Numerical and experimental analysis of penetration grouting in jointed rock masses

International Journal of Rock Mechanics & Mining Sciences 37 (2000) 1027–1037

Numerical and experimental analysis of penetration grouting in jointed rock masses J.S. Leea,*, C.S. Banga, Y.J. Mokb, S.H. Johc a

Department of Civil Engineering, Korea Railroad Research Institute, South Korea b Department of Civil Engineering, Kyunghee University, South Korea c Department of Civil Engineering, Chungang University, South Korea Accepted 18 April 2000

Abstract The reinforcement effect of penetration (or permeation) cement grouting injected into jointed rock masses is investigated in this paper. For this, anisotropic material properties of jointed rock masses with and without grouting are derived based on the mechanics of composite material. Derived anisotropic material properties are not only functions of the material properties of the intact rock and grouting, but are also related to the geometric and mechanical properties of rock joints, such as dip angle, spacing and stiffness. Two in situ seismic tests were also performed to obtain information on the ground improvement. Finally, a back analysis methodology is proposed to quantify the reinforcement effect. Here, joint stiffnesses of the rock masses are selected as the dominant parameter to be determined. The so-called back analysis shows that, after grouting, the stiffnesses of the filled joints are increased upto 6 times compared with those of the ungrouted joints. # 2000 Elsevier Science Ltd. All rights reserved.

1. Introduction Grouting is widely used to improve in situ soil/rock quality and, in this regard, various injection techniques have been developed. In terms of rock engineering, penetration grouting (also called permeation grouting) is commonly used to fill the voids of the jointed rock masses so as to improve the rock stiffness and strength and to reduce groundwater flow. Also used in the field are consolidation and fracturing grouting, although these grouting techniques are commonly applied to in situ soil rather than rock masses. In this paper, our interest is focused on penetration grouting injected into jointed rock masses, and the reinforcement effect is investigated both analytically and experimentally. Previous studies on penetration grouting have been concentrated on rheological flow models of the grout and one-dimensional channel flow [1,2] but a planar flow model [3] has also been proposed. The maximum flow distance was, therefore, of major concern. However, the reinforcement effect due to penetration *Corresponding author. Tel.: +822-3453-6571; fax: +834-34618374. E-mail address: [email protected] (J.S. Lee).

grouting has not been theoretically investigated so far and only a few studies have been published [4–7]. In Kikuchi et al. [5], a simplified Reuss–Voigt model [8] has been employed to obtain material properties of the grout-reinforced foundation and it has been found from in situ tests that Young’s modulus had been increased up to two times compared with that of the ungrouted jointed rock masses. In this study, anisotropic material properties of the grout-reinforced rock masses are derived using the mechanics of composite material. Initially, the overall material properties of reinforced rock masses involving intact rock and (vertical) grouting injected in the boreholes are considered by employing a strain energy method [9]. The joint sets filled with the penetration grouting are next introduced to obtain anisotropic material properties of the reinforced rock masses. For this, a ubiquitous joint model, together with a velocity discontinuity, is successively used according to the number of joint sets. In particular, by adopting a velocity discontinuity, the effect of joint thickness in the overall constitutive equation can be effectively excluded. The derived anisotropic material properties are found to be functions of the material properties of the intact rock and the grouting. They are also related to the geometry

1365-1609/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 5 - 1 6 0 9 ( 0 0 ) 0 0 0 4 0 - X

1028

J.S. Lee et al. / International Journal of Rock Mechanics & Mining Sciences 37 (2000) 1027–1037

and properties of the rock joints, such as dip angle, spacing and stiffness. Simplified numerical experiments are also performed to verify the reinforcement effect of the rock mass and it is shown that the equivalent strains of the reinforced rock masses are significantly decreased due to superfine grouting into the rock joints. Experimental verification of the reinforcement effect was carried out using seismic test methods. Specifically, Crosshole and spectral-analysis-of-surface-waves (SASW) tests were performed in a tunnel site where penetration grouting on top of the crown area was applied. These seismic tests can be directly used to verify the ground improvement by measuring wave velocity between two measuring points which shows that the shear moduli of the reinforced rock masses are increased by upto 14% overall. The test data are also used in a back analysis where the joint stiffnesses before and after grouting are considered as unknown parameters. Calculation of the grout-filled joints shows that the stiffnesses of the rock joints are increased upto six times compared with those of the ungrouted joints. It is assumed that the injection pressure is relatively low so that hydraulic fracturing does not occur in the field. However, future work will be focused on the fracture grouting due to high injection pressure and possibly a bifurcation theory introduced in [10] will have to be considered to characterize the fracturing mechanism. Also, in addition to the joint stiffnesses, the cohesion as well as friction angle of the grout-filled joint need to be further investigated. 2. Derivation of material properties of grout-reinforced rock masses Consider a representative rock mass having two sets of joints and assume that reinforcement of the rock masses is carried out by penetration grouting in vertical boreholes using a packer system, (Fig. 1(a)). To derive the anisotropic material properties of the groutreinforced rock masses, the following assumptions are made: *

*

*

*

*

The rock joints are fully persistent, planar and parallel to each other within a joint set. Intact rock is impermeable and all the rock joints will be completely filled with grouting material containing superfine cement. The thickness of rock joints is negligible compared with the joint spacing. After injection, intact rock and grouting are fully bonded together.  The strikes of the joint sets are parallel to the Z-axis in Fig. 1(a).

