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A robust method to determine the shear strength of cement-based injection grouts in the field
Tunnelling and Underground Space Technology Tunnelling and Underground Space Technology 21 (2006) 499–503
incorporating Trenchless Technology Research
www.elsevier.com/locate/tust
A robust method to determine the shear strength of cement-based injection grouts in the field Magnus Axelsson *, Gunnar Gustafson Division of GeoEngineering, Department of Civil and Environmental Engineering, Chalmers University of Technology, SE-412 96 Go¨teborg, Sweden Received 4 May 2005; received in revised form 20 August 2005; accepted 25 August 2005 Available online 10 October 2005
Abstract There is no standardised method to directly determine the shear strength of grouts in the field. Determining the shear strength would make it possible to calculate the penetration length of cement-based grouts and hence establish a design of the grouting procedure. By developing a new robust method that consists of a stick sinking in the grout, a direct measurement of the shear strength can be made, using the same set up as the separation test. The sink of the stick depends on the shear force interaction between the grout and the stick, and hence the shear strength of the grout can be determined. To verify the results, the shear strengths obtained with the stick are compared with measurements of the shear strength made with a rotational rheometer in the laboratory. The comparison shows good agreement; hence the stick can be used in the field to determine the yield strength of cement-based grouts. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Grout; Rheology; Yield strength; Field measurement; Grouting design
1. Introduction In underground construction, grouting is used to reduce the groundwater inflow. In hard rock, the water flow takes place in the rock discontinuities, which means that the grout has to penetrate the discontinuities to reduce groundwater inflow. The method to determine the maximum penetration length for cementitious grouts in a fracture has been described by Lombardi (1985) and Gustafson and Stille (1996). The penetration length is determined by the aperture of the fractures, the acting grout pressure and the yield strength of the grout. Hence, the only material characteristic of the grout that has to be determined to calculate the maximum penetration length is the yield strength. By determining the maximum penetration of grouts in the field, it is possible to design an effective grouting procedure. To accurately determine the yield strength, advanced and expensive apparatus such as rotational viscometers are used. However, such apparatus is *
Corresponding author. Tel.: +46 31 772 2064; fax: +46 31 772 2107. E-mail address: [email protected] (M. Axelsson).
0886-7798/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2005.08.011
not suitable for use in the field where robust and simple measurements methods are needed. There is, therefore, a need to devise robust field measurement methods, so that an effective design of the grouting procedure may be developed. To date, the most common method to determine the flow properties of the grout in the field is the Marsh cone but also the slump test, the glass capillary flowmeter, and the cohesion plate is used (e.g. Kutzner, 1996 and Warner, 2004). The slump test is most suitable for concrete, but sometimes it is used for all kinds of cementitious material (Warner, 2004). The glass capillary flowmeter is mainly used for very low viscous materials such as chemical grouts (Shroff and Shah, 1999). The cohesion plate was described by Lombardi (1985) and consists of a plate that is dipped into the grout and by measure the weight of the plate before and after the weight of the grout that adheres to the plate is determined. However, this method has not been standardised, which means that the obtained values of the cohesion has to be considered as relative and not absolute. The Marsh cone measures the apparent viscosity, i.e. the flow time is dependent on both the rheology of the
500
M. Axelsson, G. Gustafson / Tunnelling and Underground Space Technology 21 (2006) 499–503
grout and the roughness of the cone. To describe the rheological behaviour of a non-Newtonian fluid, two parameters must be known, the plastic viscosity and the yield strength, which means that two separate measurements has to be done. Roussel and LeRoy (2005) developed a method to determine the yield strength using two flow cones. However, here too the limitations in using flow cone are emphasised: if the fluid viscosity is too low, there is no linear relation between viscosity and flow time and second, if the pressure gradient is not sufficient enough to overcome the yield stress of the fluid, no flow will occur. To relate the flow properties to the yield shear strength, Lombardi (1985) developed relationships for the Marsh cone and the cohesion plate. Lombardi purposed that the Marsh cone should be combined with the cohesion plate to separately determine the viscosity and the yield shear strength. Ha˚kansson (1993) established a theoretical model for the relationship between plastic viscosity, yield strength and Marsh cone flow time. This entails that by measuring the yield strength with another method, the Marsh cone flow time can be used to determine the plastic viscosity. The methods presented above only provide an indirect measurement of the yield strength. However other properties than the yield strength can affect the measurements. The objective of this study is to develop a new measuring method that is robust and simple enough to use in the field to determine the shear strength. The method is applicable to all cement-based grouts and a value of the shear strength for the grout is obtained during the actual grouting procedure. This will give a possibility to achieve more reliable and adjustable grouting designs, since the most uncertain design parameter often is the yield strength of the grout. 2. Experimental procedure The study was performed as a laboratory study where the shear strength of grout was evaluated. The measuring equipment consisted of a stick with a weight attached at the bottom end. The stick was allowed to sink into the grout and the sink depth was measured. The obtained results were compared with the yield shear strength evaluated from measurements made with a rotational rheometer.
