## Abstract

A detailed geostructural characterization (i.e. joint aperture, spacing, filling materials and joint size) was performed to evaluate the weathered rock foundation of the Siazakh Dam site, western Iran. Rock qualities were assigned a rock mass rating classification. A positive correlation was detected between permeability and rock characteristics, and played an important role in assessing fracture media. The joint aperture had a stronger relationship to joint permeability than did other fracture characteristics. The results strongly support the contention that a new generation of permeability equations and analytical methods may be obtained in accordance with a site's geological features. In this regard an artificial neural network (ANN) is a biologically inspired computing method that is capable of predicting the permeability values of rock masses with high accuracy. ANNs showed great potential in interpreting raw data from the Lugeon test and predicting the final permeability of a test section in a borehole. A new practical approach for the evaluation of field permeability with depth in fractured rock masses is also presented.

The Siazakh Dam will be an important reservoir dam to develop the agricultural sector and produce electricity for the Kurdistan province in western Iran. The project is being carried out by the Ministry of Power on one of the tributaries of the Qizil-Uzan River. Parallel to a geological investigation of the area, a very important engineering aspect that must be taken into account in the Siazakh Dam project is the prediction of the permeability of weathered rock masses under the dam foundation. Precise hydraulic parameters should be assessed when a dam is constructed on fractured media. It is difficult to precisely relate permeability in fractured media to fracture properties, although it is well known that groundwater flow is strongly controlled by fracture properties. The relationship between permeability and fracture properties depends on the tectonic history of the rocks.

It has long been known that the permeability of jointed rocks is negatively related to depth and applied geostatic stresses (Fatt & Davis 1952; Wyble 1958; Daw *et al.* 1976; Juang & Lee 1988). Based on field investigations, equations have been derived to describe this relationship (Snow 1968): the permeability of fractured rocks is strongly related to the geometric properties of joints and the degree of weathering of the flow paths. It is obvious that this permeability change should also describe the weathering process and its influence on the rock mass. Furthermore, the coefficients of the equations must be defined for every borehole and the equation can only describe one formation: it does not perform well in the other fields. In a weathered rock mass, the applied loads (including *in situ* stresses and seepage forces) may affect the test results obtained; thus these results must be adjusted. In this case a rock mass that has an altered permeability will develop around the hole. The permeability of this plastic rock zone depends on the induced strains in this zone, which are affected by seepage flow. Seepages and stresses are mutually dependent.

The goals of this study are to (1) accurately determine the permeability in several test sections of a fractured weathered rock from the water-pressure or Lugeon test, and (2) use an artificial neural network (ANN) model to establish a relationship between permeability and fracture properties (frequency, spacing, aperture, filling materials and fracture size) of core samples, considering depth and geostatic stresses. Use of an ANN eliminates some of the problems associated with generalization of predictions of permeability distribution. The ANN was designed and trained to predict permeability with limited input data (Aminian *et al.* 2000).

## Geological setting

The study area is located between 35°45' and 36°00'N and 47°00' and 47°15'E in Kurdistan, western Iran. Site investigation was extended across a large area of the Siazakh Dam site (Fig. 1). The morphology of the landscape features gently sloping hills crossed by valleys and plains, with occasional steep rocky hills.

This study covers part of the Zagros orogenic belt at the dam site, based on a geological field survey and interpretation of outcrops and core data. In Iran, the Zagros is the result of the opening and closure of the Neotethys ocean realm along the northeastern border of the Arabian plate (Alavi 2007). The basin formed in surface deposits mainly of terraces, alluvial sediments and debris during the Quaternary Period. The solid geology of the region is dominated by sequences of sedimentary and volcanic rock outcrops, largely dating back to Cretaceous lithostratigraphic units. The Cretaceous rocks are composed of dark grey massive limestone and dolomitic limestone, which have been slightly metamorphosed. The Cretaceous units are also locally composed of dark grey shale with intercalations of trachyandesitic lava and rhyodacitic tuff, dark grey limestone and shale, with minor beds of volcanic rocks. Sequences of a polygenetic conglomerate with intercalations of marl and sandstone were deposited during the Oligocene Epoch. During the late Miocene and Pliocene Epochs, regression of the sea and the creation of mountainous relief by folding and thrusting resulted in a continental environment. Limestone with intercalations of marl and marl with intercalations of limestone, great quantities of clastic material and red beds (compared with the Qom Formation) were developed in adjacent synclines (Alavi & Mahdavi 1994). Finally, Pliocene–Pleistocene conglomerates unconformably overlie older formations.

