Information and knowledge behind data from underground rock grouting

Fei Xiao, Qian Liu, Zhiye Zhao

a Department of Civil Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

b School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore

Keywords:Field grouting data Water seepage Rock grouting Inverse modelling Data analytics Geological conditions

ABSTRACT Data related to the pre-grouting work of a large underground project are systematically analyzed to reveal the mechanism behind,to shed some light on the execution of practical grouting,and to enrich the theory of engineering geology. Grouting is generally taken as an effective way for controlling nonignorable water seepage during underground rock excavation. Though various models have been developed to guide grouting design or to specify criteria for grouting stop,it does not change the fact that grouting is still highly experience-based. Therefore,explanation of the current situation due to grouting complexity is given through step-by-step data analysis, where the impact on grouting parameters from the geological and hydrogeological conditions is investigated, and the grouting features of two tunnels located at the same depth below the sea surface are compared and discussed. Then, the data from individual grout hole are used to construct the regional geological conditions via inverse analysis. It is found that grouting of fractured rock masses is accompanied with great uncertainty, and field grouting data can contribute significantly to a better understanding of the regional geological conditions around an underground tunnel or rock cavern.

1. Introduction

Rock masses in nature are generally accompanied with complex geological characteristics,including faults, joints, dyke, etc., which are closely correlated with not only the overall quality of rock body(Windsor and Thompson,1994;Lombardi,2003;Aydan,2018),but also the corresponding hydraulic permeability (Yang et al., 2002;Saeidi et al., 2012; Xiao et al., 2019). Large amount of water can enter a tunnel under construction when encountering harsh conditions, which act as nature channels for water transportation. It could lead to project delay or economic loss, and even personal casualty loss if no special actions were taken (Brantberger et al.,2000; Lombardi 2003; Panthi and Nilsen, 2005; Emmelin et al.,2007; Wu et al., 2017; Ma et al., 2020). Therefore, grouting is introduced to reduce the hydraulic conductivity and enhance the strength of rock body, which can also lead to substantial cost reduction associated with construction and maintenance (Warner,2004; Butrón et al., 2010; Kvartsberg, 2013). However, though the grouting cost is comparatively lower than other water controlling methods (Eriksson, 2002), it can still take a large portion of the overall project budget (Hendrickson and Au, 1989). The main reason should be attributed to the complexity in itself, and thus conservative grouting design is usually preferred (Kobayashi and Stille, 2007;Rafi, 2014).

Therefore, extensive study has been conducted to enrich fundamental theory and render practical guidance to rock grouting.The term‘rock grouting’in many works usually indicates pre-excavation grouting (hereinafter it will be referred to as rock grouting or grouting instead), i.e. it comes before excavation and construction works. The object of rock grouting is fractured rock masses (Tsang and Tsang, 1987; Watanabe and Takahashi, 1993;Klimczak et al.,2010;Carter et al.,2012)and the medium used to seal fractures is flowable materials,thus the main research topics are the rheological properties and sealing capability of specific grouting materials(usually cement grout)(Håkansson et al.,1992;Yahia and Khayat, 2001; Rosquoët et al., 2003; Eriksson et al.,2004; Miltiadou-Fezans and Tassios, 2013; Mohammed et al.,2014; Rahman, 2015) and the range of grout penetration in rock body with complex geological and hydraulic characteristics(Tsang and Tsang,1987;Watanabe and Takahashi,1993;Klimczak et al., 2010; Carter et al., 2012). To improve the effectiveness of practical grouting and its economic efficiency, the first thing that comes into mind is to build models for evaluating the real-time grout penetration in targeted areas.