Fig. 1. Modeling of jointed rock masses with penetration grouting: (a) Model, (b) Case 1: intact rock + vertical grouing, (c) Case 2: Case 1 + joint set 1, (d) Case 3: Case 2 + joint set 2.

tion of rock joints is normally assumed to follow Poisson’s distribution [11] and, therefore, grout has been modeled in the past by one-dimensional flow within a pipe or channel [1]. However, the assumption can be justified when rock joints are classified into clusters or sets according to their orientation characteristics [12] and, as a result, grout can be modeled by a planar flow. In the following, anisotropic material properties of the grout-reinforced rock masses are derived from the mechanics of composite material where intact rock, vertical grout and penetration grout are the constituent materials within the composite structure, see Fig. 1.

2.1. Orthotropic material properties of intact rock and vertical grouting Firstly, orthotropic material properties for a rock system composed of intact rock and vertical grouting are derived, (Fig. 1(b)). Define a representative elementary volume (REV) involving systematic grouting and let the volume ratios of intact rock and grout material be denoted by mr and mg , respectively. If the components of overall stress/strain rates within a composite material are represented by ð1Þ

The first assumption may be questionable from the viewpoint of rock engineering since the spatial distribu-

ð1Þ

ð1Þ

ð1Þ

ð1Þ

ð1Þ

rð1Þ ¼ fsx ; sy ; sz ; txy ; tyz ; tzx gT ð1Þ ð1Þ ð1Þ ð1Þ ð1Þ ð1Þ eð1Þ ¼ fex ; ey ; ez ; gxy ; gyz ; gzx gT

ð1Þ

1029

J.S. Lee et al. / International Journal of Rock Mechanics & Mining Sciences 37 (2000) 1027–1037

then the following stress/strain relation, based on the mixture rule [8], can be established in a local coordinate system X ÿ Y ÿ Z:

Since the intact rock and penetration grouting are assumed to be fully bonded together, the following equilibrium and kinematic conditions can be introduced:

rð1Þ ¼ mr rr þ mg rg ;

ð2Þ

sy ¼ sy ¼ syj1 ;

where indices r and g represent the intact rock and the vertical grout, respectively, and the constitutive model for each constituent material which is assumed to be homogeneous and isotropic in nature is as follows: rg ¼ ½Dg Šeg ð3Þ rr ¼ ½Dr Šer ;

ex ¼ ex ¼ exj1 ;

eð1Þ ¼ mr er þ mg eg

The orthotropic material properties of the composite material can be calculated from the equilibrium as well as compatibility conditions along the interface of intact rock and vertical grouting. Following the procedure outlined in [13], the constitutive relation of the composite material can now be established: rð1Þ ¼ ½Dð1Þ Šeð1Þ ;

ð4Þ

where the calculated constitutive equation is not only a function of the Young’s moduli and Poisson’s ratios of the constituent materials, but is also related to the volume ratio of the grout. Once Eq. (4) is derived, the structural relation between constituent and composite material can be constructed as follows: r

r

ð1Þ

e ¼ ½A Še ;

g

g

ð1Þ

e ¼ ½A Še :

ð5Þ

The material properties calculated from Eq. (4) will be in ð1Þ ð1Þ ð1Þ ð1Þ ð1Þ ð1Þ ð1Þ ð1Þ ð1Þ the form of Exx ; Eyy ; Ezz ; Gxy ; Gyz ; Gzx ; nxy ; nyz ; nzx and the details of the properties as well as the structural relation can be found in [13].

