Compensation grouting in sand, fractures and compaction Compensation jointoyant dans le sable, les ruptures et le tassement

A. Bezuijen TU-Delft/GeoDelft, Delft, The Netherlands

A.F. van Tol TU-Delft/GeoDelft, Delft, The Netherlands

ABSTRACTMechanisms that are of importance for compensation grouting in sand are elaborated. Measured injection pressures are compared with pressures according to cavity expansion theory and the influence of grout blee-ding and leak off is discussed. Model experiments are described and the results of experiments are comparedqualitatively with theory. In these tests a relation between the injection pressure and the width of the fractureswas found. Furthermore it is shown that more cement in the grout mixture leads to higher injection pressures.The results indicate that the optimum cement content of a grout mixture is lower than what is common prac-tice at the moment for compensation grouting.

RÉSUMÉ Les mécanismes qui sont d'importance pour l'injection de compensation dans le sable sont élaborés. Les pres-sions d'injection sont comparées aux pressions calculées selon la théorie d'expansion de cavité et l'influence du ressuage et de la fuite de coulis au loin est discutée. Des expériences modèles sont décrites et les résultats des expériences sont comparés qualitativement à la théorie. Une relation entre la pression d'injection et la lar-geur des fractures a été trouvée. En outre on montre que plus de ciment dans le mélange de coulis mène à des pressions d'injection plus élevées. Les résultats indiquent que la teneur optimale en ciment d'un mélange de coulis est inférieure à ce qui est pratique courante à l'heure actuelle pour l'injection de compensation

Keywords: compensation grouting, model tests, sand bleeding, leak off

1 INTRODUCTION

Compensation grouting has been successfully ap-plied in several projects to prevent or to compensate for surface settlements induced by for example tun-nelling (Mair & Hight, 1994, Chiriotti et al. 2005, Christiaens et all. 2005, Klein Lugtenbelt, 2006). Compensation grouting uses hydraulic fracturing to get a heave that can compensate the settlement or to get compaction to densify the soil to improve its characteristics.

Compensation grouting is up to now predomi-nantly an empirical procedure. It is qualitatively known that the necessary injection pressure depends on the overburden pressure, the density of the sand and the properties of the grout. No model is yet available to quantify the various phenomena. Two different processes can occur when the process is applied in sandy material: fracturing of the sand by the injected grout or densification of the sand by compaction grouting. The latter occurs when a more

viscous liquid is injected and needs much higher in-jection pressures.

Model tests have been performed to acquire knowledge on the mechanisms that are of impor-tance for hydraulic fracturing and to get quantitative data on this process.

The paper starts with some theory necessary to describe the results of the model tests. After that it describes some tests that are performed in literature and the setup and results of our tests, to end with discussion and conclusions.

2 THEORY

2.1 Cavity expansion When a cavity in the soil is pressurized, it will ex-pand. The cavity expansion theory can be used to describe the expansion of the cavity as a function of the pressure for uniform expansion. Various authors have presented solutions for this problem, in most

cases elasto-plastic solutions assuming the Mohr-Coulomb model. Various solutions differ because of the flow rule that is used and the way the strains are defined (small strain or natural strain). Here we will use the solution presented by Luger and Hergarden (1988). This solution uses natural strain and assumes no dilatancy in the plastic zone, leading to the fol-lowing equations for injection pressures that lead to plastic deformations in the soil:

sin2 1 sin

0' 1 ( / )' ( .cot ) .cotp

f

R RP P c c

Q

ϕϕ

ϕ ϕ

⎛ ⎞⎜ ⎟+⎝ ⎠⎡ ⎤−

= + −⎢ ⎥⎢ ⎥⎣ ⎦

(1)

with:

'0 sin .coscQ

Gσ ϕ ϕ+

= (2)

and P’ the effective pressure in the bore hole, P’f the pressure where plastic deformation in the soil starts (P’f = σ’0(1+sinϕ)+c.cosϕ). σ’0 the effective stress around the hole, c the cohesion of the material, and ϕ the friction angle. Figure 1 shows the relation be-tween the pressure increase in the cavity and the in-crease in diameter in the cavity according to these equations. The pressure increases up to a diameter increase that is 10 times the starting diameter. The graph has various plots to show the influence of var-ious parameters. The calculations were run for the conditions of the tests that will be described later: 1 bar confining stress, poisson’s ratio of 0.33 and no cohesion. The maximum injection pressure varies from 15 to 25 bar.