Empirical,analytical(or semi-analytical),and numerical models are three general methods for grouting evaluation.As an empirical method, grouting intensity number (GIN) is famous for its GIN limiting curve,achieving grouting control via grouting pressure and grout volume taken, and it is cost and computation efficient(Lombardi,1996,1997).As for the analytical method,the governing equations derived are usually nonlinear,which requires numerical algorithm to assist the process of problem solving(Xiao et al.,2017).While numerical models, with better visualization capability, are becoming more popular for the simulation of grout penetration in fracture networks based on some self-developed programs or commercial software (Yang et al., 2002; Sochi, 2007; Saeidi et al.,2013; Xiao et al., 2019). During the process of equation solving,both analytical and numerical models face the problem of boundary condition determination,usually,either the grout injection flow rate (Dano et al., 2004; Rahmani, 2009; Hall and Hoff, 2021) or pressure is assumed as constant(Hässler et al.,1992a;El Tani,2012;Xiao and Zhao,2017),while it is easier to control the injection flow in field grouting (Warner, 2004).

Though there are various methods or models for grouting evaluation or prediction, practical field grouting is still largely experience based, as grouting of fractured rock masses is like a black box operation.On the one hand,the rock fractures or fracture networks used in most numerical models are hypothetical, while its practical distribution patterns in three-dimensional (3D) space are blind to us;on the other hand,grouting is not an inverse process of water seepage, taking as an example the process of water seepage and grout penetration associated with a grout hole, as demonstrated in Fig.1.Water inflow occurs when there is fracture connectivity between water source and a grout hole, while grout can penetrate through all fractures connected to a grout hole,indicating that more fractures could be affected by grouting(referring to Fig.1). Therefore,it does not make much sense when attempting to forecast the volume taken or grout penetration range in field grouting from any prediction models, as fracture distribution and connectivity are of random patterns, and only limited information on the real geological and hydrogeological conditions can be obtained.It does not mean that theoretical investigation on this topic is kind of futile attempt, which still can provide us with some general patterns or fundamental knowledge, but to emphasize that more attention should be paid to aspects that can better reveal or speak for the real situation,like field data related to site investigation,surface mapping,Lugeon test,and grouting.That is why more and more research on data analysis or data mining were conducted regarding practical grouting, since we can gain better knowledge on how grouting works or extra geological and hydrogeological information, via analyzing data from distributed probe holes, bore holes, and grout holes. There is a trend that researchers prefer to build prediction models from field data of one project via machine learning or just simple regression, claiming that the models developed or conclusions derived could be universal and applicable to other projects (Öge,2017; Liu et al.,2020;Zheng et al., 2020; Nilsen, 2021).

Fig.1. Stationary demonstration of (a) water seepage into and (b) grout penetration through a grout hole.

However,the generalization capability of the prediction models derived through field data analysis remains debatable, especially for assessing the volume of grout consumed at individual grout hole, because the practical geological and hydrogeological conditions vary from one project to another(Chen et al.,2019).Therefore,in the present work,rather than building some forecast models,we are trying to figure out another way for data analysis(or mining)of engineering grouting, and then to enrich the possible utilization and application of field data. We will conduct some statistical and regression analysis to show the complexity behind field grouting,and ultimately to reveal that the development of a forecast model for future application in another project is challenging. Firstly, we will give an overall introduction to an underground project for oil storage in Singapore, including the geological and hydrogeological conditions,the grout consumed at individual tunnel station and the associated cement grout used in terms of water/cement ratio.Then,data related to individual grout hole will be analyzed in terms of water inflow rate and pressure, the grout volume consumed and the associated stop pressure. Finally, we will develop an inverse model to illustrate the regional geological conditions around a tunnel.

2. Methodology

As discussed in the Introduction, personal experience plays a critical role in the design and conduction of onsite rock grouting,as individual engineers are the carrier of intangible grouting knowledge, while the data generated before, during, and after field grouting are tangible medium, which can help uncover the underlying information and knowledge. To make these touchable,grouting data will be analyzed from different angles and via various methods, which are illustrated detailedly in Fig. 2. In Section 3,global statistical analysis will be conducted in terms of “station based” data, i.e. the Q value for assessing rock mass quality, total amount of grout holes drilled and grout volume consumed at individual station, and grout mixture preference (or the water/cement ratio preferable by onsite engineers),which can give us an overview to the features of field grouting and shed some light on grouting technics. In Section 4, further statistical, correlation, and regression analyses will be conducted to determine the relationship among different parameters or processes(such as water inflow and grouting processes),considering practical grouting techniques,like the split-spacing method and grouting sequence.The impact of water inflow rate on grout take will be analyzed in detail, as the intensity of water seepage is a critical index taken by onsite engineers for determining whether to initiate or stop grouting. In Section 5,the limitation of conventional hydraulic conductivity will be discussed,and then a new standard will be proposed for assessing spatial geological conditions (mainly void spaces for containing grout mixtures,like porous rock matrix and interconnected fracture network) based on grout consumption at individual grout hole.Innovative algorithm will be introduced to convert grouting data into spatial geological database aided by data analytics and machine learning.