The closure of the Neotethys was marked by several tectonic events on the Zagros platform. The first was the Early Coniacian–Late Santonian obduction of ophiolites onto the continental crust (Alavi & Mahdavi 1994), which changed the architecture of the basin. The second event was the pronounced reactivation of deep-seated pre-existing north–south faults. Therefore, the structure of the bedrock in this area is extremely complex owing to intense compressive and tensional tectonic phases from the Miocene to the Pleistocene Epochs. The main trend of discontinuous structures, including faults and joints, is oriented NW–SE, but a NE–SW trend is also observed. The nearest (up to 20 km from the Siazakh Dam site) faults are the Kagholi, Shikh-Hydar, Kami-Cherme and Kalane faults (Geological Survey and Mineral Exploration of Iran 1990).

Groundwater occurs within Miocene rocks both in correspondence to the weathered mantle of the bedrock and at depth within arenaceous and carbonate bodies. These aquifer layers are characterized by low hydraulic conductivity. They are interbedded with and overlapped by aquiclude layers, corresponding to the clayey-marl portion of the formations. Some of the foundations of the Siazakh Dam will be within Miocene rocks.

## Site investigation

Fifteen boreholes were drilled to depths of 40–95 m along the dam axis. Three, seven and five boreholes were drilled in the right abutment, left abutment and foundation, respectively. The rocks underlying the left abutment are limestone and black shale, with massive basalts and tuff. The bedrock of the right abutment consists of shale and shale limestone. The foundation comprises limestone and shale limestone.

The region has been subjected to complex faulting, folding and fracturing. Six major faults were recognized, which strike NNW–SSE. More recent thin geological deposits are granular alluvium in the valley bottom. A geotechnical cross-section was constructed based on exploratory boreholes (Fig. 2).

## Discontinuity data

Detailed discontinuity logging of the rock cores was performed to provide the basic parameters for classification of the rock mass. Discontinuity data were collected on the three dominant rock types (shale, limestone and tuffs) according to the suggested methods of the International Society of Rock Mechanics (Brown 1981). Joint properties (e.g. length, spacing, angle of inclination, opening, type and amount of filling material) and secondary phenomena (e.g. weathering and metamorphism) affect the physical and mechanical properties of a rock mass. The structural discontinuity survey was designed to determine the discontinuity geometry identified on cored sections obtained during borehole drilling, as well as in the exposed faces and rock outcrops in the topographic terrain. Artificial fractures made by drilling were ignored for the description. A total of 3898 significant joints have been recognized at the Siazakh Dam site: 1451 joints were on the foundation, 869 on the right abutment and 1578 on the left abutment. Joint properties were evaluated by depth for each borehole. The length of these joints varies between 2 and 93 cm.

Joint spacing ranges from 0.1–0.5 m at shallow depth to 0.5–1 m below the zone of weathering, and to 2 m at depths greater than 60 m. Joint inclinations were measured with respect to the horizontal plane. Boreholes were drilled vertically. In three parts of the dam site 1242 joints between 0 and 30°, 1353 joints between 30 and 60°, 756 joints between 60 and 80° and 547 joints between 80 and 90° were found for the three rock types, containing 32%, 35%, 19% and 14% of joints respectively. Therefore, horizontal and medium gradient joints are more commonly observed. The effective opening (aperture) of joints in the bedrock ranges from 3 to 5 mm in the upper 15 m of the rock mass, decreasing to 1–2 mm at depths exceeding 30 m. Furthermore, joint openings are closer and there is more space between them as the depth increases.

From the perspective of surface joints, 7% are smooth, 65% are slightly rough and 28% are rough, as determined with a shape tracer device. Among the bedding joints, 46% are plugged with iron oxide (hematite and limonite), 13% with silt and clay minerals, 12% with calcite crystals and 29% have no filling materials. Filling materials locally formed by weathering are transported by infiltrating water in the deep zone in jointed rock masses and are deposited on the walls of the openings, which results in the rough surfaces. Infilling of the joints may possess a wide range of physical properties, especially with regard to its permeability (Li *et al.* 2008). The range of behaviour is influenced by the mineralogy, particle size distribution and water content of the site infilling materials. The average discontinuity properties of the dam site are given in Table 1.

