Esteban Díaz,Edgar Leonardo Salamanca-Medina,Roberto Tomás

Departamento de Ingeniería Civil,Escuela Politécnica Superior,Universidad de Alicante,P.O.Box 99,E-03080,Alicante,Spain

Keywords: Jet grouting Ground improvement Compressive strength Machine learning

ABSTRACT Jet grouting is one of the most popular soil improvement techniques,but its design usually involves great uncertainties that can lead to economic cost overruns in construction projects.The high dispersion in the properties of the improved material leads to designers assuming a conservative,arbitrary and unjustified strength,which is even sometimes subjected to the results of the test fields.The present paper presents an approach for prediction of the uniaxial compressive strength (UCS) of jet grouting columns based on the analysis of several machine learning algorithms on a database of 854 results mainly collected from different research papers.The selected machine learning model(extremely randomized trees)relates the soil type and various parameters of the technique to the value of the compressive strength.Despite the complex mechanism that surrounds the jet grouting process,evidenced by the high dispersion and low correlation of the variables studied,the trained model allows to optimally predict the values of compressive strength with a significant improvement with respect to the existing works.Consequently,this work proposes for the first time a reliable and easily applicable approach for estimation of the compressive strength of jet grouting columns.

1.Introduction

Nowadays,the land for construction is increasingly scarce,resulting in a greater use of underground space,reclaimed land,or inadequate soils.Under these conditions,it is necessary to improve the soil properties to meet engineering requirements with the appropriate safety conditions.Among the existing ground improvement techniques,jet grouting is undoubtedly the most powerful,versatile,and most studied technique.

Jet grouting(Yahiro and Yoshida,1973)is a technology that uses a radial injection of fluids at high speed,to erode the soil,partially replacing the eroded material and mixing it with a cementing agent(grout) to create a new material (Bell,1993,2012;Modoni et al.,2006).This grout manages to increase the strength of the treated area or reduces its deformability and/or permeability.Its applications include underpinnings,excavation support,soil improvements,auxiliary works for construction of the tunnels,slope stabilization,and groundwater control,etc.(Lunardi,1997;Modoni and Bzówka,2012;Croce et al.,2014).

According to the European standard (EN 12716,2018),jet grouting systems are classified into three categories depending on the number of fluids injected.More precisely,the types of jet grouting systems are single fluid (only grout),double fluid (grout enshrouded by air or water),and triple fluid (grout and water enshrouded by air).

The final product obtained with a jet grouting improvement depends on numerous factors,which in turn lies in the parameters of the system itself and the soil to be improved(Bell,1993;Modoni et al.,2006;Shen et al.,2013).The jet grouting technique requires understanding the characteristics of the soil,and the average geometric and mechanical properties of the soil-cement columns.The most important mechanical property of the resulting columns is the uniaxial compressive strength (UCS).The strength of a jet grouting improvement is expressed as a fraction of the UCS(usually between 0.2 and 0.3 times)considering the Tresca failure criterion(Croce et al.,2014).On the other hand,there is a scientific consensus on the variability of the strength of the jet grouting columns due to the heterogeneity of the soil and the effectiveness of the execution parameters considered during the injection(Tinoco et al.,2011;Toraldo et al.,2018).

For the above reasons,the mechanism of soil improvement by jet grouting is complex and for this reason,there are currently no reliable methods to predict the properties of the jet grouting columns.The available methods are based on extreme empirical rules or formulas with a local validity(i.e.for specific sites and with small datasets).These methods lead to conservative and unjustified designs and usually require on site verifications (Akan et al.,2015).Thus,it is necessary to develop alternative methods that can reliably predict the UCS of the jet grouting columns.

Supervised machine learning methods are a powerful toolkit for discovering robust patterns in complex datasets,demonstrating its satisfactory use in geotechnical engineering(Baghbani et al.,2022)and also specifically in the prediction of certain properties in jet grouting(e.g.Tinoco et al.,2011;Díaz and Tomás,2021;Njock et al.,2021;Shen et al.,2021).

