by creating a comprehensive framework that systematically reduces parametric uncertainties through data integration and real-time monitoring.

[0040] The system begins by building a global probabilistic model database. This database contains normalized bearing pressure-settlement data from 61 plate-loading tests from 19 different literature sources. These include both small-scale laboratory experiments and large-scale field investigations in diverse geological settings. This extensive database serves as the basis for developing a hyperbolic model that describes the relationship between bearing pressure and settlement using two key parameters, "a" and "b." The system uses Monte Carlo simulation techniques to generate thousands of normalized pressure-settlement curves, treating these parameters as statistically independent variables with a predefined log-normal distribution.

[0041] The core innovation lies in the implementation of the Bayesian inference method. This provides a mathematical framework for updating the global probability model using site-specific local data from slab load tests at the actual construction site. This Bayesian update process treats the global database as prior knowledge and incorporates local test results as probability functions. This generates posterior distributions with significantly lower uncertainties compared to the original global model. The system maintains parameter flexibility by treating one parameter as a known population parameter and updating the other using conjugate priors of the normal distribution.

[0042] The invention further improves prediction accuracy by integrating observation methods that utilize real-time construction monitoring data. During the initial construction phases, the system monitors initial load increases and the corresponding settlements of the foundations. This information is used to further refine model parameters and predict future behavior under higher loads. This observational approach enables continuous model updating throughout the construction process and enables adaptive design adjustments based on actual field performance.

[0043] The system incorporates sophisticated data processing capabilities that normalize bearing pressure and settlement values ​​to dimensionless ratios. This effectively reduces scale effects that typically compromise the accuracy of extrapolations from small-scale tests to large-scale applications. The uncertainty quantification module continuously calculates posterior distributions and provides probability density functions that can be directly applied to reliability-based design approaches. This enables engineers to make informed decisions regarding safety factors and design optimization.

[0044] The proposed system is also configured to ensure the reliability of the predictions by comparing the system results with the results of actual foundation load tests. This confirms the effectiveness of the combined Bayesian inference and observational method. The system demonstrates superior performance in predicting actual foundation behavior compared to conventional methods, with significantly reduced parameter uncertainties and improved correlation with field observations.

[0045] The design of shallow foundations on clayey soils is primarily determined by settlement criteria defined under serviceability limit conditions (SLT). To minimize uncertainties in estimating bearing pressure settlement behavior, a system is proposed that uses a multi-model probabilistic model consisting of a global probabilistic model, Bayesian inference, an observational method, and a combined Bayesian observational approach.

[0046] The system includes a global probabilistic model database created from a compiled dataset of 61 plate load tests (PLTs) from 19 literature sources. This includes 22 small-scale laboratory tests and 39 full-scale field tests. All pressure and settlement data have been normalized to eliminate scale effects. Each dataset is fitted to a hyperbolic model characterized by curve-fitting parameters to represent the normalized pressure and settlement relationships.

[0047] To adapt the model to site-specific conditions, a local data acquisition module is used. A PLT is performed at the designated site to generate local data on bearing pressure and settlement, which are used to define the likelihood function. This local data is processed by a Bayesian inference module that updates the global hyperbolic model parameters. The update focuses on refining the uncertain model parameter (λ) using a normal distribution as the conjugate prior, while retaining a known parameter (ξ) from the global model. The result is a posterior distribution with reduced variability and uncertainty.

[0048] A foundation load test (FLT) is conducted at the same location, approximately 32 meters from the PLT site. The system's observation module uses the initial data points from the FLT, representing early phases of a multi-stage construction, to predict future foundation behavior under higher loading conditions. This module estimates the most uncertain model parameter and treats other parameters with relatively low variability as probabilistically defined constants.

[0049] The system supports a combined method in which the posterior distribution generated by Bayesian inference is further refined with observational data. This integrated approach significantly reduces uncertainties in model parameters by leveraging both global prior knowledge and real-time observational data.

