Numerical simulation of the swelling behaviour around tunnels based on special triaxial tests

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Tunnelling and Underground Space Technology incorporating Trenchless Technology Research

Tunnelling and Underground Space Technology 23 (2008) 508–521

www.elsevier.com/locate/tust

Numerical simulation of the swelling behaviour around tunnels based on special triaxial tests Marco Barla

*

Department of Structural and Geotechnical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy Received 16 April 2007; received in revised form 7 September 2007; accepted 25 September 2007 Available online 26 November 2007

Abstract This paper is to contribute to the understanding of the behaviour of tunnels in swelling ground. An Italian case study of a tunnel, collapsed due to swelling of a stiff clay, is taken as an example. The stress paths during excavation of elements of ground around the opening are computed in order to evidence the significant difference to that reproduced by usual swelling tests in the laboratory. An innovative triaxial testing procedure is developed and the stiff-clay tested. A numerical simulation of the swelling phenomenon induced by the excavation of the tunnel, based on the experimental results obtained, is then compared to site observations.  2007 Elsevier Ltd. All rights reserved. Keywords: Swelling; Tunnelling; Laboratory testing; Numerical simulation

1. Introduction There are no clearly defined rules for the design of tunnels in swelling ground. Difficulties are generally met for characterisation and testing of swelling soils and rocks and for prediction of the response to tunnel excavation and support loading. This is to be recognised although significant efforts have been made in the recent past by many researchers, in particular by members of the Commission on Swelling Rock of the International Society for Rock Mechanics (Gysel, 1987; Kovari et al., 1988; Anagnostou, 1993; ISRM, 1983, 1989, 1994a,b; Wittke, 2000). Following the introduction of the most recent developments, in particular the experimental and analytical work performed at MIT by Bellwald (1990) and Aristorenas (1992), this paper is intended to contribute to the understanding of tunnel behaviour in swelling ground. During the excavation of a tunnel in saturated porous media, an element of ground near the excavation may expe-

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rience negative excess pore pressures due to unloading. As a function of the permeability of the ground, flow may occur and swelling takes place. It must be stated here that the swelling phenomenon addressed in the present paper, according to the definition given by the ISRM (1983), is a combination of physico-chemical reactions involving water and stress relief. The physico-chemical reaction with water is usually the major contribution but it can only take place simultaneously with, or following, stress relief. Swelling occurs in soil or rock where clay minerals, anhydrite or pirite/marcasite are present. In order to be able to make appropriate predictions of this behaviour, both at the design and construction stage, the tunnel engineer needs to use tools that allow him to quantify, timely and correctly, the swelling properties of the ground. To this end, different testing techniques, ‘‘at laboratory scale’’, have been proposed in the past. It appears that the oedometer test, as originally introduced by Huder and Amberg (1970) and later modified by the ISRM Commission on Swelling Rock (ISRM, 1989; Madsen, 1999), is often used. However, more recently, different authors have been studying this problem by triaxial testing (Pregl et al., 1980; Bellwald, 1990; Aristorenas, 1992). This

M. Barla / Tunnelling and Underground Space Technology 23 (2008) 508–521

et al., 1997), the room and pillar workings underground were visited. This allowed one to observe an exploratory adit in clay. The tunnel has a horseshoe shaped cross section, typical of mine tunnels excavated with the conventional method. This adit, which was excavated in 1970, has incurred in dramatic failures of the 20 cm thick unreinforced concrete liner (Rck 25), as clearly illustrated in Fig. 1. Fig. 2 shows a schematic cross-section of the Quarry, taken through boreholes CAEST3 and CAEST4, which were drilled to reach the Tertiary Flysch Complex, below

paper is intended to show how special triaxial tests can be used in order to quantify the swelling properties of the ground. These data are then used to back-analyse the swelling behaviour experienced with reference to an Italian case study. 2. The case study of Caneva–Stevena` The Caneva–Stevena` Quarry, near Pordenone, is located in the North-East of Italy. As part of a geotechnical investigation on large-scale slope instabilities in the area (Barla

Fig. 1. Typical conditions of the exploratory adit in the swelling zones at the Caneva–Stevena` site.

WASTE ROCK GREY LIMESTONE MARMORINO FLYSCH COMPLEX WATER LEVEL

EXPLORATORY ADIT (located 340 m ahead of the cross section shown)

CONTACT BETWEEN LIMESTONE AND CLAY

CAEST 4 CAEST 3 1 2 3 4 5 1 2 3

509

6

Fig. 2. Schematic illustration of a typical cross-section of the Caneva–Stevena` site showing the boreholes CAEST3 and CAEST4 (not to scale).

