Download - The influence of near face behaviour on monitoring of deep tunnels

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The influence of near face behaviour on monitoring of deep. tunnels

D'Appolonia Consulting Engineers, S.p.A., Genoa, Italy

P . K. KAISER Geomechanics Research Centre, Laurentian University, Sudbury, Ont., Canada P3E 2C6

AND N. R. MORGENSTERN

Department of Civil Engineering, University of Alberta, Edmonton, Alta., Canada T6G 2G7

Received August 8, 1990

Accepted December 27, 1990

Convergence, radial displacements, and stress changes are often recorded during the advance of a tunnel for the observational tunnel design approach. In deep tunnels, instruments must be installed from underground and can seldom be placed in undisturbed ground. Consequently, observations are only partial records of the total change induced by an excavation and the influence of the three-dimensional state near the face must be considered. This paper presents results from numerical simulations to assess face effects on monitoring data. The influence of such aspects as in situ state of stress, anisotropy, nonlinearity, and plasticity (yielding ground) are evaluated. Guidelines for underground monitoring of deformations are given.

Key words: tunnelling, monitoring, back-analysis, convergence, extensometers, numerical modelling.

La convergence, les dkplacements radiaux et les changements de contrainte sont souvent mesuris en cours d'avance- ment d'un tunnel pour l'approche (< observationnelle )) dans la construction d'un tunnel. Dans les tunnels profonds, les instruments doivent Ctre installis a partir du tunnel et peuvent rarement Ctre placCs dans le sol intact. En consC- quence, les observations ne constituent que des dossiers partiels du changement total induit par l'excavation, et l'influence de 1'Ctat tridimensionnel prks de la surface doit Ctre prise en considkration. Cet article prCsente les risultats de simulations numiriques pour Cvaluer les effets de surface sur les mesures. L'influence de certains points tels que 1'Ctat des contraintes in situ, l'anisotropie, la non-linCaritC et la plasticit6 (sol en Ccoulement) sont CvaluCs. Des rkgles pour la mesure des dCformations souterraines sont donnCes.

Mots elks : percement de tunnel, mesure, analyse a rebours, convergence, extensomktre, modClisation numCrique. [Traduit par la ridaction]

Can. Geotech. J . 28, 226-238 (1991)

1. Introduction Since Rabcewicz (1964) introduced the New Austrian

Tunnelling Method (NATM), monitoring of strains, displacements, and stresses to assess the adequacy of the design and the performance of tunnels during construction has become an integral part of the modern observational design approach. In particular, displacement measurements are frequently obtained during the excavation process and used to assess the stability of tunnels.

Monitoring programs are commonly designed for two purposes: (i) to assess tunnel safety, often by empirical approaches, or (ii) to back-analyse the ground properties and the in situ stress field for on-going design improvements (this is particularly valuable where there is some flexibility in underground operations such as in the final design of an underground power house, large tunnelling, or on-going mining operations).

The empirical stability assessment is based on a comparison of field observations with predictions from analysis or experience (Bieniawski 1984). For example, (i) the magnitude of the observed displacements is compared with those predicted for elastic ground response or with measurements taken previously in stable sections, (ii) closure rates are related to empirical values, or (iii) observed movements are compared with critical displacements or strains that would cause failure of the tunnel support or the surrounding rock. Printed in Canada / Imprime au Canada

Recently, many efforts have been directed towards devel- oping methods to back-analyze ground properties and the in situ stress state from monitoring data. Gioda and Maier (1980) back-analyzed cohesion, angle of internal friction, and in situ stresses by numerical interpretation of measurements taken during a tunnel pressurization test. The rock parameters were calculated by applying a "direct search method" for function determination. Sakurai and Takeuchi (1983) developed a finite element program for the back- analysis of elastic properties and in situ stresses based on the "inverse approach" (see also Cividini et a1 198 1; Gioda 1985). Kaiser and Zou (1990) and Kaiser et al. (1990) have successfully used stress changes to back-analyze in situ stress parameters. Even though much interest has been directed toward the interpretation of monitoring data for back- analysis purposes, little effort has been spent on investigating how the near face behaviour may affect such interpretation. This would add further insight into the back-analysis process.

A truly three-dimensional approach to study the near face behaviour for monitoring data interpretation is needed for the following reasons: (i) a better understanding of the three- dimensional conditions near the face is important for the interpretation of monitoring data because only a portion of the total displacement is actually measured in the field; (ii) displacements, particularly the progressive development

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TABLE 1. Summary and comparison with previous studies k

Constitutive relationship Support

Linear Linear condition Type of elastic elastic Excavation

Source analysis isotropic anisotropic Hyperbolic Elastoplastic Flow rule Unlined Lined modelling

de la Cruz and Goodman (1969)

Coates and Yu (1970)

Desai and Reese (1970)

Yes No - Yes

Yes

Yes

Yes No -

Yes Associated Yes No External loading

Daemen and Fairhurst (1972) Yes Variable -

elastic parameters

Yes No External loading

Descoeudres (1974) Yes Yes Associated Yes No External

loading Ranken and

Ghaboussi (1975) Hocking (1 976) Niwa et al. (1979) Schwartz and

Einstein (1980) Kaiser and

Hutchinson (1982) Panet and Guenot

(1982)

Yes Yes Yes

Yes Associated No - No -

Yev Yes Incremental Yes No - yes No -

Yes Yes Associated No Yes Incremental

Yes No Yes Incremental

Yes Associated (4 = 0°)

Yes Nonassociated

Yes Yes No External loading

Yes Yes Incremental Yes Yes This study Yes

NOTE: AXI, axisyrnmetric analysis.

of deformations associated with face advance, can reveal important properties of the rock mass medium; (iii) for lined tunnels, the effects of ground-support interaction must be modelled properly and considered for monitoring data interpretation; and ( iv) in nonlinear and nonelastic ground, the response of an opening is stress path dependent and hence an appropriate three-dimensional model of the step- by-step excavation sequence must be employed in the data interpretation process.

