Abstract
To ensure successful sealing of rock and soil, an adequate description of the system to be grouted is required as a basis for the grouting design and the selection of the grouting material. In rock, the individual fractures and the hydraulic apertures of these fractures form the basis of the Swedish grouting design concept. The hydraulic aperture is a key parameter when describing grouting behaviour and it is used to determine the extent to which the grout can enter fractures – that is, the penetrability. The hydraulic aperture also determines the penetration length, and therefore the grout parameters (e.g. yield stress and viscosity) as well as the grouting pressure and time needed to be adopted to the hydraulic aperture. Once these parameters are chosen, a suitable grouting technique can be adopted. Simple, practical rock and grout tests are important inputs to ensure correct design and performance. The aim of this paper is to present a testing procedure and provide examples from laboratory and field experience to demonstrate that the approach also works in practice.
Successful sealing of rock and soil requires an adequate description of the system to be grouted (e.g. Fransson, 2001a; Hernqvist et al., 2012; Kvartsberg, 2013) as a basis for the grouting design and the selection of the grouting material. When grouting fractured rock, the Lugeon value (e.g. Houlsby, 1990) has traditionally been used to describe the rock mass, although it describes neither the fractures nor the rock in a way that relates fully to the behaviour of the grout in the system. The basis for this Swedish grouting design concept comprises the individual fractures and the hydraulic apertures (b) of those fractures. The aperture is an important parameter when describing grouting behaviour and it is used to determine whether or not the grout can enter the fractures – that is, the penetrability. The aperture also determines the penetration length and in addition the grout parameters – for example, yield stress (τ0) and viscosity (μg); the grouting pressure and time are also important. Once these parameters are known, a suitable grouting technique can be adopted.
A design process for grouting was introduced by Gustafson et al. (2004) which is modified in Figure 1 (translated version, in Gustafson (2012)). The framework is grouting for waterproofing in crystalline rock, where the transmissivities of fractures can be assumed to follow a power-law distribution (few fractures dominate), which is also the context for this paper. The design process illustrated in Figure 1 includes (1) gathering in situ data and (2) estimating the transmissivity distribution (power law) among the fractures (4) generalising to an aperture distribution from which inflow to a tunnel can be estimated (6). Grout recipes are defined based on spread properties in (3) so that fracture apertures in (4) and fan geometry defined in (5) can be sealed to an extent that fulfils the desired maximum inflow in (6).
Figure 1. Flow chart for the design process for grouting, adapted from Gustafson et al. (2004). Each process box contain reference to the parameters of interest (italic) and a reference to the relevant section in this text (bold)
The basis for the design concept presented here comprises the hydraulic apertures of individual fractures. Corresponding penetration lengths (I) can be calculated from these apertures. Figure 2 shows a diagrammatic sketch of a cross-section of a tunnel as well as a grouting fan intersecting a number of fractures of different lengths and apertures. The theoretical sealing of a fracture requires the borehole distance L be less than twice the penetration length I (L < 2I).
Figure 2. Cross-section of a tunnel and a grouting fan intersecting fractures. For the theoretical sealing of a fracture, the borehole distance L should be less than twice the penetration length I (L < 2I)
The equations used to estimate the penetration length of a Bingham fluid in a pipe and a parallel slot or a fracture with radial (two-dimensional (2D)) flow are derived in Gustafson et al. (2013). In the example below, Equations 1–6 and a graph (Figure 3) are used to estimate the penetration length for a cement-based grout (Bingham fluid). These equations are also described in Gustafson and Stille (2005), which is based on the manuscript later presented by Gustafson et al. (2013).
Figure 3. Penetration length and grouting time: I/Imax as a function of t/t0 for a cement-based grout based on Gustafson et al. (2013). For a tD of 1·35, ID is ∼0·65, meaning that 65% of the maximum penetration length is achieved
Gustafson et al. (2013) presented a comparison between experimental data and the estimated penetration length for 1D flow (a pipe or channel). There was good agreement. Further, initial investigations in a parallel plate fracture replica constructed at the Division of GeoEngineering at Chalmers University of Technology also show good agreement for radial (2D) flow (see video clip of flow in replica, Chalmers, 2014). This work is ongoing and will be developed and evaluated further.