510

M. Barla / Tunnelling and Underground Space Technology 23 (2008) 508–521

the Cretaceous Limestone Formation, with the main purpose to obtain representative samples of the ground. It is shown in the same figure that the exploratory adit is located at a depth ranging between 40 and 60 m, with the invert in a stiff clay (Caneva clay) and the crown in a weak highly fractured limestone (locally called ‘‘Marmorino’’, which represents the mined ore). This rock can be given a Geological Strength Index – GSI according to Hoek and Brown (1997) – equal to 40–50, an unconfined compressive strength of 34 MPa and a Young’s modulus of 30 GPa. Geotechnical characterisation of the Caneva clay was achieved by means of laboratory testing. Specimens were retrieved from a number of undisturbed samples taken from the two boreholes, by a double core barrel. Samples were preserved in a PVC container. Specimens were prepared by trimming them to the desired dimensions and then sealed with cling film and wax and stored into a cooling chamber. Physical properties of the Caneva Clay are given in Table 1. Geotechnical characterisation in terms of deformability and strength parameters was achieved by means of conventional triaxial testing (Table 2). The samples tested are characterised by a significant heterogeneity in terms of the physical and mechanical properties and of the mineralogical content. The results of consolidated undrained compression triaxial tests confirm a significant degree of variability of the strength parameters (c 0 , / 0 ), depending on the location and depth of the samples tested. In general, the strength parameters appear to be greater in terms of the calcium carbonate content; also, they are likely to be influenced by the size distribution in terms of clay content. Average strength parameters in terms of effective stresses are 84 kPa for cohesion (c 0 ) and 26 for friction angle (/ 0 ). As an attempt to gaining insight into the likely swelling behaviour of the Caneva clay, the available mineralogical data have been plotted on the diagram of Fig. 3, which is generally used to identify the swelling potential of hard soils and soft rocks. The diagram combines together the mineralogical constituents of a soil/rock. Each point is drawn by a known percentage of clay minerals, quartz and carbonate content which is defined on each side of

Table 2 Material properties for the Caneva clay Porosity, n (dimensionless) Total unit weight, c (kN/m3) Dry unit weight, cd (kN/m3) Shear modulus, G (MPa) Bulk modulus, K (MPa) Effective friction angle, / 0 () Effective cohesion, c 0 (kPa) Isotropic hydraulic conductivity, kH (m/s)

0.3 22 19 30 65 26 84 1 · 109

the triangle by a clockwise scale from 0% to 100% of the particular constituent. In order to compare the Caneva clay with other soils which are known to exhibit a different degree of swelling, the data from two argillaceous soft rocks (Varicolori clay shales and Terravecchia claystone) from Sicily are reported in the same diagram. Although some caution need be used, the data points confirm that the Caneva clay exhibits a swelling potential which is between medium and high. The identification of the swelling potential of the Caneva clay, as evaluated on the basis of mineralogical content, is confirmed by the results of the oedometer tests carried out, according to the Huder & Amberg procedure, as modified by ISRM recommendations (Madsen, 1999). It is clearly shown that the Caneva clay exhibits a total vertical strain between 1.7% and 7.5% as the axial stress applied to the specimen is gradually decreased (Fig. 4) after the cell is filled with water. 3. Stress paths during tunnelling Typical stress paths due to tunnel excavation, can be adopted as appropriate input to laboratory testing. Stress paths during excavation were therefore computed with reference to the geometry of the exploratory adit at the Caneva–Stevena` site. Also, a simplified geometry of a circular tunnel (diameter, D = 10 m), supposedly excavated in the Caneva clay, is taken into account. For a fully saturated ground, it is accepted that the issue of whether undrained or drained conditions are more applicable to the tunnel problem during face advancement

Table 1 Physical properties of the Caneva claya Sample CAEST CAEST CAEST CAEST CAEST CAEST CAEST CAEST CAEST

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

Depth (m)

wn (%)

c (kN/m3)

Gs (dimensionless)

e (dimensionless)

LL (%)

PL (%)

PI (%)

CaCO3(%)

44.65–45.55 47.60–48.35 55.35–55.75 25.52–25.85 32.48–33.68 36.58–37.65 45.94–47.15 51.12–52.50 58.95–59.80