0

5

10

15

20

25

30

inje

ctio

npr

essu

re(b

ar)

10-3 10-2 10-1 100 101

relative diameter increase (-)

40 dg100 MPa35 dg100 MPa40 dg200 MPa40 dg50 MPa

Figure 1: Cavity expansion theory, injection pressure as func-tion of the increase in diameter for friction angles of 35 and 40 degrees (dg) and Young’s modulus of the sand from 50 to 200 Mpa.

The cavity expansion theory presents the maxi-mum possible pressure that a cavity can resist. An asymmetric deformation of the cavity, as a hydraulic fracture, is only possible when the pressure that is associated with this fracture is lower than the pres-sure necessary for cavity expansion. If not it will be cavity expansion that occurs. This presents the pos-

sibility to have an idea what process is going on dur-ing grouting. When the pressure is close to the cavi-ty expansion limit, the shape of the grout will be roughly symmetric. Hydraulic fracturing can be ex-pected when it is possible to inject a certain grout volume with a lower injection pressure than the cavity expansion pressure.

2.2 Conditions for fracturing For fracturing in sand it is necessary that locally the contact between the grains vanishes. Since there is no tensile strength between the grains (this is differ-ent from fracturing in rock or clay), this means that the fracture pressure must overcome the effective stress in the direction perpendicular to the fracture. Assuming again that the cavity expansion formula-tion is valid before the fracture starts, this condition can be fulfilled. The pressure in the fracturing liquid will be the same as the radial stress. According to Mohr-Coulomb the relation between the radial stress and the angular stress perpendicular on the radial stress can be written as:

1 sin1 sin rθ

φσ σφ

−=

+ (3)

Where σr is the radial stress, σθ the tangential stress and φ the friction angle of the sand. Taking for ex-ample a friction angle of 35 degrees, the tangential stress is only 0.27 times the radial stress.

Classical cavity expansion theory assumes that there will be a radial expansion, which is uniform in all directions. However, in reality the sand is never perfectly homogeneous. Looking at the scale of the grains at the boundary of the opening there will be some grains that are in closer contact and some be-tween which there is some space, see Figure 2.

Pf

σθ

sand grains

injection fluid

Pf

σθ

sand grains

injection fluid

deformationaccordingto cavityexpansion

localizeddeformation

PfPf Pf

Pf

before deformation after deformation Figure 2. Sketch with possible deformation modes of the injec-tion hole. In reality there will be more grains around the injec-tion hole. The figure just shows the principle. Such space can be sufficient to have the fluid pres-sure not only in radial but also in tangential direc-tion. Since the fluid pressure is much higher than the tangential stress this will lead to an opening of the space between the grains and a fracture can occur. If there is a beginning of a fracture then the fluid pres-

sure will penetrate further in the sand and the frac-ture will easily grow further. A fracture will stop to propagate when the pressure in the fracture tip drops due to friction losses, leak-off or increase of the vo-lume of the cavity. The influence of leak-off will be demonstrated using the results of the tests per-formed.

Plastering and the formation of a filter cake in the injection hole will hamper fracturing of the sand, be-cause now possible irregularities at the boundaries of the injection hole will be filled with plaster see Fig-ure 3. This plaster also has certain strength and therefore prevents the fluid pressure from penetrat-ing into the space between the grains.

Pf

σθ

sand grains

injectionfluid granular

material

plasteredmaterial

Figure 3. Influence of plastering.

A fracture that occurs at injection pressures much lower than the limit pressure for cavity expansion will necessarily be only a very thin fracture, because the sand will hardly deform under these low pres-sures. A fracture that occurs at higher pressures will be wider because under these higher pressures the sand will deform further.

Consequence of what is mentioned above is that fracturing in sand is only possible when the injection fluid satisfies certain conditions. It is proven that Newtonian fluids (with only a viscosity, but with no yield stress) do not really lead to fractures when in-jected in sand (de Pater et al.2003), some plastering is necessary to have a sufficient pressure gradient over the sand grains around the injection hole. How-ever, too much plastering will fill up the irregulari-ties around the injection hole and therefore also pre-vents fracturing.

2.3 Plastering Two processes lead to plastering of the sand around the injection hole: - Consolidation of the grout or grout bleeding. - Leak-off of fine particles and liquid from the grout into the sand while coarser particles are blocked by the sand grains. Grout bleeding will always occur and depends on the permeability of the grout. This permeability de-pends apart form the bentonite content also on the cement content in the grout and the kind of cement.

