Supervised machine learning models based on the architecture of the artificial neural networks, Support Vector Machine, Decision Tree Regressor and Random Forest were also used for shear resistance predictions. 𝐴𝑣 stirrup area within the distance of the stirrup distance 𝑎/𝑑 ratio of their shear span to effective depth. 𝑉𝑅𝑑 the design value of the shear resistance force 𝑉𝑅𝑑,𝑐 concrete contribution to the design shear resistance 𝑉𝑅𝑑,𝑠 contribution of the stirrup to the design shear resistance 𝑉𝑅𝑑,𝑚𝑎𝑥 the upper limit of the design shear resistance.
𝑉𝑙 contribution of the longitudinal reinforcement/penaction to shear resistance 𝑉w shear transferred across web cracks.
Background of the study
Motivation and problem statement
Research aim and objectives
Summary of chapters
- Review of shear in beams without shear reinforcement
- Shear behaviour of reinforced concrete beams without stirrups
- Deep beams
- Short Beams
- Slender Beams
- Very slender beams
- Shear transfer mechanism
- Shear in the uncracked compression zone
- Dowel action
- Aggregate interlock
- Residual tensile stress in concrete
- Shear reinforcement contribution
- Arch action
- Parameters contributing to shear strength
- Longitudinal reinforcement ratio
- Concrete strength
- Size effect
- Span - effective depth ratio
- Axial force
- Review of shear models from current national codes of design
- European Code (EC2)
- Australian code (AS 3600 - 2018)
- American Code (ACI 318-19)
- The South African national standard (SANS 10100 -1(2000))
- fib Model Code 2010
- Literature-Based shear Models
- Compression chord capacity model (CCCM)
- Modification of the SNiP Shear Model
- Mechanical Model Based on Structural Mechanics
- Structural reliability assessment
- Model uncertainty
- Uncertainty Model in the existing literature
- Reliability index and target reliability
- General probabilistic Model
- Overview of machine learning
- Application of machine learning
- Classification of machine learning algorithm
- Theory and Mathematical Intuition of Machine Learning models
- Support Vector Machine
- Artificial Neural Network
- Decision tree
- Random Forest
Aggregate jamming: (a) kinematics of a shear crack with relative opening (w) and slip (𝛿) components; and (b) contact stresses (Fernandez Ruiz et al., 2015). A maximum margin hyperplane that separates two completely separable classes with only five support vectors for the optimal solution of the optimization problem (Swamynathan, 2017).
- Regression and correlation
- Coefficient of correlation
- Distribution and cumulative frequency of dataset
- Deterministic analysis of shear resistance
- Mean value analysis
- Design value analysis
- Machine learning model building and evaluation
- Uncertainty modelling of authorial code-based and machine learning shear models
- Model factor derivation
- Model factor based on machine learning models
- Statistical moment analysis of model factor
- Demerit point analysis
- Sensitivity analysis
- Probabilistic modelling for model uncertainty
- Reliability assessment and partial calibration approach
- Global comparison of mean value shear prediction to experimental shear strength
- Comparison using the perfect line analysis
- Global comparison of shear mean value prediction to experimental shear strength with respect to
- Global comparison of shear mean value prediction to experimental shear strength with respect to
- Comparison of experimental shear strength to the EC2 and other shear design values
- Statistical analysis of model factor observations
- Statistical moment
- Histogram of model factors
- Identification of outliers
- Sensitivity analysis of model factors
- Sensitivity analysis discussion of model factors
- Choice of probabilistic model
- Demerit point analysis for design shear value
- Comparison of experimental shear strength to machine learning shear predictions (a subset of
- Comparison of predictions from machine learning models to experimental shear strength
- Comparison using the annotated heatmap
- Comparison of machine learning prediction to experimental shear strength with respect to
- Statistical analysis of machine learning model factor observations
- Histogram of model factor realizations for A. I based shear models
- Histogram of the prediction error of A. I based shear models
- Identification of outliers
- Trend Analysis of model factors derived from machine learning models
- Probability distribution function of realized A.I based shear model factor
- Performance evaluation of ML shear results
- Optimal hyperparameter of ML models selected via cross-validation
Comparison of experimental shear strength (VEXP) with predicted machine learning shear strength (VML) a) VANN, b) VSVM, c) VDT, d) VRF.