Fig. 1. Schematic drawing of the test performance. The stick consists of wood with a screw attached in the lower end. The total length of the sink of the stick is read-off and this determines the shear strength of the grout.
density of the grout, ms is the mass of the stick and g is the acceleration due to gravity. When the stick is sunk into grout there is a resistance from the grout that can be designated tip resistance. In geotechnical engineering (Terzaghi et al., 1996), the relationship for heave of a cohesive earth mass in a cut is described as, qc ¼ N c s0 A;
ð4Þ
where qc is the tip resistance, Nc is the bearing capacity factor and A is the cross section area. For a circular geometry and assuming that the length of the stick in the grout is considerably larger than the cross section area of the stick, the bearing capacity factor approaches a value of 9 (Terzaghi et al., 1996). This means that the expression of the tip resistance can be written as, qc ¼ 9 s0 pr2 .
ð5Þ
Taking into account that the tip resistance acts on the bottom surface of the stick, the total equilibrium of the forces acting according to Eqs. (1)–(5) is l 2p r s0 þ 9s0 pr2 þ l pr2 g qg ¼ ms g.
ð6Þ
Rearrangement of this expression leads to the shear strength being determined as,
2.1. Theory To be able to evaluate the yield strength, it is necessary to develop a relationship between the sink of the stick and the shear strength of the grout. Considering a stick in equilibrium with the surrounding grout, see Fig. 1, the acting forces are stated in the following equations: The shear force : l 2p r s0 .
ð1Þ
The buoyancy : l pr2 g qg .
ð2Þ
The weight of the stick : ms g;
ð3Þ
where l is the length of the stick in grout, r is the radius of the stick, s0 is the yield shear strength of the grout, qg is the
s0 ¼
ms g l pr2 g qg . 2p l r þ 9 pr2
ð7Þ
2.2. Measuring equipment In this study, the stick was made of wood with a diameter of 5.0 mm and on one end a screw with a diameter less than the stick diameter was attached. The grout was kept in a measuring glass. In Table 1, the necessary parameters for calculation of the shear strength according to Eq. (7) are presented along with the measuring equipment and the measuring accuracy.
M. Axelsson, G. Gustafson / Tunnelling and Underground Space Technology 21 (2006) 499–503 Table 1 The parameters that were measured in the study, how the parameters were measured and the accuracy Measuring equipment
Accuracy of equipment
Radius of stick, r Mass of stick, ms Density of grout, qg Sink length of stick, l
Slide-calliper Scales Mud-balance Folding rule
0.1 mm 0.0005 g 5 kg/m3 0.1 cm
.
Shear rate [s-1]
Parameter
501
γ max
.
γ min Time [s]
2.4. Reference tests To corroborate the measurements made by the stick, the obtained shear strengths were compared with measurements of the shear strength made with a rotational rheometer. The tests were performed with a Bohlin CVO200 with rotating coaxial cylinder. The measuring equipment consisted of a cylinder with a diameter of 30 mm and a grooved inner cylinder with a diameter of 25 mm. The rheometer was run with controlled shear rates that were successively changed according to pre-programmed schedules, running from high to low shear rates. The high shear rates were varied between 200 and 40 s1 and the lowest shear rate were varied between 5 and 0.3 s1. Most test series were measured at 30 different shear rates, but there were also some series with 100 shear rates. In Fig. 2, the test sequence is illustrated. The actual shear rate that the grout would be exposed to during grouting depends on the flow rate, in other words the pump and the applied pressure on the grout. Generally, the shear rate is high when the grout passes the pump, but successively decrease as the grout enters the borehole and into the fractures. This means that the realistic shear rates will be low in the rock and according to Ha˚kansson (1993), the shear rate would be below 200 s1 as the grout penetrates a fracture. 2.5. Evaluation method Cement-based grouts are often described as Bingham fluids with the generalised rheological behaviour, presented
Shear stress [Pa]
The grouting modelling material used was a crushed dolomite with the marketing name Myanit, produced by Omya in Glanshammar, Sweden. The chemical formula of dolomite is CaMg(CO3)2. The density is 2.85 g/cm3 and the pH ranges between 9.5 and 10.5. The grain size distribution is between 0 and 20 lm and the d95 value (the grain size that 95% of the grains are smaller than) is around 16 lm. The main reason for using Myanit instead of cement is that it is an inert material. This means that it will not harden with time and that the thixotropic effects would be negligible. A disadvantage of Myanit is its large tendency to bleed, especially for high water–solid ratios. The study was made on grout with different water–solid ratios in order to test the method at different shear strengths. The water–solid ratios ranged from 0.8 to 2.0 by weight.
