How to predict tunnelling-induced damage under model uncertainty in heterogenous soft ground?

Predictive analytics for Tunnelling-induced damage

In one of the previously published articles in Geostructural Design Processes (GDPs), a performance-based process for assessing risks related to tunnelling-induced settlement for large building stocks using remote sensing real-time database was discussed (https://www.dhirubhai.net/posts/ehsan-moradabadi-b4801b81_itwin-tunelling-settlement-activity-6991427772480978944-XomM?utm_source=share&utm_medium=member_desktop).

As explored in that article, evaluating the impact of tunnelling on above ground structures in urban areas highly relies on prediction of the settlement trough at surface level. Regarding a specific iTwin framework suggested for tunnelling in the mentioned article, the prediction of tunnelling-induced damage to above ground buildings includes treating uncertainties in soil properties and other system characteristics. Classically, empirical formulas are used for prediction of the settlement using the experience from previous tunnelling projects. Empirical formulas genuinely do not consider the soil-lining interaction or the method of construction and lack a theoretical background for ground movement in continuum mechanics. Analytical and numerical approaches have developed to address some of these deficits, but are not able to take account of many uncertainties involved in the process.?

In this edition of GDPs, the process of constructing stochastic discrete random finite element models to probabilistically predict the tunnelling-induced surface settlement treating the above deficits is summarised. The method, published before as a PhD thesis in 2017, proposed a single mechanism (i.e. an uncertainty and sensitivity analysis framework) in which multiple sources of uncertainty can be considered within a single model (e.g. heterogeneity of the soil profile, variability in surcharge loads, and material properties). The power of the method was then examined through application to case studies involving two large-scale, shallow tunnelling projects excavated in alluvium soil, Tren Urbano tunnel in Porto Rico subway project, USA, and Amirkabir road tunnel in Tehran, Iran. The results were compared with monitoring data, with estimations from deterministic finite element (FE) models and empirical formulas.?

While it was an effort to provide a layman summery for individuals with relevant background in structural, geotechnical and probability analyses in this edition of Geostructural Design Processes, professionals being interested to know more about the subject are highly recommended to review the main thesis to find more information and results about the method.

Process of constructing the probabilistic models for prediction of tunnelling-induced damage?

Figure 1 shows a proposed paradigm introduced for decision analysis for predicting tunnelling-induced surface soil settlement. The suggested paradigm includes four different parts: a) analysing building and contractual documents, b) probabilistic modelling and reliability analysis, c) Damage assessment and control of performance (reliability) criteria and d) mitigation plan. An effective methodology for predicting tunnelling impacts highly depends on the availability of building and contractual documents. These documents are summarised in Figure 1, generally titled ‘building and contractual documents’. The above ground investigations illustrate a real status of loading conditions of the project and indicate the loading condition of buildings and other relevant information. However, the availability of the relevant in-situ or experimental data to construct an adequate, site-specific ground database depends on the progress of the tunnelling project design or construction phase. In case the tunnelling project is in the early phase of the design or the planning, the literature review or reviewing previous case studies are usually helpful for defining the design parameters or even ground conditions.??Based on the multidisciplinary design documents of tunnelling projects, geometry and structural component of a tunnel can be defined to generate finite element model(s). These documents include all structural component and geotechnical considerations for adequately predicting the response of the ground (e.g. settlement troughs in the specific subject of the thesis, but the application can be extended to a general problem) due to tunnel’s geometry and buildings’ stiffness and loading. For practical performance assessment, involving all stakeholders of a tunnelling project, contractual ratios relate to the performance of the tunnel and acceptability level of damage can be introduced by pre-agreed performance criteria.??These pre-agreed criteria consider building’s importance factors based on regulation and the sensitivity of the project and buildings, being found in regulations and contractual documents (e.g. maximum allowable slope of the ground, maximum allowable building settlement, allowable critical principle strains in buildings and/or corresponding allowed damage categories).

