Introduction

Rock mass grouting is commonly used for rock slope stabilization, tunnel sealing, and reinforcement as well as dam foundations; however, different techniques and grout mixtures are used depending on rock fracture intensity and rock mass permeability (ISRM 1996; NTS 2011). Therefore, fractured rock mass reinforcement through grout injections requires a good knowledge of joint features such as aperture, roughness, spacing, and filling (ISRM 1996). Indeed, an effective grout penetration into fractures depends on grain size to joint aperture ratios (Axelsson et al. 2009) and is affected by many other factors such as grout hydration and flocculation, injection pressure, grout density, and the void geometry (Draganovic and Stille 2011; Pusch 1994). The optimal combination of the final grouting pressure p and the grout volume injected V (called the grouting intensity number, GIN) has been investigated by Lombardi and Deere (1993). More recently, the aperture controlled grouting method (ACG) has been proposed by Carter et al. (2012) considering the Lugeon number (Lu), based on the 3D joint geometry and hydraulic properties of the fracture network (mainly the aperture).

Water pressure tests (WPT) are traditionally used to evaluate the rock mass permeability and derive grout penetrability into joints. Among these, the Lugeon test (Lugeon 1933) is a well-known and widely used method, although it can only provide quite rough estimates of grout infiltration due to the different properties of water and grout (Ewert 1997). Although no analytical relationship between hydraulic conductivity and the grout take is known, many authors found empirical relationships (Foyo et al. 2005; Sohrabi-Bidar et al. 2016; Sadeghiyeh et al. 2013; Kayabasi and Gokceoglu 2019), some of which are based on Lu or the Secondary Permeability Index (SPI), sometimes showing high correlation coefficients (Kayabasi and Gokceoglu 2019; Sohrabi-Bidar et al. 2016). SPI provides information about rock mass hydraulic conductivity and rock mass quality based on WPT (Foyo et al. 2005). At a given pressure, SPI expresses the water infiltration rates through the surface of the injection chamber (l·s−1·m−2). Based on the SPI, Foyo et al. (2005) classified rock masses in four main classes, providing suggestions on the ground treatment needs.

Rock masses with different hydraulic properties require different types of grout compositions to achieve optimal infiltration. They vary from cement, with or without ashes, fillers and silica fumes, resins, silicates, and chemical admixtures. When considering cement grouts, important issues refer to the water-cement ratio, blend stability, and slurry properties (density, bleeding, viscosity, etc.), which affect the optimal grout penetration into fractures (Cambefort and Ischy 1964; Lombardi and Deere 1993).

With this study, we propose a simple approach for calculating the grout take needed for reinforcing a suggestive calcareous sea arch, in a highly frequented tourist resort in Southern Italy, assuming that the injected grout volume, in a unit volume of the rock mass, equals the total fractures’ volume. The study couples geo-structural surveys, water pressure, and grouting tests, carried out with both silica gel and bentonite cement. The analysis allowed evaluation of the grout’s needs for strengthening the arch. The total injectable volume in a volumetric unit of the rock mass was calculated using the software GeoGebra (https://www.geogebra.org/), adopting simplifying assumptions concerning the fracture’s aperture, spacing, and roughness. Results in terms of grout takes were compared with other approaches based on SPI available in the literature and with the experimental data from grouting tests. They show that considering the shallow depth of the injection across the thin arch structure, empirical equations based on SPI provide unrealistic results both in terms of grout masses and volumes; on the contrary, structural data, properly processed, proved more satisfactory results in agreement with the site tests.

Geological and geo-structural setting

The Natural Arch of Palinuro, located along the Cilento coast, represents an important geological singularity inserted in a beautiful landscape (Fig. 1), resulting from the interplayed role of karst and marine erosion and tectonic uplift (Sorrentino et al. 2016). The arch connects two highly frequented beaches and is often crossed by tourists, posing a severe risk for rock falls. Rock failures from the arch roof and abutment are mainly due to the complex fracture network and the wave erosive action worsened by the progressive rise of sea level. Consequently, this structure is susceptible to collapse in a few years, leaving only an isolated stack. Budetta et al. (2019) carried out geo-mechanical surveys and numerical non-linear finite element modelling, pointing out that the arch roof and its seaward abutment are the more critical areas requiring urgent interventions.