ð2Þ

ð1Þ

j1 txy ¼ txy ¼ txy ;

ð2Þ

ð1Þ

tyz ¼ tyz ¼ tyzj1

ð2Þ

ð1Þ

ez ¼ ez ¼ ezj1 ;

ð2Þ

ð1Þ

ð2Þ

ð1Þ

gzx ¼ gzx ¼ gzxj1

ð2Þ

ð1Þ

ð10Þ Also, since t1 5w1 , the following velocity discontinuities [14] of the penetration grouting can be established: g j1 ¼ fgyj1 ; gxj1 ; gzj1 gT ;

ð11Þ

where gyj1 and gxj1 ; gzj1 are the normal and shear velocity discontinuities, respectively, and the following constitutive model can be used to simulate the penetration grouting: r j1 ¼ ½K j1 Šg j1 ; with

2

K11j1 6 ½K j1 Š ¼ 4 K21j1 K31j1

ð12Þ K12j1 K22j1 K32j1

3 K13j1 7 K23j1 5: K33j1

ð13Þ

If the penetration grouting is assumed to behave elastically, K11j1 , K22j1 and K33j1 become the normal and shear stiffnesses while the off-diagonal terms can be ignored. In rock mechanics terminology, these stiffnesses can be rewritten as K11j1 ¼ KNj1 ;

K22j1 ¼ KS1j1 ;

K33j1 ¼ KS2j1 ;

ð14Þ

Furthermore, if KS1j1 =KS2j1 =KS in Eq. (14), the following equations can be used in the calculation:

2.2. Anisotropic material properties of grouted rock masses with one or two sets of joints

Eg ð1 ÿ ug Þ ; tj ð1 þ ug Þð1 ÿ 2ug Þ

KN ¼

KS ¼

ð15Þ

Eg ; 2tj ð1 þ ug Þ

The orthotropic material properties derived using the above method can be used to obtain anisotropic (monoclinic) material properties of the rock masses which include filled joints. Considering a joint set with dip angle, y1, mean spacing, w1 , and joint thickness, t1 , the following average stress/strain relation in the local coordinate system, x1 2y1 2z1 can again be established, (Fig. 1(c)):

where, Eg , ng and tj are the Young’s modulus, Poisson’s ratio and thickness of the joint, respectively. To derive the anisotropic material properties, the constitutive equation in Eq. (4) is transformed into the local coordinate system x1 2y1 2z1 and will be denoted  ð1Þ Š. From Eqs. (4), (6), (9), (10) and (12), the by ½D  Y–  Z  following constitutive equation in the global X– coordinate system can be established:

rð2Þ ¼ m1 rð1Þ þ m2 r j1 ;

 ð2Þ Šeð2Þ ; rð2Þ ¼ ½D

eð2Þ ¼ m1 eð1Þ þ m2 e j1

where the volume ratios are calculated as w1 t1 ; m2 ¼ m1 ¼ w1 þ t1 w1 þ t1 with m1 þ m2 ¼ 1:

ð6Þ

ð16Þ

where ð7Þ

rð2Þ ¼ ½Ty1 Šÿ1 rð2Þ ;

eð2Þ ¼ ½T1;y1 Šÿ1 eð2Þ

ð17Þ

and ð8Þ

If the joint thickness is negligible compared with the joint spacing, Eq. (7) can be rewritten as t1 m2 ¼ ð9Þ m1  1; w1

 ð1Þ Š½S ð1Þ Š½T1; y1 Š  ð2Þ Š ¼ ½Ty1 Šÿ1 ½D ½D 1 ð1Þ

¼ ½Dð1Þ Š½Ty1 ŠT ½S1 Š½T1; y1 Š

ð18Þ ð1Þ

with the structural relation between e ð1Þ ½S1 Š.

and e

ð2Þ

being

1030

J.S. Lee et al. / International Journal of Rock Mechanics & Mining Sciences 37 (2000) 1027–1037

Table 1 Material properties of Sandstone and superfine grout Sandstone Young’s modulus, Er Poisson’s ratio, ur Cohesion, Cr Friction angle, fr Cohesion of joint, Cj Friction angle of joint, fj Normal stiffness, KN; j Shear stiffness, KS; j Tensile strength, st;r Tensile strength of joint, st;

Grout

j

24 GPa 0.15 0.7 MPa 358 0.1 MPa 308 3.1 GPa/m 1.0 GPa/m 0.5 MPa 0.01 MPa

Young’s modulus, Eg Poisson’s ratio, ug Cohesion, Cg Friction angle, fg Normal stiffness, KN; g Shear stiffness, KS; g Tensile strength, st; g Joint thickness, tj

The anisotropic material properties of rock masses involving two sets of grouted joints can also be derived using the same procedure adopted above. The final form of the constitutive equation is  eq Še eq ; r eq ¼ ½D ð19Þ where  eq Š ¼ ½Dð1Þ Š½Ty1 ŠT ½S ð1Þ Š½T1; y1 Š½Ty2 ŠT ½S ð2Þ Š½T1; y2 Š ½D 1 1