As an example, Table 1 presents the yield stress (τ0) and viscosity (μg) of a grout as well as grouting overpressure (Δp) (grouting pressure minus the groundwater pressure) and grouting time (t) for the design of a grouting application for an investigation borehole performed at Äspö Hard Rock Laboratory, Äspö HRL, in December 2013. Due to a large inflow with a risk of influencing further investigations, the first 15 m of the borehole was grouted before drilling continued. The hydraulic characterisation that was used as a basis for the grouting design comprised inflow during drilling and transient hydraulic tests performed before grouting. The main inflow was found at a borehole length of 10·5 m and was initially 280 l/min and decreased to about 200 l/min. The estimated hydraulic aperture was, in this case, 250 μm (see Equation 7). Due to the high hydraulic head (320 m) and gradient, grouting design aimed at a stiff grout with a yield strength of 15 Pa.
|
| Hydraulic aperture, b: μm | Yield stress, τ0: Pa | Viscosity, μg: Pa · s | Grouting overpressure, Δp: MPa | Grouting time, t: min |
|---|---|---|---|---|
| 250 | 15 | 0·015 | 5 | 45 |
In the example above, sealing of an investigation borehole was the main objective so the actual penetration length was not the key issue. To obtain a theoretical overlap in a grouting fan, a borehole distance (at borehole tip) L should be suggested so that L < 2I (Figure 2). A common limit for what one can expect to seal with a cement-based grout is 50–100 μm (Gustafson et al., 2009) and, in that case, 100 μm would be used as the dimensioning aperture. As follows from Equation 1, a sufficient penetration length in this fracture would also result in the (theoretical) sealing of all fractures with larger apertures intersected by the boreholes.
A similar approach can be used for a Newtonian fluid such as silica sol (Butrón et al., 2012). Silica sol is a grouting agent that consists of nanospheres of amorphous silica dispersed in water. Mixing with a salt solution catalyses gelling of the material and the mixing proportions govern the gelling time (e.g. Funehag, 2007). Silica sol is modelled as a gelling Newtonian fluid that rheologically is only described by its viscosity development over time (i.e. no yield stress). To characterise the fluid for grouting purposes it is suggested here to use the initial viscosity (≈0·005 Pa · s) and the gel induction time (the time taken for the mix to reach the double the viscosity). Details of the different steps can be found in Funehag and Gustafson (2008).
Section 1 presented the procedure for estimating the penetration length for an investigation borehole and a grouting fan design using the ‘expected’ properties of a specific grout. The next step is to show how the parameters included in the above equations can be obtained by measuring the ‘actual’ properties of the grout.
The proposed methods used to characterise the fractured rock are short-duration hydraulic tests (of a few minutes) based on either inflow or injection of water. A graph that includes the hydraulic aperture has been developed to facilitate the selection of grout based on penetrability (see Section 2.4).
The grout properties are characterised in laboratory pre-investigations and from these investigations the grout type (e.g. cement-based grout or grout for fine-aperture sealing) with the desired properties can be selected. In the field, control measurements should be made to check that the expected properties are actually obtained. Methods used for testing the penetrability include the PenetraCone (Axelsson and Gustafson, 2010) and an invention referred to as the yield stick (Axelsson and Gustafson, 2006), which is used to test the yield stress and viscosity in combination with the traditional Marsh funnel and mud balance (e.g. API, 1990; Håkansson, 1993). The equipment is presented in Figure 4.