In this paper the results of a parametric study, based on a series of three-dimensional finite element analyses, are presented. Advancing tunnels with or without support in linear elastic isotropic, linear elastic anisotropic, and nonlinear, nonelastic media were simulated.

The purpose of this paper is to establish a series of guidelines to be used for the design of monitoring programs and to define how an advancing tunnel should be instrumented to maximize the value of information gained by the measurements. Emphasis is placed on those features that can reveal the deformation and strength properties of the geologic medium, as well as the virgin stress state in the ground. Con- vergence and radial displacement measurements taken by means of tape extensometers and multipoint radial extensometers are discussed. These monitoring techniques have been selected because they are simple, reliable, and are used most commonly in modern tunnelling.

icant parametric studies by means of truly three-dimensional as well as axisymmetric numerical models are compared in Table 1 with the work presented here. Only analyses of deep tunnels have been included in this table, but it is worth men- tioning that valuable three-dimensional modelling of shallow tunnels has been carried out by other authors (Gartung et ai. 1979; Wittke and Gel1 1980; Katzenbach and Breth 1981; Kasali and Clough 1983; Heinz 1984). Ghaboussi and Gioda (1977) and Hanafy and Emery (1980, 1982) investigated the effects of time-dependent ground properties on advancing tunnels by means of axisymmetric finite element analyses.

Niwa et al. (1979) conducted a series of three-dimensional numerical analyses by means of the boundary integral method to investigate stresses and displacements near the face of deep, unlined tunnels in linear elastic, isotropic ground. The assumption of linear elastic ground behaviour, although sometimes adequate and useful for comparison purposes, is often insufficient to model the behaviour of geologic media. To overcome this, nonlinear analyses were undertaken in this study and are compared with other recent investigations in Table 1. A truly three-dimensional approach (i.e., KO # I), as opposed to axisymmetry in most previous works, was adopted. Nonassociated flow plasticity was chosen to properly simulate the deformation behaviour of frictional materials and an incremental excavation sequence was introduced where required. The nonlinear behaviour of the ground in the prefailure regime was also investigated by an hyperbolic constitutive relationship.

An extensive study of ground-linear interaction was conducted by Schwartz and Einstein (1980) using an axisym-

2. Relation to previous studies Several researchers have conducted three-dimensional

simulations of tunnels. Some of the most recent and signif-

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CAN. GEOTECH. .I. VOL. 28, 1991 i

, ,

Case A1

- - - - - - - - - - , \

RL . . . Excavation round length DEL. . . Span length before excavation

RL+DEL. . . Span length after excavation

,Extent of tunnel before excavation (m ~nstallation of unstressed liner segment m)

+\\\\\\\\\\- Extent of tunnel after excavation A

elements. Twenty node solid elements were placed near the wall and in front of the tunnel face where high strain gra- dients were expected. Eight nodeaelements were used to model the ground far from the tunnel face. A flat tunnel

Case A3 face was incorporated into the model, and this clearly affects the predicted response in the immediate vicinity of the tunnel face.

FIG. 1. Orientation of the elastic properties to the tunnel for The relatively thin liner was modelled by means of three-

the a,lisotropic ground models (E,,E, = v, = 0.25 and dimensional isopararnetric shell elements, described by Bathe v , = 0.025). and Bolourchi (1980). The lined tunnel was subjected to pre-

liminary testing under two-dimensional plane strain condi-

metric finite element model of ground and support. Pelli et al. (1986) extended this investigation on truly three- dimensional conditions and included the influence of the excavation round length in their study. The dependence of convergence and radial extensometer records on the tunnel liner interaction, for tunnels in linear elastic ground, are discussed later.

This study presents a systematic investigation of the geometric effects near the face, the ground properties, the in situ stresses, and the support conditions on field measurements collected during tunnel excavation.

3. Description of finite element model and cases analyzed

The computer program ADINA was used for simulating unsupported and supported tunnels in isotropic and anisotropic linear elastic media (Bathe 1977). The nonlinear analyses were conducted by means of the program SAGE^^ (Chan 1986).

The finite element mesh chosen for the model represents one-quarter of the tunnel. This simplification was possible because both tunnel geometry and initial stress field were assumed to be symmetric with respect to horizontal and vertical axial planes. The initial stress field was assumed to be constant throughout and gravity was neglected. This assumption is reasonable for deep tunnels where the stress variation with depth is usually not significant relative to the magnitude of the average stress.

To obtain a reasonably accurate strain field around the tunnel, a large mesh, 8 tunnel diameters wide and 10 diameters long, was designed. The mesh was defined by 3145 nodal points and 988 three-dimensional, isoparametric solid

tions and the results obtained were found to be in good agreement with the closed form solution given by Einstein and Schwartz (1979).