Fig. 1
figure 1

Location of the investigated area and picture of the NE façade of the Natural arch. The white dotted line shows a stratigraphic boundary between thick-bedded limestone and dolostones and calcirudites (on the left) and thin-bedded calcilutites and calcarenites with chert nodules and lists (on the right)

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The arch has a maximum height at the extrados of about 20 m and a maximum thickness of about 14 m. The void height is about 12 m, the landward abutment supporting the vault has a thickness of 12 m, while the seaward abutment is 14 m thick at its base and about 7 m upward (Fig. 1).

The whole rock mass of the arch is formed by a Jurassic limestone dipping to the NE. Specifically, at the intersection between the arch vault and the seaward abutment, thick-bedded dolomitic limestones and calcirudites are overlain by well-bedded silicified calcilutites and calcarenites with chert nodules and lists. A low-angle normal fault (LANF) gently dipping towards the south, affecting the rock mass at the vault of the arch (Budetta et al. 2019), is responsible for the intense fracturing of the rock masses and the formation of cataclastic zones (Fig. 2).

Fig. 2
figure 2

Orthometric vertical structural maps of the north-eastern face of the arch’s cliff: a fractures intensity zoning according to Geological Strength Index (GSI) rock mass classification (Marinos and Hoek 2000); b map of fracture traces and exposed surfaces

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In situ surveys carried out through 15 scanlines on the arch surfaces allowed to define the geo-structural and geo-mechanical frameworks. Cm-scale virtual outcrop (VOM), reconstructed coupling terrestrial laser scanning, and UAV photogrammetry facilitated structural mapping and analyses. The adopted equipment was a Riegl VZ1000 Long range laser scanner and a custom UAV equipped with a GoPro Hero 4 Digital Camera with a 12 Mpx CMOS sensor. To the scope of the present study, VOM was used to lay vertical base map for structural mapping and visualization.

In-depth rock mass conditions were investigated through 10 boreholes (with depths varying between 1.50 and 2.00 m) drilled using portable equipment. The joint orientations and main physical properties (aperture, roughness, weathering, and infilling) were carefully investigated (Figs. 3 and 4); this allowed us to detect, in the arch area, three main joint sets that group the bedding planes (Ks) as well as tectonic discontinuities (K1 and K2) affecting the arch (Table 1). A further set (K3) crossing the north-eastern face was detected towards the lateral ends of the studied area by analyzing the VOM; however, it does not significantly affect the arch vault and abutments and is no longer treated within the present study.

Fig. 3
figure 3

Stereoplots of dominant joint sets affecting the Natural arch: A NE face; B SW face

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Fig. 4
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Main physical properties of joints affecting the Natural arch

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Table 1 Geo-structural parameters of the rock mass surveyed along the faces of the arch
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The K1 set consists of fractures steeply dipping towards ESE, which bound elongated blocks. It is sub-parallel to the primary orientation of the north-eastern face (Fig. 3) and shows persistences mainly ranging between 1 and 10 m. Joints belonging to the set K2 are steeply dipping to NE and SW, showing high persistence. The spacing of bedding planes generally ranges between 30 and 300 mm at the arch vault, with a modal value of about 75 mm (“close” spacing), and between 120 to 800 mm at the seaward abutment (Fig. 4). Regarding the other sets, the spacing generally varies from “close” to “moderate.” Both sets intersect the bedding plane Ks, thus causing a blocky-to-very blocky structure of the rock mass and favoring slab detachment from the arch roof along unsupported bedding planes (Ks), bounded by intersecting fractures. Consequently, high susceptibility to rock failure characterizes the rock mass forming the arch headstone.

Field surveys also allowed to detect the following additional physical properties:

  • Joint aperture usually vary from “partly open” to “moderately wide” (0.25–6 mm), although apertures up to 10 mm have been found along joints intersecting the arch vault.

  • Some joints are filled with sand and a few joints are filled with hard calcite veins.

  • Block volumes (Vb) mostly range between 0.7 and 11 dm3 with a mean value of about 5.0 dm3.

  • Joint roughness coefficient (Table 1), measured using the Barton comb, mainly varies from “smooth undulating,” for bedding planes (JRC values 5–10), to “smooth nearly planar” (JRC values 6–8), for joints belonging to the other sets.

  • The outcropping discontinuity traces are usually long between 1 and 25 m (“medium–high persistence”), with maximum lengths up to 30 m.

  • Exposed main joint terminations are mainly against other discontinuities (“J/J type” terminations).

  • Joint surfaces are “moderately” or “highly” weathered and present rare rock bridges.

  • The joint condition factor (jC), representing the inter-block frictional properties (Palmström 2005), ranges between 0.65 and 1.4.