Fig. 2. Structure of the present work and the associated methodologies involved.

Fig. 3. Schematic layout of the project for oil and petrochemical storage (JTC, 2021).

3. An overview of project grouting

The underground project for oil storage is located 150 m below the ground surface of Jurong Island and 130 m beneath the Banyan Basin, as demonstrated in Fig. 3, which is composed of several operation and access tunnels,and some caverns for oil storage,and all of them are right below the sea.

As a subsea project, water inflow during underground excavation is a tough issue,thus rock grouting is usually utilized and plays a critical role in water controlling. A series of valuable data were recorded and stored in some technical reports, among all the tunnels we only choose two with relatively complete data sets (hereinafter referred to as T1 and T2, respectively). According to information available in the report, the number of exaction stations,Q values,and data points(data from individual grout hole)in T1 and T2 tunnels are 25 and 18, 25 and 18, 938 and 775, respectively,indicating that each station has only one Q value and all data point at the corresponding excavation surface share the same Q value.The variation trend of Q value and number of grout holes at individual excavation surface at T1 and T2 tunnels are presented in Fig. 4. First, it can be found that the distance between any two neighboring stations is not a fixed value (which can be partially attributable to data deficiency),with the minimum and maximum values being 3 m and 17 m, respectively, though it is normally designed as 4 m per excavation. If the rock quality is good and/or the inflow rate of water is ignorable, it is highly possible that excavation will keep moving on, while it will be terminated immediately whenever the water seepage there significantly hinders the construction work undergoing.

Fig.4. Comparison between Q value and number of grout holes along the direction of excavation at (a) T1 and (b) T2 tunnels.

Normally, a station with more grout holes indicates that the water seepage control there would be more difficult, and the Q value assessed there should be relatively lower.According to Fig.4,in terms of rock quality reflected by Q value, the geological conditions of T1 tunnel are not stable along the excavation direction,while that of T2 tunnel is fluctuating within a relatively small range.Meanwhile, for both T1 and T2 tunnels, there is an obvious trend that the number of grout holes is inversely proportional to the Q value measured at individual excavation. Nevertheless, exclusion exists at several locations, some of low Q value but the grouting works stop after only a few rounds (referring to Station Nos.135 and 139.5 in T1 tunnel (Fig. 4a) and Station No.100.5 in T2 tunnel(Fig.4b)),while some of high Q value but it takes long time to seal the water inflow(referring to Station No.202.5 in T1 tunnel(Fig.4a)and Station No. 191 in T2 tunnel (Fig. 4b)). This existence of exclusion cases again proves that grouting work is a very complex process, and the grouting operation conducted at one location can lead to both regional and global impacts.

It is possible that not too much grout would be consumed at a specific station even if there is large number of grout holes,thus we further look at the total grout consumption at individual station of both tunnels, as presented in Fig. 5, where total grout volume consumed at each station of T1 (or T2) tunnel varies along the excavation direction in almost the same pattern as that of the grout hole number shown in Fig. 4. Additionally, grouting usually stops when the grout take at a hole reaches a certain value.Therefore,the grout take and number of grout holes at individual station are positively correlated.