Excavation was modelled by eliminating the "excavated" elements from the stiffness matrix and the stresses in the excavated zones were reset to zero. This generates a non- equilibrated condition at the boundary of the opening and influences the stresses in the surrounding medium. The stress adjustment was performed in a single step for the unlined tunnels in linear elastic ground. For all other cases, an incremental procedure was adopted.

3.1 Unsupported tunnels in linear elastic, isotropic ground For the unsupported tunnels in a linear elastic isotropic

medium, a Poisson's ratio of v = 0.25 was selected. The results presented in this paper are normalized with respect to the Young's modulus, E, the tunnel radius, a, and the initial vertical stress, p,. The two cases were analyzed for two different initial stress conditions:

pv # 0; ph = pa = 0 and pa # 0; p, = ph = 0 where p,, ph, and pa are the vertical, horizontal (perpendicular to tunnel axis), and axial (parallel to tunnel axis) initial stresses, respectively. The results obtained by these analyses were superimposed to determine values for selec- tively chosen initial stress distributions. For all other situations presented in the following, a stress ratio of KO = ph/pv =pa/pv = 2 was selected.

3.2 Unsupported tunnels in linear elastic, anisotropic media In layered or stratified materials, perfect symmetry of

behaviour about any axis perpendicular to the planes of stratification was assumed. Hence, the medium is trans- versely isotropic and can be characterized by four mutually

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1 229

T u n n e l Face

I I I I I I I I I

- 4 - 3 - 2 - 1 0 1 2 3 4 5 6

x / 2 a

FIG. 3. Effect of axial stress p, on tunnel wall convergence at the crown (KO = 2).

independent parameters: E l , E2, Gl , and v2, such that

An empirical relationship was adopted for G1 (Zienkiewicz 1968):

Tunnels excavated in three transverse isotropic rock con- figurations were modelled as shown in Fig. 1 (cases A1-A3). A constant modulus ratio of E2/E1 = 10, realistic for metamorphic foliated rocks (Gerrard 1977), was selected. E2 is the elastic modulus for any direction parallel to the strata. Poisson's ratios of v2 = 0.25 and v l = 0.025 were assumed.

The results are normalized with respect to the average

Young's modulus (E,, = E&2), the tunnel radius a , 2

and the vertical stress p,.

3.3 Unsupported tunnels in nonlinear and nonelastic media The effects of nonlinear ground behaviour on the pre-

failure range was investigated by assuming a hyperbolic stress-strain relationship (Konder 1963; Duncan and Chang 1970). It is defined by an initial modulus Ei and by the ultimate stress difference (al - CJ~),~,. Both vary depending on the minor principal stress a3. In this study Ei was kept constant. This is a reasonable assumption if the ultimate stress difference of the rock can be varied according to the Mohr-Coulomb failure criterion. An initial modulus of Ei = p, x lo3, a Poisson's ratio of v = 0.25, a cohesion of c = 1.7 p,, and a friction angle of d, = 30" were chosen. The unloading-reloading modulus E,, was selected to be equal to Ei.

For the studies of tunnels in yielding rock, a constitutive relationship based on ideal, nonassociated flow plasticity was adopted. In the prefailure region the model is defined by

the Young's modulus of E = p, x .lo3 and Poisson's ratio of Y = 0.25. At failure, the model is characterized by the Mohr-Coulomb failure criterion (c = 0.6 p,, d, = 30") and by zero dilation ($ = 0).

The parameters listed in the preceding section were not picked arbitrarily. They are particularly meaningful for the case study presented in a companion paper (Pelli et al. 1990).

3.4 Lined tunnels in linear elastic, isotropic media The effects of the relative stiffness between the ground

and tunnel liner, the delay of support installation, and the excavation round length on the wall convergence and radial extensometer records were investigated for tunnels in linear elastic, isotropic rock. The relative stiffness can be quan- tified by the compressibility (C) and flexibility (F) ratios (Einstein and Schwartz 1979):

where E, v, E,, and v, are the elastic parameters for the rock mass and the support, A, is the cross-sectional area, and I, is the moment of inertia of,the support per unit length of tunnel. C i s a measure of the relative diametrical stiffness of the support under axisyrgimetric loading, whereas F is a measure of the relative diametrical stiffness under antisymmetric load conditions.

In Fig. 2, the definitions of support delay (DEL) and excavation round length (RL) are presented. The delay is the distance between the leading edge of the liner and the tunnel face immediately after the installation of an unstressed liner segment (1) and immediately before excavation (note: some authors use a different definition). The length of the tunnel section excavated at each step (equal to the length of one liner segment) is called the excavation round length.

4. Near face effects on convergence measurements Convergence measurements are often recorded immedi-

ately behind the tunnel face (note: convergence means radial displacement of the tunnel wall; one side only). The initial stress distribution, the ground properties, and the near face tunnel behaviour affect these measurements as discussed in the following sections. Emphasis is placed on those aspects that have been revealed to be dominated by the three dimen- sionality of the model adopted for this study.