Rock mass hydraulic conductivity

The rock mass hydraulic conductivity was evaluated through 10 WPTs (Figs. 5 and 6 ) performed in horizontal boreholes drilled mostly perpendicular to the surfaces, with depths ranging from 1.50 to 1.80 m. The boreholes drilled on both facades of the arch mainly intersect the joints belonging to K1 system and, subordinately, Ks and K2, while the boreholes drilled in the vault mainly intersect the joints of the K2 system and, subordinately, K1 and Ks.

Fig. 5
figure 5

Ortho-mosaics of both arch rock faces exposing towards NE (a) and SW (b) showing the position of borehole and the drilling direction

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Fig. 6
figure 6

Photo of the WPT equipment captured during a test

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Boreholes were equipped with a single packer confining the testing chambers with lengths (z) mainly ranging between 0.50 and 1.00 m at the hole bottom, at depths between 1.50 and 2.00 m. Due to the small width of the structure, these depths were considered adequate for testing the hydraulic conductivity of the whole rock mass surrounding the arch. Each test consisted of a cycle of five consecutive increasing and decreasing pressure steps, during which water pressures and flow rates were measured (Fig. 7). To stabilize measurements, the steady state was kept constant for 10 min (Nonveiller 2013; Houlsby 1976). Unfortunately, abundant water leaks from superficial joints caused some difficulties maintaining the steady state, allowing only low injection pressures (between 0.4 and 2.4 bars) during tests.

Fig. 7
figure 7

Plots of some pressure tests. All of them are performed in five pressure steps. Most of them show a non-linear trend (turbulent flow), and some tests show some wash out of joints

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Lugeon numbers (Lu) were calculated from the flow rate (Q) and the water pressure (P) measured during the tests. For every pressure step at each tested borehole, Lu was calculated using the following equation (Houlsby 1976):

$${\text{Lu}}= \frac{Q \cdot 10 {\text{bar}}}{P \cdot L}$$
(1)

where Q equals flow rate (l/min), P equals water pressure (bar), and L equals length of the test chamber (m).

In such a way, block diagrams of Lugeon values were plotted for every WPT (Fig. 8). According to Houlsby (1976), all the diagrams show a turbulent flow, with some fracture wash-out at the boreholes n. 2 and n. 6. In such conditions, the suggested value for the characteristic Lu of each borehole is that calculated for the maximum pressure step (Houlsby, 1976).

Fig. 8
figure 8

Lugeon patterns for some of the performed WPT. All of them demonstrate a turbulent flow

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Lu calculated in such a way (Table 2) ranges between 237 and 804 Lu, thus suggesting high hydraulic conductivity for the rock mass.

Table 2 Representative Lugeon numbers for the tested boreholes
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Hydraulic conductivity

The hydraulic conductivity of the rock mass at each test was calculated based on the water flow values and the corresponding pressure, according to the following equation (Celico 1986):

$$K=0.159 \cdot (\frac{Q}{{l}_{{\text{e}}}} )\cdot \sqrt{(\frac{1}{r} \cdot P )}$$
(2)

where Q equals inflow discharge (m3/s); le equals length of the testing chamber (m); r equals borehole radius (m); and P equals total pressure measured in the barycentre of the testing chamber (m).

For the B10 test, showing a linear trend for Q versus P, the following equation was used (Celico 1986):

$$K= \frac{Q}{P}\cdot \frac{1}{(2\pi {l}_{{\text{e}}} )}\cdot {\text{ln}}( \frac{{l}_{{\text{e}}}}{r} )$$
(3)

Considering that water infiltration through the rock mass is episodic and water pressure close to atmospheric one, the conductivity values were calculated for the low-pressure step of each test (Table 3). It is worth observing that during the surveys, no water leakage occurred; therefore, the rock mass is almost dry most of the time. Any capillary water in minor fractures produces negative pressures, while rainfed downward water flows produce only small pressures.

Table 3 Hydraulic conductivities calculated for the tested boreholes
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K1 and K2 strongly affect the calculated hydraulic conductivity, since those are the most frequently crossing discontinuities due to the borehole orientations mainly orthogonal to the set trends.

Secondary Permeability Index (SPI)

Based on the WPT data, the Secondary Permeability Index (SPI) was calculated for every borehole using the following formula (Foyo et al. 2005)

$${\text{SPI}}=C\frac{{\text{ln}}\left(\frac{2{l}_{{\text{e}}}}{r}+1\right)}{2\pi {l}_{{\text{e}}}}\cdot \frac{V}{Ht}$$
(4)

where SPI equals Secondary Permeability Index (l/s·m−2) of borehole test surface; C equals a constant depending upon viscosity for a given rock temperature (at 10 °C, C = 1.49·10−10); le equals length of the test section (m); r equals borehole radius (m); V equals water volume absorbed (l); t equals duration of each pressure level (s); H equals total pressure expressed as water column (m).