## Rock mass classification

The first rock mass classification was presented by Ritter (1879). This classification was presented for experimental design of tunnel and support systems.

Later Terzaghi (1946) presented a descriptive classification of rocks; this is the first rock classification system and was used for many years in the USA for the design of rock loads carried by steel sets. This classification method is suitable for estimating the load on steel arched frames, but is not suitable for other support methods such as shotcrete systems.

Deere *et al.* (1966) presented another strategy for classifying rock masses (rock quality designation; RQD) based on rock quality. This index is based on the percentage recovery of cores, which is the ratio of the total proportion of solid parts of the core whose length is equal to or greater than 10 cm to the total length of the drilling. This qualitative rock index (RQD) has been used extensively in various designs and has also been useful in the choice of tunnel maintenance system. The International Rock Mechanics Association has recommended that the diameter of the core be at least 54 mm and recovered with a core barrel.

Barton *et al.* (1974) and Bieniawski (1989) changed drastically the rock engineering perspective. The latest version of the geomechanical classification, the rock mass rating (RMR; Bieniawski 1989) was used to summarize the geological and geotechnical data and provide design tools (Table 1). This classification system uses six parameters, all of which were measured from outcrops or cores: uniaxial compressive strength (UCS) of intact rock material; RQD; spacing, condition and inclination of discontinuities; and groundwater condition (Mert *et al.* 2011). Ratings are summed to give an RMR value for each rock formation, ranging from zero (very poor) to 100 (excellent). At the dam site, shale has a poor RMR and limestone and tuff have a fair RMR (Table 1).

## Rock mass strength

The point load strength test was used to quantify the *in situ* strength of rock masses on either cored sections or cut blocks. The test is derived from the Brazilian test, in which a disc of rock core is compressed by application of a concentrated load between a pair of truncated conical plates until failure. The compressive stress at failure, *σ*_{ci}, is then calculated according to Marinos *et al.* (2005). The UCS of intact rock, *σ*_{ci}, can be measured using the procedure of ASTM (2002).

The presence of geological structure within a rock mass (e.g. joints, shears) requires consideration of the combined influence of intact rock blocks and discontinuities. However, laboratory testing is usually restricted to intact rock samples. This led to the development of a system that links rock mass properties to observations of rock mass characteristics. Hoek & Brown (1988) used the RMR to describe the quality of a rock mass. The empirical criterion has been re-evaluated and expanded over the years owing to the limitations in Bieniawski's RMR classification and the equations used by the Hoek–Brown criterion for very poor quality rock masses (Hudson *et al.* 1992). Hoek & Brown (1997) proposed a new rock mass classification called the geological strength index (GSI). The GSI value was found to be a better input parameter for the Hoek–Brown failure criterion to estimate the strength and deformation modulus of jointed rock masses.

The most up-to-date version of this classification represents a new derivation for the relationship between the input parameters and GSI. The generalized form of the non-linear Hoek–Brown failure criterion was expressed by Hoek *et al.* (2002). *m*_{b}, *s* and *a* are constants determined for the rock mass using the GSI (Hoek *et al.* 2002). Once the GSI has been estimated, these three constants that describe the rock mass strength characteristics are calculated (Table 2). The value of the Hoek–Brown constant for the rock mass, *m*_{b}, depends on the Hoek–Brown constant of intact rock, *m*_{i}. The constants *s* and *a* can be calculated respectively, for a GSI >25 (Table 2).

The RMR and GSI classification systems are based on the quantitative properties of a given rock mass. Among the various empirical correlations that have been made between RMR and GSI classifications, the most applicable was proposed by Hoek & Brown (1997). The above-mentioned parameters of rock mass strength criteria for the three rock formations are presented in Table 2.

Most of the geotechnical software involves the use of the Mohr–Coulomb failure criterion, so determination of equivalent angles of friction (*φ*′) and cohesive strengths (*c*′) is necessary for each rock mass (equtions (1) and (2), respectively):

A computer program ‘Rock Lab’ was developed to determine rock mass strength parameters by using the GSI determined from the RMR version of Bieniawski (1989) and Mert *et al.* (2011). In this research, this software is used to determine rock mass parameters, and the values of *φ*′ and *c*′ for the three types of rocks under study are presented in Table 3. These parameters were used for rock strength classification when preliminary and reconnaissance information was required. Therefore, they were not used for design or analytical purposes.