Fig. 2. The pre-programmed test sequence for the measurements with the rheometer. Each shear rate was kept constant for approximately 5 s before measurements. The maximum shear rate was between 40 and 200 s1 and the minimum shear rate was between 0.3 and 5 s1.
Shear stress [Pa]
2.3. Grouting material
τ0
a
Shear rate [s-1]
b
τ0
Shear rate [s-1]
Fig. 3. (a) Appearance of an ideal Bingham fluid with shear rate on the xaxis and shear stress on the y-axis. In order to get a Bingham fluid in motion, the applied stress must exceed the yield strength, s0. (b) Non-ideal Bingham fluid with an actual lower yield strength than evaluated according to a Bingham fluid. Most fluids exhibit a true yield strength lower than evaluated.
in Fig. 3(a). The flow curve is plotted with the shear rate on the x-axis and the shear stress on the y-axis. This is a simplified model and the yield strength is extrapolated from the flow curve. However, the ‘‘true’’ yield strength is often lower than the extrapolated one, see Fig. 3(b), but there is a problem in measuring the true value of the yield strength since lower shear rate will give lower yield strength (Ferguson and Kemblowski, 1991). In other words, the assumed yield value depends on the lowest shear-rate data available and hence it is not an absolute value. In order to evaluate the yield strength from the rheometer, the method with extrapolated yield value was used. 3. Results A total of 52 evaluations of the shear strength with sticks and the rotational rheometer were done in the test series. The evaluation of the yield strength from the rotational rheometer was based on extrapolation of the flow curve as exemplified in Fig. 4, where the measured curve is fitted with a straight curve. The rheological studies confirmed that Myanit can be described reasonably well as a Bingham fluid and hence is suitable to use as an experimental substitute for cement-based grouts. The assumption that Myanit would not show any thixotropic behaviour was also confirmed by the rheometer measurements. In Fig. 4, a test is shown where the test have run from low shear rates to high shear rates and back to low shear rates again. A large difference between the sequences would have indicated thixotropic characteristics.
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M. Axelsson, G. Gustafson / Tunnelling and Underground Space Technology 21 (2006) 499–503
and the lowest shear strength measured both with the rheometer and the stick.
7 6 5
4.1. Material
4 3 2 1 0 0
10
20
30
40
50
60
Shear rate [1/s]
Fig. 4. Measurements of the rheological characteristics made with a rotational rheometer. The test have run from low shear rates to high shear rates and back to low shear rates in order to test if the material shows any thixotropic behaviour. Since the lines are rather similar the conclusion is that the material is not thixotropic. In the diagram is a curve fitted that imitates an ideal Bingham fluid.
16 Y=0.9226*X R 2=0,966
Shear strength from stick [Pa]
14
During the test series, it was found that the surface of the stick is of great importance, due to the necessary adhesion between the stick and the grout. When a material has a too smooth surface or a very wet surface, the necessary adhesion cannot be obtained. In the test series, the weight of the stick was measured accurately, an important factor since the weight of the stick strongly affects the results. Measurements of the density with the mud-balance were made both before and after measurements, and the result showed good agreement. There was also good agreement between measurements made at different mixes with the same water–solid ratio. The measurements with the stick were made with two different sticks and for each measuring occasion more than one measurement was made with each stick. Myanit seems to be an applicable substitute for cement, the rheological behaviour is relatively similar to cement and the description as Bingham fluid seems reasonable.
12
4.2. Evaluation of data 10 8 6 4 2 0 0
2
4 6 8 10 12 Yield shear strength Bohlin [Pa]
14
16
Fig. 5. Cross plot of the shear strength measured with the rheometer on the x-axis and measurements made with sticks on the y-axis. In the figure is also a trend line with a regression value of 0.966.
In Fig. 5, a cross plot is presented where the yield shear strength obtained from the Bohlin rotational rheometer is compared with the value of the shear strength obtained with the sticks. In the figure, a trend line is fitted to the obtained values. The trend line has an inclination of 0.92, which means that the values obtained by the stick are generally slightly less than the values obtained with the rheometer. The trend line has a regression value of 0.966 and the maximum deviation from the trend line is approximately 20%. 4. Discussion and conclusion As can be seen in Fig. 5, the spread between measurements made with the same water–solid ratio is relatively small, often within 1–2 Pa difference between the highest
Using extrapolation to determine the yield strength from the rotational rheometer overestimates the yield value. In order to be consistent, the extrapolation method was used with a curve fit generated from the measured data. It seemed reasonable to use an extrapolation of the Bingham curve, since it is along this curve that the shear rates will change in real grouting situations. Measurement of a yield value at low shear rates (going toward zero) would underestimate the shear strength for the rest of the curve, see Fig. 6. The shear rate that the grout is exposed to as the stick sinks through the grout can be estimated approximately by assuming that the shear rate is proportional to the sink velocity of the stick divided by the sheared length.