Considering that sufficiently high pressures must be achieved during grout injection, the representative SPI was calculated using the pressure and flow rate of the highest-pressure step of each test. Consequently, the calculated SPI values (Table 4) range between a minimum value of about 5.4·10−12 l/(s·m2) and a maximum value of about 1.6·10−11 l/(s·m2), the average value being 9.6·10−12 l/(s·m2), indicating that rock volumes fall within the class D (“very poor quality”), thus requiring extensive grouting treatment.

Table 4 Secondary Permeability Index calculated for the tested boreholes
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Rock mass groutability

For a first estimate of the rock mass groutability, some boreholes used to evaluate hydraulic conductivities were arranged for grouting tests (Fig. 9). Two grouts were tested: (1) a microfine binder suspension and (2) a bentonite cement.

Fig. 9
figure 9

Photo of the equipment used for the grouting tests

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The first is a silica gel, having low viscosity, composed of sodium–potassium silicate with an acrylic resin as a dispersing agent to produce a stable suspension grout, obtained by adding water to the silica gel with a ratio of 1:3. This grout type shows a compressive strength of about 69.4 MPa, after 28 days (ASTM C88-55 T: http://www.astm.org/Standards/C88.htm). It was injected into two boreholes where the fracture intensity and limited thickness of the rock mass did not allow to reach injection pressures higher than 4.0 bar. In fact, abundant grout leakages from rock surfaces occurred whenever testing chambers depths were less than 1.30 m. Smaller leakages were observed at greater depths where the rock mass absorbed most of the cement paste, allowing an injecting flow rate of about 3.0 l/min.

The second is a pozzolanic cement (containing up to 45–64% of Portland cement and pozzolans) enriched with bentonite to enhance the cement’s cohesion and viscosity and penetrability and reduce bleeding phenomena. This grout type shows the following main rheological properties: bleeding less than 4%, viscosity (marsh cone funnel) varying between 35 and 45 s, and compressive strength of about 32.0 MPa, after 28 days. This grout (water to cement ratio of 1:2) suffered the same leakage when injected in shallow rock mass volumes, although to a lesser extent; therefore, injection pressures reached 9.0 bar with a flow rate of about 1.5–2.0 l/min. The grout was injected at the borehole bottom (length = 0.50 m) in two steps, the second of which followed the grout consolidation. The total weight of injected grout was 30 kg. Considering a “theoretical” yield of 1.6 kg/dm3, declared by the manufacturer, 30 kg corresponds to 18.75 l.

Both the empirical relationships suggested by Kayabasi et al. (2015) and by Sohrabi-Bidar et al. (2016) were used to calculate the grout take from SPI. In addition, a deterministic approach based on geo-structural data surveyed in the field was used to calculate the grout take, derived from the volume of the fractures openings to be filled. Such an approach is based on each joint set’s average volumetric joint density and mean aperture.

As a first attempt, the abovementioned empirical equations of Kayabasi et al. (2015) (Eq. 5) and Sohrabi-Bidar et al. (2016) (Eq. 6) were used to estimate the grout take need for the arch reinforcement from the SPI parameter:

$${G}_{t}=5030\;Ln \left(SPI\cdot {10}^{13}\right)-1880.7$$
(5)
$$G_t=4.9276\cdot e^{\left(0.0153\cdot\text{SPI}\cdot10^\wedge14\right)}$$
(6)

The first equation provides the grout take as kilograms of grout per meter of the borehole. The second equation has been found by a normalization of the measurement data with respect to the injection pressure and provides the grout take as liters of grout per meter of borehole per bar of injection pressure. Given the values of SPI calculated for the arch (Table 4), grout take values have been calculated assuming injections in 15 boreholes drilled in the vault and 15 in the landward pier; each borehole has been considered 5 m long. The values provided were unphysical in terms of masses (Eq. 5) and mainly in terms of volumes (Eq. 6), (Table 5 and 6). In this regard it should be noted that the authors themselves affirm that the empirical equations for Gt predictions have serious uncertainties, especially in karstic environments (Kayabasi and Gokceoglu 2019) and that the coefficients of determination for the best-fitted relations are low (Sohrabi-Bidar et al. 2016).