[0050] A comparison module evaluates the predictive performance of the four modeling approaches: 1. The global probability model is based exclusively on compiled literature data. 2. The Bayesian inference model updated with local PLT data. 3. The observational method that predicts stance behavior based on early FLT observations. 4. The combined Bayesian observational model, which merges local PLT-based Bayesian updates with early-stage FLT data.

[0051] The system shows that the fourth model, which integrates Bayesian inference and observational method, achieves the highest accuracy in predicting the actual behavior of foundations at higher loads and has the lowest uncertainty in the hyperbolic model parameters.

[0052] The system provides a robust and adaptive approach for determining the allowable bearing pressure for shallow foundations on clay soils. By integrating global knowledge with site-specific measurements and real-time observation data, the system offers a comprehensive probabilistic design methodology that supports serviceability-oriented design with reduced uncertainty and improved predictive capability.

[0053] In one embodiment, the invention relates to a system that uses a hyperbolic model to represent the settlement behavior of foundations resting on clay soils. The model uses normalized parameters, in particular the settlement ratio and the pressure ratio, to minimize scale effects and enable consistent application across different test setups. Normalization is based on expressing the bearing pressure in terms of the soil's uniaxial compressive strength and the settlement as a ratio to the test slab width. This ensures that data from different test scales are comparable, regardless of whether they are small-scale laboratory tests or large-scale field tests.

[0054] To define the global model, a comprehensive database of 61 plate load tests conducted on clayey soils under varying geological and soil conditions was compiled. These tests include both small-scale tests in the laboratory or in controlled field environments and large-scale in-situ tests. The collected data were fitted to the hyperbolic model to obtain curve-fitting parameters that were used to characterize the normalized bearing pressure-settlement curves. The use of normalized pressure and settlement values ​​is further justified by common practice in estimating foundation settlements from PLTs on clayey soils, which supports the applicability of settlement ratios to minimize economies of scale. Each test in the database was therefore converted to a dimensionless format prior to curve fitting.Statistical analysis of the hyperbolic model parameters revealed different behavior. One of the parameters showed relatively low variability across the global dataset, while the other showed significantly higher variability. This difference in variability is consistent with the results of similar axial load tests for bored piles. Further investigation into the possible dependence of these parameters on other variables, such as slab width and uniaxial compressive strength, revealed no clear trend. The scatter observed in the data plots confirmed that changes in parameter values ​​related to these variables are random. Therefore, both parameters were treated as random variables in the global model. To statistically represent the uncertainty of these parameters, a bivariate random vector was formulated.Consistent with previous literature on pile foundations, both parameters were modeled using marginal lognormal distributions, as they are inherently non-negative. Frequency distributions and cumulative distribution functions confirmed the suitability of lognormal fits, although certain deviations were observed, particularly for the parameter with higher variability. Nevertheless, both parameters were assumed to follow lognormal distributions for modeling. Joint probability distributions were constructed for the natural logarithm of the parameters to further quantify their combined behavior. Additionally, a correlation analysis was performed to evaluate the dependence between the two parameters. The results of this analysis showed mixed trends across different datasets.Small-scale tests showed a weak negative correlation, while large-scale tests showed a negligible positive correlation. The overall dataset yielded a low positive correlation coefficient. Based on standard thresholds for correlation strength, the calculated values ​​fall into the weak correlation category. The substantial scatter in the dataset, combined with the small magnitude of the correlation coefficients, supports the assumption that the two parameters are statistically uncorrelated in the present study. This modeling framework underpins the global probabilistic model of the system and provides the basis for further integration with Bayesian updating and observational methods for reducing uncertainty in the site-specific design of shallow foundations on clayey soils.