4.1 Effects of virgin stress field Usually, only partial displacements are recorded in the

field because of inaccessibility of the rock ahead of deep tunnels. Panet and Guenot (1982) suggested that for KO = 1 and linear elastic rock (Poisson's ratio = 0.4), the measured convergence values should be increased by 27% to obtain the total radial displacement (including the deformation ahead of the face). This rule is not generally applicable for conditions with KO # 1. For KO = 2, for instance, the recommended 27% increase provides a reasonably accurate result of the tunnel springline (side wall) but is completely inappropriate for the tunnel crown or roof (Fig. 3, for pa 2 p,) where some outward (positive) movement, rather than closure, takes place right at the tunnel face.

Since displacements at the crown are very small when compared with the relatively large movements at the springline, KO values back-calculated using the 27% rule and the ratio of radial displacements at the crown and springline

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FIG. 4. Effect of axial stress pa on partial tunnel wall convergence measurements at crown (KO = 2; initial reading at tunnel face (x/2a), = 0; total two-dimensional normalized partial wall displacement = - 0.54).

would lead to an error not exceeding 15%. Therefore, if the rock mass can be assumed to behave as an isotropic, linear elastic medium, the ratio of the convergence measurements obtained at the crown and springline can lead to a good estimate of KO. Furthermore, for those cases where a reasonable assumption for p, can be made based on the depth of overburden, the value of ph can also be estimated.

Another important aspect affecting convergence measurements, neglected by conventional two-dimensional approaches, is the magnitude of the axial initial stress pa. The influence of the axial stress on the shape of the radial displacement curves at the tunnel crown wall is shown in Fig. 3 for KO = 2 (i.e., ph/pv = 2 = constant andp, varied independently). Although the total radial movement is not affected by pa, the relative displacement between the tunnel face and a point far behind it changes substantially as the axial stress is increased. By increasing pa, an increase in inward movement (negative) is obtained ahead of the tunnel, whereas minor closure or outward movement is observed at the flat face. This has a significant influence on the interpretation of field data because the convergence profile ahead of the tunnel face is unknown. In Fig. 4, partial wall displacement curves, as recorded immediately behind the tunnel face, are shown for different axial stress values. These curves would be recorded if measurements were started exactly at the tunnel face and show that, for relatively high pa values, the monitored displacement may actually become larger than the total radial closure as predicted by two-dimensional analyses.

The effect of pa on the total convergence is much less pronounced at the tunnel springline. Furthermore, the partial convergence profiles near the tunnel face and at the springline are virtually unaffected by pa as can be observed from Fig. 5. This consideration is very important, as the shape of these curves near the tunnel face contain information for the back-analysis of the modulus of the ground. In particular, the shape of the radial displacement curve in

Frc. 5. Effect of axial stress paion partial tunnel wall convergence measurements at springline (KO = 2; initial reading at tunnel face (x/2a), = 0; total two-dimensional normalized partial wall displacement = - 3.0).

the proximity of the tunqel face can be used to define the elastic modulus of the rock mass. For this purpose, the measured convergence profile can be fitted with three- dimensional numerical results obtained assuming a linear elastic rock mass behaviour and a reasonable value for the Poisson's ratio.

Several practical implications evolve from these observations.

(i) The convergence measurements are significantly affected by the initial stress distribution, in particular by the magnitude of the initial axial stress. This parameter must be considered during data interpretation.

(ii) A good estimate of the initial stress field may be obtained based on convergence measurements if the rock mass can be assumed to behave in an isotropic, linear elastic manner.

(iii) The shape of the convergence profiles as well as the convergence magnitude in the direction of the maximum principal stress (at the tunnel springline for KO > 1) display low sensitivity to the magnitude of the axial stress. There- fore, if pa is not known with sufficient accuracy, these measurements should be selected for the back-analysis of the rock mass deformation properties.

4.2 Effects of zero reading delay So far, it has been assumed that the initial convergence

measurements are taken at the tunnel face. This is physically impossible and the zero readings are, in reality, recorded at some distance behind the face. This delay affects the magnitude of the monitored partial displacements. It is also strongly dependent on the Poisson's ratio of the rock immediately ahead of the tunnel face.

A set of partial wall displacement curves is plotted in Fig. 6 for the springline and for KO = 2. Each curve represents measurements relative to a different zero reading location, ( ~ / 2 a ) ~ , from 0 to 0.75. For instance, for the solid curve the zero reading was taken at the tunnel face,

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FIG. 6. Effect of zero-reading location (x/2a), on partial tunnel convergence measurements at springline (KO = 2).

FIG. 7. Effect of axial stress pa on partial tunnel convergence measurements at crown (KO = 2; delayed initial reading at (x/2a), = 0.25).

( ~ / 2 a ) ~ = 0, and for the dashed line the zero reading was taken one-half radius behind the face, ( ~ / 2 a ) ~ = 0.25. Near the tunnel face, where the displacement gradient is very high, small delays in installing convergence points cause drastic reductions in the measured radial displacements. If this delay is not considered accurately during the data interpretation process, an under- or over-estimate of the in situ stresses and an over- or under-estimation of the rock deformability will be obtained.

The sensitivity of the convergence profiles to the magnitude of pa (discussed in the previous section) becomes more dominant if the delay in the zero reading is increased. This is demonstrated by Fig. 7 where the convergence at the tunnel crown for different pa values is shown for a one-half radius reading delay (compare with Fig. 4).

For anisotropic rock masses, the effect of the zero reading delay also depends on the orientation of the elastic properties of the medium with respect to the tunnel axis. In Fig. 8, total convergence curves at the tunnel springline are shown in normalized form for four cases. The convergence profile for a tunnel in linear elastic, isotropic ground is compared with the three cases A1-A3 (anisotropic ground; see Fig. 1).