More specific the amount of calcium influences the permeability of the grout. The more calcium is present in the grout the higher its permeability. Cal-cium changes the coagulation structure as is ex-plained more in detail by Mitchell (1977) and is ap-plied on grout by Sanders (2007). The bleeding process can be described by theory developed by Bolton and McKinly (1997). Bezuijen et al. (2007) present values for the permeability for various types of grout. Leak-off with blocking of the courser par-ticles depends on the materials in the grout and again on the calcium concentration.

When leak-off is the dominant mechanism (and not the grout bleeding mentioned above) this can be described as will be explained below. Assume that the grout mixture that flows through both a grout cake that is forming due to the leak-off and through the sand behaves as a Bingham liquid. The liquid will start to flow when there is a difference in pie-zometric head over the grout cake and the sand. As-suming a one dimensional situation, see Figure 4, this can be written as (for v>0, flow into the sand):

Rqssk

qsk

qs++++=Δ 1111

2

2

1

1 ααφ (4)

Where Δφ is the difference in piezometric head, s1 the thickness of the grout cake, s2 the distance the liquid has penetrated into the sand, k1 and k2 the permeability of the cake and the sand respectively for the penetrating liquid, q the specific discharge, α1 and α2 factors for the cake and the sand respec-tively that determine the drop in piezometric head caused by the yield stress in a Bingham liquid and R the flow resistance from the soil around the fracture. The last 3 parameters may need some explanation.

The ‘standard’graph to explain a Bingham liquid is shown in Figure 5A: the shear rate remains zero until a shear stress, above that there is a linear rela-tion between shear rate and shear stress. The conse-quence for the flow of a Bingham liquid through a granular material is shown in Figure 5B. A certain minimum gradient is needed to start the flow of a Bingham liquid though the soil. This minimum gra-dient, depends on the liquid and on the soil and are the factors α1 and α2 for the flow through the cake and through the sand respectively. The resistance R is present in this equation because the grout that pe-netrated into the sand replaces the pore water. The flow resistance that this pore water encounters is the term R.

The model has been used to simulate the 1 di-mensional penetration of a 5% bentonite liquid with 0.5% of quartz floor in fine sand. The model takes into account that a cake of quartz floor developed during the penetration, which hampers the fluid flow. The bentonite particles are so small that they will flow through the sand pores. Using the model,

the calculated penetration is too small, when the most realistic parameters are used. However, by in-creasing the permeability of the sand (by reducing the viscosity of the bentonite and decreasing the grain size) a good fit appears possible, see Table 1 and Figure 6.

grout mixturewith particles

externalcake

grout mixturewithout particles

pore water

flow directionsand

Figure 4: Sketch leak off and cake formation. The cake grows during the flow because the sand filters the fine particles from the grout.

τ

γ.

q

iA B

Bingham

Newton

Newton

Bingham

Figure 5. Shear stress and shear strain in both a Newtonian and Bingham liquid (A) and consequence for flow in soil (B).

0.000

0.005

0.010

0.015

0.020

0.025

grou

tpre

netra

tion

insa

nd(m

)

0.0 0.5 1.0 1.5 2.0

time (s)

measuredm. valuesbest fit

Figure 6: 1-dimensional penetration experiments compared with calculations. The curve with “m. parameters” show the re-sult using the measured parameters, see Table 1. Table 1: Parameters used in calculation of the penetration depth. The italic numbers are changed to make the fit.

Parameter m. values best fit dimensionInj. Press D15 sand Porosity sand Visc. water Visc. bentonite Yield strength Perc. quartz fl. D15 quartz fl. Porosity quartz

400 90 0.4 1e-6 1.3e-5 100 0.5 10 0.5

400130 0.4 1e-6 6e-6 105 0.5 10 0.5

kPa μm - m2/s m2/s Pa % μm -

This result confirms that there are two mechanism that can create a grout cake, bleeding and leak-off of a part of the grout.

3 EXPERIMENTAL SET-UP

A circular container with a diameter of 0.9 m was used for the tests (see Figure 7). This container was filled with saturated sand up to 0.84 m height. A PVC plate was placed on top of the sand sample. There was an air tight connection between the plate and the container by means of a rubber ring. This makes it possible to pressurize the sand sample, us-ing air pressure, simulating sand at a larger depth. The injection opening is comparable to the system developed for compensation grouting. A pipe with a rubber sleeve has been used (see Figure 8). The sleeve will only allow outflow of the grout when the grout pressure is higher than the soil pressure. The injection nozzle was located 0.37 m above the bot-tom of the tank.