On one hand,these machine learning techniques perform better as the number of training data increases,so it is of paramount importance to collect an extensive amount of UCS data.On the other hand,if local datasets are used,the obtained predictions will normally have a limited validity,and can be rarely generalized to other cases out of this local area.Consequently,the data must be collected worldwide,covering the greatest casuistry of the variables considered in the training process of the algorithm.The main objective of this work is to develop a tool for estimation of the UCS which can easily be applied in design phases.Therefore,not all the parameters involved in the jet grouting process can be considered,since some of them are rarely known at the design level.For this,a global and extensive dataset (854 records) of UCS and other parameters involved in the technique have been collected for different treatments conducted in different parts of the world.The compiled dataset covers all jet systems,most used energy ranges,and soil types.This paper is structured as follows:it first studies the state of the art regarding the UCS in jet grouting.Later,the characteristics of the considered database are described in detail.The paper then goes on to analyse and discuss machine learning techniques’performance,when these are applied to predict the UCS of jet grouting samples.Next,the main results obtained are studied and interpreted by evaluating the accuracy of the predictions performed.Finally,the main conclusions derived from the research are summarized.

2.Uniaxial compressive strength in jet grouting

Although the jet grouting technique has acquired notable technological advances in the equipment,there are limited calculation guidelines to estimate the physical and mechanical properties of jet grouting columns.Regarding the standards,there are no clear procedures for estimation of the properties of jet grouting improvements focusing on general principles for the execution works (e.g.EN 12716,2018).

There are several expressions to obtain the UCS from parameters measured in situ,in columns already constructed,such as the Pwave velocity of the ultrasonic test or the unit weight of the column(e.g.Fang et al.,1994;Croce and Flora,1998;Akin,2016).However,these methods must be carried out after the improvement;therefore at the design level,they have a limited utility.

Bell and Burke (1994) pointed out that the value of UCS in jet grouting columns can cover a wide range,varying from about 1 MPa to extreme values of 30 MPa,where higher strengths are associated with low water-cement ratios(W/C)and more granular soils,while lower strengths are associated with higher watercement ratios and more clay soils.In turn,a high water content of a soil (e.g.organic soils and/or peats) can increase the watercement ratio of the treatment,resulting in a decrease in strength(Guler and Secilen,2021).

Van der Stoel (2001) carried out extensive experimental research on jet grouting columns executed with single and double systems in sandy and clay soils in Amsterdam,the Netherlands.The research concluded that the UCS strongly depends on the watercement ratio,the soil type,and the jet grouting system,obtaining a systematically lower strength of material created with the double system than that created with the single system.The latter was also corroborated by various authors(e.g.Xanthakos et al.,1994;Wanik et al.,2017;Modoni et al.,2019).Therefore,it seems clear that the single system yields higher strength values than the other jet grouting systems.

Langbehn (1986) related the UCS of columns conducted under the single system with the soil type and the amount of cement per meter of column.Similarly,Croce et al.(2014) proposed an abacus with indicative ranges of UCS for different soils depending on the amount of injected cement,showing a higher strength in coarsegrained soils than that in fine-grained soils.It is well-known that this issue is also presented in concrete,where the compressive strength is dependent on the aggregate quality.This dependence of the UCS value on the soil type is evidenced in several studies (e.g.Modoni et al.,2019;Guler and Secilen,2021).

Gladkov et al.(2011)found that the UCS increases with cement consumption,but only up to 650-750 kg/m3,a fact that is also corroborated in test fields in Chile (Ayarza and Vukotic,2014).Nikbakhtan and Osanloo (2009) concluded that the UCS value increases with the grout pressure,and proposed a formulation based on triple fluid systems from 58 data from a specific site.Based on 18 data from the previous study,Nikbakhtan and Ahangari (2010)proposed additional expressions based on lifting and rotation speeds,grout pressure,and cement water ratio.

Tinoco et al.(2014) carried out a study of UCS in 472 samples directly extracted from jet grouting columns.This study,involved the effects of different variables(both the soil and the technique),in the predictive models considered.The work analysed the performance of several machine learning algorithms,concluding that support vector machine (SVM) provides the best performance(with anR2of 0.51).This is the most ambitious study to date,with a large database that eliminates the local character of existing formulations.However,the proposed SVM algorithm is extremely difficult to apply at the design level due to the large number of involved parameters,or because of no abacus or formulas to facilitate its use.

Other expressions to predict UCS values are those proposed by Akan et al.(2015),who studied the relationship between UCS and several parameters of execution of the technique (i.e.grout pressure,water pressure,water flow,lifting and rotation speeds,and cement-water ratio),using statistical models of multiple linear regression from some data of the study of Nikbakhtan and Ahangari(2010) mentioned above(18 data from the same site).It should be noted that although the studies based on Nikbakhtan and Ahangari(2010) offered a positive correlation between the grout pressure and the UCS,there are other works where a negative correlation is demonstrated (e.g.Aksoy,2020;Hasan and Canakci,2022).

