Abstract
Purpose
A common design driver for pipe-jacking projects is the jacking force required to advance the tunnel boring machine and pipe string. Empirical methods are popular in industry but are well known to lack accuracy, while there is a strong desire to supplement such approaches with robust data-driven techniques, typically small construction datasets present significant challenges.
Design/methodology/approach
To address this challenge, this paper develops a physics-constrained neural network predictive model for pipe-jacking forces. Information used as input into the model includes principal design information and soil type.
Findings
The physics constrained model was found to predict jacking force to a higher accuracy than current industry practice and better discern meaningful patterns in data than a purely data-driven artificial neural network. The results reveal promising performance for this initial dataset such that there is motivation, as a longer-term objective, to train the present approach on a more comprehensive drive database for more reliable and cost effective solutions for new projects.
Originality/value
Novel contributions include (a) a bespoke framework to constrain a neural network using a pipe-jacking mechanistic model which includes stoppage-induced friction increases, (b) built-in model uncertainty for greater confidence in model outputs, (c) new historical drive data for model training and (d) one-hot encoding of soil type as a model input. The model is calibrated and validated against 14 tunnel drives across four different sites with four distinctive ground types.
Keywords
Citation
Rayner-Philipson, M., Sheil, B. and Zhang, P. (2025), "Prediction of pipe-jacking forces using a physics-constrained neural network", Machine Learning and Data Science in Geotechnics, Vol. 1 No. 1, pp. 24-34. https://doi.org/10.1108/MLAG-06-2024-0004
Publisher
:Emerald Publishing Limited
Copyright © 2024, Malachi Rayner-Philipson, Brian Sheil and Pin Zhang.
License
Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/by/4.0/legalcode
Introduction
Pipe-jacking is fast becoming the primary construction method for buried utility infrastructure. A key concern in both design and construction is that jacking forces may exceed the prepared-for capacity, resulting in jacking pipe/launch shaft damage and/or costly tunnel boring machine (TBM) recovery. Uncertainty in jacking forces – amplified by the influence of work stoppages – necessitates redundant intermediate shafts and/or inter-jacks at great expense (Atalah et al., 1994; Sheil, 2021).
Early predictive methods are predominately empirical, involving multiple regression analyses or probability based formulae (Auld, 1982; Ripley and Ripley, 1989; Chapman et al., 1999; Pellet-Beacour and Kastner 2002; Sofianos et al., 2004; Staheli, 2006). While widely adopted in industry, such methods are known to be inaccurate and over-conservative (Li et al., 2019). Rcent numerical modelling research has simulatd the pipe-jacking process with greater fidelity, including the mechanics at the pipe-soil interface (Yen and Shou, 2015; Li et al., 2019; Ji et al., 2019). However, predictions using these numerical methods are highly influenced by user-defined inputs, introducing greater uncertainty, as well as rarely being transferable to different contextual cases. Thus, numerical simulations are rarely used as a benchmark.
Data collected from modern TBMs presents a new opportunity for improved machine learning (ML) predictive methods (Sheil et al., 2020). For traditional large-diameter tunnelling, applications of ML to TBM performance prediction have soared, e.g. hybrid artificial neural networks (ANNs) (Armaghani et al., 2017), deep neural networks (Koopialipoor et al., 2019) and support vector regression (Mokhtari and Mooney, 2020). In contrast, applications of ML to pipe-jacking are scant, particularly to predict jacking force. Recent efforts have included the use of Gaussian process regression (Sheil, 2021) and particle swarm optimisation (Zhou et al., 2023) with reasonable degrees of success. However, those methods are purely data-driven and thus remain prone to spurious predictions, particularly when trained on typically small construction data sets.
The paper addresses this need by introducing a new physics-constrained neural network for pipe-jacking force prediction. Novel contributions of our study include (a) a bespoke framework to constrain a neural network using a mechanistic model which includes stoppage-induced friction increases, (b) built-in model uncertainty for greater confidence in model outputs, (c) new historical drive data for model training and (d) one-hot encoding of soil type as a model input. The present results are benchmarked against a purely data-driven ANN and the industry-standard empirical relationships that were used for the original design of the test drives.
Data
Case studies
Table 1 summarises the 14 case studies used in this paper, where D is the outside pipe diameter and z is the depth to the tunnel axis. Here, soil types are categorised as:
weak to strong rock and stiff to very stiff clay;
gravels;
sands; and
very soft to soft tidal flat deposits and silts.