[0055] In one embodiment, the system includes a Monte Carlo simulation module that evaluates the variability of the bearing pressure and settlement response using probabilistic modeling. Based on the prescribed lognormal statistical distributions of the hyperbolic model parameters a and b, which are assumed to be statistically independent, a Monte Carlo simulation is performed to generate 10,000 unique parameter pairs. This large sample size is chosen to ensure an accurate statistical representation of the normalized bearing pressure and settlement curves. The resulting ensemble of curves exhibits significant variability, primarily due to the uncertainty associated with the hyperbolic model parameter b. This reflects the system's ability to capture the inherent randomness of the soil response under loading conditions.In accordance with design practice, the system evaluates the serviceability limit state (SLS). This is defined as the condition at which the foundation's ability to perform its intended function is impaired. The SLS can include various factors such as deformation, cracking, vibration, or wear. However, in the current implementation of the system, excessive settlement is considered the sole SLS criterion, as this is most relevant for foundations made of clayey soil. To facilitate SLS-based design, the system uses four predefined settlement ratio values ​​to represent serviceability thresholds. These ratios serve as benchmarks for the probabilistic analysis of foundation performance under various acceptable settlement levels.For each defined SLS condition, the Monte Carlo simulation module generates relative frequency distributions of the normalized bearing pressure (pressure ratios) corresponding to the simulated parameter pairs. These distributions are then fitted with lognormal probability density functions to represent the probabilistic variability of the pressure ratio under each SLS condition. The Monte Carlo simulation results enable the system's uncertainty quantification module to analyze the distribution properties of the pressure ratio, such as mean and standard deviation, at different SLS levels. This supports reliability-based design by providing input to the design optimization module for determining allowable bearing pressures with quantified uncertainty.

[0056] In one embodiment, the Bayesian inference module provides a systematic framework for integrating site-specific local data with globally derived probabilistic information to improve the accuracy and reliability of model parameter estimation in the bearing pressure domain. The system applies Bayesian inference to update global probabilistic model parameters using site-specific data from field plate compression tests (PLT) at various serviceability limit states (SLS). The global database includes normalized bearing pressure-settlement data fitted to a hyperbolic model. From this, the pressure ratio values ​​at various serviceability limit states are characterized using log-normal distributions.In the Bayesian update process, the system assumes that the global parameter (denoted by ξ), estimated from a large and diverse global dataset, is known and constant. The parameter to be updated (λ) is considered uncertain and is therefore treated as a random variable. Since λ can take both negative and positive values, it is modeled with a normal distribution, which serves as a conjugate prior distribution. This assumption is consistent with standard practice in Bayesian analysis and allows for closed-form expressions for the posterior mean and standard deviation of λ. The global estimates of the mean of λ and the variance are derived from the lognormal distribution parameters associated with the global dataset. These global parameters serve as prior estimates in the Bayesian framework.Local PLT field data collected at each site provide updated information in the form of a likelihood function. This likelihood is based on the hyperbolic model fitted to the site-specific PLT data and yields the expected λ values ​​at the defined SLS levels. The associated variability at each SLS level is assumed to be equal to the corresponding global ξ value. By incorporating the local PLT data as a likelihood function, the Bayesian inference module updates the mean and standard deviation of λ to generate posterior distributions. These posterior distributions are characterized by lower uncertainty compared to the previous ones and are better adapted to the actual site-specific conditions.The updated posterior distributions of λ were then compared with actual field observations from a foundation load test (FLT) conducted at the same site. The system demonstrated that the posterior distributions obtained by Bayesian updating exhibited significantly lower variability and better matched the actual foundation behavior observed in the FLT. This confirms the system's ability to reduce parameter uncertainty and improve prediction accuracy by combining global model knowledge with local field data through Bayesian inference.