More recently,Guler and Secilen (2021) studied five cases of applying the single system in Turkey,and compared 12 UCS data with the percentage of sand in the soil prior to the improvement,as well as with the standard penetration test (NSPT) value.They pointed out that the UCS increases with the soil strength measured through theNSPTand the sand content in the soil.

3.Database

3.1.Selection and study of variables

The big datasets covering usual ranges of the involved variables help machine learning models to achieve a better generalization.Therefore,it is essential to collect an extensive amount of data worldwide to eliminate the local component of the predictions.The dataset must include data related to the parameters of execution of the technique,as well as the textural and mechanical characteristics of the soil before improvement.Consequently,the compiled database has been based mainly on scientific works,including some data extracted from the experience of the authors,which are summarized in the study of Salamanca-Medina (2022).In this work,the local characteristic of the existing formulations mentioned above is demonstrated,being these formulations fed with the records of the compiled database,offering extremely low performances (R2is lower than 0.15).

It should be noted that the collection of existing works contains a large number and great heterogeneity in the available predictor variables.The main aim of this work is to develop a tool for estimation of the UCS of easy application in design phases.If all the parameters involved in the jet grouting process are considered,it would be of limited usefulness in the design phase.Regarding the cement content,it is typically prefixed in the improvements by the designers so that it usually adjusts to the optimum value.It should be recalled that the cement content increases to a certain value and then an increase in the quantity of cement would not yield a notable effect on the UCS (Gladkov et al.,2011).Other parameters such as the age of the grout do not have excessive incidence,because the samples are tested at least 28 d after the execution of the improvement,which is the usual practice since several works have shown a behaviour similar to concrete (Burke,2004;Tinoco et al.,2011).

In short,the final selection criterion involves discarding variables,either their values are clearly limited by the execution technique or they are not available at the design level (e.g.unit weight of the column or amount of cement per meter of column).Considering these criteria,we will try to achieve a model with great predictive power for use at the design stage,and with variables that have already been related to the UCS in previous works.In this way,the data were classified according to the jet grouting system (i.e.single,double,and triple).In relation to the soil texture,they were grouped considering the ASTM D2487 (2017) standard,which divides inorganic soils into coarse-grained without fines,coarsegrained with fine,and fine-grained.This classification reflects the distinct erosive behaviours of the different soils against the jet and it has been used in other works of jet grouting (e.g.Flora et al.,2013).However,a fourth group,including organic soils,has been added.This soil type has a strong effect on the UCS value of jet columns because of (i) the high water content;and (ii) the high content of organic matter,which delays the process of setting and hardening of the cement grout,reducing its strength (Topolinski,2019;Du et al.,2021).Table 1 shows the different types of soils considered in this work,and the equivalence in the unified soil classification system (USCS),as well as the class assigned for each soil type.The strength of these four soil classes is quantified from theNSPT.

Table 1Soil classification considered in this work.

The final database includes the following predictive variables:jet system,soil type,blowing count of standard penetration test,water/cement ratio,rotation speed,and grout pressure.These variables are usually available in the design phase and they have been related to the UCS in previous works.Starting from the definitive database with the six predictor variables and the variable to be predicted,an exploratory analysis has been carried out.This analysis has enabled to explore the distribution and identify characteristics such as outliers,discontinuities,concentrations of values,and shape of the distribution,etc.

It should be noted that,within the predictor variables,there are continuous and categorical variables,such as the type of jet and the type of soil.In machine learning,it is usual to assign values to categorical variables.For the jet system,the values 1,2,and 3 were assigned to the single,double,and triple systems,respectively.Regarding the type of soil,the assigned values can be consulted in Table 1.

Table 2 shows the main statistics of the selected variables,where is observed that all the variables have 854 data except for the rotation speed,which has 743 due to the absence of this information in the consulted works.Fig.1 depicts the histograms of the distribution and the density plots of the variables included in the dataset.Regarding the jet system,the single system predominates with 566 records,while the double system has 162,and the triple system 126.Regarding the soil type,there are 120 data for coarsegrained soils without fine,328 for coarse-grained soils with fine,372 for fine-grained,and 34 for organic soils.Concerning the UCS values,they are concentrated below 10 MPa,being in the 75th percentile of 7.4 MPa,following a clearly log-normal distribution(see Fig.2).

Fig.1.Histograms of distribution and density plots of the variables considered in the present work: (a) Jet system;(b) Soil type;(c) Nspt;(d) W/C;(e) Grout pressure (bar);(f)Rotation speed (rpm);and (g) UCS (MPa).

