Enhancing Geotechnical Design with DeepEX Statistical Analyses
- deepexcavation
- 3 days ago
- 6 min read
Reliability Analysis VS Deterministic Design
Introduction
In geotechnical engineering, uncertainty is not the exception, it is the rule. Soil is a naturally variable material, and its properties can change significantly even within a single project site. Deterministic analysis, which relies on single “characteristic” values for soil parameters, often simplifies this variability into a single calculation. While practical, this approach can obscure the real range of possible outcomes, sometimes leading to designs that are either overly conservative or unconsciously risky (Phoon & Kulhawy, 1999). To address this issue, reliability-based design has emerged as a powerful approach. Instead of asking “Is my factor of safety greater than 1.5?”, engineers can now ask: “What is the probability that this system will perform safely under the expected variability of soil and loads?” DeepEX brings this capability directly to the user’s desktop.
Why Reliability Analysis is Superior to Deterministic Design
Deterministic analysis uses single “best estimate” or conservative values for soil and load parameters and produces one factor of safety. This often leads to designs that are either over-conservative (driving up costs) or unintentionally unsafe if the chosen parameters do not adequately represent variability. In contrast, reliability analysis treats soil and load parameters as random variables with defined probability distributions and evaluates design performance across a range of possibilities.
The advantages of reliability analysis over deterministic analysis include:
· Quantification of risk, providing both factor of safety and probability of failure.
· More optimized designs, reducing unnecessary conservatism and costs (Baecher & Christian, 2003).
· Transparent communication of risk to stakeholders.
· A more realistic representation of soil behavior and uncertainty (Fenton & Griffiths, 2008).
DeepEX’s Capabilities for Statistical & Reliability Analyses
DeepEX incorporates advanced statistical tools seamlessly within its geotechnical modeling environment. With minimal additional input, engineers can:
· Assign distributions (e.g., normal, log-normal, uniform) to soil strength, stiffness, and load parameters.
· Run Monte Carlo simulations to evaluate a wide range of scenarios.
· Obtain reliability indices and probabilities of failure, alongside traditional factors of safety.
· Visualize design performance across thousands of simulated cases, making uncertainties clear and actionable.
This integration empowers engineers to perform both conventional deterministic checks and reliability-based analyses in a single, streamlined workflow.
From Theory to Practice
To illustrate how this works in a real project, let’s consider an excavation design example. We’ll walk through the process of:
1. Defining soil parameter distributions.
2. Running statistical analysis within DeepEX.
3. Interpreting results such as probability of excessive wall deflection or basal heave.
Model configurations
To illustrate the application of DeepEX’s reliability analysis features, consider a 7 m deep excavation supported by a sheet pile wall system. The wall is braced by an anchored deadman wall located behind the excavation, providing restraint against horizontal movement.
The soil profile consists of multiple layers with varying geotechnical properties. The representative soil parameters are provided in Table 1. For the probabilistic analysis, soil parameters were modeled as random variables following a Normal Distribution with truncation. A lower bound of mean – 2.4·σ and an upper bound of mean + 2.5·σ were imposed to reflect realistic variability while excluding extreme outliers.
Table 1- Shear strength properties with mean and standard deviation values.
Statistical analysis set up
The soil parameter distributions are defined within DeepEX using the Statistical Parameters and Modelling for Soils interface, where users can assign mean values, standard deviations, and truncation limits for each property. As illustrated in Figure 1, parameters such as friction angle, cohesion, and undrained shear strength were modeled with Normal distributions (with truncation). The software also provides alternative statistical models, including Log-normal and Beta distributions, which allow engineers to better capture skewed or bounded behaviors of soil properties. These statistical definitions form the foundation of the probabilistic analysis, enabling DeepEX to run Monte Carlo simulations in which soil parameters are sampled systematically. This workflow captures the natural variability of ground conditions and quantifies its influence on excavation performance measures such as wall deflection, bending moments, anchor forces, and basal stability.
Figure 1. Window to define the distribution of the soil parameters in DeepEX.
The model was defined in several steps to replicate the construction stages of the excavation. In the final stage, the complete soil stratigraphy and the retaining system are represented. Figure 2 illustrates the final model configuration together with the soil profile, providing a clear view of the excavation geometry and subsurface conditions used in the analyses. A Limit Equilibrium Method (LEM) analysis is used in this example to perform both the stability evaluation and the statistical assessment.
Figure 2. Excavation model and soil stratigraphy in DeepEX.