Tests were performed with Baskarp sand (d50 = 130 μm). The sand was wet pluviated into water in the container. The loose sand was densified by drop-ping the whole container over a few centimetres several times depending on to the required density. The sand was ‘pre-stressed’ by applying a high ver-tical pressure before the test to achieve a higher K0. This pre-stressing was only partly successful. The K0 achieved with this procedure was around 1. Dur-ing grout injection K0 rises rapidly to values well above 1 and even to 4.5 in the case of dense sand. Pore pressure transducers and total stress transducers were installed at various locations in the container, see Figure 9.

air pressure100 kPa

groutreservoir

groutpump

plungerfilter

sand

filter

chamber filled with water

waterlevel drainage

water level

TAM

480

360

900

Figure 7. Set-up of the experiments. Note that changes in pore volume and sand volume can be measured as changes in the water levels (dimensions in mm).

Special attention was paid to the measurement of

the volumes. The increase in volume of the sample due to the injection and the drainage of pore water was measured continuously during the tests, more details on the measurements of the volume can be found in (Kleinlugtenbelt, 2005 and Sanders, 2007).

tube

rubberring ring

rubberinjectionholes

Figure 8. Injection system with rubber sleeve. The steel rings were placed on the tube to prevent grout flow along the tube.

-50

0

Z(m

m)

-300 -200 -100 0 100Y (mm)

PVHinj

1234

Figure 9. Position of the instruments with respect to the injec-tion tube (inj). P are the pore pressure gauges, V measures the vertical pressure and H the horizontal.

Grout was injected by means of a plunger pump.

This pump pumped water and by means of a bladder the grout was pumped into the system (the sketch in Figure 7 does not show the bladder). The bladder system was installed to avoid damage to the pump by the granular particles in the grout. The maximum injection pressure of the injection pump was 40 bar. The grout was allowed to harden for one day after the test before the sand was washed away and the shape of the injected grout became visible. There was no hardening of the grout in the tests without cement, or with only a little amount of cement. After these tests the capillary forces in the sand were used to see the shape of the fracture.

4 RESULTS

All tests were performed using a confining pressure of 100 kPa and a water pressure of only a few kPa in the sand. For an overview of the tests performed see, Kleinlugtenbelt (2005) and Sanders (2007). Some tests are also described by Bezuijen et al. (2007). Here we will present only a summary of the test re-sults using the tests shown in Table 2.

The injection pressure appears to vary with the injection fluid and the amount of cement present in the bentonite, see Figure 10. This figure shows the injection pressure for an injection, Test 4, with cross-linked gel (an injection fluid used in the oil in-dustry to create fractures) and the injection of some

tests where the injection fluid consists of 5% bento-nite and an increasing amount of cement. It is clear that in general the injection pressure increases with the amount of cement although Test 7 and 10 does not fit. For these tests the density of the sand was a bit lower (Rd around 60% instead of 65%). Figure 10 shows that the injection pressure can differ a fac-tor 2 with different grout/cement mixtures. The dif-ference is even bigger when X-linked gel us used.

Table 2. Parameters of Tests performed.

No

Yield stress (Pa)

Visc (Pas)

perccem (%)

Perm.

x10-12 (m/s)

Peak press. (kPa)

4 n.d. n.d. 5.6 750 6 51 21 0.5 50 1700 7 68 22 5 600 1200 8 83 6.4 10 600 1900 9 64 9.6 20 750 2900 10 98 6.4. 50 1000 2350 Notes: Yield stress = the yield stress of the grout, Visc = the viscosity of the grout, Perm = the permeability of the grout fil-ter cake, peak pressure = the maximum pressure measured, n.d = not determined.

-5

0

5

10

15

20

25

30

inje

ctio

npr

essu

re(b

ar)

0 5 10

time (s)

Test 4Test 6Test 7Test 8Test 9Test 10

Figure 10: Injection pressures for various tests

The tests in which a bentonite slurry with a rela-tively low cement content was used (Test 6, 7 and 8) led to lower injection pressures. Here the injection pressure fluctuates, see Figure 10. Long thin fractures were observed in the tests with lower injection pressures and shorter and wider frac-tures in the tests with higher injection pressures; see Figure 11 and the injection pressures shown in Fig-ure 10.

Comparing the results obtained with injections with different grout-cement mixtures it appeared that there was a maximum in the efficiency (volume in heave divided by the volume injected) of the grout-ing process. Using a grout mixture of 5% bentonite, the efficiency was at maximum for a cement percen-tage of 10 (percentage of the water). Efficiency re-duces both with a lower and higher amount of ce-ment.

Figure 11. Fractures obtained using X-linked gel (Test 4), 5% of cement in 5% bentonite slurry (Test 7) and 50% cement (Test 10).