Table 5 Statistics of the calculated unitary grout take
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Table 6 Statistics of total grout take amounts
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Evaluation of grout take from geo-structural data

Here, we propose a simple approach for calculating the grout take assuming that the injected grout volume, per unit of rock mass volume, equals the total fractures’ volume. Excluding leakage phenomena, the unit fracture volume (Vj) represents an upper limit for the grout take since the grout migration could be hindered along tight or filled joints.

In the evaluation process, the following simplifying assumptions were adopted:

  • Within each set, joint surfaces are considered almost parallel to each other, smoothed and not in contact at any point.

  • Grout mix completely passes from the injection valves into the fractures.

  • Both the fracture length, usually much larger than the bedding spacing orthogonal to them, and the type of terminations cause a general fracture interconnection, and, therefore, their active role in rock mass hydraulic conductivity and groutability.

  • The in-depth joint aperture is related to the mean value measured at rock-exposed surface.

  • Possible karst phenomena causing enlargement of joint apertures are neglected.

With reference to fracture hydraulic conductivity and, especially, to the groutability, filling primarily acts in reducing the available volumes. In this study, therefore, since the aim has been to provide a maximum value of Vj, the effect of the filling was neglected as joint filling was very episodic and only locally detected.

To implement this approach, in addition to the orientation of the joint sets, the joint aperture, spacing values, volumetric joint count (Jv), and JRC are also critical input parameters.

The number of fractures in a cubic meter of rock mass was calculated based on Palmstrom’s volumetric joint count (Eq. 7, Palmstrom 1982), which provides the number of joints per unit of volume (Jv):

$${J}_{v}=\frac{1}{{S}_{1}}+\frac{1}{{S}_{2}}+\frac{1}{{S}_{3}}+\dots$$
(7)

where S1, S2, and S3 are the spacings of the joints belonging to each system, so 1/Si is the joint frequency.

The voids’ volume (Vj) was evaluated considering each joint delimited by smooth and parallel surfaces placed at a distance equal to the aperture.

The determination of the volume for a single joint intersecting a cube having an edge length equal to 1 m is a problem of a solid geometry. For joints parallel to the face of the cube, the problem is trivial since the volume is obtained by multiplying the area of a square having a side of 1 m (area = 1 m2) by the aperture. The problem is still simple for a joint with a trend parallel to an edge of the cube and forming a given θ angle (dip) with the cube’s top face (Fig. 10). In this case, the intersection of the joint walls with the cube identifies two parallel rectangles with a base length of 1 m and a side length equal to 1 m/cosθ. However, joints of different families can intersect the cube with any orientation with respect to the cube faces and edges, so that the shape of the joint walls can vary from triangular to trapezoidal or hexagonal and have larger or smaller extensions. To evaluate the range of variation of the average joint extension for each system in a cubic meter, the software GeoGebra (https://www.geogebra.org/) was used (see Appendix). Bundles of parallel and variously oriented joints were considered, and the calculated average intersection areas range between 0.50 and 1.0 m2 per cubic meter (see Appendix). Average joint extensions in the cubic meter were considered around 1 m2 (equal to the face of the cube). Although individual joints inclined to the cube faces can have larger (or smaller) extensions, the average value calculated for each joint set was between 0.5 and 1 m2 (see Appendix).

Fig. 10
figure 10

Area of the joint wall (from Wyllie 1999—modified)

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To calculate the void volume, the average surface for the joints of each set, in cubic meter, was multiplied by the characteristic aperture of the set. Two values were considered for the aperture of each system: the physical aperture E (averaged on field measurements) and the hydraulic aperture e, obtained from E and the JRC with the following equation e = E2/JRC2,5 (Barton et al. 1985; Rutqvist and Stephansson 2003). Directly using the E implies the assumption that fractures are delimited by planar surfaces, favoring a greater penetration. Lower values generally characterize the e values since they consider the irregularities of the fractures, which could result in lower penetration grout and lower takes.

For a generic joint set Ki, the void volume VVi in a cubic meter of rock can be calculated as

$${V}_{{\text{Vi}}}=\frac{1}{{S}_{{\text{i}}}}\cdot {A}_{{\text{i}}}\cdot 1 {{\text{m}}}^{2}$$
(8)

where Ai and 1/Si are the fracture aperture and frequency of the ith set, respectively.