## Deformation modulus of rock mass

The *in situ* rock mass deformation modulus (*E*_{rm}, GPa) is an important parameter in monitoring deformation at the dam foundation (Table 3). It was obtained from the triaxial test on core specimens and calculated with equation (3) (Hoek & Diederichs 2006):*E*_{i} is the deformation modulus of the intact rock obtained in the laboratory (GPa), and it should be recalled that *D* was considered as zero for this site project.

## Rock mass permeability

### Lugeon test method

Site permeability is one of the main design considerations for dam and reservoir drainage systems. A constant water-pressure test in the field, referred to as the Lugeon test or packer test, is used for isolated sections between the packer and the bottom of a borehole (Fig. 3). The test was carried out by lowering the packer to the required depth and inflating it with nitrogen. The length of the packer, when expanded, should be at least five times the borehole diameter (Shmonov *et al.* 2011). The test is carried out in stages (e.g. ABCBA 0.1–0.3–0.5–0.3–0.1 MPa), cycling up to a maximum head and then down again. The maximum head value applied in the Lugeon test is determined by the maximum height of the dam reservoir during operation and the layout specifications. The maximum head in this case is assumed to be 0.5 MPa. Lugeon tests were carried out in boreholes 4, 8, 10 and 12 according to Figure 2.

At each stage, the pressure is held constant and the volume of water taken in the section of burial is measured over a specific period. If the measured volumes over two consecutive readings are more than 10% different, then an additional measurement should be made for a new period before the pressure is changed (Eid 2007). The permeability is calculated from the volume of flow and using the net dynamic head applied to the test section:*H*_{T} is the net pressure head, causing flow into the rock (m), *P* is the Bourdon gauge reading converted to head (m), *H* is the height of the Bourdon gauge above the midpoint of the test section to the ground level (m), *H*_{g} is the height of the natural groundwater level above the midpoint of the test section (m) and *H*_{f} is the friction head loss in the pipes (m).

Head loss must be obtained by calibrating every piece of equipment or from calibration curves. Around a test well, permeability can be calculated from the solution for steady-state laminar flow in homogeneous and isotropic media. Basically, a steady-state equation should be used when the steady state is achieved (Kiraly 1969; Shmonov *et al.* 2011). The coefficient of permeability (*k*, m s^{−1}) for test section lengths (*L*, m) greater than 10 times the radius of the test section (*r*, m) and between one and 10 times the radius of the test section can be calculated with equations (5) and (6), respectively. *L* is usually selected such that adequate hydraulic information can be obtained with variations of joint development:*Q* is the constant rate of flow into the section (m^{3} s^{−1}), *H*_{T} is the pressure head of water in the test section (m) and *r* is the radius of the test section (m).

Where cycled tests are conducted, with a pressure pattern as mentioned above, results are graphically presented either as a head v. flow (Lugeon) diagram or a head v. permeability diagram. Interpretation of these diagrams has been presented in the literature (Dick 1975; Lancaster-Jones 1975; Pearson & Money 1977; Ghabezloo *et al.* 2009). Practically, the results fall into three groups.

Figure 4 top: Darcy's law indicates that flow will be directly proportional to pressure, therefore prediction of the horizontal line on the head v. permeability plot yields a straight line passing through the origin;

Figure 4 middle: permeability increases with increasing pressure;

Figure 4 bottom: permeability decreases with increasing pressure.

The best way to determine the permeability of rock masses is to carry out *in situ* tests. Lugeon tests were performed during the site investigation for the design of the Siazakh Dam. Water pressure tests were conducted in five out of 15 boreholes along the axis of the dam site. Boreholes were drilled to a maximum depth of about 68 m, with a radius of 15.2 cm. Test intervals were up to 2 m in length, sealed from the bottom to the top of the borehole at different depths. Five consecutive pump-in tests (single Lugeon) at constant water pressures between 0.1 and 0.5 MPa were performed, with a stage duration of 10 min. The longer the duration, the more effective the test (water injection flow rate stops changing). The joint spacing was measured corresponding to the water pressure at each 2 m section.

The five Lugeon values were plotted and compared with Figure 4. It was determined that group 1 (laminar flow) values are accepted as the permeability reported from the tests. Equation (13) was deemed most applicable to calculate the permeability because the water inflow rate was constant and test hole *L* (2 m) was more than 10 times the radius (15.2 cm). The interconnections between discontinuities and the amount of saturation are important parameters in permeability measurement (Wong *et al.* 2013).

