Enterprise AI Analysis
A comparative machine and deep learning approach for predicting ultimate bearing capacity of shallow foundations in cohesionless soil
This study developed a Python-based framework to predict the ultimate bearing capacity of shallow foundations on cohesionless soil, employing machine learning (ML) and deep learning (DL) techniques. Utilizing a comprehensive dataset of 116 footing experiments, Eleven ML models (Gaussian Process Regression (GPR), Extreme Gradient Boosting (XGBoost), Gradient Boosting Machine (GBM), Random Forest (RF), Categorical Boosting (CatBoost) etc.) and five DL models (Artificial Neural Network (ANN), Deep Neural Network (DNN), etc.) trained and compared against traditional methods. Input parameters included foundation dimensions and soil properties. Results demonstrated that ML and DL models significantly outperformed traditional equations, achieving higher accuracy. Ensemble methods like GPR, XGBoost, GBM, RF, and CatBoost exhibited superior performance, with Coefficient of Determination (R²) values above 0.988 and a Mean Absolute Percentage Error (MAPE) below 5.07%. Conversely, traditional methods showed lower accuracy, with R² values ranging from 0.684 to 0.82 and MAPE exceeding 19.63%. Taylor diagram analysis confirmed the improved performance of ML and DL. Additionally, a SHapley Additive exPlanations (SHAP) analysis highlighted foundation depth and soil friction angle as the most influential parameters, consistent with geotechnical principles.
Executive Impact at a Glance
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Average R² (Ensemble ML Models)
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Average MAPE (Ensemble ML Models)
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Traditional Methods R² Range
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Traditional Methods MAPE Exceeded
Deep Analysis & Enterprise Applications
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Machine Learning
Deep Learning
Traditional Methods
AI Opportunities
Machine Learning Models Overview
Machine learning models excelled in predicting ultimate bearing capacity, with ensemble methods showing particularly strong performance and robustness.
Gaussian Process Regressor (GPR)
Characteristics: Probabilistic predictions with uncertainty estimates. Handles complex non-linear relationships. Computationally expensive, sensitive to kernel choice. Poor scalability for large datasets. Best for small datasets, scientific modeling, Bayesian optimization.
Performance: Training R²: 1.0, MAPE: 5.84%. Testing R²: 0.972, MAPE: 11.27%.
Extreme Gradient Boosting (XGBoost)
Characteristics: High accuracy and scalability. Handles missing values. Regularization to prevent overfitting. Requires careful hyperparameter tuning. State-of-the-art performance for structured data.
Performance: Training R²: 1.0, MAPE: 0.65%. Testing R²: 0.977, MAPE: 13.14%.
Light Gradient Boosting Machine (LightGBM)
Characteristics: Extremely fast and memory efficient. Handles large datasets and categorical features. Can overfit on small datasets. Faster than XGBoost with comparable accuracy.
Performance: Training R²: 0.976, MAPE: 33.68%. Testing R²: 0.928, MAPE: 26.86%.
Gradient Boosting Machine (GBM)
Characteristics: High accuracy. Handles non-linear relationships. Robust to outliers. Computationally expensive. High accuracy but slower than XGBoost/LightGBM.
Performance: Training R²: 1.0, MAPE: 0.86%. Testing R²: 0.976, MAPE: 10.65%.
Random Forest (RF)
Characteristics: Robust to overfitting. Handles high-dimensional data. Provides feature importance. Less interpretable than single trees. High accuracy, slower than boosting methods.
Performance: Training R²: 1.0, MAPE: 0.85%. Testing R²: 0.959, MAPE: 15.15%.
Categorical Boosting (CatBoost)
Characteristics: Handles categorical data natively. Robust to overfitting. GPU support for fast training. Requires tuning. High accuracy, especially for categorical data.
Performance: Training R²: 1.0, MAPE: 7.46%. Testing R²: 0.958, MAPE: 15.26%.
AdaBoost Regressor (AdaBoost)
Characteristics: Improves weak learners. Simple to implement. Robust to overfitting. Sensitive to noisy data. Good accuracy for small datasets, struggles with noise.
Performance: Training R²: 1.0, MAPE: 6.57%. Testing R²: 0.942, MAPE: 16.99%.
K-Nearest Neighbors (KNN)
Characteristics: Simple and intuitive. No training phase. Handles non-linear data. Computationally expensive for large datasets. Good for small datasets, slow for large.
Performance: Training R²: 1.0, MAPE: 0.85%. Testing R²: 0.970, MAPE: 20.23%.
Bagging Regressor (BR)
Characteristics: Reduces variance and overfitting. Combines multiple models for robustness. Computationally expensive. Improves stability and accuracy of base models.
Performance: Training R²: 0.997, MAPE: 16.94%. Testing R²: 0.949, MAPE: 18.56%.
Decision Tree (DT)
Characteristics: Easy to interpret and visualize. Handles mixed data types. No need for feature scaling. Prone to overfitting, high variance. Good for small datasets, prone to overfitting.
Performance: Training R²: 0.999, MAPE: 8.42%. Testing R²: 0.958, MAPE: 17.01%.
Support Vector Machine (SVM)
Characteristics: Handles non-linear relationships using kernels. Robust to outliers. Provides probabilistic predictions. Computationally expensive, requires careful hyperparameter tuning. High accuracy for small datasets, slow for large.
Performance: Training R²: 0.999, MAPE: 10.87%. Testing R²: 0.975, MAPE: 13.13%.
Deep Learning Models Overview
Deep learning models also showed strong predictive capabilities, offering a robust approach for complex geotechnical problems.
Artificial Neural Network (ANN)
Characteristics: Input layer, one or more hidden layers, output layer. Fully connected. Versatile and flexible. Can model complex, non-linear relationships. Computationally expensive. Prone to overfitting. Black-box nature. General-purpose tasks.