ð20Þ

eq

and r is the equivalent stress vector involving vertical as well as two sets of penetration grouting. The constitutive equation in Eq. (20) is not only a function of the material properties of intact rock and grout, but is also related to the properties of the rock joints such as stiffness, dip angle and spacing. 3. Analysis of the reinforcement effect The reinforcement effect of the penetration grouting introduced above is numerically analyzed in this section. For this, experimental data on the material properties of sandstone including the joint set properties are used. Table 1 is a summary of the data used in the example. In Table 1, the material properties of sandstone are obtained from [15,16] and those of superfine (cement) grout are from [17], while the stiffnesses of penetration grouting can be calculated from Eq. (15). To demonstrate the reinforcement effect of the penetration grouting, assume a uniaxial compression test in the jointed rock masses and consider the equivalent strain, e eq , introduced in Eq. (19). The equivalent strain within REV, in our case, can be an indicator of the reinforcement effect of the jointed rock mass since the properties of ungrouted or grouted rock joints are explicitly accounted for. Figs. 2(a) and (b) illustrate the change of equivalent strain of the jointed rock masses according to the number of joint sets and to the joint spacing. In case of two sets of joints, the material properties of the second joint set are assumed to be the same as the first joint set. Also shown in the figure is e eq of the grout-reinforced rock masses where

30 GPa 0.17 0.9 MPa 308 32 GPa/m 12 GPa/m 0.5 MPa 1 mm

the volume ratio of the vertical grouting, mg , equals 0.2. Clearly, the grouting effect is significant in both cases, especially when the joint spacing is 1.0 m, the ratios of strain reduction in one and two sets of joints are about 10 and 17 times, respectively, from the following equation: ratio of strain reduction ¼

ejeq egeq

;

ð21Þ

e geq are the equivalent strain of ungrouted where e eq j and  and grouted rock mass, respectively. It is noted from Fig. 2 that e eq of the grout-reinforced rock masses is the same regardless of joint spacing and number of joint sets because the penetration grouting is assumed to be scattered within representative elementary volume and is fully bonded together with intact rock. It is also noted that the effect of volume ratio, mg , is not a major factor since the overall equivalent strain is almost the same regardless of the injection volume of vertical grouting. The effect of joint thickness is next considered. During the derivation of constitutive equation in Eq. (20), the tj term is effectively eliminated and, therefore, the thickness term has no influence on the overall behavior of the rock masses. Although the stiffness of grout will be modified as the thickness is changed, Eq. (15), the effect of joint thickness and, therefore, the thickness of grout is negligible and will not influence on the overall behavior of the rock mass. Finally, the elasto-plastic material behavior of groutreinforced rock masses is investigated by considering uniaxial compression and uniaxial tension tests on the grout-reinforced rock masses. For this, tensile strengths, cohesions and friction angles of the intact rock, rock joint and grout in Table 1 are used in the conventional Mohr–Coulomb yield condition. When one set of joint is assumed to exist, the threshold value of the compressive stress with which plastic yielding of the constituent material occurs is illustrated in Fig. 3(a). In our case, the plastic yielding leads to the plastic failure by nature and, therefore, the threshold stress becomes the ultimate stress. Fig. 3 shows that, as the compressive

J.S. Lee et al. / International Journal of Rock Mechanics & Mining Sciences 37 (2000) 1027–1037

1031

sets of orthogonal joints are considered, similar failure modes can be foreseen, (Fig. 4(a) and (b)). From Figs. 2–4, it has been demonstrated that the proposed ubiquitous joint model can be effectively used to evaluate the reinforcement effect of the penetration grouting when one or two sets of joints exist. Also shown in the figures were the failure modes of the groutreinforced rock mass in terms of the threshold values. In the next section, field tests on the penetration grouting are explained and the results, together with the proposed analytical model, will be used to evaluate the joint characteristics before and after grout injection is performed.

4. Field measurements by seismic techniques In the following text, two seismic test procedures are introduced to obtain material properties of the unreinforced and reinforced in situ rock masses. These tests are theoreticaly similar to each other, although the crosshole test is sometimes considered to be more reliable for obtaining information at a specific location. All the tests have been performed twice, i.e., before and after the grouting was injected into the crown area of the tunnel.

Fig. 2. Change of equivalent strain with varying spacing: (a) one set of joints, (b) two sets of orthogonal joints.

stress starts to increase, the vertical grouting fails first and subsequently the intact rock fails. The penetration grouting finally fails when a favorable dip angle is encountered. However, when the dip angle is less than 308, the penetration grouting will not fail. It is noted that the numerical experiment under consideration is an idealized case and, once one of the constituent materials fails, the rock mass will not sustain further loading. Similar experiment using uniaxial tensile stress is shown in Fig. 3(b). Like in Fig. 3(a), when the dip angle is greater than 708, tensile failure will not occur in the penetration grouting although the vertical grouting and the intact rock fail subsequently. However, if the dip angle is less than 108, the intact rock fails after penetration grouting fails in a tensile mode. When two

Fig. 3. Ultimate uniaxial stresses in grouted rock masses: one set of joints: (a) compression test, (b) tension test.