FORM Sensitivity Factor
1 If COV% of model uncertainties > COV% of geometric and material properties, model uncertainty is dominant. In addition, the choice of the probability distribution function influences the reliability predictions of investigated shear models and is a good indicator of a model's performance. The derived model factor statistics were used as an indicator of the uncertainty in the reliability prediction of shear models.
The scatter around the mean = 0.30 and the variation in shear prediction = 27% revealed the degree of uncertainty of the 𝑉𝐸𝐶2 shear method. In general, the sensitivity to shear parameters poses an issue of adequate calibration of the size effect in the ACI shear method. Safety issues related to the performance of the mechanical compression chord capacity (CCC) model at a high slenderness ratio (very slender beams) and a high amount of longitudinal.
Although conservative, the model factor realization statistics of 𝑉𝐶𝐶𝐶 are somewhat satisfactory with a mean value of 1.14, a standard deviation of 0.28 and a coefficient of variation of 0.25. The investigation showed that the performance of the modified SNiP cutting method raises alarming economic concerns. This overconservatism is the result of the neglect of important shear parameters since the modified SNiP shear method includes only very basic shear parameters.
The insensitivity of the shear model 𝑉𝑁𝐿𝑇 to the main shear parameters is indicative of its robustness and reliability in prediction in the considered parametric range. The procedures highlighted in the work of Konig et al. 2012) should be adopted to correctly incorporate the effect of the partial safety factor of model uncertainty for the modified SNiP shear method.
Selection of Target Reliability Index β
Model Uncertainty Partial Factor related to SANS shear resistance model for beams without
Overview
The inability of investigated shear models to adequately replicate trends as seen in experimental observations indicates significant underlying uncertainties inherent in the shear strength models for beams without shear reinforcement. The identified uncertainties may result from model oversimplification or neglect of important shear parameters leading to an overestimation or underestimation of shear strength and an inconsistent prediction across the parametric range. The prediction of displacement reliability for a studied model is based on its insensitivity to the considered range of displacement parameters, marginal or no bias in the mean value of realizations of model factors, minimal coefficient of variation, a low dispersion of model factor realizations around the mean and also the ratio between maximum model factor and minimum (𝑀𝐹𝑚𝑎𝑥⁄𝑀𝐹𝑚𝑖𝑛) must be minimal.
Further investigation revealed that there was no clause in national codes or author publications that the investigated models were calibrated to account for the intentionally structured trends associated with increasing shear strength parameters. Uncertainties discovered after a thorough evaluation of the considered models have given rise to safety and economic concerns, as will be discussed in the following sections. The performance of the shear model should not result in excessive conservatism or significant non-conservative estimates, as an overly conservative estimate leads to uneconomic performance of the shear models, while a significant non-conservative prediction raises concerns about the safety performance of the shear models.
Accomplishments of research objectives
An in-depth knowledge of the underlying principles or phenomenon used in the formulation of the considered shear capacity models together with the included constraints is a form of bias. Mathematical intuition behind the development of supervised machine learning models and deep neural networks with implementation in python (an object-oriented programming language) and the use of python library packages such as Pandas, NumPy, Sci-Py, machine learning library (Sci-Kit) and Neural Network -library packages such as TensorFlow and Keras API. Proper application of structural reliability assessment methods that include concepts such as deterministic assessments, probabilities and statistics.
The resulting model factors were parametrically related to significant shear design parameters for observed trends and were found to be sensitive to some shear parameters, although mechanical models appeared to be less sensitive to shear parameters. Correlation and regression analysis showed negligible, mild and significant sensitivity of model factors to important parameters affecting shear strength. After the reliability investigation, a partial factor was derived for the EC2 and SANS shear models, in addition to the justification in the last part of Section 5.3, to account for the model uncertainties in the shear models.
Finally, a general probabilistic model suitable for a futuristic full reliability assessment of shear models without shear reinforcement was identified for both non-AI-based models and A.I-based models and will be recommended in the following section.
Limitation of research
Assessment of model uncertainty for shear reliability
The model factor 𝑀𝐹𝑀𝐴𝑆𝑀 associated with the shear method 𝑉𝑀𝐴𝑆𝑀 has a mean value of 1.11 and a standard deviation of 0.28, confirming that the MASM mean shear function generally underpredicts shear performance. The significant sensitivity to 𝑝𝑙 indicates the neglect of this term, while the sensitivity to the compressive strength of concrete is due to incomplete information when deciding to replace compressive strength with tensile strength under the assumption that “tensile strength of concrete and not compressive strength of concrete should be considered when designing a shear model . Overall, the modified SNiP shear capacity approach significantly underpredicts shear capacity with a mean of 1.65, a standard deviation of 0.52, and a coefficient of variation of 0.31.