The testing procedure suggested is described further in the subsections below and includes the following.
| • | Investigation of grout properties (μg, τ0 and penetrability) in the laboratory. | ||||
| • | Estimation of the penetration length and adaptation of the borehole geometry. | ||||
| • | Checking grout properties in the field. | ||||
| • | Use of hydraulic tests in grouting boreholes as a basis for grout selection. | ||||
The PenetraCone is presented in Axelsson and Gustafson (2010). This device is used to measure the penetrability of cementitious grouts (Figures 4 and 5). The measuring device consists of two conical cylinders where a gap between the cones resembles the opening between parallel plates (a simplification of a fracture). The gap can be adjusted by turning the inner cone and it is measured using a dial indicator gauge attached to the inner cone. The measurement begins with a large open gap, and the gap is then reduced until the grout flow changes from continuously flowing to dripping (bfilter), which indicates that filtration of the cement will begin. Measurement continues by reducing the gap until the dripping ceases and the flow stops completely (bstop).
Figure 4. The four measurement devices. From the left, the PenetraCone, the Marsh funnel, the mud balance (at the back) and the yield stick, including the measurement graph (see also Figure 6) (picture by Nina Zanders)
Figure 5. Sketch of the PenetraCone (dimensions in mm). Top: fully closed. Bottom: opened 10 mm rendering a 1 mm slot for the grout to flow through
In Axelsson and Gustafson (2010), six different grout mixes were used with water-to-solid ratios of 0·8–1·4 and three different values of d95, (30, 20 and 16 μm). d95 is the grain size below which 95% of the grains fall. The ratio between bfilter and d95 of the grouts was in the range 1·5–6·5 (the highest figure may be due to difficulty mixing the 16 μm grout). For a water-to-cement ratio of 1·0 and above, the bstop to the grain size of the grout was 0·5–1·8, whereas for a water-to-cement ratio of 0·8 this relationship was 2·0–5·0. This indicates that the value of bstop is generally around the largest grain size of the grout except for the thicker grout mixes. The value of bfilter should be related to the value of bcritical obtained using a penetrability meter (or similar) since they both describe the initiation of the filtration process of a grout (e.g. Eklund and Stille, 2008).
Fransson (2009) and Gustafson et al. (2009) present how grout can be selected based on a fracture hydraulic aperture assessment and they argue that an effective fracture hydraulic aperture would appear to be useful for grout penetration. As an example, Gustafson et al. (2009) investigate the penetration of cementitious grout close to a penetration threshold using a variable aperture and a median (effective) hydraulic aperture that is successively decreased down to an assumed penetrability limit for the grout. This results in a local cluster only being filled with grout. For silica sol or other non-granular grouting materials that allow fine-aperture sealing, penetrability is not an issue since it can penetrate much smaller fracture apertures.
The ‘density’, or the specific gravity, is measured using a ‘mud balance’ (API Recommended Practice 13B-1 (API, 1990)). The mud balance is a balance scale with a 210 ml cup and a piston with a rider attached. At equilibrium, the specific gravity is determined directly on the piston at the position of the rider. The device is well established and was originally developed for routine testing of drilling mud in the oil recovery industry.
The ‘yield stick’ is as described previously – a method for measuring the ‘yield stress’ of cementitious grouts and is presented in Axelsson and Gustafson (2006) (Figures 4 and 6). They compare shear strengths obtained using the yield stick with shear strength measurements made using a rotational rheometer in the laboratory. The comparison shows good agreement. The yield stick has been used in the field as a tool to check that the desired properties are actually obtained.
The method consists of a stick with a controlled weight together with its specific measurement (and evaluation) sheet. The stick is placed in the grout and the sink depth is proportional to the yield stress of the grout. The measurement sheet and an example of a measurement using the stick are shown in Figure 6. By placing the stick on the measurement sheet, the yield stress can be determined directly. In the example shown in Figure 6, the density of the grout is 1520 kg/m3 and the grey part on the stick represents the sink depth. The yield stress in this case would be 15 Pa.