Cement grout is the most common material used for controlling underground water seepage, hence the water/cement ratio (WC)used is usually of great interest. It is generally thought that dilute materials (grout with higher WC) will be utilized for grouting first and then dense material (grout with lower WC), but does it mean that all situations follow this “engineering practice”? Therefore,data analysis on the grout materials of different WC values is conducted to shed some light upon this question, and the results are demonstrated in Fig.6.Unexpectedly,there is a limited number of stations used grout materials with more than one WC,and cement grout with WC equal to 1 is preferred in most of the stations at both T1 and T2 tunnels. Nevertheless, there are still some differences between T1 and T2 tunnels considering stations with multiple cement grout utilized (or grout of different WC values). The two stations of T1 tunnel (Station Nos. 81.5 and 176.5) rank top two stations consuming the most grout and the associated Q values are among the lowest two; while only three of the four stations of T2 tunnel (Station Nos. 56.5, 64, 72 and 191) are of the highest grout take,and only two of them are of the lowest Q value and the Q value evaluated at Station No.191 is even the highest of all.

Fig. 5. Total volume of grout consumed at individual station of T1 and T2 tunnels.

Fig.6. Cement grout of different WC values utilized at individual station of(a) T1 and(b) T2 tunnels.

Fig.7 further presents the grouting data from individual grout hole grouped by WC, where the distribution of samples categorized by WC can be seen via the main figure in the middle, while the variations in Pgand Vgare displayed in two boxplots on the right and bottom sides, where Pgis the grouting end pressure and Vgis the corresponding grout take at each grout hole. For T1 tunnel,96.38%of all holes are sealed with WC of 1,and the Pgand Vgin 95.45% of all data points fall in the ranges of 21.31-33.74 bar (1 bar =100 kPa) and 0-1586.9 L, respectively, with Pg≥30 bar satisfied in 26.55% of all cases. For T2 tunnel, only 73.68% of all holes are sealed with WC of 1, and the Pgand Vgin 95.45%of all data points fall in the ranges of 19.52-32.33 bar and 0-2130.81 L, respectively, with Pg≥30 bar satisfied in only 13.03% of all cases.

It can be concluded that grouting is a complex process,and both the geological conditions and grouting features are remarkably different from each other even for two tunnels constructed almost in the same region.The reason can be attributed to the fact that the grout consumed at a specific tunnel station is not only affected by the rock quality assessed by Q value at individual excavation surface, but also by the geological conditions of rock masses closely linked to that station and the antecedent grouting.

4. Analysis of grouting characteristics

To achieve better grouting or water controlling effect,engineers need to make grouting strategy,which includes the determination of fan geometry and grout material, and grouting monitoring, etc.(Eriksson et al., 2009). Grout holes are usually arranged in a fan with certain spacing between adjacent holes within a specific excavation surface (Kawasaki et al., 1998; Lombardi, 2003), as illustrated in Fig.8.Meanwhile,to enhance the sealing quality or to ensure the grouting effectiveness, the spacing among grout holes should be close enough to form overlapping, but it should not be too close to avoid hydraulic jacking (Warner, 2004). Additionally,there is also overlapping between any two neighboring stations to reduce the risk of nonallowable water inflow during rock excavation.

Fig. 7. Statistical information of grouting data from individual grout hole categorized by different WC values for (a) T1 and (b) T2 tunnels.

According to the split spacing principle, major fractures will be sealed at first by primary holes, while minor fractures could be sealed with secondary (and probably succeeding) holes, which is supposed to split the space equally between grout holes under primary and secondary rounds(referring to Fig.8)(Liu et al.,2020).It is possible that more rounds of grout holes would be drilled and grouted to meet the allowable water inflow requirements. After categorizing the grouting data at individual station of T1 and T2 tunnels based on split-spacing method, the results of which are presented in Fig. 9, we can find that more than one round of grouting work was conducted at most of the stations for both tunnels, among which 60% has tertiary round of grouting.Compared with the total number of grout holes at individual excavation station,the number of grouting rounds can better reflect the associated difficulty for controlling water seepage, as it has closer correlation with the total volume of grout consumed at each station.

Fig. 8. Schematic diagram of grouting fan (split-spacing method).