FIG. 8. Normalized tunnel wall displacement, u,/u,,,,, at the springline (KO = 2; cases A1-A3 (Fig. b) and isotropic, elastic case).

If the zero readings were taken one-half radius behind the tunnel face, marked by a vertical line in this figure, only portions of the conv,ergence "behind the face would be measured. For cases A1 and A2 with flatter convergence curves than for the isotropic case, 51 and 43% of the displacements would be measured. On the other hand, only 21% of the total displacement would be recorded for case A3, owing to the very high convergence gradient near the face associated with the low shear stiffness on the axial planes (containing the tunnel axis).

In summary, the following observations are important for a monitoring program.

(i) The zero readings should be taken at the tunnel face or the amount of delay must be defined accurately. If blast damage is induced at the tunnel face, its extent must be evaluated and considered.

(ii) The sensitivity of the convergence measurements to delay varies considerably depending on the orientation of the rock strata or the elastic parameters of the rock mass.

4.3 Other effects of rock mass anisotropy For tunnels in linear elastic, isotropic media, the stress

ratio KO can be calculated by measuring convergences at the crown and at the springline. However, if the rock mass is anisotropic, the assumption of isotropy may lead to substan- tial errors in the back-calculated KO value. For case A1 (KO = 2, see Fig. l), a convergence ratio of u ~ ( ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ) / u ~ ~ , , , , ~ ~ = 0.75 is faund that would lead to a predicted KO = 0.87 (instead of 2) if a two-dimensional closed form solution based on isotropic elasticity were used. For case A2, a relatively large inward displacement takes place at the springline, whereas the tunnel crown moves outward. A displacement ratio of 8.45 is found and, hence, a KO = 4.5 would be calculated. If the total displacements were considered, including convergence ahead of the tunnel face, an even more erroneous KO value would be predicted.

The magnitude of the rock mass stiffness in the direction of the tunnel axis affects the shape of the convergence pro-

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C a s e A 3 I

FIG. 9. Radial wall displacement at the crown and springline for case A3 (KO = 2).

files in a similar manner as pa. The convergence profiles at crown and springline are shown in Fig. 9 for case A3 where the low stiffness direction is parallel to the axis of the tunnel. Some outward movement takes place at the tunnel face, especially at the crown. An analogy with tunnels in isotropic rock, excavated under high axial stresses, is apparent by comparison with the results presented in Fig. 3.

These observations lead to the conclusion that either the initial stress distribution or the degree of anisotropy of the rock mass must be known before the convergence data can be interpreted with confidence. The initial stress ratio and the elastic parameter ratio produce very similar effects on the wall displacements.

4.4 Effects of nonlinear ground behaviour The increase of rock mass deformability associated with

confinement reduction near the tunnel wall, as well as yielding, increases the amount of closure detected during face advance and changes the shape of the convergence curves. The normalized convergence at the tunnel springline is plotted in Fig. 10a for the linear elastic, the hyperbolic, and the elastoplastic rock model. Yielding causes significant convergence differences, with respect to the linear elastic case, only behind the tunnel face where the strength of the rock mass is exceeded. The increase in convergence owing to yielding is much more pronounced at the tunnel crown (Fig. lob) because of the high concentration of deviatoric stress at this location. For these reasons KO values back- analyzed by adopting the procedure mentioned in section 4.1 (i.e., assuming linear elastic rock behaviour) will lead to less extreme values (closer to unity) than in reality. Therefore, for rock masses exhibiting nonlinearity, a direct back- analysis of the stress ratio KO, independent of rock properties, is not possible.

The shape of the near face portion of the convergence profile can reveal the elastic modulus of the rock mass even for nonlinear elastic and moderately yielding rocks. In Fig. 11, three partial convergence curves for tunnels in linear elastic, hyperbolic, and elastoplastic rock are plotted. It can be

FIG. 10. Wall displacements for linear-elastic, hyperbolic, and elastoplastic rock (KO = 2): ( a ) at springline and (b) at crown.

observed that the curves are virtually identical up to about (x/2a) = 0.1 behind the tunnel face (point A in Fig. 11) and very similar up to (x/2a) = 0.25 behind the face (point B). For these three cases, the ratios E/a p, (read Ei in place of E for the hyperbolic case) are identical and major differences of the convergence profiles only occur relatively far behind the excavation front, where high deviatoric stresses develop. The initial part of the convergence curves at the tunnel springline is almost unaffected by moderate nonlinearity and reflects the elastic properties of the rock mass.