Since numerical models employed to generate performance functions of a tunnel under investigation are highly complex nonlinear finite element models, it was assumed herein that the models have neither a closed form solution nor characterised output probability functions. Thus, for investigating the models under uncertainty, Monte Carlo Simulation (MCS) can be applied, and the effects of uncertain random input variables for this complex system can be evaluated by introducing sampling from a non-close form Finite Element Model.

The whole computational sequences of the suggested framework needed to apply to a project can be summarised as below:?

A. Statistical analysis to define the distribution function of each important parameters of the problem and to interpret the random field parameters of each layer of the soil profile including distribution functions of characteristic material properties and their correlation structures.??

B. Sensitivity analysis?

Propagate reasonable finite number of random vectors by sampling from uniform distribution functions using Latin Hyper cube sampling or other available??efficient smart sampling, and for each generated random vector simulate the following then:??

I. Produce??finite number of parametric FE models of the problem under investigation, and calculate bellows for each model:??

i. Generate discrete random field with the geometry parameters of the problem based on the concept of the random functionality described in section 3.4.2 of the thesis.?

ii. Map the random variable of each local domain of random field to the corresponding mesh in the generated FE model.?

iii. Execute the model appropriate times to generate a histogram of random finite element model’s response (see section 5.5 of the thesis for how to select an appropriate number).?

iv. Construct the weighted histograms from all different types of models (i.e. satisfying equation 3.7 of the thesis)

b. Calculate, the averages, maximums and minimums of the histograms?

c. Perform regression analysis, Partial Ranked Correlation Coefficient (PRCC) and Standardised Ranked Regression Coefficient. (SRRC) analysis and to calculate p-values, PRCC and SRRC indexes for each parameter corresponding to the outputs of the previous step??

d. Interpret the results to capture the most import input parameters??

e. Increase the number of simulations if needed and repeat steps a to d??

C. Reliability analysis?

a. Update the uniform density function of each important parameter to non-uniform (if appropriate) and assume a nominal value for the rest.?

b. Propagate??reasonable numbers of random vectors by sampling from probability distribution functions of important parameters using LHS, and simulate bellows for each generated random vector.?

I. Generate finite numbers of parametric FE models of the problem under investigation, and calculate bellows for each model:??

i. Generate discrete random field with the same geometry parameters of the problem based on the concept of the random functionality described in section 3.4.2. of the thesis

ii.??Map the random variable of each local domain of random field to the corresponding meshes in the FE models generated.??

iii.??Execute the model for appropriate finite times to generate a histogram of desired outputs of random finite element models.?

II. Construct weighted probability mass function histograms from all models??

III. Fit a known form probability density function to each histogram of the previous step?

IV. Calculate reliability curves from the lower bound of each cumulative distribution functions derived from the previous step assuming an appropriate factor as probability of loss

c. Generate the cumulative mass functions??of the whole system??

d. Fit a known form probability distribution function to each histogram of the previous step to derive the reliability curves

e. Check the limit state functions (i.e. equation 3.15 of the thesis), assuming an appropriate probability of loss

?f. Bayesian updating if needed??

I. Construct the likelihood function of the observations, if available.?

II. Update reliability curve of system using likelihood functions, if needed

The above suggested framework was successfully implemented to two different large scale projects in Alluvium soil. Figure 2 shows the application of the method in prediction of reliability curves of surface settlements of Amirkabir Road Tunnel??in Tehran, Iran, Figure 3 illustrates the?graphical abstract of how the method applied to Tren Urbano subway project in Porto Rico, USA.

Compared to the results of classical Finite Element Method and empirical approaches, application of the new probabilistic approach provides better understanding of the development of the settlement trough at surface level in both case studies. The output parameters for the tunnelling-induced settlement trough (volume loss and maximum settlement) are in good agreement with actual monitoring data in both case studies. Notably, the prediction result of the empirical formula in the first case study is conservative and for the second one is quite non-conservative. The new approach, on the other hand, provides more accurate predictions and insights into the effect of different sources of uncertainty.

To find more about the method and the case studies, please find the published thesis below:

https://library.ucd.ie/iii/encore/record/C__Rb2142718?lang=eng

To find more about Geostructural Design Processes, find the other newsletters below??:

https://www.dhirubhai.net/newsletters/6985944134142283776/