Generally, within each round of grouting, grout holes are sealed one by one due to the limitations of space and grouting technology,as well as to avoid grout travel(Prager,1986).For specific zones with excessive water ingress, more than one hole can be injected simultaneously (hereinafter referred to as a grouting sequence) to accelerate water controlling, thus to save construction time (Liu, 2020).Hence, this sequence-by-sequence grouting strategy is used in the present project, where water seepage during excavation is a challenging issue.The normal process of grouting is to drill a grout hole first and then to measure the corresponding water inflow rate:(1)if there is heavy water inflow,the measurement would be terminated,and grouting would be initiated immediately;(2)if the water inflow rate is within the allowable range, then backfill of the grout hole would be conducted; otherwise (3) grouting would be carried out after the measurement and not be stopped until the water inflow rate drops below the allowable range.It is evident that water inflow and grouting are tightly linked,hence the relationships among four parameters involved in this process are of interest:water inflow rate(Qw) and pressure (Pw), and grout take (Vg) and stop pressure (Pg).The relationships among these four parameters corresponding to individual grout hole in T1 and T2 tunnels are presented in Fig.10,where the diagonal plots in Fig.10 are for illustrating the univariate distribution of each parameter. No observable correlations between any two parameters can be found,except that between Qwand Pw.Pwincreases linearly with increasing Qwunder most of the data points from T1 tunnel, while only part of all data points from T2 tunnel satisfy this pattern. Moreover, all the water pressures measured in both tunnels are capped at 10 bar, and no higher pressures can be found,which can partly explain the lower degree of correlation for T2 tunnel.

Fig.9. Statistics of grouting based on split-spacing method at individual station of (a)T1 and(b)T2 tunnels.In the legend,R1 to R7 indicate the primary to septenary round of grouting.

Apart from the above analysis,the following formula is used to quantitatively assess the correlation relationship between any two parameters:

where ρv1v2is the Pearson’s coefficient of correlation;v1and v2are any two of these four parameters;Cov(v1，v2) = Ev1v2-Ev1Ev2is the covariance between two variables; Ev1, Ev2and Ev1v2are the expectations of parameters v1, v2and v1v2, respectively; and σv1and σv2are the standard deviations of parameters v1and v2, respectively.

According to the coefficient of correlation ρv1v2of all data points listed in Table 1, we can see that Qwand Pw, and Qwand Vgare highly correlated, compared with other parameter pairs. High water inflow measured Qwcan lead to high water pressure Pwand high grout take Vg, the former is easy to be understood, but the latter is not, as grouting through a grout hole is not an inverse process of water seepage as discussed in Section 2. Pearson’s correlation coefficient is not used for analysis here,because individual variable has approximately a normal distribution, and the relationship between any two variables is neither curvilinear nor monotonic (referring to Fig.10). Additionally, the data are continuous but not ordinal.

Fig.10. Correlation analysis of water seepage and grouting with data from individual grout hole of (a) T1 and (b) T2 tunnels.

Table 1 Pearson’s correlation coefficient to identify strongly correlated parameter pair for T1 and T2 tunnels.

Therefore, further investigation should be conducted on the relationship between Qwand Vgin terms of different grouting sequences, as the relationship revealed from analysis of individual grout hole is not remarkable (referring to Fig. 10). Taking as examples Station No. 81.5 at T1 tunnel and Station No. 191 at T2 tunnel, as they are the most difficult station for grouting and own more sequences of grouting under each round of grouting. Statistical analyses of grout data under each round of grouting grouped by grouting sequences are presented in Figs.11 and 12,where“S”is short for “Sequence”, representing one grouting sequence. A vertical bar stands for a round of grouting, and its height, denoted as Hr, is the sum of Qwor Vgof all grout holes within that round of grouting. A color block inside any vertical bar stands for a single grouting sequence and its height,denoted as Hs,is the sum of Qwor Vgof all grout holes within that grouting sequence. The vertical black line, located at the top of each color block, represents the standard deviation of Qwor Vgwithin that grouting sequence: the deviation is large (small) when there is a long (short) line, while there is no line if only one hole is drilled.