Appendix 1 outlines key assumptions and limitations.
Data processing
Measurements of jacking force recorded by the TBM are processed to remove spurious data, as shown in Figure 1. Periods of inactivity are defined by a jacking force <50 kN, or zero cutterhead revolutions per minute (RPM), cutterhead torque or advance rate, as is common in TBM data processing for ML (Zhang et al., 2019; Erharter et al., 2019). To remove outliers, a rolling mean of a window of fifty data points is adopted (Erharter et al., 2019; Zhou et al., 2023).
For case studies with multiple soil types, soil boundaries are identified using clustering in a cutterhead RPM-torque parameter space. For example, Figure 2 shows how the soil boundary is identified in the training data for case studies Al2 and B5 using the RPM. In contrast, input data used for model testing are sourced only from design information available prior to a tunnel drive so that benchmark comparisons are valid. Hence, the soil type used to test the model is derived from the same borehole data that informed the jacking force prediction in the original tunnel design.
Physics-constrained machine learning (PCML) model
Artificial neural network
The PCML design incorporates an ANN within an empirical framework, as shown in Figure 3. The value of the output neurons of the ANN correspond to τ (skin friction between pipe and ground), and c and a (model constants). Along with the typical design information, these parameters are used in the empirical framework to predict jacking force. The ANN input features include soil type and “geohash”. Soil type is a categorical one-hot encoded input where each category is converted into a binary vector, where 1 indicates the presence of a category; this avoids bias by ensuring no inherent order in the labelling. Geohash is a compact numerical location encoding that combines both latitude and longitude coordinates into a single string of digits, allowing grouping of nearby projects.
For the present ANN, sensitivity analyses revealed that two hidden layers with 25 neurons each, ReLU activation functions between the input and hidden layers and a “softplus” activation function before the output neurons gave the best performance. The use of a more complex neural network architecture and a non-linear activation function yields similar accuracy in jacking force prediction but incurs higher computational costs while increasing the risk of overfitting for small data sets. Model uncertainty is considered using Monte Carlo (MC) dropout with probability of p = 0.1 and using 100 initialisations (Zhang et al., 2021; Zhang et al., 2022). The performance of the PCML model is benchmarked against a purely data-driven ANN shown in Figure 4. This benchmark ANN uses the same model input information but as separate features, identical hidden architecture and a single output neuron that is the jacking force prediction. Root mean squared (RMS) error loss convergence was found to be achieved after 500 epochs, as shown in Figure 5.
Empirical framework
Figure 6 shows the components contributing to the total jacking force, FJ, which is defined as:
To account for varying soil types along the length of the drive, the skin friction force is calculated as:
The face force arising from the hydrostatic groundwater pressure at the tunnel axis, u, is:
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Stoppage-induced jacking force increases have been shown to be proportional to the logarithm of the stoppage duration (Pellet-Beaucour and Kastner, 2002; Phillips, 2023). The force increase is caused by an increase in friction around the pipe string and is thus calculated as:
Analysis framework
Figure 7 summarises the present workflow. Tenfolds of leave one out cross validation (LOOCV) were used to evaluate the model performance. It is noteworthy that case study Al2 is standalone in that there are no other projects from the same site in the training data. Table 2 lists those drives forming the validation set and those forming the test set.
Results and discussion
Jacking force predictions for case studies Al2, B7 and HA from the validation set and B6 from the test set are shown in Figure 8. Results are shown for the three different predictive methods (industry empirical design, unconstrained ANN and the present PCML compared to the measured jacking force. The 95% confidence interval for the PCML model is also superimposed on the plots. For the ANN and PCML model, the mean predicted jacking force is plotted assuming zero stoppages (Fs = 0). Of the three predictive methods, the PCML model produces the most accurate and reliable predictions; in practice, this will help inform optimised inter-jack installation [as in Figure 8(a)] and provide advanced warning of excessive jacking forces [as in Figure 8(d)].
The PCML model better estimates jacking force for the early stages of a drive due to the inclusion of FM in the mechanistic model [as in Figure 8(c)]. For the latter stages of a drive, the PCML model better predicts skin friction, reflected in the gradient of the jacking force-distance plot [as in Figure 8(a)]. One notable exception is case study Ak4 where the PCML model over-estimates the model constant, c, as shown in Figure 9. Here, the model extrapolates outside the training space, a consequence of the training data originating from a shallower depth than the deeper Ak4 case study.