Fig.2.Correlation matrix and scatter plots for each variable considered.

Table 2Main statistical parameters of the considered variables.

3.2.Data processing

As mentioned above,prior to the processing of the data,it is necessary to encode the categorical variables(i.e.the jet system and the soil type).Encoders are used to convert categorical data into numbers,which can be better understood by the predictive models.In our case,a one-hot-encoder type (Pedregosa et al.,2011) was used to avoid the model thinks that the values assigned to a variable have some kind of order or hierarchy.

Once the categorical variables have been encoded,an outlier detection analysis was performed using the one-class SVM algorithm (Sch?lkopf et al.,1999).It is a classification method used to detect the outliers and anomalies in a dataset.The one-class SVM is based on the traditional SVM,a type of supervised machine learning algorithm that can be applied for regression or classification tasks.The most important concept behind SVM is to find a hyperplane that maximizes the distances between the different classes existing in the dataset.With the hyperplane defined,new data can be classified by locating on which side of the hyperplane they fall on.In terms of one-class SVM,there is only one class,and it defines the hyperplane for the normal data points,and classifies thedata located outside the hyperplane as outliers.Once this algorithm was applied,39 outliers were removed from the dataset.From this point,the dataset is divided into training dataset and validation dataset,starting with an 80/20 division.Hereon,as mentioned above,all the variables have the same number of records except for the variable rotation speed,with which 743 data are available.Therefore,a strategy of imputation of values is proposed.However,in order to avoid conditioning the performance of the algorithm,the imputation is only carried out in the training dataset.In this way,the validation will be done with real data without imputation and thus the algorithm will be evaluated with a set of untreated data.For the imputation of values,a multivariate feature imputation algorithm has been chosen(Van Buuren and Oudshoorn,2000;Little and Rubin,2019).This technique models each feature with missing values as a function of other features and uses that estimation for imputation.The workflow followed in this work is outlined in Fig.3.

Fig.3.Flowchart with the work procedure performed.

4.Model construction

Once the database is defined,a comparative performance analysis of various machine learning algorithms is carried out.Typically,to compare the different models and select the most appropriate model for a specific problem,the cross-validation technique is used.In fact,cross-validation is a “re-sampling”procedure for evaluating a model by making“k”groups of data and obtaining“k"different performance scores(in our casek=5).The coefficient of determination (R2) was chosen as the performance measure.

Once the initial selection process has been defined,a series of algorithms to be evaluated is chosen.Specifically,the algorithms used are linear regression (LR),lasso regression (LSR),elastic net(EN),K-nearest neighbours (KNN),regression trees (RT),multilayer perceptron (MLP),adaptive boosting (AB),gradient boosting regression (GBR),random forests (RF),and extremely randomized trees(ET).

Fig.4 shows the rainclouds obtained in the cross-validation process in terms of theR2value.It should be clarified that a raincloud plot is basically a mixture of half-violin,boxplot and strip plots,and enables to extract full statistical information about the analysis carried out.This plot allows to display the five-number summary statistics as the minimum,first quartile,median,third quartile,and maximum (boxplot),distribution shape (violin plot),sample size and location of the individual data points (strip plot).

Fig.4.Raincloud plots of all algorithms.

As can be seen,the four best algorithms in terms of their performance are RT,GBR (Friedman,2001),RF (Ho,1995),and ET(Geurts et al.,2006),and the LSR algorithm is the worst.The four algorithms exhibiting the best performance are based on decision trees.RT is a simple algorithm and GBR,RF and ET are ensembles created with decision trees,with slight differences in their ensemble tactic(bagging or boosting),in the selection of cut points to split nodes,and in the use of bootstrap replicas or the whole original sample.