16.2 12.5 – 17.0 10.7 13.8 9.2 13.3 11.9

21.4 21.9 20.5 21.3 22.9 22.4 22.8 22.0 23.2

2.69 – – 2.76 – 2.84 2.8 – 2.83

0.53 0.30 – 0.49 0.29 – 0.4 – –

63 53 40 46 39 39 46 33 34

23 13 10 12 9 21 21 21 19

40 40 30 34 30 18 25 12 15

1.9 41.0 – 13.9 – 22.3 38.7 – 23.9

a wn, natural water content; c, unit weight; Gs, specific gravity; e, void ratio; LL, liquid limit; PL, plastic limit; PI, plasticity index; CaCO3, calcium carbonate content.

M. Barla / Tunnelling and Underground Space Technology 23 (2008) 508–521

511

100% QUARTZ

A = HIGH SWELLING POTENTIAL B = MEDIUM SWELLING POTENTIAL C = LOW SWELLING POTENTIAL

= CANEVA CLAY (CAEST3) = CANEVA CLAY (CAEST4) = TERRAVECCHIA CLAYSTONE = VARICOLORI CLAY SHALES

A

B

C

100% CLAY MINERALS

100% CARBONATE CONTENT

Fig. 3. Diagram of the swelling potential for the Caneva clay.

8

Total axial strain [%]

7

Edo1

6

Edo2

5

Edo3 Edo4

4

Edo5 3 2 1 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Vertical stress [MPa] Fig. 4. Total axial strain due to water absorption versus vertical stress for the five Huder–Amber modified oedometer tests (EDO) performed on the Caneva clay.

depends primarily on the ground permeability, the rate of excavation and the size of the tunnel (Mair and Taylor, 1997). If consideration is given to hard soils and argillaceous rocks with permeability lower than 109 m/s (as for the Caneva clay e.g.), undrained conditions are assumed to hold true at least for the time duration required effectively for a ground element at the tunnel contour to experience the stress path. There is no drainage during construction and volume changes are zero. The stress path at points around a tunnel as face advancement takes place can be well described by the use of the stress path method, as proposed by Lambe (1967). This has been done by different authors on the basis of numerical analyses or closed form solutions (Ng and Lo, 1985; Steiner, 1992; Barla, 2000).

The total stress path (TSP) and effective stress path (ESP) are here examined by means of numerical methods in plane strain conditions, using the finite difference code Flac (Itasca, 1996a). The analyses were performed for an hydrostatic stress field (Ko = 1) and according to an elastic perfectly plastic stress–strain law for the ground, according to the Mohr– Coulomb model. The assumption of a hydrostatic stress field is introduced as no direct observation from the site is available. The stress state is considered constant versus depth and boundary conditions are introduced to the edges of the mesh as shown in Fig. 5, for the circular tunnel case. The excavation of the tunnel was simulated by reducing the normal internal pressure at the tunnel contour from the in situ state of stress to zero, in undrained conditions.

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M. Barla / Tunnelling and Underground Space Technology 23 (2008) 508–521

Fig. 5. Mesh and boundary conditions for 2D and 3D analyses for the circular tunnel case.

to the circular tunnel, while the TSP is characterised by a decrease of the total mean stress for the sidewall (S 0 ) and invert (I 0 ) in the case of the horse shoe shaped tunnel. At failure, the TSP decreases as negative excess pore pressure develops in the plastic zone around the tunnel. It is recognised that the stress paths described are determined by using a simplified constitutive law and in situ stress condition. It is beyond the scope of this paper to get a deeper insight into these aspects of the problem. A further numerical step was performed only to seek the effect of the advancing tunnel face (i.e., analysing the problem in three dimensional conditions), considering suitable for this scope a linearly elastic isotropic behaviour and a circular tunnel. The finite difference code Flac3D (Itasca, 1996b) was used and the analyses were carried out in total

The initial vertical and horizontal stresses are 1 MPa and the initial pore pressure is 300 kPa. The TSP and ESP during excavation of typical points around the tunnel (sidewalls, crown and invert), at 1 m distance from the tunnel contour, are described on the [s–t] plane, where s ¼ mean total normal stress ¼ ðrv þ rh Þ=2; t ¼ deviatoric stress ¼ ðrv  rh Þ=2; s0 ¼ mean effective normal stress ¼ s  u; rv and rh are the vertical and the horizontal total stresses, respectively, and u is the pore water pressure. In case the horizontal stress becomes larger than the vertical stress this results in a negative t. Fig. 6 shows the results of the numerical analyses, both for the horse shoe shaped section and for the circular one. It can be seen that the TSP and ESP at the sidewalls (S), crown (C) and invert (I) are vertical for that pertaining

