Grouting aims to reduce the permeability of rock mass below the required value and has been widely used in rock engineering field for a long time

M. Ashraf, M. Ashraf

T. Yamamoto, T. Yamamoto

Y. Mito, Y. Mito

English

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Harmonising Rock Engineering and the Environment – Qian & Zhou (eds)© 2012 Taylor & Francis Group, London, ISBN 978-0-415-80444-8Numerical modeling for the evaluation of grout penetration in fractured rock massesY. MitoDepartment of Urban Management, Graduate School of Engineering, Kyoto University, JapanM. AshrafSchool of Civil Engineering, Universiti Sains Malaysia, MalaysiaT. YamamotoKajima Corporation, JapanABSTRACT: Grouting aims to reduce the permeability of rock mass below the required value and has been widely used inrock engineering field for a long time. However, the injection procedure needs several empirical decision makings and it israther difficult to reliably confirm the achievement of improvement, because the grout penetration process is not sufficientlyclarified. This study proposes a stochastic prediction method of spatial distribution of rock hydraulic properties after groutingin fractured rock mass by using the grout penetration process model. The goal achievement probability under the specifictarget permeability is computed with the help of geostatistical interpolation method. The applicability of the method is verifiedthrough the several field applications.Subject: Modelling and numerical methodsKeywords: numerical modelling, Rock joints, fluid flow, site characterization1 INTRODUCTIONThe materials stored in underground rock storage facility havegradually diversified over time (e.g. high-pressure gas stor-age, high level radioactive waste repository, etc.). In orderto store these materials, a more reliable storage functioningis required and rock hydraulic properties around the cavernmust be improved sufficiently. Especially, it is important topredict and evaluate the spatial distribution of rock hydraulicproperties after grouting in fractured rock mass for the reliablegroundwater control.Grouting aims to reduce the permeability of rock massbelow the required value and has been widely used in rockengineering field for a long time. However, the injection proce-dure needs several empirical decision makings and it is ratherdifficult to reliably confirm the achievement of improve-ment, because the grout penetration process is not sufficientlyclarified.This study proposes a stochastic prediction method of spa-tial distribution of rock hydraulic properties after grouting infractured rock mass by using the grout penetration processmodel. The applicability of the method is verified through theseveral field applications.2 NUMERICAL MODELING OF GROUT FLOW2.1 ModelingConsidering the balance between the gravity force of a cementparticle in suspension and drag force of a cement particle(Date, 2003, Aoki, 2003), terminal settling velocity of cementparticle in suspension v is calculated bywhere dp = diameter of particle; δp = specific gravity of parti-cle; δ= specific gravity of suspension; and CD = 24/Re = dragcoefficient in the case of turbulent flow; Re = Reynoldsnumber.Since volume of sediments in parallel plates produced in aunit period of time is constant, we havewhere s(t) = width of sediments produced during the periodfrom t to t +t, which is proportional to v; and d(t) = rangeof sedimentation during the period from t to t +t.Based on the law of conservation, s(t) can be written as,where, E(t) = kinetic energy of particles in suspension at t;and F = drag force of suspension.On the other hand, obeying cubic law, flow rate q(t) duringthe period from t to t +t is given by,483where b(t) = distance between plates (aperture) at t; andi = hydraulic gradient.Velocity of suspension at t, u(t) is givenbyFrom equations (3)(4) and (5), finally we can haveSubstituting equation (6) forand substituting equation (7) for (4)(5)(6), we can obtainq(t + 1), u(t + 1) and s(t + 1). Thus, the change of flow rate asa function of time, total grout take, total time for injection, andso on can be simulated by following such iteration procedureuntil aperture b(t) becomes 0.The above process expresses the suspension flow nearthe borehole. To express the suspension flow in rock mass,the radial flow model is introduced. The suspension flowdecreases in velocity in inverse proportion to distance formthe centre of borehole. The discrete elements are establishedalong the radial lines to analyze the penetration of suspension.In each element, flow rate and grout width are calculated bythe iteration using equations (4) (5) (6) and (7) .In applying the above procedure to rock mass, aperture dis-tribution of the fractures intersecting the injection hole mustbe required in order to determine b(0). However, if all aper-tures can be represented as a mean value, the flow rate of therock mass can be expressed aswhere N = number of the fractures intersecting the injec-tion hole; fB(b) = probability density function of aperture,bM = averaged aperture.As a result, the flow rate in the field tests can be simulatedusing equation (8). The number of fractures is determined byreferring the fracture spacing data from borehole televisionsystem. Averaged aperture can be obtained from cubic lawwith the spacing data.2.2 Model validationThe applicability of the proposed grout penetration modelis examined through the several field applications. Fig-ure 1 shows the illustrations of the comparison betweenthe theoretical plots of flow rate obtained from the anal-ysis with the proposed model and the actual field data.Figure 1(a) shows the injection case at the constant pressure.Figure 1(b) shows the injection case in the high permeablerock mass under the flow rate control. Figure 1(c) shows theinjection case with the change in W/C ratio during the injec-tion. As shown in