S hea r s t r es s [P a ]
Shear stress [Pa]
8
τ 0, B τ 0, R
Shear rate [s-1] Fig. 6. The difference between the flow curves by applying an extrapolation of the Bingham curve, s0, B and the yield strength from very low shear rates, s0, R. The flow curve would be underestimated if the value from the low shear rates were applied.
M. Axelsson, G. Gustafson / Tunnelling and Underground Space Technology 21 (2006) 499–503
In conclusion, the method to determine the yield strength of a grout by letting a stick sink into the grout seems to be a robust method to measure the yield strength in the field. By performing standard measurements on the grout such as determining the density with mud-balance, measuring the flow time in the Marsh cone and measuring the separation in a measuring glass, the stick method yields a valuable complement. Performing these tests in the field yields a complete characterization of the necessary material parameters to characterize the grout. A reliable value of the yield strength is also necessary to predict the penetration length of cement-based grouts and hence make it possible to achieve designs of the grouting procedure.
0.16 0.15 0.14 0.13
τ 0 =0 .0 1 Pa
0.12
τ 0 =1 Pa τ 0 =2 Pa
Sink [m]
0.11 0.1
τ 0 =3 Pa
0.09
τ 0 =5 Pa
0.08 0.07 0.06 0.05 0.04
503
τ0 =8 Pa τ 0 =10 Pa τ 0 =15 Pa τ 0 =20 Pa
0.03
Acknowledgements
0.02 0.01 0 1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
Density grout [kg/m3]
Fig. 7. Diagram to determine the yield strength with known density and measured sink of the stick. The grout density is determined with a mudbalance and with known weight and diameter of the stick, the sink of the stick yields the shear strength directly in the field.
This results in a shear rate between 0.2 and 2 s1 which is in the same range as the lowest measured shear rates with the rheometer. The shear rate obtained as the stick sink through the grout is ceasing towards zero shear rate. This is the same process that is obtained as the grout penetrates and finally stops in a fracture. 4.3. Application A suitable method for measuring the yield strength of grout in the field has to be simple to use as well as robust. The method of using a stick to measure the yield strength seems to full-fill both these demands. The measurement with the stick can be done in the same measuring glass as the separation test is performed in today. This means that no special measuring device has to be manufactured except for the stick itself. To determine the density of grout, the mud-balance is used in the field. This means that all the necessary parameters are known if a standard stick with known diameter and weight is used. In Fig. 7, a diagram is presented where known density and sink of the stick yields the shear strength of the grout. By measuring the sink of the stick, a value of the yield strength is immediately obtained in the field.
The work has been carried out at the Division of GeoEngineering at Chalmers University of Technology within the group of Grouting and Characterization. The study is a part of the project ‘‘Inner erosion of fracture filling and grouting agents’’, financed by Formas. The laboratory equipment were manufactured and facilitated by the laboratory technicians Aaro Pirhonen and Peter Hedborg. The use of the Bohlin rheometer was introduced by Oskar Esping, Division of Building Technology at Chalmers University of Technology and Johan Funehag, Division of GeoEngineering. The modelling grouting material was supplied by Omya in Glanshammar, Sweden. References Ferguson, J., Kemblowski, Z., 1991. Applied Fluid Rheology. Elsevier Applied Science, London, Great Britain. Gustafson, G., Stille, H., 1996. Prediction of groutability from grout properties and hydrogeological data. Tunnelling and Underground Space Technology 11 (3), 325–332. Ha˚kansson, U., 1993. Rheology of fresh cement-based grouts. Doctoral Thesis, Department of Infrastructure and Environmental Engineering, Division of Soil and Rock Mechanics, Royal Institute of Technology, Stockholm, Sweden. Kutzner, C., 1996. Grouting of Rock and Soil. A.A. Balkema, Rotterdam, The Netherlands. Lombardi, G., 1985. The role of cohesion in cement grouting of rock. In: Proceedings, Quinzie`me Congre`s des Grands Barrages, Lausanne, Switzerland, pp. 235–261. Roussel, N., LeRoy, R., 2005. The Marsh cone: a test or a rheological apparatus. Cement and Concrete Research 35 (5), 823–830. Shroff, A.V., Shah, D.L., 1999. Grouting Technology in Tunnelling and Dam Construction. A.A. Balkema, Rotterdam, The Netherlands. Terzaghi, K., Peck, R.B., Mesri, G., 1996. Soil Mechanics in Engineering Practice. Wiley, New York, USA. Warner, J., 2004. Practical Handbook of Grouting. Wiley, New Jersey, USA.