The values of the output neurons generated by the PCML model for the validation and test sets for each soil type are presented in Table 3. The range in values results from the inclusion of the geohash feature and is also dependent on the variation in training data due to the LOOCV approach. This is most significant for soil types c and d, which feature in at least one project in the validation set for only a single-case study.
As shown in Figure 8, the empirical design method provides relatively poor performance, with examples of both significant over-estimates and under-estimates of the measured jacking force; this is attributable to the difficulty of capturing τ within a prescriptive design approach. The results also show that the ANN, in failing to capture meaningful relationships between input data and jacking force, exhibits underfitting of the measured jacking force.
The performance metrics for the three different predictive methods are given in Table 4. These results show that the PCML model provides improved predictions compared to the empirical design prediction for all but the Ak4 case study. Importantly, there are no apparent differences in the PCML prediction accuracy between the validation set and the test set indicating rigorous model training, enabled by the empirical constraints. Importantly, PCML training was 94.9% faster than the benchmark ANN.
Figure 10(a) and (b), shows (i) the mean jacking force during normal tunnelling and (ii) an upper bound line to show the predicted increase in jacking force after stoppage intervals of twelve hours and one week as predicted by the PCML model compared with the measured jacking force for case study Ak1 from the validation set and case study HE from the test set, respectively. The 12-h stoppage interval reflects the most common upper bound for the case studies considered, enabling a fair comparison. The plots demonstrate the PCML model’s capability to obtain different jacking force predictions for different stoppage durations. Note: Appendix 2 contains the jacking force predictions for all case studies. There are some instances where the 12-h stoppage PCML prediction underestimates the measured data; it is worth noting that this may be due to multiple site factors and not simply poor model calibration.
Conclusion
This paper has presented a novel method of predicting jacking force for pipe-jacked tunnel drives using a PCML approach. PCML jacking force predictions were benchmarked against both industry design predictions and those obtained from a purely data-driven ANN. The PCML model was found to predict jacking force to a higher accuracy than current industry practice and better discern meaningful patterns in data than the ANN. The PCML model produced an average decrease of 216 and 534 kN in mean absolute error of jacking force predictions compared with the industry design and ANN approaches, respectively. The ability to account for stoppage-induced jacking force increases as well as model uncertainty enabled useful upper bound estimates to be determined from the PCML model. With a view to its future application in industry, training the present model on a more comprehensive pipe-jacked tunnel database is warranted to improve generalisation across a wider range of soil and site conditions.
Figures
Project information
ID | Location | Date | D (m) | Length (m) | zmin − zmax (m) | Ground conditions (soil type coding) |
---|---|---|---|---|---|---|
Al2 | Athlone (IRE) | Oct 2023 | 1.490 | 537 | 4.2–12.8 | Alluvial clays and silts – soft grey slightly gravelly clayey sandy SILT (d) Alluvial sands and gravels – loose grey fine SAND (c) |
Al3 | Athlone (IRE) | Feb 2024 | 1.490 | 346 | 8.2–13.6 | Alluvial clays and silts – soft grey slightly gravelly clayey sandy SILT (d) Glaciofluvial gravels – loose to dense greyish brown slightly silty sandy GRAVEL (b) |
Ak1 | Arklow (IRE) | May 2022 | 1.490 | 478 | 4.0–5.5 | Alluvial sands – medium dense, brown gravelly SAND (c) |