Fig.11. Comparison between(a)water inflow rate Qw and(b)grout take Vg of grouting sequences(S1 to S9)within each round of grouting(R1 to R7)at Station No.81.5 of T1 tunnel.

According to Figs.11 and 12, the overall variation trends of Qwand Vgunder different rounds of grouting(i.e. the value of Hr) are quite similar for Station No. 81.5 at T1 tunnel, while they are significantly different from each other for Station No. 191 at T2 tunnel.However,for both stations,the variation patterns of Qwand Vgunder individual grouting sequence are similar but not identical,as the proportion of the same color block in a vertical bar(denoted as Hs/Hr) evaluated under Qwin Fig.11a (or Fig.12a) does not always resemble that under Vgin Fig.11b (or Fig.12b). For instance,regarding the blue portion of R1 bar, Hs/Hris around 1/3 and far less than 1/10 in Fig.10a and b, respectively, while the associated Hs/Hrof R2 bar is around 1/2 in both figures.From the perspective of grouting sequence, the conclusion derived above also works for other rounds of grouting under both stations, which are taken as special cases for the purpose of better explanation,thus it does not necessarily represent the potential patterns with respect to other stations.

Fig. 12. Comparison between (a) water inflow rate Qw and (b) grout take Vg of grouting sequences (from S1 to S7) within each round of grouting (from R1 to R5) at Station No.191 of T2 tunnel.

To better assess the potential relationship,regression analysis of Qwand Vgunder all grouting sequences at T1 and T2 tunnels are presented in Fig.13a and b,respectively.It is observable that there is positive correlation between Qwand Vg, and the Pearson’s coefficient of correlation for T1 and T2 tunnels are 0.767 and 0.785,respectively, which are far higher than that evaluated with data from individual grout hole, as listed in Table 1.

The regression model is assessed by the coefficient of determination (R2), which indicates that only 58.8% and 61.6% of the variance in the grout take Vgis predictable from the associated water inflow rate Qwin terms of T1 and T2 tunnels,respectively,implying that approximately 40% cases cannot be forecasted.

Therefore, the correlation between the grout take Vgand the water inflow rate Qwdoes exist. The correlation is strong when evaluated in terms of individual grouting sequence, but no causal relationship between them can be affirmed. In other words, high(or low) water inflow rate does not necessarily lead to large (or small) volume of grout consumption, which again reveal the complexity of grouting and that these two processes are not reversible (referring to Fig.1).

Fig.13. Regression analysis of water inflow rate Qw and grout take Vg in all grouting sequences at (a) T1 and (b) T2 tunnels with coefficient of determination (R2) of 0.588 and 0.616, respectively.

5. Inverse modelling of geological conditions

From the above analysis, though some interesting and meaningful patterns have been revealed from the field data, but the variance in some parameter(s)can only be partially explained by the variance in other parameter(s),due to its complexity associated with the unknown geological and hydrogeologic conditions.In engineering practice, the hydraulic conductivity K of regional rock masses(assumed to be homogeneous and isotropic) is usually evaluated through data measured with a probe hole, as illustrated in Fig.14,according to the following formula(Fernández,1994;Xu et al.,2015):

where Dpand Lpare the diameter and length of the probe hole,respectively; while Qpand Hpare the water inflow rate and hydraulic head measured on site, respectively.

Eq. (2) can also be used to assess the hydraulic conductivity of rock masses surrounding a grout hole(referring to Fig.1a),utilizing the water inflow rate and pressure obtained before grouting.Then,it raises the question of whether it is possible to evaluate the geological conditions of rock masses around a grout hole, especially,distribution features of the associated fracture network.One way to answer this question is to figure out if there are any parameters or process that involves as many fractures as possible.

From the comparison analysis given in Fig.1, we find that the fractures directly or indirectly associated with the grouting process account for a much larger portion of fractures distributed around a grout hole, in comparison with that linked with the process of water seepage. Therefore, data from individual grout hole for fracture sealing can help deconstruct the hidden geological conditions, such as rock mass quality in macro-scale, fracture zone in meso-scale, and large rock fractures in micro-scale.