In this way,these four algorithms are selected,and their internal parameters are tuned,already operating with the training and validation datasets.Tuning is the process of maximizing the model’s performance.In this case,a Bayesian optimization technique was used.This technique runs models many times with different sets of hyperparameter values,but it evaluates the past model information to select hyperparameter values to build the newer model.After tuning these algorithms,and since they are all tree-based models,it is a good practice to check the performance of these models with and without encoding the categorical variables.It is well known that in this type of models,a one-hot-encoding,could result in a decrease in the performance metrics,mainly due to two drawbacks: (i) one-hot-encoding induces sparsity into the dataset,and(ii)from the splitting algorithm’s point of view,all the encoded variables are independent,and,hence,the tree is very unlikely to select one of the encoded variables closer to the root.The results of this analysis showed that the value ofR2in the validation dataset is improved by at least about 2.5% in all the compared models.Thus,the next steps will be developed with the models without encoding the categorical variables.Once this process is completed,the results are expressed using the diagram proposed by Taylor(2001)(see Fig.5).The Taylor diagram is a twodimensional diagram designed to graphically represent the performance of several models.This diagram allows to quantify the correspondence degree between the modelled and the observed behaviours by means of three statistics simultaneously: (a) the correlation coefficient (azimuthal angle);(b) the centred rootmean-square error (RMSE),presented by circles centred on the point on thex-axis marked with a star and defined as“ref”;and(c)the standard deviation represented onx-andy-axis and measured as the radial distance from the considered point to the origin.

Fig.5.Taylor chart for the four best algorithms selected.Note that the dashed line represents the standard deviation of the reference sample.

As can be seen in Fig.5,the results are quite close to each other due to the similarity of the four algorithms.However,the metrics are slightly better in the case of the ET algorithm,which exhibits a higher correlation coefficient,a lower centred RMS difference,and a standard deviation closer to the standard deviation of the original data(“ref”value in Fig.5).Therefore,this algorithm is chosen as the one with the best performance.Once selected,the trainingvalidation process is repeated for percentages varying in fractions of 10% up to 50/50 (i.e.50/50,60/40,70/30 and 80/20),obtaining the best results for the percentage 80/20 originally used.With this algorithm already tuned,the predictions presented in the following section are obtained.

To replicate the model,the adopted parameters are included in Table 3.

Table 3Valued adopted for tuning parameters of ET model (Pedregosa et al.,2011).

The performance metrics obtained in both the training and validation datasets are indicated in Table 4.

Table 4Summary of accuracy parameters of the adopted model ET.MAE is the mean absolute error.

As can be seen,theR2in the validation set is 0.85 and the algorithm deviates on average from the predictions by only±1.3 MPa.On the other hand,the algorithm shows very similar metrics both in the training and in the validation datasets.This issue confirms the lack of overfitting and the generalization capability of the model.It should be noted that with the selected algorithm,the analysis has also been carried out without removing the outliers,obtaining a lower metrics(i.e.R2of 0.74 and 0.76 in the training and validation datasets,respectively).

The complete code of the model has been uploaded in open access (https://huggingface.co/spaces/EstebanDC/UCS_JG),jointly with a graphic application that has been deployed to facilitate its practical use by geotechnical professionals who are not familiar with machine learning.This app enables jet grouting designers to easily calculate the UCS from the inputs using the developed algorithm.

5.Results

The definitive algorithm,configured with the best hyperparameters,has been used to evaluate its accuracy through the comparison between the measured and predicted UCS values of the whole dataset.Fig.6a contains the point clouds with lines of absolute error of±2 MPa and±3 MPa.Fig.6b displays the residuals obtained in the analysis by means of a distribution histogram.On the one hand,the figure clearly reveals that the model predictions are close to the real values(identity line).On the other hand,only a 10% of predictions is outside the absolute error range of±3 MPa and slightly below 20% outside the range of ±2 MPa.This shows an optimal performance of the algorithm,when considering the high dispersion of the variables exposed in previous sections.Another interesting fact is that the algorithm has a slight trend to predict conservative values (nearly 55% of the predictions underestimate the UCS)and also the largest errors in absolute value are located on the safe side,being both aspects clearly observed in the residual’s histogram (Fig.6b).Likewise,the sum of the positive residuals,which corresponds to those values predicted on the safe side,is 544 MPa,and the sum of the negative residuals is 506 MPa,confirming a slight trend of the algorithm to predict in a safe way.

Fig.6.Relationship between the UCS of jet grouting predicted versus measured values by ET model: (a)Point cloud with the identity line (1:1 line) and lines of absolute error of±2 MPa and ±3 MPa;and (b) Frequency histogram and density distribution curve of the residuals obtained.