Ak4 | Arklow (IRE) | Nov 2022 | 1.866 | 101 | 9.2–10.1 | Alluvial sands – dense brown slightly silty fine to course SAND (c) |
B1 | Blanchardstown (IRE) | Aug 2021 | 1.866 | 602 | 3.6–5.6 | Glaciofluvial gravels – medium dense dark grey sandy clayey fine to course subrounded GRAVEL (b) |
B5 | Blanchardstown (IRE) | Jul 2021 | 2.224 | 387 | 5.4–12.4 | Glaciofluvial gravels – dense grey sandy GRAVEL (b) Glacial till – stiff brown slightly sandy slightly gravelly CLAY (a) |
B6 | Blanchardstown (IRE) | Aug 2020 | 2.224 | 156 | 2.8–8.0 | Glaciofluvial gravels – dense grey sandy GRAVEL (b) |
B7 | Blanchardstown (IRE) | Oct 2020 | 2.224 | 546 | 3.5–14.4 | Glaciofluvial gravels – dense grey sandy GRAVEL (b) Argillaceous limestone – weak to strong indistinctly bedded dark grey LIMESTONE (a) |
B8 | Blanchardstown (IRE) | Jan 2021 | 2.224 | 314 | 9.3–15.4 | Glaciofluvial gravels – dense grey sandy GRAVEL (b) Argillaceous limestone – weak to strong indistinctly bedded dark grey LIMESTONE (a) Glacial till – very stiff brown slightly sandy slightly gravelly CLAY (a) |
HA | Hull (UK) | Feb 2021 | 1.490 | 165 | 3.3–3.9 | Tidal flat deposits – very soft to soft laminated greyish brown slightly sandy CLAY (d) |
HB | Hull (UK) | Feb 2021 | 1.490 | 49 | 3.1–3.4 | Tidal flat deposits – very soft to soft laminated greyish brown slightly sandy CLAY (d) |
HC | Hull (UK) | Jan 2021 | 1.490 | 141 | 2.9–3.6 | Tidal flat deposits – very soft to soft laminated greyish brown slightly sandy CLAY (d) |
HD | Hull (UK) | May 2021 | 1.490 | 195 | 2.4–3.4 | Tidal flat deposits – very soft to soft laminated greyish brown slightly sandy CLAY (d) |
HE | Hull (UK) | April 2021 | 1.866 | 265 | 2.5–3.9 | Tidal flat deposits – very soft to soft laminated greyish brown slightly sandy CLAY (d) |
Source: Table by authors
Training and test sets
Validation | Test |
---|---|
Al2 | Al3 |
Ak1 | B6 |
Ak4 | HB |
B1 | HE |
B5 | |
B7 | |
B8 | |
HA | |
HC | |
HD |
Source: Table by authors
Output neuron values generated by PCML model
Soil type | τ (kPa) | C | a (× 10−5 kPa) | ||||||
---|---|---|---|---|---|---|---|---|---|
Avg | Min | Max | Avg | Min | Max | Avg | Min | Max | |
a | 0.27 | 0.14 | 0.34 | 0.46 | 0.26 | 0.57 | 3.11 | 2.36 | 3.91 |
b | 1.69 | 1.47 | 1.79 | 0.51 | 0.39 | 0.61 | 2.34 | 1.23 | 3.31 |
c | 0.66 | 0.32 | 1.23 | 1.44 | 0.64 | 2.44 | 3.40 | 1.49 | 4.68 |
d | 0.35 | 0.23 | 0.49 | 3.09 | 1.63 | 3.79 | 6.05 | 2.99 | 9.84 |
Source: Table by authors
Performance metrics table for different designs
Empirical design |
Unconstrained ANN model |
PCML model |
|||||
---|---|---|---|---|---|---|---|
Set | ID | R2 | MAE (kN) |
R2 | MAE (kN) |
R2 | MAE (kN) |
Validation set |
Al2 | −11.90 | 628 | −15.79 | 865 | −0.20 | 191 |
Ak1 | −33.94 | 944 | −8.79 | 488 | −0.26 | 112 | |
Ak4 | −1.25 | 117 | −48.77 | 636 | −20.7 | 418 | |
B1 | −1.13 | 1101 | −0.68 | 929 | −0.01 | 712 | |
B5 | 0.65 | 375 | −1.02 | 891 | 0.76 | 304 | |
B7 | −1.47 | 679 | −1.26 | 712 | 0.02 | 418 | |
B8 | 0.66 | 301 | −1.15 | 855 | 0.75 | 278 | |
HA | −4.03 | 147 | −167 | 986 | 0.12 | 53 | |
HC | −5.62 | 169 | −221.46 | 1069 | −0.01 | 44 | |
HD | −1.09 | 135 | −82.45 | 1097 | −0.06 | 89 | |
Test set | Al3 | −0.36 | 392 | −44.64 | 845 | 0.24 | 293 |
B6 | −1.58 | 778 | −0.58 | 480 | 0.24 | 393 | |
HB | −14.73 | 221 | −237.43 | 892 | −0.16 | 32 | |
HE | −6.49 | 489 | −0.41 | 184 | 0.35 | 115 |
Source: Table by authors
Table of assumptions
Section | Assumption |
---|---|
Database | Four distinct soil groupings defined in this paper are: (1) rock and stiff clay, (2) gravel, (3) sand and (4) very soft to soft tidal flat deposits and silts. These general categories, chosen as part of a proof-of-concept approach, ensured sufficient and evenly spread data across different ground conditions. Development of the model would see the inclusion of a more comprehensive database encompassing wider ranging soil categories with distinct soil mechanics parameters |