0.8 C

0.6

C’ S

0.4

S’

I

ESP TSP Strength envelope

σh=0

I’

S

t/so [-]

0.2

S' 0 0

0.2

0.4

-0.2 -0.4

I'

0.6

PLASTIC ZONE

0.8

1

1.2

C/I/C'

x

-0.6 Δu

ELASTIC ZONE

σv=0

-0.8

s'/so s/so [-] Fig. 6. TSP and ESP for points S and S 0 (sidewalls), C and C 0 (crown) and I and I 0 (invert) for the effective stress analysis.

M. Barla / Tunnelling and Underground Space Technology 23 (2008) 508–521

513

Fig. 7. Stress paths for points S (sidewalls), C (crown) and I (invert) for the total stress analyses.

stress conditions (i.e., water pressure is zero). For 3D analyses tunnel excavation was simulated by removing elements inside the tunnel in sequence (steps of 0.05 D length) in the longitudinal direction. All other conditions were consistent with the plane strain analysis. The different stress paths obtained from plane strain and 3D analyses are compared in Fig. 7. No account is taken of the out of plane stress component, when describing the stress paths in the s–t plane. This is however considered in the three dimensional calculations carried out. The Kirsch closed form solution for a circular hole in a linearly elastic plate, subjected to an isotropic or anisotropic state of stress is also considered (Timoshenko and Goodier, 1951). The results of the 3D computations exhibit a different trend of behaviour. As the tunnel face approaches a monitored section n, the mean total normal stress increases. An arrow, along the 3D stress path, shows the state of stress obtained when the face of the excavation crosses the n section. As soon as the face of the excavation overpasses the n section, the mean total normal stress suddenly decreases and goes back to the initial value. This takes place because of an abrupt decrease in the horizontal stress (rh). It is of interest to note that between the highest and the lowest value of s, the excavation proceeds for a distance of approximately 1/3 of the tunnel diameter. The behaviour is similar, however with an opposite sign for the stresses, at the crown/invert. On the basis of these results it can be observed that the excavation is accompanied by a continuous change of the mean total normal stress even for an isotropic initial state of stress. 4. Experimental programme The aim of the different laboratory techniques developed so far is to quantify the ground swelling properties in order to provide the tunnel engineer with the necessary input data for appropriate prediction of ground behaviour. An important aspect in laboratory testing is the need to repro-

duce as close as possible the in situ ground behaviour, since the results obtained show a tendency to be influenced from the testing conditions adopted. Based on the numerical analyses described above, Fig. 7 shows that the modified Huder and Amberg (1970) oedometer test, which is generally used to characterise the swelling ground behaviour, does not reproduce the correct stress path experienced by the ground in the near vicinity of the tunnel. This stress path, in particular near the face of the excavation, can be properly described only by accounting for three dimensional conditions. Triaxial tests are probably a better compromise than the oedometer test and therefore were used in the present study to determine relevant parameters describing the swelling potential. 4.1. The experimental procedure To mimic the stress paths described, by adopting experimental techniques fairly common in practice, a test procedure to be applied in a triaxial apparatus was developed. It consists of six phases: specimen preparation and set-up, flushing, saturation, consolidation, undrained stress path phase and drained phase. The set-up of the specimen is done with the dry setting method (Lo Presti et al., 1999) in order to prevent it from swelling when occasionally gets in contact with water. Up to the consolidation phase, the procedure adopted is that of a typical triaxial test with the precaution to inhibit swelling when the specimen gets in contact with water (i.e., during the flushing phase). The stress path or shearing phase is carried out in undrained conditions, given the intention to simulate ‘‘at laboratory scale’’ the stress conditions in the near vicinity of the tunnel, during face advancement. As previously stated, for the stiff clay tested, undrained conditions are assumed to hold true during the complete excavation of the tunnel. During the shearing phase the specimen can be subjected to the stress paths described above enabling one to closely