The assessment showed that applying the SANS shear method at a high shear span to an effective depth ratio (very slender beams) is an unsafe practice as all the predictions at this high slenderness ratio provided increasingly unconservative estimates, thus the shear capacity exaggerated. Of all the shear models considered in this study, code-based models (such as EN 2003, ACI 318, AS 3600, Fib Model Code 2010 and SANS10100), author models (such as CCC, MASM, NLT and the modified SNiP shear model) and machine learning -based shear models (ANN, SVM, RF and DT), 𝑉𝑁𝐿𝑇 is the best predictor of shear capacity. 𝑀𝐹𝑁𝐿𝑇 was the most favorable candidate in terms of statistical moments with a mean of 1.02, a standard deviation of 0.16 and a coefficient of.
Investigations from machine learning shear predictions showed that all A.I-based shear methods were a good predictor of shear capacity in terms of mean value, distribution of data points, presence of outliers, and sensitivity to the cutting parameters. The highest bias seen in the machine learning cutoff result was in the case of 𝐹𝑆𝑉𝑀 which was only 7% conservative, this is relatively small compared to the first conservatism in 𝑀𝐹𝐴𝐶𝐼 = 31% conservative, 𝐶 = 31% conservative, 𝐶%. Although the only shortcoming of 𝐹𝑆𝑉𝑀 and 𝑀𝐹𝐷𝑇 was their descriptive statistics showing the variability of 𝑀𝐹𝑆𝑉𝑀 and 𝑀𝐹 0 with a relatively large variation coefficient of 0.0. 7 respectively.
Unlike 𝐹𝑆𝑉𝑀 and 𝑀𝐹𝐷𝑇, the intercept predictions from 𝑀𝐹𝐴𝑁𝑁 and 𝑀𝐹𝑅 of 1.00. Both 𝑀𝐹𝐴𝑁𝑁 and 𝑀𝐹𝑅𝐹 are arguably reliable in predicting shear, but 𝑀𝐹𝐴𝑁𝑁 is the better predictor due to its less sensitivity to shear parameters.
Recommendations
- Main recommendations from the dissertation
- Recommendations for future research
The degree of dispersion around the mean value is significantly smaller compared to the other investigated cutting models as seen in Table 4.1. The marginal measure of the distribution indicates that there is no shape or negligible degree of uncertainty associated with 𝑉𝑁𝐿𝑇. Furthermore, such a model can be adopted as a probabilistic model in future reliability evaluations of alternative shear design methods.
Out of all the displacement models considered in this study, the displacement method based on structural mechanics proposed by Ngoc Linh Tran (𝑉𝑁𝐿𝑇) meets the requirements of a good model as mentioned above and is considered to be the best predictor of shear capacity. While considering soft computation, 𝑉𝐴𝑁𝑁 and 𝑉𝑅𝐹 fulfill the demand for a suitable model and can also be used as a probability model for reliability analysis. The mechanical model of Ngoc Linh Tran is proposed as a probabilistic model for future reliability assessments of alternative shearing techniques, as the study showed that it was the best predictor of shear strength as it correctly reflects shear failure and has the lowest level of uncertainty in its model factor. Statistics.
In general, a mechanical model based on structural mechanics theory, fracture mechanics, and crack theory should be evaluated for reliable shear predictions and adopted by national codes instead of conventional empirical models that have many assumptions and neglect important shear parameters, resulting in uncertainties. The investigation carried out in this study showed that the EC2 shear method overpredicts the shear at larger beam depths, leading to unsafe designs. Therefore, for safe design practices, it is recommended that the current state of the EC2 shear method not be used to assess the shear capacity of beams > 500 mm deep until the size effect concern is addressed after appropriate calibration.
The mechanical model proposed by Tran (2020) should be used as a general probabilistic model for the complete reliability assessment of any alternative shear design arrangement for beams without shear reinforcement. The underestimation of the shear capacity according to the ACI shear methods for beams without shear reinforcement requires a good reliability calibration.