To reach the goal,we first introduce a new standard to evaluate the geological conditions based on the volume of grout consumed at individual grout hole, quantified with a scale Sgc(hereinafter referred to as Sgcstandard)ranging from 0(bad)to 100(excellent).

Fig. 14. Schematic diagram of a probe hole measuring the hydraulic permeability of fractured rock masses.

The Sgcstandard is derived through parameter normalization and rearrangement:

where min(Vg), max(Vg) and norm(Vg) represent the minimum,maximum and normalized grout take, respectively.

Aided by the Sgcstandard proposed, we can have a better understanding of the onsite geological conditions. Taking as an example the spatial distribution of grouting data on the excavation surface of Station No. 202.5 at T1 tunnel, the original data are presented in Fig.15a, where both the size and color of a circle are used to visualize the grouting intensity(or the grout take)at a grout hole. From Fig.15a, the profile of three grouting fans can be easily figured out,while grouting hole drilled following the split-spacing principle mainly appears on the right side, where there are high water seepage and grout take.In comparison with the visualization of grouting features, the grouting data are first assessed by the proposed Sgcstandard and then further processed with surface interpolation, thus deriving the surface-based geological conditions,as presented in Fig.15b.Therefore,the geological conditions at any location of the excavation surface can be known once the corresponding coordinates are given.

Nevertheless, the surface-based geological conditions only utilized a small portion of information that can be extracted from the grouting data, because most of the grout holes are generally more than 10 m long and drilled in spatially varying directions,as can be seen from Fig.16. The length of a grout hole is Ln, and the length between the starting point Snand an arbitrary point inside Anmis lnm,where the subscripts m and n represent the mth arbitrary point inside the nth grout hole.

Suppose the coordinates of the starting and end points of the nth grout hole are(xSn，ySn，zSn)and(xEn，yEn，zEn),respectively.Then,the coordinate of the mth arbitrary point inside can be calculated as

where φ represents x,y or z.Anmbecomes the starting or end point when lnm/Lnequals 0 or 1.

Fig. 16. Spatial distribution of grout holes (revised from Barton and Quadros, 2019).The starting and end points are indexed by Sn and En, respectively; and Anm labels an arbitrary point in a grout hole.

Though m is an arbitrary number, we can determine its value based on the information collected during hole drilling, like the position where there are large fractures, or highly fractured rocks,or large water inflow,etc.,otherwise the values of m and lnm/Lnare set as 1 and 0.5 (by default), respectively.

Assume that the grout consumption at the mth point inside the nth hole (where the total grout take is Vn) is Vnm, we have the following continuity equation:

Under a given Vnm, geological conditions around the mth point(Sgc)nmcan be assessed via Eq. (3).

Fig.15. Data from individual grout hole of Station No.202.5 at T1 tunnel used for(a)visualization of spatial grouting intensity and(b)evaluation of geological conditions based on Sgc standard.

Fig.17. Cluster analysis of grouting data without being classified based on known geological or hydrogeological information for (a) T1 and (b) T2 tunnels.

Table 2 Summary of grouting data categorized via cluster analysis.

It is possible that some geological conditions, such as highly fractured zones, dikes, or water bearing zones, could be detected during the site investigation stage. Then, data from some grout holes hitting these geological features can be classified according to specific features. The remaining data not categorised will go through cluster analysis, the results of which are illustrated in Fig.17.The grouting data from both tunnels are grouped into three clusters, the characteristics of which are summarized in Table 2,where the ranges of Vgand Pgare assessed excluding some outliers.Three clusters ranging from left to right are renamed as I,II and III,which correspond to low, medium, and high grout consumption,respectively, and all three categories have distinctive features.Categories I and II of both tunnels account for the majority, the associated ranges of Vgare quite similar,while the pressure ranges are quite different. As for Category III of both tunnels, the corresponding pressure ranges become similar again. All the results obtained from the above analysis can be taken as “known information” and thus the input and output for machine learning(Suwansawat and Einstein, 2006; Mahdevari and Torabi, 2012;Toghroli et al., 2014; Liu et al., 2020).