It follows from these observations that (i) for KO > 1, convergence at the tunnel crown is more sensitive to material nonlinearity than at the springline, because of the high stress concentration occurring at the crown and (ii) even for those cases where moderately nonlinear behaviour is exhibited by the rock mass, the shape of the initial part of the radial displacement curves can reveal the magnitude of the elastic

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L inear Elast ic

'\ \--- &-

6 relative stiffnesses: (1) C = 1.41 and F = 24387; (2) C = 4.7 and x / 2 a F = 9032; (3) F = 14.10 and F = 243875 (after Pelli et al. 1986;

Frc. 11. Partial wall displacement at the springline for linear- = 2; = 0.25; DEL = O; RL = 2a).

elastic, hyperbolic (Ei = E,,; c = 1.7 p,; C$ = 30°), and elastoplastic rock ( c = 0 . 6 ~ " ; 4 = 30°, $ = 0°, i.e., no volume 4

change at failure) (KO = 2; initial reading at tunnel face 3

( X / U ) ~ = 0). ... C w g Tunnel Face

modulus of the rock independently of the ultimate rock mass - I

response. Therefore, the same fitting procedure as outlined 6 6 0 0 in section 4.1 can be applied for back-analysis purposes. On 5 , u

the other hand, a direct back-analysis of KO, independent g , -, of rock properties, is not possible for rock masses exhibiting ; 2 nonlinear behaviour. N - - 2 .- - z 4.5 Effect of support ;j -3

The presence of a support also influences the convergence -4

measurements collected during face advance and must be considered for monitoring data interpretation. - 5

The effect of the relative support stiffness on the con- -4 -3 -2 - I o I 2 3 4 5

vergence curve is illustrated by Fig. 12 for three different x 120

a fixed (DEL = O ) and FIG, 13. Convergence curves for three cases with variable round length (RL = 2a), the relative stiffness ratios C and delays and round lengths: DEL = 0, R~ = 2a, as in Fig. 12; F (Einstein and Schwartz 1979) were varied as depicted in (4) DEL = 0, RL = la; ( 5 ) DEL = la, RL = la (after Pelli et al. the figure caption. Decreasing the compressibility ratio C 1986; K, = 2; = 0.25; c = 1.41 and F = 24387). reduces the final convergence. The flexibility ratio F does not display any significant effect. Even though the liner is placed immediately behind the excavation face, the convergence up to about one radius behind the tunnel face is (ii) A thin concrete liner (liner thickness up to 5% of tun- not altered by the support. nel radius and concrete modulus 15 times higher than for

Figure 13 demonstrates for a liner with constant relative the rock) does not affect the convergence curve immediately stiffness the dependence of the convergence profiles on the behind the tunnel face and, therefore, field observations can delay and excavation round length. Reducing the delay and be used for the back-analysis of the ground properties round length causes the final convergence to decrease. The without considering support interaction. convergence rate is not affected much by the action of the (iii) In tunnels with heavy temporary support, even the liner in the proximity of the tunnel face. The stress transfer initial portion of the convergence profile may be affected mechanism that characterizes the shape of the convergence by the liner. In this case, three-dimensional numerical anal- curves in lined tunnels is discussed in more detail by Pelli ysis would have to be carried out to establish the effect of et al. (1986), but the following important observations are the liner-rock interaction mechanism on the convergence reinforced by these figures. curves and to assist the back-analysis process. However, it

(i) The action of the liner causes a decrease in convergence must be pointed out that heavy, stiff liners are seldom depending on the relative stiffness of the support, the magni- applied close to the tunnel face because the modern tunnel- tude of the delay of liner activation and the excavation round ling philosophy relies on the self-supporting ability of the length. rock mass.

-2.5 - v ' a, N .- - -3.0 - 0 E I

0 -3.5 - Z

-4.0

5

4

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$ 2 - 0 - a- I -

: & - 6 0 - --. g , - I -

L

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-4 -

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- - - Elastoplastic \ -

- - - - - - - - - - - - - - - - - - - - - - - - - - - _ _ - c G p e r b o l i c

I I I I I

x / 2 a

FIG. 12. Convergence curves for three cases with variable 0 I 2 3 4 5

' i ,

.r. --: - -

I I 1

-4 -3 -2 -1

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- 4- Dkection of Mining

t Tunnel Face

crown \\> i i',, - _ _ -1.. -- 6 -- - _0_!4?-~

',,,,,I::z ------ 3 ----------- z -- -.-----. 2 --..-------.--

\\ ,-- I,---./- -... kc; E. - .-3.-. -. -.

---2

k ~ p r l n g l l n e

I I I I

0 1 2 3 4

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234 CAN. GEOTECH. J. VOL. 28, 1991 ,

FIG. 14. Partial relative displacement measurements ( a ) at crown and ( 6 ) at springline ( K O = 2; pa = p,; initial reading at ( ~ / 2 a ) ~ = 0 , 0.25, and 0.5).

5. Near face effects on multipoint extensometer records Multipoint extensometers are commonly placed in radial

boreholes to measure relative displacements in the ground around a tunnel. Valuable information on the properties of the geologic medium can be extracted from such extensometer records, provided that the monitoring program is properly laid out and the effects of the various parameters introduced earlier are well understood.

In the following sections, the sensitivity of extensometer records to ground behaviour, initial stress state, and support interaction is discussed, and various factors that should be considered for the design of a monitoring program are emphasized.

5.1 Effects of initial stress state and zero reading delay In deep tunnels, radial extensometers can be placed only

behind the tunnel face, thereby providing a partial picture of the total displacement field. Partial relative displacements for the tunnel crown and springline (KO = 2 and pa = p,), with zero readings taken at the tunnel face (solid lines) are plotted in Figs. 14a and 14b. The datum is assumed at an infinite distance from the tunnel wall. Hence, a correction must be applied to the diagram if a comparison with real data, with a datum at a finite distance, has to be made. At the tunnel crown the mobilized portion of the ground is not very deep and could be monitored by an extensometer

extending to only three t u h e l radii. 9 the other hand, at the springline relatively large deformations are detected as far as five or more radii away from the tunnel wall. For isotropic and linear elastic rock, the difference in shape of the relative displacement profiles at the crown and springline can provide an indication of the KO value. Again, fitting of measurements with three-dimensional numerical results can be adopted as the most direct tool for interpretation.