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M. Barla / Tunnelling and Underground Space Technology 23 (2008) 508–521

follow what the ground experiences in the field. If the stress path is followed up to a certain t value, lower than failure, it is then possible to simulate a new phase. With the stress level constant versus time and creep completed (creep rate De < 0,05%/day), the drainage valve can be opened and water can flow in or out from the specimen, depending on the value of the pore water pressure reached during the undrained phase. This new drained phase corresponds to that experienced by an element of ground at a certain distance from the tunnel contour or during a standstill and can be adopted to study the swelling behaviour of the ground versus time, as will be shown in the following. 4.2. Testing equipment To perform the triaxial tests described in this paper, two triaxial apparatuses (GDS and SRTA), developed at the Politecnico di Torino, were used. For a detailed description of them refer to Lo Presti et al. (1995), for the GDS, and to Lo Presti et al. (1998), Barla (1999) and Barla et al. (1999), for the SRTA. Both equipments have a very stiff cell structure and consist of two end platens connected by three tie rods located inside a perspex pressure cell. The triaxial cells are equipped with local measurement devices for the axial and radial strain, external measurement of the axial strain, pressure transducers for the cell pressure and the pore pressure, a load cell located inside the pressure chamber and a volume variation indicator. Lateral and axial pressure control is obtained by means of single channel pneumatic digital controllers, with a resolution of 0.5 kPa, designed to be programmed by an external personal computer. A multichannel conditioning system is used for data acquisition. The data are automatically transferred via HPIB connection from the conditioning system to a PC so that one can control the whole test procedure by PC due to a user made program developed to manage the different phases. The GDS apparatus can reach maximum values of 2.5 MPa for the axial stress and 1 MPa for the confining

pressure while the SRTA has a maximum capacity of 25 MPa for the axial stress and 2 MPa for the cell pressure. 4.3. Simulation of different stress path conditions by triaxial testing The specimens were subjected to the stress paths computed above with the intent to simulate, ‘‘at laboratory scale’’, the ground behaviour around the tunnel during face advancement. The stress paths adopted are those computed for the circular tunnel case. The initial state of stress considered during testing was taken as isotropic (Ko = 1), even though the clay deposit under study gives a certain degree of over consolidation. A total of 12 triaxial tests were performed, as shown in Table 3. The saturation degree of all samples was checked by computing the Skempton’s B value. High B values were difficult to achieve, at the applied back pressure, due to the nature of the stiff clay and the sampling conditions. Tests CNV1 to CNV4, CNV8, CNV9, CNV11 and CNV12 were performed with the intent to reproduce the behaviour at the sidewalls with undrained compression tests. As indicated in Fig. 8, the s = constant compression TSP was imposed to tests CNV2, CNV3, CNV4, CNV11 and CNV12. While the CNV2 test was carried out up to failure, the CNV3, CNV11 and CNV12 stress paths were interrupted at a value of the mobilised deviatoric strength factor f = t/tfailure < 1. At this point the drainage valve was opened and the swelling deformations measured. The CNV4 test was carried out in drained conditions. The stress path computed by three dimensional numerical analyses was followed for tests CNV8 and CNV9. At a value of f = 0.5, in order to compare the results with test CNV3, the CNV8 stress path was interrupted and the drainage valve opened, while the CNV9 test was taken up to failure. Tests CNV6, CNV7 and CNV10 were performed to investigate the behaviour at the crown/invert with undrained extension tests. At different values of the mobilised factor f (see Table 3) the drainage valve was opened.

Table 3 Triaxial tests performeda Name

Sample

Depth (m)

wn

Type of test

B (dimensionless)

r0c (kPa)

ec (dimensionless)

B.P. (kPa)

tmax (kPa)

s0max (kPa)

Du (kPa)

f (dimensionless)