Finally,the surrogate model derived via machine learning can be used to assess the geological features under hypothesized φAnm,Vnm,etc. (Zhang and Goh, 2016), together with optimization algorithm developed for reverse analysis. Thus, the parameter array[φAnm，Vnm，(Sgc)nm] and geological features derived after optimization can form a geological database, which can be taken as reference document for future projects nearby and routine maintenance. All the steps involved in the process on how to generate a geological database from raw data and some hypotheses are demonstrated in Fig.18.

The detailed geological conditions around the T1 tunnel evaluated after systematic analysis are visualized in Fig.19b,where there are four special zones: Zone I (relatively low), Zone II (extremely low),Zone III(very low)and Zone IV(low).Compared with the data from the original data points illustrated in Fig.19a, the 3D visualization can give us a better understanding of the regional rock mass quality, including both magnitude and the associated distribution range. With this geological database available, special attentions can be paid and/or actions can be taken in advance when there are new underground projects constructed nearby.

Fig.18. Steps for deriving the geological conditions of rock masses affected by grouting based on reverse analysis and machine learning.

To validate the geological database obtained,the geological and hydrogeological conditions constructed with data from site investigation and various probe holes are presented in Fig. 20. The geological database in Fig.19 is interpreted with geological and/or hydrogeological information from Fig.20,as listed in Table 3.Due to the complex geological and hydrogeological conditions encountered by Station No.81.5,large number of grout holes were drilled and the total volume of grout consumed is very high, but few among these holes consumed large amount of grout,indicating that the geological condition around individual hole is of similar characteristics or homogeneous, that is why the rock mass quality is indexed as relatively low according to the Sgcstandard. According to Table 3, Zone II of extremely low rock mass quality is well predicted.Zone III located around Station No.202.5 is 20 m and 60 m from the second and third water bearing zones, respectively, indicating that there are large fractures or faults directly or indirectly connected to the two water bearing zones.Similarly,the rock mass quality of Zone IV located between Stations Nos.229 and 243 is low,as it is close to the third water bearing zone.Probably because the void spaces at the third water bearing zone have been sufficiently filled by grout injected at previous stations, grout consumption at Station No.267 is not that high,though it is located well inside the zone.

6. Conclusions

In the present work,an overview was made to an underground project for oil or petrochemical storage, in terms of geological and hydrogeological conditions, the grout consumption at each excavation surface, etc. Then, statistical, correlation and regression analyses were conducted with data from individual grout sequence or hole. Finally, we proposed an inverse analysis model to convertgrouting data of this project into a geological database. Following conclusions are drawn as follows:

Table 3 Interpretation of geological conditions along T1 tunnel.

Fig.19. Visualization of(a)original data point from grout holes distributed at individual excavation surface and(b)geological conditions of T1 tunnel assessed via Sgc standard after optimization.

Fig. 20. Tough geological and hydrogeological conditions crossed by T1 tunnel.

(1) Sealing rock fractures around a grout hole is not reversible process of water seepage via the same hole.

(2) Grouting is a complex process, and both the geological conditions and grouting features can be remarkably different from one another even for neighbouring tunnels. The grout consumed at a specific excavation surface is not only affected by the quality of regional rock masses, but also by the antecedent grouting.

(3) Results from data analysis reveal that grout consumption is correlated with water inflow rate. The correlation is strong when evaluated in terms of individual grouting sequence,which, however, does not indicate a causal relationship. In other words, high (or low) water inflow rate does not necessarily lead to large (or small) grout consumption. The direct cause of high grout volume consumed is the number of fractures directly or indirectly connected (fracture connectivity) with grout holes and the corresponding fracture apertures.

(4) Geological database can be built with data from individual grout hole drilled during underground construction based on reverse analysis, which can provide visual information for future projects located nearby.

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 thank NTU-JTC Industrial Infrastructure Innovation Centre (I3C) and Nanyang Centre for Underground Space for allowing us to use the Jurong Rock Cavern data for the data mining analysis, and the “Start-up Funding for New Faculty” provided by the Nanjing University of Aeronautics and Astronautics.