1032

J.S. Lee et al. / International Journal of Rock Mechanics & Mining Sciences 37 (2000) 1027–1037

from the boring log as well as cores, where the average dip angle and joint spacing are set to 608and 0.1 m, respectively, and these values are confirmed by the additional two boreholes drilled during crosshole test. To evaluate the performance of LW grouting, two seismic measurement methods, namely the Crosshole [18] and SASW [19] tests were performed before and after the injection. As shown in Fig. 5, the crosshole test was performed using two boreholes having 4 m distance, and SASW test was undertaken at two measurement arrays, SA1 and SA2, which are 4 m apart and parallel to the axis of the tunnel. 4.2. Crosshole test

Fig. 4. Ultimate uniaxial stresses in grouted rock masses: two sets of joints (a) compression test, (b) tension test.

4.1. Field description and overview of measurements The case example tunnel under consideration is a part of the Korean high-speed rail route and located 23 km south of Seoul, South Korea. During site investigation, the field conditions were found to be unfavorable to the conventional tunneling method and it will be subjected to an excessive deformation during excavation. It was also found that the nearby abutment and piers of a highway bridge which cross the tunnel section should not be ignored during excavation. A pilot tunnel having a 3 m diameter was, therefore, chosen to excavate the tunnel center, and modified LW (Labile Wasser) grouting was next injected from the pilot tunnel so that the surrounding soil and jointed rock masses above the crown and shoulder area of the main tunnel could be stabilized. Right after the LW grouting was hardened, the main tunnel was advanced progressively. The crown area of the main tunnel is 26 m below the ground level, while the adjacent abutment and the nearest pier of the bridge are 12.5 and 21 m from the main tunnel, respectively. LW grouting was systematically injected so that the thickness of the grouting area above the final section of the main tunnel would be 5 m in a regular pattern. The geological profile of the tunnel section is composed downward of engineering fill, weathered soil, weathered rock and soft rock. A significant joint set is identified

The crosshole test requires careful installation of the boreholes. In this regard, two boreholes having an inner diameter of 75 mm were drilled vertically and an NXsized PVC casing was placed in each borehole. The borehole was about 26 m deep and it was carefully grouted to ensure tight contact between the PVC casing and the adjacent rock mass. The grouting material was made up of water, Portland cement and hardening accelerator with a mixing ratio of 1 : 1 : 0.15. The grouting material was injected again into the borehole when all the water was drained after one or two days. The purpose of the two-phase grouting was to acquire high-quality data by establishing a firm contact between PVC casing and adjacent rock masses. The shrinkage of the grouting material after curing was also prevented by adding an expansion agent into the grouting mixture. Fig. 6 illustrates the configuration of the crosshole test. Also shown in the figure is the stratification of the profile which was identified through the geologic logging in the boreholes. According to the boring log, the top 16 m was an engineering fill, the layer between 16 and 25 m was identified as the weathered soil (residual soil), and the layer below 25 m was found to be weathered rock.

Fig. 5. Location of field test (23 km south of Seoul).

J.S. Lee et al. / International Journal of Rock Mechanics & Mining Sciences 37 (2000) 1027–1037

Fig. 6. Cross-sectional area including boreholes.

The crosshole test, which complies to ASTM standards (ASTM D4428/D4428M), was performed using a mechanical source and a velocity transducer. The mechanical source used in the crosshole test has the capability of generating P- and S-waves. As shown in Fig. 7, the source is clamped to the PVC casing with the pneumatic pressure and wedging system, while the forced movement of the weight in the vertical direction generates SV waves polarized in the positive and the negative direction. The mechanical source also generates P-wave through the jaw in the wedging system. A 3-D receiver unit having three geophones embedded inside is used to capture the propagated P- and S-waves, two for the horizontal direction and one for the vertical direction. The crosshole testing was performed at the starting depth of 26 m and measured upward at 0.5 m intervals. At each depth, P- and S-wave measurements were made; in the case of P-wave measurement, the compression wave propagating in the direct ray path from the source was detected using a horizontal geophone aligned with the direct ray path. For S-wave measurement, the upand down-hits of the mechanical source were repeated to identify the S-wave arrival. This test is normally checked by visualizing the butterfly wing pattern in the time record. However, it has been noted that the PVC casing was slightly damaged during the grout injection and some of the test results were not retrievable from the measurement. 4.3. SASW measurements The Spectral-Analysis-of-Surface-Waves (SASW) method is an in situ seismic method to evaluate shear stiffness profiles of geotechnical, pavement and structural systems. The profile of the material being tested is typically presented in terms of a stack of horizontal layers and,