CNV1 CNV2 CNV3 CNV4 CNV5 CNV6 CNV7 CNV8 CNV9 CNV10 CNV11 CNV12

CAEST4-3 CAEST4-3 CAEST4-3 CAEST4-3 CAEST4-5 CAEST4-5 CAEST4-5 CAEST4-3 CAEST3-1 CAEST3-1 CAEST3-1 CAEST4-4

37.51 37.28 37.06 36.91 51.19 51.35 51.49 36.90 45.17 44.87 45.42 46.48

14.5 13.4 11.5 14.1 14.3 13.1 12.3 11.2 9.4 20.5 10.8 10.2

CIU CIU-2D CIU-2D CID-2D CIU EIU-2D EIU-2D CIU-3D CIU-3D EIU-2D CIU-2D CIU-2D

0.94 0.87 0.90 0.95 0.93 0.99 0.90 0.90 0.77 0.88 0.77 0.48

718 650 670 657 200 815 750 635 1150 695 647 645

0.48 0.39 0.39 – – – – 0.33 0.27 0.49 – 0.25

243 350 310 320 0 200 380 350 553 405 307 369

270 452 245 135 470 317 318 234 317 132 374 335

558 1000 728 661 669 632 595 656 735 479 743 785

286 348 60 0 – 175 164 100 43 124 101 134

1 1 0.5 1 1 0.8 0.8 0.5 0.7 0.3 0.8 0.7

a

wn, natural water content; r0c ¼ consolidation effective stress; ec, void ratio at the end of consolidation; B.P., back pressure; CIU, consolidated isotropically undrained compression test; EIU, consolidated isotropically undrained extension test, 2D, 3D, indicates the stress path followed during shearing.

M. Barla / Tunnelling and Underground Space Technology 23 (2008) 508–521

515

0.5 ESP TSP - uo Strength envelope

0.4

CNV12

0.3

CNV3

CNV9

S

CNV8

0.2

t/so [-]

CNV2

CNV11

0.1 0 -0.1 -0.2

0.5

0.7

CNV10

0.9

1.1

1.3

1.5

1.7 C

CNV7 CNV6

-0.3

I

-0.4

(s-uo)/s'o, s'/s'o [-] Fig. 8. TSP and ESP for the tests intended to simulate the behaviour at the sidewalls (S) and at the crown/invert (C and I). Only undrained tests are shown. s0o ¼ initial effective mean stress.

The CNV5 specimen was sheared under a conventional compression loading stress path. The comparison of TSP and ESP in Fig. 8 allows one to clearly appreciate the excess pore pressure change which occurs during each test. It is clearly shown that the excess pore pressure Du, negative at the sidewalls of the tunnel, is instead positive at the crown/invert. The final value of Du attained in each case at the end of the shearing phase is directly related to the stress level t. Some further comments are possible if a closer view is taken to the tunnel problem, with the excavation process being simulated with the tests performed. If we refer to tests CNV2 and CNV3, according to the stress paths followed, a final t/so value equal to 1 would correspond to the excavation completed in the cross-section of interest. The CNV2 specimen is shown to have failed at t/so = 0.45, with a negative excess pore pressure Du = 348 kPa. This is to say that the state of stress induced around the tunnel when the excavation process is completed, would lead to the development of a failure zone with a negative excess pore pressure, unless a confining pressure was applied on the tunnel contour. The CNV3 test was interrupted before failure for f = 0.5 with a negative excess pore pressure Du = 60 kPa. This simulates the fact that the tunnel excavation is not completed and the advancing face is at a small distance from the cross-section of interest, where the ground element undergoing the test is supposed to be located. The same type of behaviour would be experienced by a ground element at a certain distance from the tunnel contour, in a cross section where excavation has however been completed. It is noted that the results obtained in such a case are quite similar to those exhibited by the CNV2, CNV11 and CNV12 tests (Fig. 9). If the attention is now posed on the CNV8 and CNV9 tests, which were carried out specifically to simulate three

dimensional conditions during face advancement, the results obtained in terms of the excess pore pressure differ from the previous tests described. Due to the different TSP, along the first segment (where both the axial and confining pressures in the triaxial cell increase), the excess pore pressure is positive. For higher t/so values (i.e., after the tunnel passes the cross section of interest) the excess pore pressure becomes negative. For the CNV8 specimen, at the end of the test, the excess pore pressure was positive with a value of 100 kPa. On the contrary, for the CNV9 specimen, which was taken up to failure, the negative excess pore pressure was 43 kPa. As can be seen, while for the two dimensional conditions the negative excess pore pressure develops at a t/so value of 0.3, when the influence of the advancing face is taken into account (i.e., in three dimensional conditions) a greater value of t/so is necessary to induce a negative excess pore pressure depending on the shape of the TSP. Moreover, towards failure, in both cases, as a negative excess pore pressure around the tunnel results in a water inflow towards it, volumetric strain is likely to occur as dilation due to the stress relief and the interaction between water and the swelling minerals present in the ground. To investigate this behaviour the drainage valve was opened at the constant final state of stress, measuring the axial, radial and volumetric deformations versus time. This drained phase is reproduced with the intent to study the time dependent response, when the excavation is completed (the face of the tunnel is far away from the section under study) or during a standstill. Fig. 10 illustrates, for all tests, the plot of the volumetric deformation (evol) versus time, obtained by either direct measurement of volume change in the specimen (i.e., volume of water entering-positive or exiting-negative the specimen) or computation of the first invariant of strain in terms of ea and er.