Finally,the relative importance of the selected variables was evaluated using two different methods: (i) the traditional feature importance automatically calculated by the algorithm,and (ii) the SHapley Additive exPlanations (SHAPs) values (Lundberg and Lee,2017).In the first approach,once the algorithm has been trained,the relative importance scores for each input feature can be obtained (e.g.Zhang et al.,2021a,b).A higher value represents a stronger influence on the prediction.The analysis results are shown in Table 5,indicating that the variables with the highest influence on the UCS are the rotation speed and the soil type.Conversely,the variables with the least influence are theW/Cratio and the grout pressure.Complementarily,the SHAP method has been applied,providing a unified approach to explain the output of any treebased model with a clear advantage over other methods.The results are depicted in Fig.7 by combining feature’s importance with feature’s effects.In this plot,each point is one SHAP value for a prediction and a feature.In they-axis,the features ranked in descending order of importance are shown.In thex-axis,the SHAP values are displayed.It should be indicated that a value of zero represents no contribution to the prediction,whereas the contribution is increased as the SHAP value moves away from zero.Finally,colour denotes high(red)to low(blue)feature values.Thus,the general sense of features’directionality impact can be obtained based on the distribution of the red and blue dots.

Fig.7.Relative feature importance with SHAP values in ET algorithm.

Table 5Importance analysis of variables.

The variable with the greatest impact on the UCS is the rotation speed with a negative correlation,in agreement with the study results of Akan et al.(2015).To get an effective mixing of the ground with the stabilizer,the rotation speed of the rods must be rather slow in order to gain a homogeneous distribution of the jet in the improved area.The second most influential variable is the soil type,which has a somewhat smaller impact and also correlates negatively.It must be remembered that soils assigned to class 1 are coarse-grained soils without fines,which offer greater UCS because they are more similar to aggregates of good characteristics in concrete(Croce et al.,2014).

Next,the greatest impact on the UCS is given by the jet system,which shows a negative correlation.It should be noted that class 1 is assigned to the single system that traditionally provides greater UCS (e.g.Xanthakos et al.,1994;Van der Stoel,2001).

The next parameter is theNSPTthat shows a positive correlation in agreement with the work of Guler and Secilen (2021).Concerning the grout pressure,the correlation is more diffuse,in agreement with the reviewed literature in which there is no scientific consensus about its influence on the UCS.In fact,the values are grouped around zero,although with a slight negative correlation,according to various authors (e.g.Aksoy,2020;Hasan and Canakci,2022).Finally,the variable with the least impact on the UCS value is theW/Cratio,which also has a negative correlation with the UCS,as demonstrated in many studies (e.g.Akan et al.,2015;Van der Stoel,2001).

In view of the results,it can be concluded that the algorithm has mostly understood the relationship of every independent variable with the UCS,in agreement with technical literature.A brief summary of the feature importance analysis performed with the two approaches considered has been tabulated in Table 5.

6.Conclusions

In the present study,supervised machine learning techniques have been applied to predict the UCS of jet grouting columns.To this end,the largest data collection from UCS measurements of jet grouting columns to date has been carried out.The analysis of this database shows a high variability of the UCS values in relation to the potential predictor variables,a fact already noticeable in previous works.This high variability made it impossible to approach the problem by using ordinary statistical techniques.Therefore,machine learning algorithms provide an excellent tool to discover a priori unknown relationships.As a result of the performed machine learning analysis,the ET algorithm was selected due to its performance (R2of 0.85 and MAE of 1.3 MPa).The predictions of this algorithm lean slightly towards the safety side (i.e.predicts conservative values of UCS)and approximately 80% of them are below an absolute error of ±2 MPa,demonstrating a relatively low dispersion in the predictions in comparison with the uncertainties provided by the existing methods to predict UCS.Complementarily,a study to quantify the importance of the variables involved in the prediction of the UCS was carried out,proving that the greatest impact is given by the rotation speed,the soil type,and the jet system.To provide the work with a greater practical application and facilitate its use by geotechnical engineers at the design level,an open access online application has been deployed from the code generated and shared on: https://huggingface.co/spaces/EstebanDC/UCS_JG.

It is important to note that if the database is completed with other variables that have confirmed to have an influence on the UCS(e.g.the cement content or some additional operational parameter)in various previous works and with new records,the prediction of UCS could be improved.However,given the metrics achieved in this work and the high dispersion of the input variables,we understand that this work represents an important step forward in determination at the design level of one of the most important parameters in jet grouting improvements.

It should be indicated that the results presented here are valid for the ranges of the variables considered in this work(see Section 3)and for samples tested at least 28 d after the execution of the jet grouting columns.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors wish to express their gratitude to Grupo Terratest S.A.and the Japanese Jet Grouting Association for their assistance with the field data.On the other hand,we would like to thank Tim Matthews (OLA English) for his support on the English language review.This work has been supported by the Conselleria de Innovación,Universidades,Ciencia y Sociedad Digital de la Generalitat Valenciana (CIAICO/2021/335).