1033

Fig. 7. Crosshole test system.

the shear wave velocity as well as the thickness of each layer are determined from the analysis of field measurements (Fig. 8). The SASW measurement is performed by generating a stress wave on the surface. To generate the stress wave, a hand-held hammer, a heavy drop weight, a bulldozer or an electro-magnetic shaker is often required and, in our case, a hand-held hammer as well as a 70 kg drop weight were used as the impact source, while a hand compactor was used as the vibrating source. The propagated stress wave can be measured by a geophone or an accelerometer depending on the material tested. The waves are recorded at two locations where the positions of two receivers are such that the distance from the source to the first receiver should be the same as the distance between two receivers. In this study, the receiver spacings selected for the measurements are 0.5, 1.0, 2.0, 4.0, 8.0, 15.0 and 30.0 m since the shear stiffness profile down to 30 m level was required. 4.4. Results of field measurements In the case of the crosshole test, P- and S-wave velocities around the crown area have been measured. The shear moduli were next calculated from the determined S-wave velocities and Fig. 9 shows the change in the S-wave velocities before and after grouting. From the variations of the S-wave velocities before and after grouting, it can be concluded that S-wave velocity is increased up to 30 m/s which is equivalent to 11–14% increment in S-wave velocity. Although the shear wave velocity is slightly increased in the upper part of the grouted area (19 m deep), some regions in the grouted area do not show any significant velocity increment. This is partly because the PVC casing has been damaged during grout injection from the pilot tunnel and partly because the traffic vibration from the nearby highway has deteriorated the data

1034

J.S. Lee et al. / International Journal of Rock Mechanics & Mining Sciences 37 (2000) 1027–1037

Fig. 8. SASW test lines SA1 and SA2.

Fig. 9. Variation of S-wave velocity before and after grouting (Crosshole test).

Fig. 10. Variation of S-wave velocity before and after grouting (SASW test at SA1).

1035

J.S. Lee et al. / International Journal of Rock Mechanics & Mining Sciences 37 (2000) 1027–1037 Table 2 Variations of the shear moduli according to test methods Method

Depth (m)

Shear modulus before grouting (MPa)

Shear modulus after grouting (Mpa)

Increment (%)

Crosshole test

19 22 16 18

353 387 449 540

405 430 505 599

14 11 12 11

SASW test

quality. Therefore, the S-wave data after grouting are selectively chosen in Fig. 9 to avoid confusion. From the SASW measurement, the phase velocity dispersion curves have been obtained and, through the inversion analysis of the curves, the S-wave velocity profile can be plotted (Fig. 10). The resulting S-wave velocity profile is in good agreement with the stratification from the boring log. A little difference of the S-wave velocities between crosshole test and SASW measurements is unavoidable since the center of the SASW measurement array is about 20 m away from the crosshole location. Also, the deviation of two test results may not be negligible because the material properties of two locations are found to be different. From the general point of view, the crosshole test gives the local material properties at a specific point, while the SASW measurements provide the overall material properties of the area under consideration. The results of the SASW measurements show that S-wave velocities have been increased up to 40 m/sec throughout the depth from 14 to 30 m. The increment of the stiffness at the depth of 14 m indicates that the penetration of the grouting material could be further reached beyond the planned depth (19 m). In short, the overall increment of the shear moduli estimated by the SASW test is in the range 10–13%.

During the back analysis, the material properties of the in situ rock which is composed of intact rock and rock joints are calculated from the test results before grouting. Using these data, the reinforced stiffnesses of the grout-infiltrated rock joints are finally calculated from the constitutive relations introduced in this study.

5. Back analysis of reinforcement effect

5.2. Material properties of grouted rock joints

In this section, a back analysis of the reinforcement effect has been proposed by utilizing shear moduli obtained from the seismic tests. Table 2 shows the typical variation of the shear moduli below the ground level and, regardless of the test method, the ratios of increment are almost the same. However, when the measuring depth is beyond 20 m, the shear moduli using the SASW test are almost twice higher than those by the crosshole test. As explained before, the difference lies in the fact that the shear moduli deduced from SASW test are, by its nature, the averaged value of the measurement spacing; furthermore, the location of the crosshole test is 20 m away from the SASW test site. In this regard, the results of the crosshole test at 22 m depth are adopted and, from these, the material properties of the reinforced rock masses will be estimated.