incorporating Trenchless Technology Research
www.elsevier.com/locate/tust
A robust method to determine the shear strength of cement-based injection grouts in the field Magnus Axelsson *, Gunnar Gustafson Division of GeoEngineering, Department of Civil and Environmental Engineering, Chalmers University of Technology, SE-412 96 Go¨teborg, Sweden Received 4 May 2005; received in revised form 20 August 2005; accepted 25 August 2005 Available online 10 October 2005
Abstract There is no standardised method to directly determine the shear strength of grouts in the field. Determining the shear strength would make it possible to calculate the penetration length of cement-based grouts and hence establish a design of the grouting procedure. By developing a new robust method that consists of a stick sinking in the grout, a direct measurement of the shear strength can be made, using the same set up as the separation test. The sink of the stick depends on the shear force interaction between the grout and the stick, and hence the shear strength of the grout can be determined. To verify the results, the shear strengths obtained with the stick are compared with measurements of the shear strength made with a rotational rheometer in the laboratory. The comparison shows good agreement; hence the stick can be used in the field to determine the yield strength of cement-based grouts. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Grout; Rheology; Yield strength; Field measurement; Grouting design
1. Introduction In underground construction, grouting is used to reduce the groundwater inflow. In hard rock, the water flow takes place in the rock discontinuities, which means that the grout has to penetrate the discontinuities to reduce groundwater inflow. The method to determine the maximum penetration length for cementitious grouts in a fracture has been described by Lombardi (1985) and Gustafson and Stille (1996). The penetration length is determined by the aperture of the fractures, the acting grout pressure and the yield strength of the grout. Hence, the only material characteristic of the grout that has to be determined to calculate the maximum penetration length is the yield strength. By determining the maximum penetration of grouts in the field, it is possible to design an effective grouting procedure. To accurately determine the yield strength, advanced and expensive apparatus such as rotational viscometers are used. However, such apparatus is *
Corresponding author. Tel.: +46 31 772 2064; fax: +46 31 772 2107. E-mail address: [email protected] (M. Axelsson).
0886-7798/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2005.08.011
not suitable for use in the field where robust and simple measurements methods are needed. There is, therefore, a need to devise robust field measurement methods, so that an effective design of the grouting procedure may be developed. To date, the most common method to determine the flow properties of the grout in the field is the Marsh cone but also the slump test, the glass capillary flowmeter, and the cohesion plate is used (e.g. Kutzner, 1996 and Warner, 2004). The slump test is most suitable for concrete, but sometimes it is used for all kinds of cementitious material (Warner, 2004). The glass capillary flowmeter is mainly used for very low viscous materials such as chemical grouts (Shroff and Shah, 1999). The cohesion plate was described by Lombardi (1985) and consists of a plate that is dipped into the grout and by measure the weight of the plate before and after the weight of the grout that adheres to the plate is determined. However, this method has not been standardised, which means that the obtained values of the cohesion has to be considered as relative and not absolute. The Marsh cone measures the apparent viscosity, i.e. the flow time is dependent on both the rheology of the
500
M. Axelsson, G. Gustafson / Tunnelling and Underground Space Technology 21 (2006) 499–503
grout and the roughness of the cone. To describe the rheological behaviour of a non-Newtonian fluid, two parameters must be known, the plastic viscosity and the yield strength, which means that two separate measurements has to be done. Roussel and LeRoy (2005) developed a method to determine the yield strength using two flow cones. However, here too the limitations in using flow cone are emphasised: if the fluid viscosity is too low, there is no linear relation between viscosity and flow time and second, if the pressure gradient is not sufficient enough to overcome the yield stress of the fluid, no flow will occur. To relate the flow properties to the yield shear strength, Lombardi (1985) developed relationships for the Marsh cone and the cohesion plate. Lombardi purposed that the Marsh cone should be combined with the cohesion plate to separately determine the viscosity and the yield shear strength. Ha˚kansson (1993) established a theoretical model for the relationship between plastic viscosity, yield strength and Marsh cone flow time. This entails that by measuring the yield strength with another method, the Marsh cone flow time can be used to determine the plastic viscosity. The methods presented above only provide an indirect measurement of the yield strength. However other properties than the yield strength can affect the measurements. The objective of this study is to develop a new measuring method that is robust and simple enough to use in the field to determine the shear strength. The method is applicable to all cement-based grouts and a value of the shear strength for the grout is obtained during the actual grouting procedure. This will give a possibility to achieve more reliable and adjustable grouting designs, since the most uncertain design parameter often is the yield strength of the grout. 2. Experimental procedure The study was performed as a laboratory study where the shear strength of grout was evaluated. The measuring equipment consisted of a stick with a weight attached at the bottom end. The stick was allowed to sink into the grout and the sink depth was measured. The obtained results were compared with the yield shear strength evaluated from measurements made with a rotational rheometer.