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M. Barla / Tunnelling and Underground Space Technology 23 (2008) 508–521

300 200 CNV8

100

Δu [kPa]

CNV9

0

CNV12 CNV3

CNV11

-100 S

-200 -300

CNV2

-400 0

0.1

0.2

0.3

0.4

0.5

t/so [-] Fig. 9. Excess pore pressure versus t/so for tests intended to simulate the behaviour at the sidewalls (S).

0.4 Drainage opening

0.2

CNV7 CNV8

CNV10 CNV6

0

ε vol [ % ]

CNV3

CNV11

-0.2 -0.4

CNV3 CNV3 CNV6

-0.6

CNV3

CNV7

CNV12

CNV8 CNV8

-0.8

CNV10 CNV11 CNV11

-1

CNV13 CNV13

-1.2 1

10

100

1000

10000

100000

1000000

log time [min] Fig. 10. Volumetric deformation after drainage opening by either computation of the first invariant of strain (dotted line) or direct measurement of volume change (continuous line).

It is of interest to point out the different trends of behaviour exhibited by the specimens, depending on the excess pore pressure values attained at the end of the undrained phase. This excess pore pressure dissipates, under a constant state of stress, in a few hours. Specimens with negative excess pore pressure at the end of shearing, exhibit a dilatant behaviour (swelling), while a contracting behaviour (consolidation) is shown by the others.

test, can be drawn as shown in Fig. 11. It is noted that, for the tests performed, when the excess pore pressure is positive the volume decrease is not significantly dependent on the excess pore pressure value. On the contrary, when the excess pore pressure is negative, the volumetric strain is relatively high due to the swelling behaviour of the clay. Two further considerations on the results obtained can be added as follows.

4.4. Evidences from laboratory investigation Based on the results of the special triaxial tests described, a relationship among the excess pore pressure (Du), present in the specimen at the end of the undrained shearing phase, and the total volumetric strain (evol), measured at the end of the drained phase of the same

 evol @ 0 when Du = 0, i.e., no volumetric strain without variation of the excess pore pressure.  It is reasonable to expect that for high negative excess pore pressure values the volumetric strain tends to a relatively constant value (dotted line in Fig. 11). For the case under study it was assumed that evol,max = evol,edo @

M. Barla / Tunnelling and Underground Space Technology 23 (2008) 508–521

-5 -4

Maximum vertical strain in the oedometer

Numerical simulation Triaxial tests (computation) Triaxia l tests (direct)

⎛ Δu ⎞ + 4⎟ ⎝ 38 ⎠

ε vol = −2 + 1.5 ⋅ arctan⎜

-3 εvol [%]

517

-2 CNV3

-1 CNV10

0 1 400

CNV7

CNV12 CNV11

CNV6 CNV8

200

0 -200 Δu [kPa]

-400

-600

Fig. 11. evol–Du relationship determined by the experimental results on the Caneva clay. Also shown is the comparison to numerical analyses results.

4.5%, i.e., the average total vertical strain achieved during a Huder-Amberg oedometer test is taken to be the horizontal asymptote and upper limit also for the volumetric strain achievable in the triaxial cell. The two above considerations might be questioned. However, these allow one to reach a more comprehensive data interpolation which can be described by the following equation:   Du evol ¼ 2 þ 1:5 arctan þ4 : ð1Þ 38 A better description of the evol–Du curve may obviously be obtained with additional triaxial tests, which however could not be carried out for the case study described as no additional samples were available. The curve shown in Fig. 11 is only valid for the particular state of stress after consolidation at which the triaxial tests were performed, which is intended to reproduce the in situ state of stress. It can be reasonably anticipated that the evol–Du curve will vary versus the in situ state of stress, being the volumetric strain both a function of the negative excess pore pressure at the end of the undrained phase as well as of the effective stress acting during the drained phase. 5. Numerical simulation of swelling The results of the special triaxial tests described above can be used to simulate the phenomenon that likely took place around the exploratory adit excavated at the Caneva–Stevena` site. With this aim, numerical analyses were performed to reproduce the behaviour of the Caneva clay during both the undrained and the subsequent drained swelling/consolidation phase at the laboratory and in situ scale. Again, the finite difference Flac code was used.