Similar to the convergence measurements, the radial extensometer records are also affected by the magnitude of the initial axial stress pa and by the zero reading delay. Small radial compression may be observed in measurements of this kind if relatively low pa values are encountered (not shown in figure).

Readings for various zero reading locations are presented in Fig. 14. If the extensometers were installed one-half radius or more behind the tunnel face, zero displacement or even some relative compression would be recorded at the crown (Fig. 14a) and very little relative displacement would be observed at the springline (Fig. 146). Delayed readings affect not only the magnitude of the measured relative displacements but also the shape of the displacement profiles. Depending on the distance from the tunnel face at which the instruments are placed, steeper or flatter profiles may be obtained. This is due to the fact that points located at different distances from the tunnel axis displace at different rates.

In summary, knowledge of the initial stresses is beneficial to properly determine the length and orientation of radial extensometers. On the other hand, by placing various instruments around the excavation and fitting the relative displacement profiles to the results of three-dimensional numerical analyses, the direction of the initial stresses normal to the tunnel axis and KO can be back-analysed (if the rock behaves in a linear elastic isotropic manner). For those cases where a reasonable assumption for p, can be made based on the depth of overburden, the absolute value of ph can also be estimated. The axial stress may dominate extensometer records at the tunnel crown (for KO > l) , especially if the zero reading is taken with some delay. The instruments should therefore be placed very close to the tunnel face and at various locations around the tunnel.

5.2 Effects of ground anisotropy The relative partial displacement profiles calculated for

the tunnel crown are plotted in Fig. 15 for cases A l , A2, and A3 (Fig. 1). The displacements ahead of the tunnel face are not considered (partial values) so that these data can be compared directly with measurements taken by means of multipoint extensometers placed immediately at the tunnel face ( ( ~ / 2 a ) ~ = 0).

The displacements calculated for case A1 are largest, owing to the low modulus in the vertical direction. For case A2, outward movement is found owing to the combina- tion of high elastic modulus and low radial stress in the vertical direction.

It can be observed that no displacements are detected for case A3 at r/a in excess of four, while for cases A1 and A2 significant movement occurs for r/a > 6. It follows again that the initial stress distribution (see previous section) and the orientation of the elastic parameters affect the straining process in a similar manner.

In a previous section the outward movement, occurring at the tunnel face, for case A3 was discussed. Such behaviour

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PELLI ET AL. 235

FIG. 15. Partial relative displacement measurements at the crown for cases A1-A3 ( K O = 2; ( x / 2 a ) , = 0; Fig. 1 ) .

is particularly pronounced at the tunnel crown (for KO > 1) and may dominate extensometer records taken immediately behind the tunnel face. The interpreter may be led to erroneous conclusions if the tunnel crown is the only monitoring location (for KO > 1). Particularly at the crown, the shape of the relative displacement curves is affected by the orientation of the elastic properties of the ground. Relatively flat curves, with large radial displacements far from the tunnel wall, are found if the axis of the tunnel and the orientation of the maximum elastic modulus correspond. If the minimum elastic modulus controls deformation along the axis, the radial displacements at the tunnel crown are concentrated near the wall of the tunnel, similarly to the isotropic case (Fig. 14).

5.3 Effects of nonlinear ground behaviour In Fig. 16a, the relative displacements at the tunnel spring- - 1.5

line for a homogeneous linear elastic, a hyperbolic, and an I 2 3 4 5 6

elastoplastic case are presented. Although the magnitudes r / a

of the displacement profiles are different for the three cases, FIG. 16. Partial relative displacement measurements ( a ) at the curves are virtually identical in shape. Therefore, the springline and ( b ) at crown for linear-elastic, hyperbolic, and relative movement between the head (at A) of a multipoint elastoplastic rock ( K O = 2; initial reading at tunnel face extensometer installed at the springline and a deep seated (x /2a lO = 0).

anchor (at B) gives very little indication of the nonlinear behaviour in these cases.

On the other hand, very different profiles are obtained at the tunnel crown (Fig. 16b). For the linear elastic case, the smallest displacement is observed at the wall. For r/a > 1.25 (to right of point C), the radial displacements for the linear elastic case are larger than for the elastoplastic case. For r/a > 1.9 (to right of point D), larger displacements occur for the linear elastic than for the hyperbolic case. The intersection (at C) corresponds approximately with the boundary of the plastic zone.

In conclusion, multipoint radial extensometers placed immediately behind the tunnel face give little indication of nonlinear ground behaviour if located at the tunnel springline (KO > 1). On the other hand, at the tunnel crown higher stress concentrations occur near the wall and the thickness of the plastic zone can be detected if relatively

shallow extensometers with closely spaced anchors are installed.

5.4 Effect of the support One example of radial displacement profiles (relative to

a fixed point far from the opening) calculated from results of the three-dimensional analysis (linear elastic rock with a liner; C = 1.41; F = 24,387) is presented for the springline in Fig. 17. An apparent or relative compression zone is observed near the wall for this lined case. The causes have been discussed in detail by Pelli et al. (1986) and field observations consistent with these results, at least in trend, have been presented by Kaiser and MacKay (1983). The compression zone is more noticeable if the liner is activated close to the face and is associated with the stress concentration in the proximity of the leading edges of the liner segments.