### Interpretation of rock mass permeability

#### Using empirical equations.

Snow (1970) assumed that the joint permeability is isotropic. The data available from the Siazakh Dam site were also interpreted to indicate isotropic permeability, assuming that a rock mass possesses a cubic system of joints. Spacing (number of joints) was measured from the core log data in boreholes for every 2 m section, each with a defined permeability. Zones with too many fractured gouge and breccia occurrences could not be determined and were not used for determining the correlation between permeability and joint characteristics. This method gives an average value of *k* in the measuring zone (Eid 2007; Baghbanan & Jing 2008).

The interpretation of field measurements has been discussed by many researchers. Assuming homogeneous rock with a constant boundary condition, a number of empirical functions have been utilized relating the loss of permeability to depth. Snow (1970) observed that the permeability of a jointed rock mass follows a logarithmically declining trend with depth (*z*) (equation 7):*d* and average opening *e* are introduced into the rock mass. They have an initial isotropic permeability of intact rock *k*_{o}. The new permeability, *k*, in the direction of the fracture is given by equation (9) (Zhang *et al.* 2007):*e* is average opening (m), *n* = 1/*d* is the number of fractures per unit length in the new set (*d* in metres) and *v*_{w} is the kinematic viscosity of water (m s^{−1}).

If there are *N* sets of fractures introduced into the rock mass, the total volumetric strain relative to the initial rock at zero differential stress is given by equation (10):

Equations (9) and (10) may be combined in two different ways to give equations (11) and (12):*n* is constant, then *e* is constant, then

When the peak strength of the rock mass is exceeded and strain is continued in the strain-softening zones, it is expected that both *n* and *e* will increase. Brown & Bray (1982) proposed that, in the plastic zone, *η* is the constant of proportionality and must be obtained from field experiments. However, extreme values of *η* can be used for design purposes.

Considering the seepage flow pattern in a jointed rock mass in the radial direction and using Darcy's Law, the pore pressure increment at any radius *r* is given by equation (14):*γ*_{w} is the unit weight of water (N m^{−3}), *p*_{W} is the pore-water pressure and *q* is the seepage flow rate per unit length of the borehole.

Therefore, pore pressure at any radius *r*_{b} and any pressure *p*_{b} of the plastic and elastic zones can be described by equations (15) and (16), respectively:*R* is the radius of the borehole (m) and *h*_{1} is the distance of the borehole section from the groundwater table (m).

The permeability of a rock mass calculated from the Lugeon test is commonly used to define the apparent permeability (equation 17), wherein the effects of drilling and seepage force are neglected:*r*_{e}, after some modifications, leads to the initial hydraulic conductivity of the rock mass. The effects of altered permeability of the plastic zone around the borehole are taken into account. This metric is called the adjusted permeability (equation 18):

On the basis of data obtained from the Siazakh Dam site, the *k*_{apparent} of jointed sedimentary rocks can be estimated by plotting the mean *k* against the mean depth in the measuring zone. The *k*_{apparent} seems to follow a logarithmically declining trend with depth at the dam site (Fig. 5 and equation 21):

Using the adjustment procedure (equation 19) for the considered rock masses, equation 22 was derived:

Plots of water pressure v. flow (l min^{−1}) during Lugeon tests show an idealized flow path, which varies continuously with joint openings (Houlsby 1976; Bell 1992). The flow paths change when the joints are subjected to different stress conditions, because an imposed stress will deform discontinuities in a rock mass. This means that geostatic stresses have a significant influence on the permeability of a rock mass. Therefore, the permeability is related to the stress field and thus decreases significantly with an increase in effective confining stress (Fatt & Davis 1952; Wyble 1958; Daw *et al.* 1976; Juang & Lee 1988). Permeability at the dam site varied over 10 orders of magnitude between 70 m (high stress) and at shallow depths (low stress) (Fig. 5). On the basis of *in situ* permeability tests and joint frequency determination, joint spacings increased with depth (Fig. 6), whereas joint openings decreased (Fig. 7). Other investigations on core samples concluded that discontinuities with significant joint apertures persist at depth. Therefore, no systematic variation is apparent over the range of depths normally encountered during civil engineering operations.

Price (2015) proposed that jointed rocks resulting from unloading and uplift are of most significance to groundwater flow. Below a surface zone where joint frequency increases as a result of weathering and the effect of stress relief, *k* increases simultaneously. However, joint intensity remains approximately constant from 30 m down, as shown in Figure 8. Decreasing joint frequency may be estimated at the end of the weathering zone.