It is assumed that measured jacking force data reflect real jacking forces experienced on site. Risk of spurious readings, as a result of tunnel boring machine parameters being incorrectly initialised, were minimised by taking the following precautionary measures: 1 – Coordination with the tunnel engineer 2 – Analysis of “actual” skin friction to identify irregular data 3 – Use of the PCML model presented in this paper to cross-validate measured data with that of other drives |
|
Data processing | A data entry corresponding to a sensor reading of zero for any of either RPM, cutterhead torque or advance rate, or a measured jacking force of less than 50 kN is assumed to relate to a period of inactivity, such as a pipe change, and hence deemed invalid |
A rolling mean of window size 50 is adopted to smooth outliers while preserving true variations of jacking force, for example, those arising from stoppage intervals. For example, a false peak reading of jacking force is recorded when the jacking rams reach max length | |
A change in soil type is identified in the training data as a step change in RPM. Boundary RPM values were chosen by inspection as follows: Case study Al2: if RPM > 6, soil type = 3. If RPM < 6, soil type = 4 Case studies B1, B5, B7 and B8: if RPM > 11, soil type = 1. If RPM < 11, soil type = 2 |
|
Neural network | The probability that a connection between neurons is severed when the neural network is initialised is p = 0.1. Dropout is active for both hidden layers in the neural network |
Empirical formulae | The horizontal stress induced by the soil on the TBM face is highly variable, dependent on the ground conditions, stability of the soil face in front of the TBM and driving style of the TBM operator. Face force is small compared with the frictional component, justifying the grouping of the resistive forces induced by the soil and a simple approximation of face force equating face pressure to hydrostatic pressure, u |
Stoppage time is defined as the time difference between consecutive valid data entries. Stoppage-induced jacking force increases for stoppages of less than one hour duration are assumed insignificant and ignored (Phillips, 2023) | |
When tunnelling resumes following a stoppage, a dummy stoppage time for subsequent data entries mimics friction dissipation. The dissipation of additional friction for a stoppage of 48 h duration is assumed to occur linearly over a length equal to the distance between adjacent bentonite stations, b. The dummy stoppage time is calculated as:![]() where △t′ is the original stoppage time, △x is the chainage difference since tunnelling resumed and, typically, b = 12m. For calculated dummy stoppage times of less than 1 h, additional induced jacking forces are assumed to dissipate instantaneously |
Source: By authors
Appendix 1
Appendix 2
References
Armaghani, D.J., Mohamad, E.T., Narayanasamy, M.S., Narita, N. and Yagiz, S. (2017), “Development of hybrid intelligent models for predicting TBM penetration rate in hard rock condition”, Tunnelling and Underground Space Technology, Vol. 63, pp. 29-43.
Atalah, A.L., Bennett, D. and Iseley, T. (1994), “Estimating the required jacking force”, Proc., Annual Conf. of the North American Society of Trenchless Technology. Bowling Green, OH: ScholarWorks@BGSU.
Auld, F.A. (1982), “Determination of pipe jacking loads”, Proc., Pipe Jacking Association.
Erharter, G.H., Marcher, T. and Reinhold, C. (2019), “Application of artificial neural networks for underground construction–chances and challenges–insights from the BBT exploratory tunnel Ahrental Pfons”, Geomechanics and Tunnelling, Vol. 12 No. 5, pp. 472-477.
Ji, X., Zhao, W., Ni, P., Barla, M., Han, J., Jia, P., Chen, Y. and Zhang, C. (2019), “A method to estimate the jacking force for pipe jacking in sandy soils”, Tunnelling and Underground Space Technology, Vol. 90, pp. 119-130.
Koopialipoor, M., Tootoonchi, H., Jahed Armaghani, D., Tonnizam Mohamad, E. and Hedayat, A. (2019), “Application of deep neural networks in predicting the penetration rate of tunnel boring machines”, Bulletin of Engineering Geology and the Environment, Vol. 78 No. 8, pp. 6347-6360.