Fig. 1. Schematic drawing of the test performance. The stick consists of wood with a screw attached in the lower end. The total length of the sink of the stick is read-off and this determines the shear strength of the grout.
density of the grout, ms is the mass of the stick and g is the acceleration due to gravity. When the stick is sunk into grout there is a resistance from the grout that can be designated tip resistance. In geotechnical engineering (Terzaghi et al., 1996), the relationship for heave of a cohesive earth mass in a cut is described as, qc ¼ N c s0 A;
ð4Þ
where qc is the tip resistance, Nc is the bearing capacity factor and A is the cross section area. For a circular geometry and assuming that the length of the stick in the grout is considerably larger than the cross section area of the stick, the bearing capacity factor approaches a value of 9 (Terzaghi et al., 1996). This means that the expression of the tip resistance can be written as, qc ¼ 9 s0 pr2 .
ð5Þ
Taking into account that the tip resistance acts on the bottom surface of the stick, the total equilibrium of the forces acting according to Eqs. (1)–(5) is l 2p r s0 þ 9s0 pr2 þ l pr2 g qg ¼ ms g.
ð6Þ
Rearrangement of this expression leads to the shear strength being determined as,
2.1. Theory To be able to evaluate the yield strength, it is necessary to develop a relationship between the sink of the stick and the shear strength of the grout. Considering a stick in equilibrium with the surrounding grout, see Fig. 1, the acting forces are stated in the following equations: The shear force : l 2p r s0 .
ð1Þ
The buoyancy : l pr2 g qg .
ð2Þ
The weight of the stick : ms g;
ð3Þ
where l is the length of the stick in grout, r is the radius of the stick, s0 is the yield shear strength of the grout, qg is the
s0 ¼
ms g l pr2 g qg . 2p l r þ 9 pr2
ð7Þ
2.2. Measuring equipment In this study, the stick was made of wood with a diameter of 5.0 mm and on one end a screw with a diameter less than the stick diameter was attached. The grout was kept in a measuring glass. In Table 1, the necessary parameters for calculation of the shear strength according to Eq. (7) are presented along with the measuring equipment and the measuring accuracy.
M. Axelsson, G. Gustafson / Tunnelling and Underground Space Technology 21 (2006) 499–503 Table 1 The parameters that were measured in the study, how the parameters were measured and the accuracy Measuring equipment
Accuracy of equipment
Radius of stick, r Mass of stick, ms Density of grout, qg Sink length of stick, l
Slide-calliper Scales Mud-balance Folding rule
0.1 mm 0.0005 g 5 kg/m3 0.1 cm
.
Shear rate [s-1]
Parameter
501
γ max
.
γ min Time [s]
2.4. Reference tests To corroborate the measurements made by the stick, the obtained shear strengths were compared with measurements of the shear strength made with a rotational rheometer. The tests were performed with a Bohlin CVO200 with rotating coaxial cylinder. The measuring equipment consisted of a cylinder with a diameter of 30 mm and a grooved inner cylinder with a diameter of 25 mm. The rheometer was run with controlled shear rates that were successively changed according to pre-programmed schedules, running from high to low shear rates. The high shear rates were varied between 200 and 40 s1 and the lowest shear rate were varied between 5 and 0.3 s1. Most test series were measured at 30 different shear rates, but there were also some series with 100 shear rates. In Fig. 2, the test sequence is illustrated. The actual shear rate that the grout would be exposed to during grouting depends on the flow rate, in other words the pump and the applied pressure on the grout. Generally, the shear rate is high when the grout passes the pump, but successively decrease as the grout enters the borehole and into the fractures. This means that the realistic shear rates will be low in the rock and according to Ha˚kansson (1993), the shear rate would be below 200 s1 as the grout penetrates a fracture. 2.5. Evaluation method Cement-based grouts are often described as Bingham fluids with the generalised rheological behaviour, presented
Shear stress [Pa]
The grouting modelling material used was a crushed dolomite with the marketing name Myanit, produced by Omya in Glanshammar, Sweden. The chemical formula of dolomite is CaMg(CO3)2. The density is 2.85 g/cm3 and the pH ranges between 9.5 and 10.5. The grain size distribution is between 0 and 20 lm and the d95 value (the grain size that 95% of the grains are smaller than) is around 16 lm. The main reason for using Myanit instead of cement is that it is an inert material. This means that it will not harden with time and that the thixotropic effects would be negligible. A disadvantage of Myanit is its large tendency to bleed, especially for high water–solid ratios. The study was made on grout with different water–solid ratios in order to test the method at different shear strengths. The water–solid ratios ranged from 0.8 to 2.0 by weight.