So far, the material properties of the intact rock and the stiffness of the ungrouted joints have been estimated. The material properties of the grouted rock joint can also be estimated using a similar procedure. By introducing Eq. (18) again, the grout-reinforced joint stiffnesses can be inversely estimated from the values of field tests in Table 2. For this, the amount of injected grout is set to 20% of the representative elementary volume from the field data. Using the same approach used in the above, i.e., varying the stiffness values of the reinforced joint, the shear modulus of the reinforced rock masses can be calculated. This value is next compared with the field data on the shear modulus, 431 MPa, and finally the stiffness of the reinforced rock joint is found to be around 205 GPa/m. This means that the stiffness due to

5.1. Material properties of in situ rock In this section, parametric studies have been performed to estimate the material properties of in situ rock masses. For this, the constitutive relations introduced in Eqs. (16)–(20), as well as a trial and error method, are employed. Initially, the joint spacing and dip angle of the significant joint set are set to 0.1 m and 608, respectively, from the boring log information and the remaining joints are not taken into account due to lack of consistency. By changing the values of Young’s modulus and joint stiffness of the in situ rock, the estimated shear modulus before grouting, 387 MPa, is found to be almost the same as the tested value in Table 2, i.e., 388 MPa. The Young’s modulus of the intact rock and joint stiffness at this stage are 1150 MPa and 34.5 GPa/m, respectively, see Case 3 in Table 3 for the estimation procedure. The estimated joint stiffness is found to be the typical value of the siltstone [15] and the field condition confirms the assumption.

1036

J.S. Lee et al. / International Journal of Rock Mechanics & Mining Sciences 37 (2000) 1027–1037

Table 3 Cases of parametric studies before grouting Case

Young’s modulus (intact) (MPa)

Shear modulus (intact) (MPa)

Normal stiffness of joint (MPa/m)

Estimated shear modulus ( jointed) (MPa)

1

1100 1150 1200 1100 1150 1200 1100 1150 1200

423 442 462 423 442 462 423 442 462

345 345 345 3450 3450 3450 34 500 34 500 34 500

232 243 253 271 282 292 372 387 402

2

3

penetration grouting is almost six times higher than the original value. It is noted here that the injected grouting material is assumed to be completely penetrated into the fully persistent joints.

6. Model assumptions and field conditions So far, both analytical and experimental studies on the penetration cement grouting injected into the jointed rock masses have been performed. Rather than estimation of the viscous flow of the cement grouting, the emphasis in our studies was placed on the reinforcement effect due to penetration grouting and on the stiffness changes of the grout-reinforced rock joints by considering a tunnel structure under construction. The proposed model is based on the idea of ubiquitous joint concept in which rock joints are grouped into sets according to their mean length and mean orientation. Therefore, if the distribution of the rock joints follows a complete spatial randomness in a stochastic geometry terminology [12], the reinforcement effect of the penetration grouting will be difficult to estimate. However, the proposed model does not have any limitation on the intersection angle between joint sets. In practice, the major joint sets having nonnegligible joint thickness can be identified with the boring logs and accompanying cores, and the proposed model can, therefore, be applied to the design process of the ground improvement without significant bias. The other assumption made in the formulation was the full persistency of the joint sets. In this case, if the joint sets are not persistent and if the injection pressure is rather high, a possible fracturing mode at the tip of the joint is expected and a different mechanism has to be considered. Although a concept of the fracturing grouting can be incorporated in the proposed model, e.g. [20], the distribution of the non-persistent joints within rock masses is hard to obtain and, therefore, the realistic calculation of the reinforcement effect due to fracturing grouting is a big challenge in the injection process.

The proposed model can be employed in the stability analysis of a tunnel reinforced with the penetration grouting. Currently, the anisotropic material properties of the jointed rock masses reinforced with cement grouting can be plugged into the commercial software and the elastic analysis of the tunnel excavations is possible. However, the elasto–plastic analysis of the grout-reinforced tunnel requires the updated cohesion and friction angle of the joint sets. An artificial joint filled with cement grouting can be used in the laboratory experiment, more elaborate testing device will be necessary to obtain information on the improved values of the parameters above. Finally, the elasto–plastic analysis of grout-reinforced rock masses can be performed based on the mechanics of composite material. In this case, an anisotropic yield function introduced in Ref. [21] or a classical yield function for each constituent material together with a sub-iteration scheme [13] can be considered.

7. Conclusions The effect of penetration cement grouting which is often used to reinforce highly jointed rock masses is quantitatively analyzed in this study. To derive the anisotropic material properties of the grout-reinforcement, a mixture rule together with a ubiquitous joint model has been successively applied to the jointed rock masses, and the velocity discontinuity is also employed to model the penetration grouting. From the analyses of the model structure, the following conclusions are made: *

*

The anisotropic material properties of the groutreinforced rock masses are functions of the material properties of the intact rock and the grout. These are also related to the geometric and mechanical characteristics of the rock joints, such as spacing, dip angle and stiffnesses. As the uniaxial stress is applied, the vertical grouting fails first and intact rock and penetration grouting fail subsequently.