Figure 6. Measurement using the yield stick. The grey part of the stick shows the sink depth of the stick into the grout. In a grout with a density of 1520 kg/m3, the yield stress for the tested grout can be determined directly as 15 Pa
The text in Figure 7 describes steps 1–3 when estimating grout viscosity (μg) from measurements using the yield stick, Marsh funnel and mud balance. In this example, the grout density is 1520 kg/m3, the yield stress is 15 Pa and the Marsh funnel flow time (efflux time) is between 40 and 50 s. The viscosity is determined directly on the y-axis and is found to be in the interval 0·015–0·025 Pa · s.
Figure 7. Example of measurement of viscosity using the known yield stress, density and Marsh funnel flow time. An example evaluation is shown with the arrows and notes 1–3. Graph 2 is from Håkansson (1993)
The fluidity of grouts or the Marsh funnel flow time can be measured using the ‘Marsh funnel’. There are different funnel variants, but in API Recommended Practice 13B-1 (API, 1990) a funnel with an outlet of 4·75 mm and a volume of 1·5 l is used. The outflow time for 1 l is measured.
The device can be checked to ensure the water has a flow time of 28 s (at 21°C). Håkansson (1993) developed a graph showing the relationship between the Marsh funnel flow time and the viscosity (Graph 2, Figure 7). The graph was developed for a funnel with dimensions according to API 13B-1 and a volume of 1 l. To calculate the viscosity, the density and the yield stress of the grout need to be known.
The rheological properties of grout are estimated here using basic tests. Interesting additional testing and follow up would be in-line measurements as suggested in, for example, Rahman et al. (2015).
The transmissivity (T), can be approximated by the specific capacity (Q/dhw), when using short-duration tests (Fransson, 2001b) such as a water pressure test (WPT) (ISO, 2012). Figure 9 also includes data (flow Q and difference in head dhw) from four Swedish experiments or construction projects (Table 2). Experiments and data are described further in the next section.
Figure 8. Sketches of NIM and WPT performed in a tunnel. Flow Q and change in head dhw = dpw/ρg are measured in different ways. The pressure pw (Pa) corresponds to the depth of the tunnel H = pw/ρg
|
| Depth: m | Flow, Q: l/min | dhw: m | Grouting pressure, p: MPa | Hydraulic aperture, b: μm | Penetrability: comments | b/d95 | |
|---|---|---|---|---|---|---|---|
| Äspö HRL pillar | 100 | 0·1 | 25 | 0·2–0·4a | ≈ 50 | Very limited | 4 |
| d95: 12 μm | |||||||
| Äspö HRL TASQ (tunnel) | 450 | 2·5 | 340 | Δp: 1–2 | ≈ 60 | > 50 μm but not below 30 μm | 4 |
| d95: 16 μm | |||||||
| Nygård (tunnel) | 50 | 0·1–4·2 | 110 | 2·5a | < 100 | Very limited | 3 |
| d95: 30 μm | |||||||
| Äspö HRL investigation borehole | 420 | 200 | 320 | 8·2 | ≈ 250 | Good | 8 |
| d95: 30 μm |
a Low water pressure: grouting pressure close to grouting overpressure
For hydraulic apertures larger than 100 μm, a regular Scandinavian grouting cement with a d95 of about 30 μm is expected to have full penetrability (type A, Figure 9) while for apertures smaller than 50–100 μm the penetrability is limited. Knowing the flow (l/min) and the (difference in) hydraulic head (m), the hydraulic aperture and type of grout are identified directly using the grout type selection graph (Figure 9). For the investigation borehole at Äspö HRL (Table 1), where penetration length was previously estimated, flow was 200 l/min and the hydraulic head was 320 m. This would, as can be seen, result in an aperture of 250 μm (Equation 7). For a pillar experiment in crystalline, fractured rock also at Äspö HRL (see Section 3 and Table 2), the flow QWPT is ∼0·1 l/min and the difference in head dhw is 25 m, resulting in a hydraulic aperture of about 50 μm. These two are examples of fractures where penetrability plays a key role. For the 250 μm aperture fracture, the grout (d95 = 30 μm) was expected to penetrate easily. For the 50 μm fracture a more limited penetration could be expected (d95 = 12 μm).