Fig. 2. The pre-programmed test sequence for the measurements with the rheometer. Each shear rate was kept constant for approximately 5 s before measurements. The maximum shear rate was between 40 and 200 s1 and the minimum shear rate was between 0.3 and 5 s1.
Shear stress [Pa]
2.3. Grouting material
τ0
a
Shear rate [s-1]
b
τ0
Shear rate [s-1]
Fig. 3. (a) Appearance of an ideal Bingham fluid with shear rate on the xaxis and shear stress on the y-axis. In order to get a Bingham fluid in motion, the applied stress must exceed the yield strength, s0. (b) Non-ideal Bingham fluid with an actual lower yield strength than evaluated according to a Bingham fluid. Most fluids exhibit a true yield strength lower than evaluated.
in Fig. 3(a). The flow curve is plotted with the shear rate on the x-axis and the shear stress on the y-axis. This is a simplified model and the yield strength is extrapolated from the flow curve. However, the ‘‘true’’ yield strength is often lower than the extrapolated one, see Fig. 3(b), but there is a problem in measuring the true value of the yield strength since lower shear rate will give lower yield strength (Ferguson and Kemblowski, 1991). In other words, the assumed yield value depends on the lowest shear-rate data available and hence it is not an absolute value. In order to evaluate the yield strength from the rheometer, the method with extrapolated yield value was used. 3. Results A total of 52 evaluations of the shear strength with sticks and the rotational rheometer were done in the test series. The evaluation of the yield strength from the rotational rheometer was based on extrapolation of the flow curve as exemplified in Fig. 4, where the measured curve is fitted with a straight curve. The rheological studies confirmed that Myanit can be described reasonably well as a Bingham fluid and hence is suitable to use as an experimental substitute for cement-based grouts. The assumption that Myanit would not show any thixotropic behaviour was also confirmed by the rheometer measurements. In Fig. 4, a test is shown where the test have run from low shear rates to high shear rates and back to low shear rates again. A large difference between the sequences would have indicated thixotropic characteristics.
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and the lowest shear strength measured both with the rheometer and the stick.
7 6 5
4.1. Material
4 3 2 1 0 0
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20
30
40
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60
Shear rate [1/s]
Fig. 4. Measurements of the rheological characteristics made with a rotational rheometer. The test have run from low shear rates to high shear rates and back to low shear rates in order to test if the material shows any thixotropic behaviour. Since the lines are rather similar the conclusion is that the material is not thixotropic. In the diagram is a curve fitted that imitates an ideal Bingham fluid.
16 Y=0.9226*X R 2=0,966
Shear strength from stick [Pa]
14
During the test series, it was found that the surface of the stick is of great importance, due to the necessary adhesion between the stick and the grout. When a material has a too smooth surface or a very wet surface, the necessary adhesion cannot be obtained. In the test series, the weight of the stick was measured accurately, an important factor since the weight of the stick strongly affects the results. Measurements of the density with the mud-balance were made both before and after measurements, and the result showed good agreement. There was also good agreement between measurements made at different mixes with the same water–solid ratio. The measurements with the stick were made with two different sticks and for each measuring occasion more than one measurement was made with each stick. Myanit seems to be an applicable substitute for cement, the rheological behaviour is relatively similar to cement and the description as Bingham fluid seems reasonable.
12
4.2. Evaluation of data 10 8 6 4 2 0 0
2
4 6 8 10 12 Yield shear strength Bohlin [Pa]
14
16
Fig. 5. Cross plot of the shear strength measured with the rheometer on the x-axis and measurements made with sticks on the y-axis. In the figure is also a trend line with a regression value of 0.966.
In Fig. 5, a cross plot is presented where the yield shear strength obtained from the Bohlin rotational rheometer is compared with the value of the shear strength obtained with the sticks. In the figure, a trend line is fitted to the obtained values. The trend line has an inclination of 0.92, which means that the values obtained by the stick are generally slightly less than the values obtained with the rheometer. The trend line has a regression value of 0.966 and the maximum deviation from the trend line is approximately 20%. 4. Discussion and conclusion As can be seen in Fig. 5, the spread between measurements made with the same water–solid ratio is relatively small, often within 1–2 Pa difference between the highest
Using extrapolation to determine the yield strength from the rotational rheometer overestimates the yield value. In order to be consistent, the extrapolation method was used with a curve fit generated from the measured data. It seemed reasonable to use an extrapolation of the Bingham curve, since it is along this curve that the shear rates will change in real grouting situations. Measurement of a yield value at low shear rates (going toward zero) would underestimate the shear strength for the rest of the curve, see Fig. 6. The shear rate that the grout is exposed to as the stick sinks through the grout can be estimated approximately by assuming that the shear rate is proportional to the sink velocity of the stick divided by the sheared length.