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236 CAN. GEOTECH.

0

Unlined Tunnel ------ o f Case4-DEL-0 R L = l a

Case 5 - DEL= la R L = l a

-3.5 ! I I I I 1 I 2 3 4 5 6

r / a

FIG. 17. Total displacement profiles at the tunnel springline for unlined tunnel and cases 4 and 5 of Fig. 13.

As discussed in a previous section, a relative compression zone may also be detected in unlined tunnels depending on the in situ stress distribution and on the zero reading delay.

For most tunnelling situations, such compression zones occur only very locally, immediately behind the support, and the shape of the remaining part of the curve is virtually unaffected by the action of the support. The later portion of the profile can therefore be used for back-analysis purposes without consideration of the support action. The presence of the compression zone is of great practical significance because most extensometer readings are related to the movement of the anchor head, which is most likely located inside the compression zone. Different displacement profiles will be detected depending on the exact position of the anchor head. Extensometers with closely spaced anchors close to the tunnel wall must be used to detect the radial compression zone and to allow proper interpretation of the measurements or the data must be related to the deepest anchor point. This later method of presentation should be used in practice.

6. Conclusions and practical implications The results of this investigation lead to the following con-

clusions and recommendations for monitoring, where the utilization of field observations for the purpose of back- analyses is of value.

(i) Today, an analysis of three-dimensional face effects of tunnelling in rock is a practical undertaking and should be made as an integral part of designing a monitoring program and for interpreting field observations.

(ii) Convergence measurements and extensometer records obtained at various locations along a tunnel allow to back- analyze KO (=ph/pv) provided that the rock mass can be assumed to be isotropic and linear elastic. Furthermore, for those cases where a reasonable assumption for p, can be made based on the depth of overburden, the value of ph can also be estimated. However, it is difficult to back- analyze initial stresses and ground properties at the same

J. VOL. 28, 1991

time if nonisotropic or nonlinear rock mass behaviour is encountered. In particular, various corhbinations of oriented deformabilities and initial stress distributions may provide reasonable fittings of the field data (i.e., there is no unique solution).

(iii) By considering convergence and extensometer records obtained in the direction of the maximum principal field stress (tunnel springline for KO > l), the elastic modulus of the rock mass can be back-analyzed independently of the ultimate rock mass behaviour. Particularly suitable for this purpose are data collected in the proximity of the tunnel face, where the rock mass is less affected by nonlinearities. The back-analysis procedure involves fitting of field data to results from three-dimensional linear elastic numerical analyses, normalized as described in this paper. On the other hand, convergence and extensometer records placed at the springline (for KO > 1) do not reveal clearly the effects of yielding and failure that may take place more extensively at the tunnel crown.

(iv) Measurements taken in the direction of the minimum principal stress (tunnel crown for KO > 1) are highly sensitive to the magnitude of the initial axial stress and the rock modulus in the axial direction. Th'erefore, they are not suitable for back-analysis of the elastic properties of the medium unless reasonable estimates df pa and E (axial) can be obtained. Measurements taken at the tunnel crown do, however, allow to investigate the extent of the plastic zone by comparing the radial extensometer records with results from three-dimensional linear elastic models. In fact, the shape of the radial relative displacement profiles becomes steeper in the proximity of the tunnel wall when yielding takes place. If a good estimate of the stress field is available and the medium can be assumed to be eventually isotropic, a reasonable value of the elastic modulus can be obtained by fitting the radial displacements measured at the boundary of the plastic zone to results from three-dimensional elastic simulations.

(v) The action of a tunnel liner causes a decrease in convergence depending on the relative stiffness of the support, the magnitude of the delay of liner activation, and the excavation round length. A thin concrete liner (thickness up to 5% of tunnel radius with a concrete modulus 15 times higher than for the rock mass) does not affect the convergence curve immediately behind the tunnel face. Therefore, the data in the near face zone can be used for the back- analysis of the ground properties without considering support interaction.

( iv) For a proper back-analysis, it is recommended that at least four convergence points and radial extensometers be placed at each instrumented section and in the direction of the minimum and maximum principal (radial) stresses. If the stress orientation is unknown, the number of instruments should be increased and spaced more closely.

(iv) The convergence and radial displacement measurements should be started immediately behind the tunnel face and the entire displacement profile should be recorded by frequent readings (daily and after every excavation step). Much information is contained in the rate of deformation and its change with tunnel advance.

(viii) Multipoint extensometer anchors should be closely spaced near the tunnel wall such that local effects in the proximity of the excavation boundary, owing to support interaction or initial stress state, can be identified clearly.

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PELLI ET AL. 237 , ' I ( ix ) An accurate preliminary estimate of the in sit24 Stress GIODA, G. 1985. Some remarks on back-analysis and characteriza-

is beneficial for an optimal positioning of instruments. tion problems in geomechanics. Proceedin"g, 5th International The analyses presented here demonstrate that back- Conference on Numerical Methods in Geomechanics, Nagoya,

analysis is a complex task and tha t instruments must be Japan, vol. 1, 47-61. carefully located and monitored frequently t o provide mean- GIoDA, G., and MAIER, G. 1980. Direct search solution for an ingful da ta for practical use. inverse problem in elasto-plasticity: identification of cohesion,

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