Figure 9. Grout type selection graph based on penetrability, including the flow Q, the change in head dhw (m), intervals of hydraulic aperture b and grout types A (e.g. a cement-based grout) and B (e.g. a grout for fine-aperture sealing). The broken line (here 100 μm) should be adapted to the grout types used. Data from the four sites included in Table 2 are also shown
Several tunnelling projects have shown that using the hydraulic aperture as a basis for grout selection is a good approach. A general rule is that cementitious grouts can penetrate fractures that are around three times d95 (e.g. Butrón et al., 2010; Martinet, 1998). The pillar experiment (Table 2 and Figure 9) performed at a depth of ∼100 m in crystalline rock at Äspö HRL (Eriksson, 2002; Fransson, 2001a; Funehag and Fransson, 2006) identifies a clear difference between the very limited penetration (penetrability) of a cement-based grout (micro-cement d95 = 12 μm) and the larger penetration for silica sol in a fracture with a hydraulic aperture of 50 μm. The results from another tunnel at Äspö HRL (TASQ) using a cement-based grout (d95 = 16 μm) confirmed that fractures of around 50 μm and larger, but not below 30 μm, had been sealed (Hernqvist et al., 2009). The limited penetration identified here suggests that 3d95 may not be sufficient (here, b/d95 ≈ 4 when d95 is 12 and 16 μm, cf. Table 2). Previous results – for example, from Axelsson and Gustafson (2010) and Eklund and Stille (2008) – indicate that for grout with a small d95, the minimum aperture (or slot) that can be grouted increases, possibly as an effect of aggregate formation.
Another example that points in the same direction is the Nygård tunnel in south-west Sweden (Butrón et al., 2010; Gustafson et al., 2008), where all the boreholes in one of the investigated grouting fans had estimated hydraulic fracture apertures below 100 μm. The main grouting-induced reduction in transmissivity was seen in the roof, where silica sol was used. Only a minor reduction was identified in the boreholes in the floor of the tunnel where a cement-based grout was used (d95 = 30 μm). A conclusion drawn from these projects is that fractures with an estimated hydraulic fracture aperture below 50–100 μm are not likely to be groutable with a cement-based grout. This conclusion is supported by a grouting test in the fracture replica at Chalmers University of Technology, where practically no penetration was achieved at an aperture setting of 80 μm using a grout with d95 = 30 μm (3d95 = 90 μm). To improve the result, a grout for fine-aperture fractures is suggested.
For the investigation borehole at Äspö HRL, a 250 μm fracture aperture was estimated and this was expected (and found) to be groutable with a grout having a d95 of 30 μm (3d95 = 90 μm). In this case, a stiff cement-based grout comprising Injektering 30 (ordinary Portland cement with d95 = 30 μm) and GroutAid (an additive to cement made of silica fume dispersed in water that acts as an accelerator) was injected into the borehole. The recipe selected was the one utilised in a tunnel at Äspö HRL in 2008 that was developed to obtain a low pH (<11) in the leachate (Bodén and Sievänen, 2005). A decrease in flow from over 200 l/min to less than 1 l/min was achieved. For the investigation borehole, key grouting aspects were penetrability (the ability of the grout to enter the fracture), grout penetration and erosion due to the high gradient.
In three of the four cases in Table 2, fairly low grouting pressures were used to reduce the risk of jacking the fractures. However, analyses of grouting data for the Nygård tunnel indicate that there is a risk of fractures opening if high pressures are used (Fransson et al., 2010). Due to the high rock stresses at the considerable depth of the TASQ tunnel, such deformations would mainly be expected close to the tunnel. The grouting pressure for the grouting of the investigation borehole was fairly high (82 bars (8200 kPa)) but the depth of the tunnel suggests that rock stresses are high. The design and selection process presented here assumes constant (non-deformable) fracture apertures (Gustafson et al., 2013).