S hea r s t r es s [P a ]
Shear stress [Pa]
8
τ 0, B τ 0, R
Shear rate [s-1] Fig. 6. The difference between the flow curves by applying an extrapolation of the Bingham curve, s0, B and the yield strength from very low shear rates, s0, R. The flow curve would be underestimated if the value from the low shear rates were applied.
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In conclusion, the method to determine the yield strength of a grout by letting a stick sink into the grout seems to be a robust method to measure the yield strength in the field. By performing standard measurements on the grout such as determining the density with mud-balance, measuring the flow time in the Marsh cone and measuring the separation in a measuring glass, the stick method yields a valuable complement. Performing these tests in the field yields a complete characterization of the necessary material parameters to characterize the grout. A reliable value of the yield strength is also necessary to predict the penetration length of cement-based grouts and hence make it possible to achieve designs of the grouting procedure.
0.16 0.15 0.14 0.13
τ 0 =0 .0 1 Pa
0.12
τ 0 =1 Pa τ 0 =2 Pa
Sink [m]
0.11 0.1
τ 0 =3 Pa
0.09
τ 0 =5 Pa
0.08 0.07 0.06 0.05 0.04
503
τ0 =8 Pa τ 0 =10 Pa τ 0 =15 Pa τ 0 =20 Pa
0.03
Acknowledgements
0.02 0.01 0 1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
Density grout [kg/m3]
Fig. 7. Diagram to determine the yield strength with known density and measured sink of the stick. The grout density is determined with a mudbalance and with known weight and diameter of the stick, the sink of the stick yields the shear strength directly in the field.
This results in a shear rate between 0.2 and 2 s1 which is in the same range as the lowest measured shear rates with the rheometer. The shear rate obtained as the stick sink through the grout is ceasing towards zero shear rate. This is the same process that is obtained as the grout penetrates and finally stops in a fracture. 4.3. Application A suitable method for measuring the yield strength of grout in the field has to be simple to use as well as robust. The method of using a stick to measure the yield strength seems to full-fill both these demands. The measurement with the stick can be done in the same measuring glass as the separation test is performed in today. This means that no special measuring device has to be manufactured except for the stick itself. To determine the density of grout, the mud-balance is used in the field. This means that all the necessary parameters are known if a standard stick with known diameter and weight is used. In Fig. 7, a diagram is presented where known density and sink of the stick yields the shear strength of the grout. By measuring the sink of the stick, a value of the yield strength is immediately obtained in the field.
The work has been carried out at the Division of GeoEngineering at Chalmers University of Technology within the group of Grouting and Characterization. The study is a part of the project ‘‘Inner erosion of fracture filling and grouting agents’’, financed by Formas. The laboratory equipment were manufactured and facilitated by the laboratory technicians Aaro Pirhonen and Peter Hedborg. The use of the Bohlin rheometer was introduced by Oskar Esping, Division of Building Technology at Chalmers University of Technology and Johan Funehag, Division of GeoEngineering. The modelling grouting material was supplied by Omya in Glanshammar, Sweden. References Ferguson, J., Kemblowski, Z., 1991. Applied Fluid Rheology. Elsevier Applied Science, London, Great Britain. Gustafson, G., Stille, H., 1996. Prediction of groutability from grout properties and hydrogeological data. Tunnelling and Underground Space Technology 11 (3), 325–332. Ha˚kansson, U., 1993. Rheology of fresh cement-based grouts. Doctoral Thesis, Department of Infrastructure and Environmental Engineering, Division of Soil and Rock Mechanics, Royal Institute of Technology, Stockholm, Sweden. Kutzner, C., 1996. Grouting of Rock and Soil. A.A. Balkema, Rotterdam, The Netherlands. Lombardi, G., 1985. The role of cohesion in cement grouting of rock. In: Proceedings, Quinzie`me Congre`s des Grands Barrages, Lausanne, Switzerland, pp. 235–261. Roussel, N., LeRoy, R., 2005. The Marsh cone: a test or a rheological apparatus. Cement and Concrete Research 35 (5), 823–830. Shroff, A.V., Shah, D.L., 1999. Grouting Technology in Tunnelling and Dam Construction. A.A. Balkema, Rotterdam, The Netherlands. Terzaghi, K., Peck, R.B., Mesri, G., 1996. Soil Mechanics in Engineering Practice. Wiley, New York, USA. Warner, J., 2004. Practical Handbook of Grouting. Wiley, New Jersey, USA.