[0057] In one embodiment, the system leverages these early load-settlement data from foundation load tests (FLTs) to implement an observational method module that enables the prediction of future foundation behavior at higher loads. In this system, prior parameter estimation was achieved using Bayesian inference, with global model parameters updated based on site-specific data from plate load tests (PLTs) to reflect local soil conditions. A subsequent foundation load test (FLT) was conducted at the same location, approximately 32 meters from the PLT site, to validate the updated model. To refine the uncertainty in the hyperbolic model parameters, the observational method module specifically targets the most uncertain parameter, parameter b, which significantly influences the initial slope of the bearing pressure-settlement curve.The system estimates this parameter using the first few data points from the FLT. Once parameter b is determined from early observations, it is fixed in the model, leaving parameter a as the remaining source of uncertainty. With parameter b fixed, the system uses global probability distributions of parameter a to generate updated probability density functions (PDFs) for the pressure ratio at various serviceability limit states (SLS) and ultimate limit states (ULS). These PDFs incorporate both prior knowledge from global data and local insights from field observations, thus enabling a more accurate probabilistic prediction of foundation behavior. The previously obtained posterior distributions from the Bayesian update with PLT data are adopted as prior distributions for a second Bayesian update based on the results of the observational method.This sequential Bayesian update process, supported by the system's uncertainty quantification module, calculates new posterior means and standard deviations for the parameter λ, assuming that the other parameter ξ remains known. The system demonstrates that integrating the observational method significantly reduces the model's uncertainty by producing posterior distributions with reduced standard deviations. This improved certainty increases the reliability of the predicted pressure ratios at all defined limit states. The resulting PDFs, generated after applying Bayesian inference to the observational data, serve as the basis for probabilistic and reliability analysis of foundation behavior under different loading scenarios.According to the principles of the observation method, the refined information can be used by the system's design optimization module to support design changes or modifications in real time, thus ensuring safe and reliable foundation performance on clay soils.

[0058] The improved hyperbolic model system predicts the bearing pressure, which depends on the load-settlement behavior of shallow foundations on clayey soils. The model parameters, denoted as a and b, are treated as independent lognormally distributed variables without correlation, supporting their use in a probabilistic framework. Using Bayesian inference, the global model parameters were updated using data from local plate load tests (PLT), thereby reducing the uncertainty of the parameter λ. The observational method, which used data from early stages of a foundation load test (FLT), contributed to the correction of the parameter b and further reduced the model uncertainty. The combination of Bayesian inference and the observational method resulted in the most accurate predictions of foundation behavior and the most significant uncertainty reduction.The system showed that the pressure ratio values ​​at different settlement levels are lognormally distributed and closely agree with actual observations. The global model, updated with site-specific PLT or FLT data, can reliably predict foundation behavior on homogeneous loamy soils. While this study focuses on loamy soils, the approach can be extended to other foundation types and soil conditions.

[0059] The drawings and the foregoing description illustrate examples of embodiments. Those skilled in the art will recognize that one or more of the described elements may well be combined to form a single functional element. Alternatively, certain elements may be separated into multiple functional elements. Elements of one embodiment may be added to another embodiment. For example, the order of the processes described herein may be changed and is not limited to the manner described herein. Furthermore, the actions of a flowchart need not be performed in the order shown; nor do all actions need to be performed. Also, actions that are not dependent on other actions may be performed in parallel with the other actions. The scope of the embodiments is in no way limited by these specific examples.Numerous variations, whether explicitly stated in the specification or not, such as differences in structure, dimensions, and use of materials, are possible. The scope of the embodiments is at least as broad as indicated in the following claims.

[0060] Advantages, further benefits, and solutions to problems have been described above with reference to specific embodiments. However, the advantages, advantages, solutions to problems, and any components that may result in or enhance an advantage, advantage, or solution are not to be construed as critical, required, or essential features or components of any or all of the claims. REFERENCES 100 A system for reducing uncertainties in the analysis of the bearing pressure-settlement relationship of spread footings on clay. 102 Global Probabilistic Model Database 104 Module for Fitting Hyperbolic Models 106 Monte Carlo simulation module 108 Local data acquisition module 110 Bayesian Inference Module 112 Observation module 114 Data processing unit 116 Uncertainty Quantification Module 118 Validation module 120 Design Optimization Module