the figures, the theoretical plots are closedto the field data. Figure 1(c) shows the compound case underthe conditions of (b) and (c). Thus, it is found that the flowbehaviors of suspension can be simulated by the iteration pro-cedure using equations (4) (5) (6) and (7). Thus the proposedmodel is validated.Figure 1. The illustrations of comparison between the theoreticalplots of flow rate obtained from the analysis with the proposed modeland the actual field data (line).3 PREDICTION METHOD OF IMPROVEMENTIn this section, the authors propose a stochastic predictionmethod of spatial distribution of rock hydraulic propertiesafter grouting by using grout penetration process modeldeveloped in Section 2.3.1 Geostatistical estimation of hydraulic conductivityOrdinary Kriging, one of geostatistical interpolation methodis employed to estimate the spatial distribution of hydraulic484Figure 2. The calculation method of goal achievement probability.Figure 3. The computed goal achievement probability and the measured Lugeon value under the target Lugeon values of 1Lu (a), 2Lu (b),and 5Lu (c). White circles show the plots whose measured Lugeon value is greater than the target Lugeon value while black circles showthose less than the target Lugeon value.conductivity before grouting. Logarithm of hydraulic conduc-tivity data observed in the injection holes are used as theinput data. Ordinary Kriging provides not only the estimatedvalue but also the estimation variance everywhere in the space.This means we can have the confidence intervals of hydraulicconductivity at the arbitrary point in the space.3.2 Calculation of goal achievement probabilityIt is impossible to grasp the real spatial distribution hydraulicconductivity because the estimated value generally includeserror. Thus we consider obtaining the probability thathydraulic conductivity at the arbitrary point is under therequired value (target hydraulic conductivity: e.g. targetLugeon value).Figure 2 shows the concept of the method. At first, we canhave probability density function of true hydraulic conductiv-ity as shown in Figure 2(a) from the estimated value and theestimation variance calculated by Ordinary Kriging. In thisfigure, the target hydraulic conductivity is also plotted.Assuming fracture spacing can be obtained, we can haveprobability density function of true fracture aperture and thetarget aperture as shown in Figure 2(b) by applying cubic lowto the values shown in Figure 2(a).From the grout penetration process model, we can havethe grout width after grouting at the arbitrary point. There-fore, the area of distribution under sum of target aperture andgrout width is the goal achievement probability by groutingas shown in Figure 2(c).Thus, we can obtain the probability that hydraulic conduc-tivity at the arbitrary point is under the required value.4 VERIFICATION OF THE PRIDICTION METHODThe proposed prediction method is verified through the fieldapplications. The 84 values of hydraulic conductivity aftergrouting at 5 different sites are predicted by the proposedmethod and then the values of goal achievement probabilityunder the specific goal achievement values are computed. Thestudy sites are as follows;– N dam (granite)– O dam (rhyolite)485Figure 4. The computed goal achievement probability and the measured achievement ratio under the target Lugeon values of 1Lu (a),2Lu (b), and 5Lu (c).– C dam (andesite)– G dam (andesite)– M dam (conglomerate and sandstone)The sets of Lugeon values obtained from the grouting testsfor consolidation grouting are used for the verification. Thegoal achievement values at the secondary to quaternary holesare predicted by using the Lugeon values of primary to tertiaryholes, respectively.Figure 3 shows the computed goal achievement probabil-ity and the measured Lugeon value under the target Lugeonvalues of 1Lu (a), 2Lu (b), and 5Lu (c), respectively, andFigure 4 shows the computed goal achievement probabilityand the measured achievement ratio under the target Lugeonvalues of 1Lu (a), 2Lu (b), and 5Lu (c). From these figures itis found that the measured achievement ratio is almost sameas the computed goal achievement probability except for thatin the class consisting of small number of data irrespective ofthe difference of the target Lugeon value. This fact shows thatthe goal achievement probability at the arbitrary point, whichallows performing the risk assessment, can be appropriatelyobtained by the proposed method.5 CONCLUSIONThis study proposed a stochastic prediction method of spa-tial distribution of rock hydraulic properties after grouting infractured rock mass by using the grout penetration processmodel. The goal achievement probability under the specifictarget permeability can be computed with the help of geosta-tistical interpolation method. The applicability of the methodhas been verified through the several field applications.REFERENCESAoki, K., Mito,Y., Kurokawa,Y.,Yamamoto,T., Date, K. & Wakita, S.2003, Development of dynamic grouting technique for theimprovement of low permeable rock masses, The 1st Kyoto Inter-national Symposium Underground Environment, Kyoto, Japan.Aoki, K., Mito Y., Yamamoto T., Date K. & Wakita S., 2003, Evalu-ation of dynamic grouting effect for Low-permeable rock. ISRM2003–Technology roadmap for rock mechanics, South AfricanInstitute of Mining and Metallurgy.Date K., Wakita, S., Yamamoto, T., Nakashima, Y., Hoshino, Y.,Aoki, K. & Mito, Y. 2003, Development of dynamic groutingtechnique for the ground improvement, Reclaiming the Under-ground Space, Proceedings of the ITA World Tunneling Congress,Amsterdam.486

Numerical modeling for the evaluation of grout penetration in fractured rock masses

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Numerical modeling for the evaluation of grout penetration in fractured rock masses

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