To perform the probabilistic stability analyses, a sufficient number of realizations must be defined, with each iteration generating a new set of soil property values sampled from the chosen statistical distributions. Figure 3 presents the setup in DeepEX, where the user specifies the number of Monte Carlo iterations and the confidence level to be applied. In this example, a 95% confidence level was selected, ensuring that the minimum wall properties are derived from the confidence level moments. This approach allows the analysis to not only reflect the inherent variability of soil behavior but also to provide statistically reliable bounds for design parameters such as wall deflection, bending moments, and anchor forces.
Figure 3. Statistical analysis options in DeepEX.
Model Verification and Output Interpretation
Figure 4 presents the results of the deterministic analysis, showing the bending moment distribution along the retaining wall and the corresponding effective horizontal soil pressure diagram. The moment diagram indicates the internal structural response of the wall, highlighting the maximum bending demand near the excavation base and at the support level. The horizontal pressure plot illustrates the interaction between the soil and the wall, distinguishing the active and passive pressure zones that govern equilibrium. Together, these outputs provide essential insight into how the wall resists soil loads and how stress redistribution occurs as excavation progresses, forming the basis for the subsequent probabilistic stability assessment.
Figure 4. Results of the Moments and Horizontal pressures for the LEM analysis DeepEX.
The outcomes of the probabilistic analysis are presented as percentage distributions within defined intervals. Figure 5 illustrates the statistical results for the factor of safety (FS) against embedment rotation of the sheet pile wall. Each bar in the histogram represents the frequency of occurrence of a given FS range across all Monte Carlo simulations, expressed as a percentage of total realizations. The red line indicates the lower bound, here corresponding to an FS value of 4.81. This graphical representation not only highlights the variability in performance but also provides insight into the probability of reaching or exceeding critical safety thresholds.
Figure 5. Statistics graph against FS embedment rotation for example in DeepEX.
In addition to the factor of safety against embedment rotation, DeepEX provides a comprehensive suite of statistical verification results that cover both the structural response of the wall and the overall stability of the excavation. These include moment, shear, and displacement results, as well as multiple factors of safety related to wall embedment and global behavior.
Specifically, the software reports probabilistic distributions for:
· Moment Results – representing the range and likelihood of maximum bending moments along the wall, which allows evaluation of how uncertainty in soil properties affects structural demand.
· Shear Results – showing the statistical variation in shear forces with depth, identifying zones where extreme values are most probable.
· Displacement Results – illustrating the probability distribution of wall deflections and ground movements, which helps assess serviceability performance under variable ground conditions.
· FS Wall Embedment Rotation, Passive, and Length (L) – providing probabilistic safety margins for rotational stability, passive resistance, and embedment adequacy. These indicators reveal how variability in soil parameters influences the reliability of the wall’s embedment design.
· Basal Stability Results – quantifying the probability of basal heave or deep-seated failure, particularly important in excavations within soft or sensitive soils.
· FS Slope Stability – giving the statistical distribution of the global factor of safety for the entire excavation system, integrating soil–structure interaction and spatial variability.
Together, these results allow engineers to quantify the reliability of each performance criterion rather than relying solely on deterministic single-value checks. By expressing outcomes as percentage distributions, DeepEX helps identify not only the mean or characteristic response but also the probability of reaching critical thresholds, providing a more informed and risk-based basis for design verification.
Concluding Remarks
By embracing statistical and reliability analyses, geotechnical engineers can move beyond the inherent limitations of traditional deterministic design, which often masks the influence of soil variability behind a single factor of safety. Instead, probabilistic approaches provide a richer, more realistic understanding of how uncertainties in soil properties and loads affect excavation performance.
With DeepEX, this shift is not only possible but also fully integrated into everyday practice. The software allows engineers to assign statistical distributions to soil parameters, run Monte Carlo simulations, and interpret performance through statistical analyses and reliability indices. This capability empowers design teams to identify the likelihood of critical events, optimize material use, and communicate design risks with greater transparency to stakeholders.
Ultimately, the adoption of reliability-based analysis within DeepEX translates into safer designs, more cost-effective construction strategies, and a modern geotechnical workflow that aligns with the increasing demand for risk-informed engineering solutions.
References
Phoon, K.K., & Kulhawy, F.H. (1999). Characterization of geotechnical variability. Canadian Geotechnical Journal, 36(4), 612–624.
Baecher, G.B., & Christian, J.T. (2003). Reliability and Statistics in Geotechnical Engineering. John Wiley & Sons.
Hasofer, A.M., & Lind, N.C. (1974). Exact and invariant second-moment code format. Journal of the Engineering Mechanics Division, 100(1), 111–121.
Fenton, G.A., & Griffiths, D.V. (2008). Risk Assessment in Geotechnical Engineering. John Wiley & Sons.
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