J.S. Lee et al. / International Journal of Rock Mechanics & Mining Sciences 37 (2000) 1027–1037 *

*

Crosshole and SASW tests were performed near a tunnel structure in Korea involving LW grouting on top of the crown area. The shear wave velocity of the reinforced area was found to have increased by upto 11–14%. Using the shear modulus values obtained in the field test, the material properties of the in situ rock and reinforced rock joint have been inversely calculated. It is found that the stiffness of the rock joint is increased by upto six times when the grouting material is fully penetrated into the joints.

So far, penetration grouting with relatively low injection pressure has been considered. However, when high injection pressure is applied, a possible fracturing mode of the intact rock or rock joint is unavoidable and grouting through newly fractured rock joints is expected. Future work will, therefore, be focused on fracturing and grouting and its reinforcement effect on rock masses. Also, reinforcement of in situ rock is not limited to the increment of the joint stiffness; rather, the strength in terms of the friction angle and cohesion of the rock joint could be more important factors as far as tunnel stability is concerned. The material characteristics such as friction angle and cohesion need to be further investigated and additional experimental work will be necessary.

[6]

[7]

[8] [9] [10]

[11]

[12]

[13]

[14] [15]

[16]

References

[17] [18]

[1] Ha¨ssler L, Ha˚kansson U, Stille H. Computer-simulated flow of grouts in jointed rock. Tunnelling Under Space Tech 1992;7:441–6. [2] Gustafson G, Stille H. Prediction of groutability from grout properties and hydrological data. Tunnelling Under Space Tech 1996;11:325–32. [3] Hausmann MR. Engineering principles of ground modification. New York: McGraw-Hill, 1990. [4] Lombardi G, The role of cohesion in cement grouting of rock. In Commision Int des Grands Barrages, Lousanne, 1985. Q.58R.13. [5] Kikuchi K, Mito Y, Adachi T. Case study on the mechanical improvement of rock masses by grouting. In: Yoshinaka R,

[19]

[20]

[21]

1037

Kikuchi K, editors. Proceedings of the International Workshop on Rock Foundation, 1995. p. 393–7. Nicholson DP, Gammage C, Chapman T. The use of finite element methods to model compensation grouting. In: Bell AL, editor. Proceedings of Grouting in the Ground, 1992. p. 297–312. Schmertmann JH, Henry JF. A design theory for compaction grouting. In: Borden RH, Holtz RD, Juran I, editors. Proceedings of Grouting, Soil Improvement and Geosynthetics. New York: ASCE, 1992. p. 215–28. Hill R. Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 1963;11:357–72. Gerrard C. Reinforced soil: an orthorhombic material. J Geotech Eng, ASCE, 1982;108:1460–74. Vardoulakis I, Sulem J, Gurnot A. Borehole instabilities as bifurcation phenomena. Int J Rock Mech Min Sci Geomech Abstr 1988;25:159–70. Einstein HH, Baecher GB. Probabilistic and statistical methods in engineering geology. Part I: exploration. Rock Mech Rock Eng 1983;16:39–72. Lee JS, Veneziano D, Einstein HH. Hierarchical fracture trace model. In: Hustrulid WA, Johnson GA, editors. Proceedings of the 31st US Rock Mechanics Symposium, 1990. p. 261–8. Lee JS, Pande GN. Analysis of stone-column reinforced foundations. Int J Numer Anal Methods Geomech 1998;22: 1001–20. Pietruszczak S, Niu X. On the description of localized deformation. Int J Numer Anal Methods Geomech 1993;17:791–805. Bandis SC, Lumsden AC, Barton NR. Fundamentals of rock joint deformation. Int J Rock Mech Min Sci Geomech Abstr 1983;20:249–68. Franklin JA, Dusseault MB. Rock engineering. New York: McGraw-Hill, 1989. Widmann R. ISRM: commission on rock grouting. Int J Rock Mech Min Sci 1996;33:803–47. Mok YJ, Paik YS, Im SB, Quality assessment of grouting by using seismic testing. Proceedings of the KGS 98 National Conference, Seoul, Korea, 1998. p. 85–92. Joh SH, Advances in data interpretation technique for spectralanalysis-of-surface-waves (SASW) measurements. PhD thesis, Department of Civil Engineering, University of Texas at Austin, USA, 1996. Lee JS, Bang CS, Choi IY. Analysis of borehole instability due to grouting pressure. In: Amadei B. et al., editors. Proceedings of the 37th US Rock Mechanics Symposium, 1999. p. 217–23. Krieg RD, Brown KH. Anisotropic plasticity with anisotropic hardening and rate dependence. J Eng Mech ASCE 1996;122: 316–24.