Works performed at Chalmers University of Technology in Gothenburg (e.g. Axelsson, 2009; Funehag, 2007; Funehag and Gustafson, 2008; Gustafson et al., 2013) and at the Royal Institute of Technology in Stockholm (e.g. Eklund and Stille, 2008; Eriksson, 2002; Håkansson, 1993; Hässler, 1991) show that the developed theories can be used to estimate the penetration length for both a gelling Newtonian fluid such as silica sol and a cement-based grout with Bingham fluid properties.
This paper deals with grouting of sparsely or moderately fractured rock, and in this case a radial flow approach as presented here is reasonable. For a densely fractured rock, or a soil, a 3D flow system is likely to be a better description and the grouted volume would also be related to this type of system (e.g. Sturk et al., 2013). In both cases, the maximum penetration can be described using the equilibrium between grout pressure and friction against the surrounding medium (e.g. Axelsson et al., 2009; Gustafson et al., 2013; Hässler, 1991; Kutzner, 1996). Water-bearing fracture systems like those above could be referred to as being different hydrogeological settings, and awareness of the flow dimension of the system at hand is key when designing grouting work.
The concept presented here includes a fracture aperture estimated from hydraulic tests as a key component. Comparing this approach directly with other methods – for example, grouting intensity number (GIN) (Lombardi and Deere, 1993), which involves grouting pressure and volume of grout – is difficult since they have different parameter set ups. The GIN can be related to a penetration length (I), introducing a factor K referred to as a groutability factor (e.g. Brantberger et al., 2000). In Brantberger et al. (2000), this factor is used to take into account the influence of geology by incorporating the assumed number of fractures using grout and the proportion of them being open. Another way to describe the geological material is to use the Lugeon value (e.g. Houlsby, 1990). This is defined as the loss of water in litres per minute and per metre borehole at an overpressure of 1 MPa. This gives a result of an average value describing the ability of the geological material to transmit water but describes neither the rock mass nor the fractures. The work presented here aims at a relevant physical representation of fractured crystalline rock that can capture penetrability and penetration length in fractures having a power-law size distribution.
The field measurement methods presented here are a combination of well-established methods and more recently developed methods. All tests have been performed as part of field tests for the TASS tunnel at Äspö HRL (Funehag and Emmelin, 2010). The results are promising and the different test methods have been tested separately in other experiments and tunnelling projects.
In this paper, the importance of using an understanding of the fracture system to be grouted as a basis for selecting a grouting design is highlighted. An adequate design can be produced using the relevant parameters and focusing on the requirements set for the particular tunnel. The important inputs for both design and performance are simple, practical tests on the rock and the grout. This paper presents a testing procedure and provides examples from laboratory and field experience that show that the approach works.
Acknowledgements
The authors express their appreciation to the Royal Institute of Technology in Stockholm, Sweden, for their collaboration and to the Swedish Nuclear Fuel and Waste Management Co., SKB and the Äspö HRL for supporting experiments and providing valuable data. They are also grateful for financial support provided over the years and for valuable help from their division. They are truly grateful to Professor Gunnar Gustafson, who is no longer with them.
| b | hydraulic aperture |
| bfilter | gap in a PenetraCone where grout flow changes from continuous flow to dripping |
| bstop | gap in a PenetraCone where grout dripping ceases and the flow stops |
| dhw | difference in hydraulic head |
| dpw | difference in water pressure |
| d95 | grain size below which 95% of the grains fall |
| g | acceleration due to gravity |
| I | penetration length |
| ID | dimensionless penetration length |
| Imax | maximum penetration length |
| L | borehole distance |
| pw | water pressure |
| pWPT | injection pressure for a water pressure test (WPT) |
| Q | flow |
| QNIM | flow, natural inflow measurement |
| QWPT | flow, injection |
| T | transmissivity |
| t | grouting time |
| tD | dimensionless grouting time |
| t0 | characteristic time |
| Δp | grouting overpressure (grouting pressure minus water pressure) |
| Θ | parameter for estimating penetration length |
| μg | viscosity of grout |
| μw | viscosity of water |
| ρ | density |
| τ0 | yield stress/strength |