5 DISCUSSION

When the injection pressure is close to the cavity expansion pressure as a fracture occurred, this frac-ture will widen, because the pressure in the fracture is high enough to push the parts of the fracture from each other. For low injection pressures the parts of the fracture will not be pushed apart, leading to thin-ner fractures. For the same volume injected in both cases, the wider fractures will be shorter than the thinner fractures to obtain the same volume.

The maximum that was found in the efficiency of the grouting process is likely to be caused by the two processes leak off and bleeding described in the chapter Theory. Leak off is the dominant process for very low values of the cement content, The same holds for grout bleeding. The permeability of the grout cake increases at larger cement contents be-cause the delicate ‘house of card’ structure that is formed by bentonite in water is destroyed by the cement (Sanders, 2007). The fluctuation in the injec-tion pressure as is shown for the tests 6, 7 and 8 is assumed to be caused by the leak off that occurred in these tests. It is assumed that a new fracture led to an increase of the leak off resulting in a pressure drop. Figure 6 shows that leak off leads to rapid penetra-tion of grout material at the sand boundary, but the penetration nearly stops after some time. This means that in a new fracture there will be a lot of penetra-tion (and thus a pressure drop), the pressure increas-es again when the leak off decreases.

The grout mixtures used in compensation grout-ing projects normally have a higher percentage of cement than the grout mixtures tested in this re-search. It is therefore likely that these mixtures will not lead to fractures when used in homogenous sands, but to compaction of the sand. Field expe-riences (Kleinlugtenbelt, 2006) led to the same con-clusion.

6 CONCLUSIONS

The theoretical and experimental research described in this paper has led to the following conclusions: - The properties of the grout mixture have an influ-ence on the fractures that occur in a hydraulic frac-ture test. Both injection pressure and shape of the fractures depend on the properties of the mixture. - Both leak off and grout bleeding seem to be of im-portance for the shape of the fractures. Fine particles at the boundary between the fluid and the sand can hamper the formation of fractures. - There appears to be an optimum in the efficiency of the compensation grouting process. In these tests this was reached using 10% cement. With less ce-ment the efficiency decreases due to increased leak off, with more cement the permeability of the grout cake increases leading to more bleeding. - When the injection pressure is close to the maxi-mum pressure according to cavity expansion theory, then quite wide fractures will occur. Fractures will be thinner for lower injection pressures. - Performing an injection at a constant volume rate it is possible to determine leak off from the pressure reading. A fluctuating pressure indicates leak off.

REFERENCES

Bezuijen A., Sanders M.P.M., Hamer D., Tol A.F. van. (2007). Laboratory tests on compensation grouting, the influence of grout bleeding.; Proc. WTC, Prague.

Bezuijen, A. & Brassinga, H.E. 2001. Blow-out pressures measured in a centrifuge and in the field Proc. XIII ECSMGE 2001, Istanbul.

Bolton M.D. & McKinley J.D., 1997, Geotechnical properties of fresh cement grout – pressure filtration and consolidation tests, Géotechnique 47, No 2, 347-352.

Chiriotti, E., Avgnina N., Grasso P. 2005. Compensation grout-ing for TBM tunneling beneath shallow cover. Proc. 5th Int. Symposium Geotechnical aspects of underground con-struction in soft ground, Amsterdam 2005.

Christiaens M., Hemerijckx E., Vereerstraeten J.C. 2005. Tun-nelling under the city centre of Antwerp. A new under-ground Railway link for the HSL Paris-Brussels-Amsteram. Proc. 5th Int. Symposium Geotechnical aspects of under-ground construction in soft ground, Amsterdam 2005.

Kleinlugtenbelt (2005) Compensation grouting, laboratory tests in sand. Msc. Thesis, Delft University of Technology.

Kleinlugtenbelt. (2006) Privat communication Luger H.J. & Hergarden H.J.A.M.,1988. Directional drilling in

soft soil: influence of mud pressure, Proc. No-Dig ’88, Washington.

Mair R.J. & Hight D.W. 1994. Compensation grouting. World Tunnelling, Nov. 361-367.

Mitchell, J.K. 1976, Fundamentals of soil behaviour, Universi-ty of California, Berkely

Pater C.J. de, Bohloli B., Pruiksma J., Bezuijen A., 2003 Expe-rimental study of hydraulic fracturing in sand; Delft Uni-versity of Technology.

Sanders M.P.M. (2007) Hydraulic fracture grouting, laborato-ry tests in sand. Msc. Thesis, Delft University of Technolo-gy. January.