Therefore, the total void volume can be calculated referring to the physical (E) and hydraulic (e) joint apertures as:

$${V}_{{\text{Vphy}}}=\sum \frac{1}{{S}_{1}}\cdot E \cdot 1 {{\text{m}}}^{2}$$
(9)
$${V}_{{\text{Vhyd}}}=\sum \frac{1}{{S}_{{\text{i}}}}\cdot e \cdot 1 {{\text{m}}}^{2}$$
(10)

According to the previous assumptions, the volumetric grout take Gt corresponds to the volumetric void volume VV.

Table 7 reports results regarding the individual joint sets and rock masses characterizing the main rock faces and the arch vault.

Table 7 Joint set parameters used for modelling the void volumes and grout takes with resulting values for the main exposure of the rock mass
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The grout take Gt calculated for every cubic meter of rock mass ranges between a lower value of 2.5 l and an upper value of 57 l per cubic meter of rock. Such values appear to agree with the volume of the grouting tests.

Discussion

Geo-structural surveys allowed to assess the degree of jointing of the arch affected by three joint sets from whose orientations different elongated blocks with small dimensions take origin. Furthermore, considering joint intersections at the vault and a LANF near the extrados causing an intense fracturing and the formation of cataclastic zones, the rock mass permeability is very high. Karst dissolution of joint surfaces and severe weathering in a very aggressive environment such as the marine also deeply increase the permeability. Tangible confirmation of the above comes from WPTs which gave hydraulic conductivity values of about 10−4 m/s. During the water tests, abundant water leaks from superficial joints caused some difficulties to maintain the steady state, allowing only low injection pressures. This is also attributable to the small transverse width of the structure partially intersected by the horizontal boreholes drilled on both facades. As a result, during grout injections, significant leakages occurred considering both the silica gel suspension and bentonite cement.

The grout takes in terms of masses and volumes resulting from the empirical approaches suggested by Kayabasi et al. (2015) and Sohrabi-Bidar et al. (2016), respectively, gave unrealistic high values, especially considering the thin structure of the arch, thus pointing out the inapplicability of such approaches to our case study. On the other hand, Jones et al. (2018) found different relationships between SPI and grout take for different rock mass structures in the same dam site, suggesting that the empirical relationships may only have a local valence. Moreover, such relationships have been found mainly for foundations and abutments of dams, involving large rock volumes at considerable depths, where the high confining pressures contrast joint opening, resulting in joints considerably tighter compared to surficial ones.

The deterministic approach based on geo-structural field surveys provided more realistic grout volumes consistent with the results of grouting tests, which resulted in the most reliable approach also considering the arch’s thin, shallow, and highly fractured structure. The suggested method can be used in the case of rock masses affected by joints with medium–high persistence and constant aperture, into the volume of interest. The small thickness of the arch and rock mass layout characterized by three continuous joint systems almost perpendicular to each other allowed to consider a substantial hydraulic connection between the joints. Despite the simplifying assumptions adopted, concerning the physical characters of injected fractures as well as grouting procedures, the suggested approach allowed to establish that the estimated cement take ranges between 2.5 and 57 l/m3 depending on the local jointing state of the rock mass, in good agreement with the tests carried out with low injecting pressures of bentonite-cement grouts.

Conclusions

The study here discussed concerns of a unique geological case where a natural rock arch of particular landscape value, in a highly frequented tourist resort, needs urgent reinforcement for landscape preservation and landslide risk mitigation.

Given the aesthetic value of the geological structure and peculiarities of the rock mass, the arch vault and abutment grouting are considered viable solutions to strengthen the whole structure. The study, therefore, investigated with different approaches the most relevant parameters needed for an optimal grouting strategy, comparing the results with on-site grouting tests. This is particularly significant for the arch setting because its thin structure and high jointing degree can induce grout leakages and the rock mass damage if grouting pressures, and types are not correctly calibrated.

To validate grout take modelling site, grouting tests were carried out on different boreholes and with different grout types. The comparison of modelling and test results, based on grout take volumes, pointed out that grout volume estimations from geo-structural data provided the most reliable results. As weathering and karst dissolution of joint surfaces deeply increase the hydraulic conductivity, extensive use of highly dense and viscous slurries is required (bentonite-cement grout). Moreover, injections should be performed by fiberglass’s Manchette tubes in boreholes (diam. 100–120 mm; max depth 3 m) arranged in a quincunx, whose spacing will be defined during design.

Considering the jointing degree of the rock mass, mainly in the vault of the arch, also, fiberglass bolts should be inserted in the boreholes. To reduce the environmental impact, the bolt heads should be hidden by rock chips.