Performance: Training R²: 0.999, MAPE: 11.69%. Testing R²: 0.975, MAPE: 14.37%.
Deep Neural Network (DNN)
Characteristics: Multiple hidden layers between input and output. Fully connected. Hierarchical feature learning. State-of-the-art performance in many domains. Computationally expensive. Requires large datasets. Hard to interpret. Image recognition, NLP, speech recognition, and complex pattern recognition.
Performance: Training R²: 0.997, MAPE: 20.32%. Testing R²: 0.963, MAPE: 16.73%.
Convolutional Neural Network (CNN)
Characteristics: Convolutional layers, pooling layers, fully connected layers. Local connectivity. Excellent for spatial data. Reduces parameters via weight sharing. Computationally expensive. Requires large datasets. Limited to grid-like data. Image classification, object detection, video analysis, and medical imaging.
Performance: Training R²: 0.993, MAPE: 32.34%. Testing R²: 0.962, MAPE: 22.06%.
Recurrent Neural Networks (RNN)
Characteristics: Recurrent connections with loops. Hidden state to capture temporal dependencies. Handles sequential data. Models temporal dependencies effectively. Suffers from vanishing/exploding gradients. Computationally expensive. Time-series forecasting, NLP, speech recognition, and video analysis.
Performance: Training R²: 0.966, MAPE: 61.37%. Testing R²: 0.940, MAPE: 26.21%.
Feedforward Neural Network (FFNN)
Characteristics: Input layer, hidden layers, output layer. No cycles or loops. Simple and easy to implement. Handles static data well. Cannot model sequential data. Prone to overfitting. Limited to small datasets. Classification, regression, and pattern recognition for static data.
Performance: Training R²: 0.994, MAPE: 26.52%. Testing R²: 0.967, MAPE: 22.33%.
Traditional Bearing Capacity Methods Overview
Traditional methods, while foundational, showed lower accuracy compared to ML/DL models due to simplifying assumptions.
Terzaghi
Characteristics: Based on Prandtl's plastic failure theory. Considers soil cohesion, effective stress, and friction angle. Relies on several simplifying assumptions.
Performance: Testing R²: 0.684, MAPE: 19.63%.
Meyerhof
Characteristics: Extended Terzaghi's equation by incorporating shape and depth factors. Still relies on simplifying assumptions, leading to potential inaccuracies.
Performance: Testing R²: 0.80, MAPE: 23.08%.
Hansen
Characteristics: Further refinement of bearing capacity theory with additional shape and depth factors. Improved applicability over basic Terzaghi, but still assumption-based.
Performance: Testing R²: 0.81, MAPE: 23.08%.
Vesić
Characteristics: Comprehensive theory including additional factors for various soil and foundation conditions. Aims for broader applicability but maintains theoretical assumptions.
Performance: Testing R²: 0.82, MAPE: 24.89%.
Eurocode 7 (EC7)
Characteristics: European standard for geotechnical design. Provides design rules and factors for bearing capacity. Part of a broader framework for structural design.
Performance: Testing R²: 0.77, MAPE: 20.93%.
Egyptian Code (ECP)
Characteristics: Local code for soil mechanics and foundation design. Offers guidelines and equations for bearing capacity in regional contexts. Similar structural form to other classical methods.
Performance: Testing R²: 0.77, MAPE: 20.93%.
Identified AI Opportunities
The study highlights several key areas where AI can drive significant advancements in geotechnical engineering:
- Automated foundation design optimization
- Real-time monitoring and adaptive bearing capacity assessment
- Integration with BIM for intelligent construction planning
- Predictive maintenance for existing infrastructure based on soil-structure interaction
- Risk assessment and uncertainty quantification in geotechnical projects
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XGBoost Training R² for Ultimate Bearing Capacity Prediction
Enterprise Process Flow
Data Collection (116 Footing Experiments)
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Data Preprocessing & Splitting (70% Train, 30% Test)
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Hyperparameter Tuning (Bayesian Optimization)
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Model Training (ML & DL Algorithms)
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Performance Evaluation (R², MAPE, RMSE, etc.)
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Feature Importance Analysis (SHAP)
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Prediction of Ultimate Bearing Capacity
| Method Category | Key Advantages | Prediction Accuracy (R² Range) |
|---|---|---|
| Ensemble ML (e.g., XGBoost, GBM) |
|
0.972 - 0.9999 |
| Traditional Theories (e.g., Terzaghi, Meyerhof) |
|
0.684 - 0.82 |
SHAP Analysis: Key Influential Parameters
A SHapley Additive exPlanations (SHAP) analysis highlighted foundation depth (D) and soil friction angle (φ) as the most influential parameters for ultimate bearing capacity prediction, aligning well with established geotechnical principles. This reinforces the interpretability of advanced AI models in engineering contexts, providing actionable insights into critical design factors.
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Your AI Implementation Roadmap
Our structured approach ensures a seamless transition and maximum value realization for your AI initiatives in geotechnical engineering.
Phase 1: Data Integration & Model Prototyping
Consolidate existing geotechnical data and begin developing initial ML/DL models. Focus on demonstrating feasibility and accuracy on historical datasets.
Phase 2: Validation & Customization
Validate prototype models with site-specific data and customize algorithms for unique project requirements. Integrate explainable AI (SHAP) for transparent decision-making.
Phase 3: Deployment & Monitoring
Deploy validated models into engineering workflows and establish continuous monitoring for performance and data drift. Provide training for geotechnical engineers on AI tool usage.
Phase 4: Optimization & Scalability
Refine models with new data, explore advanced feature engineering, and scale the AI framework across multiple projects for maximum enterprise impact.
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