Claims

[1] A system for reducing uncertainty in the analysis of the bearing pressure-settlement relationship of shallow foundations on clay, consisting of: a global probabilistic model database configured to store normalized bearing pressure-settlement data from a variety of plate load tests (PLTs) conducted at multiple geographical locations; a hyperbolic model fitting module configured to fit bearing pressure-settlement data to a hyperbolic model with parameters; a Monte Carlo simulation module configured to generate a variety of normalized pressure-settlement curves based on statistical distributions of the hyperbolic model parameters; a local data acquisition module configured to receive site-specific plate load test data from a construction site; a Bayesian inference module configured to update global model parameters using the site-specific plate pressure plate test data as a likelihood function; an observation module configured to predict foundation behavior at higher loads based on initial load-settlement data from foundation load tests (FLTs); a data processing unit configured to normalize bearing pressure and settlement values ​​to dimensionless pressure ratio and settlement ratio quantities; and an uncertainty quantification module configured to calculate posterior distributions with reduced uncertainties; The system is configured to combine Bayesian inference with observational methods to enable accurate prediction of stance behavior and reduce uncertainties in model parameters. [2] The system of claim 1, wherein the global probabilistic model database comprises: data from 61 plate load tests compiled from 19 literature sources; 22 small-scale laboratory tests and 39 full-scale field tests; normalized bearing pressure and settlement data to reduce economies of scale; and hyperbolic curve fitting parameters a and b for each test data set. [3] The system of claim 1, wherein the Monte Carlo simulation module is configured to: assume hyperbolic model parameters to be statistically independent based on low correlation coefficients; generate 10,000 pairs of the parameter values ​​with prescribed log-normal distribution; simulate normalized pressure-settlement curves for probabilistic analysis; and define serviceability limit state (SLS) criteria based on settlement ratio values. [4] The system of claim 1, wherein the Bayesian inference module is configured to: use global data as prior knowledge for parameter estimation; incorporate local PLT data as a likelihood function; update the parameter to be updated (λ) using the normal distribution as the conjugate prior distribution; maintain the known population parameter (ξ); and generate posterior distributions with reduced variability compared to prior distributions. [5] The system of claim 1, wherein the observation module is configured to monitor initial load increments and corresponding settlements during the construction phases; use the first few data points from the foundation load tests to estimate the parameter with the highest uncertainty; retain low uncertainty parameters as uncertain random variables; predict future foundation behavior at higher loads based on initial observations; and generate pressure ratio distributions at different limit states. [6] The system of claim 1, wherein the data processing unit is configured to fit site-specific bearing pressure-settlement data to a hyperbolic model, calculate dimensionless pressure ratios and settlement ratios to reduce economies of scale, determine statistical parameters of lognormal distributions under multiple SLS conditions, and process field measurement data for real-time analysis. [7] The system of claim 1, wherein the uncertainty quantification module is configured to: calculate the posterior mean and standard deviation of the parameter λ using Bayesian equations, compare prior, likelihood and posterior distributions, quantify uncertainty reduction by reduced standard deviation in posterior distributions, and generate probability density functions (PDFs) for reliability analysis at corresponding limit states. [8] The system of claim 1, further comprising: a validation module configured to compare the predicted behavior with actual foundation load test results, verify the accuracy of the Bayesian update through field observations, validate the predictions from observational methods against measured settlements, and confirm the effectiveness of the combined methods through actual foundation performance data. [9] The system of claim 1, wherein the system is further configured to perform sequential Bayesian updating by using posterior parameters from the PLT analysis as prior parameters for observation updating; combine global database knowledge with local, site-specific information; integrate real-time construction monitoring data for continuous model refinement; and provide probabilistic design parameters for foundation engineering applications. [10] The system of claim 1, further comprising: a design optimization module configured to: apply final probability density functions for probabilistic foundation analysis; enable design revision and modification based on observational principles; support reliability-based design approaches using updated model parameters; and provide uncertainty-quantified bearing capacity and settlement predictions for the design of strip foundations on clayey soils.

Images