Li, C., Zhong, Z., Liu, X., Tu, Y. and He, G. (2019), “Numerical simulation for an estimation of the jacking force of ultra-long-distance pipe jacking with frictional property testing at the rock mass–pipe interface”, Tunnelling and Underground Space Technology, Vol. 89, pp. 205-221.
Mokhtari, S. and Mooney, M.A. (2020), “Predicting EPBM advance rate performance using support vector regression modelling”, Tunnelling and Underground Space Technology, Vol. 104, p. 103520.
Pellet-Beaucour, A.L. and Kastner, R. (2002), “Experimental and analytical study of friction forces during microtunneling operations”, Tunnelling and Underground Space Technology, Vol. 17 No. 1, pp. 83-97.
Phillips, B. (2023), “Soil-lubricant-structure interface mechanics for microtunnelling” (Doctoral dissertation, University of Oxford).
Ripley, K. and Ripley, K.J. (1989), “The performance of jacked pipes” (Doctoral dissertation, University of Oxford).
Sheil, B. (2021), “Prediction of microtunnelling jacking forces using a probabilistic observational approach”, Tunnelling and Underground Space Technology, Vol. 109, p. 103749.
Sheil, B.B., Suryasentana, S.K. and Cheng, W.C. (2020), “Assessment of anomaly detection methods applied to microtunneling”, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 146 No. 9, p. 04020094.
Sofianos, A.I., Loukas, P. and Chantzakos, C. (2004), “Pipe jacking a sewer under athens”, Tunnelling and Underground Space Technology, Vol. 19 No. 2, pp. 193-203.
Staheli, K. (2006), Jacking Force Prediction: An Interface Friction Approach Based on Pipe Surface Roughness, GA Institute of Technology, GA.
Yen, J. and Shou, K. (2015), “Numerical simulation for the estimation the jacking force of pipe jacking”, Tunnelling and Underground Space Technology, Vol. 49, pp. 218-229.
Zhang, P., Jin, Y.F. and Yin, Z.Y. (2021), “Machine learning–based uncertainty modelling of mechanical properties of soft clays relating to time‐dependent behavior and its application”, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 45 No. 11, pp. 1588-1602.
Zhang, Q., Liu, Z. and Tan, J. (2019), “Prediction of geological conditions for a tunnel boring machine using big operational data”, Automation in Construction, Vol. 100, pp. 73-83.
Zhang, P., Yin, Z.Y. and Jin, Y.F. (2022), “Bayesian neural network-based uncertainty modelling: application to soil compressibility and undrained shear strength prediction”, Canadian Geotechnical Journal, Vol. 59 No. 4, pp. 546-557.
Zhou, H., Huang, S., Zhang, P., Ma, B., Ma, P. and Feng, X. (2023), “Prediction of jacking force using PSO-BPNN and PSO-SVR algorithm in curved pipe roof”, Tunnelling and Underground Space Technology, Vol. 138, p. 105159.
Further reading
Chapman, D.N. and Ichioka, Y. (1999), “Prediction of jacking forces for microtunnelling operations”, Tunnelling and Underground Space Technology, Vol. 14, pp. 31-41.
Jung, J.H., Chung, H., Kwon, Y.S. and Lee, I.M. (2019), “An ANN to predict ground condition ahead of tunnel face using TBM operational data”, KSCE Journal of Civil Engineering, Vol. 23 No. 7, pp. 3200-3206.
Lin, P., Wu, M., Xiao, Z., Tiong, R.L. and Zhang, L. (2024), “Physics-informed deep reinforcement learning for enhancement on tunnel boring machine’s advance speed and stability”, Automation in Construction, Vol. 158, p. 105234.
Mokhtari, S., Navidi, W. and Mooney, M. (2020), “White-box regression (elastic net) modelling of earth pressure balance shield machine advance rate”, Automation in Construction, Vol. 115, p. 103208.
Sheil, B.B., Suryasentana, S.K., Templeman, J.O., Phillips, B.M., Cheng, W.C. and Zhang, L. (2022), “Prediction of pipe-jacking forces using a bayesian updating approach”, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 148 No. 1, p. 04021173.
Zhang, P., Yin, Z.Y. and Sheil, B. (2024), “Multifidelity constitutive modeling of stress-induced anisotropic behavior of clay”, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 150 No. 3, p. 04024003.
Acknowledgements
The authors gratefully acknowledge the support provided by Ward and Burke Construction Ltd.