#### Using neural networks.

The ANN model is an attractive tool in geo-engineering applications owing to its ability to model non-linear multivariate problems. There are three layers in each model: (1) the input layer, which consists of the independent variables, where no calculations are made; (2) the hidden layer, in which calculations of optimization are made, the number of hidden neurons is changed and the best number of hidden layer is selected; (3) the output layer, in which the results are given; this must be predicted by the neural network and the performance of the selected model is obtained from this output layer. The number of input and output layers is determined by the characteristics of the application (Shi *et al.* 1998). Each layer consists of a number of processing units (neurons) and each unit is fully interconnected with weighted connections to units in the subsequent layer. In this investigation, a sigmoid transfer function is used and a hidden layer and a linear transition function are used in the output layer; in other words, a two-layer feed-forward network is used.

Input data to the ANN consisted of depth values. Model output is compared with permeability, which is calculated from the Lugeon test. One hidden layer was used for designing the network, but the number of hidden neurons was changed to find the most appropriate network topology. The number of hidden neurons (NHN) in the network determines the degree of our learning. The back-propagation learning algorithm was used to train the neural networks. This algorithm executes the patterns in two steps. At the first step signals produced from the input layer flow forward to the output layer. Then, from the difference between the calculated and desired output, the error of each output neuron is computed. At the second step weights in the hidden layers and output layer are adjusted to reduce the difference between the calculated and desired output (Rumelhart *et al.* 1985). The network performance may be evaluated quantitatively in terms of the correlation coefficient (*R*) and mean square of errors (MSE).

The input data will be used in the input layer of the network and are divided into three groups in a random manner. The first group consists of 70% of the input data. In this group data will be used to train. The second group consists of 15% of the remaining input data. In this group data will be used to validate. The third group consists of 15% of the input data that are not used in the first or second group. In this group data will be used to test. In Table 4 the results for the MSE and *R* are given. The MSE and the *R* both have acceptable results; MSE values are fairly small and near zero and the *R* values are near unity, which indicate a good prediction. It can be seen from Table 4 that the best case is achieved when NHN is equal to five. According to Figure 9 we can see that the minimum MSE is achieved at epoch 6 when NHN is equal to five.

From this development model it can be seen that a correlation coefficient of 0.92 is achieved in the training. The correlation coefficient for the validation period was 0.94. A correlation factor of 0.96 was achieved for the test period. Figure 10 shows these correlations.

## Discussion and conclusion

Analyses of data collected during the site investigation of the Siazakh Dam site provided useful information regarding the geometrical and geomechanical properties of the discontinuities in the rock mass in the abutments and the foundation of the dam. Steep joint sets were more commonly observed in rock masses with six major faults, which strike NNW–SSE, and have subvertical dip angles. Hence, they are amenable to grouting by vertical boreholes. The Hoek–Brown failure criterion was used to estimate *in situ* rock mass strength parameters and the modulus of deformation for preliminary investigation and reconnaissance of the dam site.

Lugeon tests indicated that permeability of the limestone, shale and tuff formations decreases with depth. A new method is proposed to adjust the permeability for weathered and bad to fair quality rock masses at great depths.

At the Siazakh Dam site, water flow is confined to a network of joints and tends to be laminar. Flow through joints depends on the joint properties (opening, spacing, interconnection and filling materials) and is strongly related to the weathering zone at shallow depths. At greater depths, beyond the influence of weathering, the openings may be filled with different materials. Joint spacing depends primarily on geostatic stresses; thus, permeability varies by more than 10 orders of magnitude within the same depth interval.

As a result of geostatic stresses, which act normal to the plane of discontinuities, the walls of the discontinuities are in contact at greater depths, which restricts the flow of water. This is the best indication of grouting depth. There is evidence of a decrease in permeability with depth, but it is hard to justify an empirical equation for this relationship. No systematic variation with depth is evident.

Furthermore, in this work we have presented a study of the use of neural networks multilayer perceptrons (MLP) for the prediction of the permeability. With this model, the correlation coefficient is almost equal to unity, which represents a good relationship between the values of the neural network model and the measured values of permeability.

## Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

*Scientific editing by Stephen Buss; Sophie Messerklinger*

- © 2019 The Author(s). Published by The Geological Society of London. All rights reserved