Reliable Parameter Determination for Salt Rock Mechanics Constitutive Models through a Multi-step Calibration Strategy

Core Concepts

A multi-step calibration strategy is presented to reliably determine a single set of representative material parameters for salt rock constitutive models based on multiple deformation datasets.

Abstract

The content discusses the development of a comprehensive constitutive model to capture the complex nonlinear deformation physics of salt rocks, including transient, reverse, and steady-state creep.
The key highlights are:

A multi-step direct calibration procedure is proposed to determine a single set of representative material parameters by including experimental data one at a time and solving a multi-objective optimization problem.

A regularization term is added to the loss function to ensure similar fitting quality across all experiments.

The Particle Swarm Optimization (PSO) algorithm is employed to solve the optimization problems.

Synthetic experimental data is used to assess the performance of the proposed calibration strategy, as relevant experimental datasets are lacking.

Global sensitivity analysis is performed to identify the most influential material parameters and understand the potential challenges in the optimization process due to the presence of local minima.

The calibration strategy is tested by first calibrating each synthetic experiment individually, and then calibrating the entire set of experiments as they become available.

The results show that the proposed calibration approach is robust and the model accuracy improves as more data is included in the calibration process.

Stats

The synthetic experimental data used in this study includes the following key metrics:

Axial and radial stresses applied to the salt rock samples
Corresponding axial, radial and volumetric strains measured over time

Quotes

None

Key Insights Distilled From

A multi-step calibration strategy for reliable parameter determination of salt rock mechanics constitutive models

by Herm... at arxiv.org 03-29-2024

https://arxiv.org/pdf/2403.19426.pdf

Deeper Inquiries

How can the proposed calibration strategy be extended to account for the presence of tertiary creep and damage in salt rocks

To extend the proposed calibration strategy to account for tertiary creep and damage in salt rocks, modifications to the constitutive model and optimization process would be necessary.

Constitutive Model Adjustment:

Tertiary Creep: Including a tertiary creep model component in the constitutive model to capture the long-term, accelerating deformation behavior observed in salt rocks under sustained loading conditions.
Damage Model: Introducing a damage model to account for the progressive degradation of the material due to cyclic loading, which can lead to changes in stiffness and strength over time.

Optimization Process Enhancement:

Additional Parameters: Incorporating parameters specific to tertiary creep and damage mechanisms into the calibration process.
Objective Function: Modifying the objective function to include metrics that assess the model's ability to capture tertiary creep and damage effects.
Data Integration: Integrating experimental data that specifically characterize tertiary creep and damage behavior to refine the calibration process.

By adapting the constitutive model and optimization approach to address tertiary creep and damage, the calibration strategy can provide a more comprehensive representation of the mechanical behavior of salt rocks under varying loading conditions.

What are the potential challenges in applying this calibration approach to real experimental data, where measurement uncertainties and sample heterogeneities may be more pronounced

Applying the proposed calibration approach to real experimental data poses several challenges due to the complexities and uncertainties inherent in laboratory testing of salt rocks:

Measurement Uncertainties:

Variability in experimental setups and instrumentation can introduce uncertainties in the collected data, affecting the accuracy of the calibration process.
Addressing measurement errors and ensuring data quality is crucial for reliable parameter determination.

Sample Heterogeneities:

Natural variations in salt rock samples can lead to heterogeneity in material properties, requiring careful consideration during calibration.
Developing strategies to account for sample-to-sample variability and ensuring the calibration process is robust across different sample types.

Model Complexity:

The multi-parameter constitutive model used for calibration may introduce challenges in determining the optimal parameter set, especially when dealing with real-world data with inherent noise and variability.

Computational Resources:

Real experimental datasets may be larger and more complex, requiring significant computational resources for optimization and analysis.

Addressing these challenges would involve rigorous data preprocessing, robust optimization algorithms, and thorough validation procedures to ensure the reliability and accuracy of the calibration results.

How can the insights from the global sensitivity analysis be leveraged to further improve the optimization process and ensure convergence to the global minimum

Insights from the global sensitivity analysis can be leveraged to enhance the optimization process and improve convergence to the global minimum in the following ways:

Parameter Prioritization:

Focus on optimizing parameters that exhibit strong correlations with the loss function, as identified through sensitivity analysis, to prioritize adjustments that have a significant impact on model performance.

Constraint Formulation:

Incorporate constraints based on the sensitivity analysis results to guide the optimization process towards regions of the parameter space that are more likely to lead to improved model fits.

Adaptive Algorithms:

Implement adaptive optimization algorithms that dynamically adjust the search strategy based on the sensitivity of parameters, allowing for more efficient exploration of the parameter space.

Ensemble Methods:

Utilize ensemble optimization methods that combine multiple optimization runs with different parameter settings to enhance exploration and exploit the identified correlations for improved convergence.

By integrating the findings from the sensitivity analysis into the optimization strategy, the calibration process can be fine-tuned to efficiently navigate the parameter space and achieve more robust and accurate model parameter determinations.