To describe the undrained behaviour, an effective stress analysis (no flow being allowed) was performed with the groundwater option available with Flac. The drained phase instead was simulated by using the relationship (1), based on laboratory results. Volumetric strain is applied to each element of the grid, as a function of the excess pore pressure computed by the code in the corresponding undrained analysis. The stress–strain behaviour at the end of the swelling process is determined by iterating the analysis to equilibrium, without coupling flow and mechanical computations. In order to implement the curve (1) in the numerical code, the method of Noorany et al. (1999) was used. With this approach, within the Flac code, a volume strain increment in a certain zone of the model is created by applying a corresponding variation of the stress state. In order to obtain a desired volumetric strain (evol), in a single element, the total stress components (rx, ry and rz) of that element are increased as follows:   G Drx ¼  K þ evol 3   G Dry ¼  K þ evol ð2Þ 3   2 Drz ¼  K  G evol 3 where K and G are, respectively, the bulk and shear modulus of the ground. The approach is valid for all constitutive laws in which incremental elastic stresses are computed using Hooke’s law. In a plasticity analysis with Flac, the above stresses should be applied in increments which remain small compared to a characteristic yielding stress point for the simulation and cycled to equilibrium at each increment. The evol value for each element is calculated as a function of Du by Eq. (1) and the corresponding total stress increments are applied to the finite difference mesh to obtain the desired behaviour.

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5.1. Numerical simulation of laboratory tests According to the procedure described above, the triaxial tests results were simulated by numerical modelling. An axisymmetric mesh accounting for the geometry of the cylindrical specimen tested in the triaxial apparatus was constructed (Fig. 12). The mesh comprises 50 elements and reproduces a quarter of the specimen. A linearly elastic perfectly plastic Mohr–Coulomb model was used to simulate the constitutive behaviour of the Caneva clay (Table 2). The model was run to reproduce each phase of the laboratory test: the undrained shearing phase and the drained phase. The initial stress state and saturation corresponding to the in situ conditions were applied to the specimen. This state of stress (corresponding to the end of the consolidation phase in the laboratory test) is characterised by a total vertical stress of 1 MPa, a stress ratio Ko = 1 and a pore pressure of 0.3 MPa. Shearing of the specimen was simulated by applying a vertical velocity on the top plate and varying it linearly to zero to the base of the mesh (i.e., the middle of the specimen). The same specimen was sheared by imposing a constant total mean stress. During iterations, the applied confining pressure is computed as a function of the total vertical stress and updated in order to keep constant the value of the total mean normal stress during the test. Flow is not permitted in order to simulate undrained conditions. According to the experimental procedure developed, each simulated test is interrupted before failure, at different levels of mobilised strength. Fig. 12 shows, as an example, the TSP and ESP for a simulated compression test stopped at f = 0.67 and for a simulated extension test stopped at f = 0.9. It is recognised that the constitutive law used is not able to completely describe the development of the excess pore pressure in the laboratory tests, especially for small values of the mobilised strength. Nevertheless, this law was considered to be suitable for the purpose of the present study. At the end of the undrained phase, the specimen is characterised by a constant excess pore pressure and an applied

total state of stress which is maintained constant during the drained phase. To simulate the swelling behaviour, the volumetric strain (evol) for the actual Du is calculated by Eq. (1). The corresponding stress increments (Drx, Dry and Drz) are computed with Eq. (2) and applied to the elements in the mesh. This is done by means of a user made Fish function. Stresses are applied by small increments. The analysis is run to equilibrium at each step. Pore pressure and saturation are fixed as flow is not allowed to take place. Different stress conditions derived by the undrained phase were simulated in order to describe the entire evol–Du curve (isotropic linearly elastic behaviour is considered when the intent is to describe non-realistic evol–Du data). The results in Fig. 10 are shown to be in good agreement with the experimental values. 5.2. Numerical simulation of the swelling phenomenon at the tunnel scale The method developed so far has been applied to simulate the swelling behaviour of the ground around the exploratory adit of the Caneva–Stevena` site. A close view of the plane strain finite difference mesh used in the analyses is shown in Fig. 13. Appropriate boundary conditions were applied. The effect of gravity was not taken into account and the initial state of stress was considered to be isotropic and constant within the model. As a crude approximation, full saturation was assumed to hold true in the model. The excavation of the adit was simulated under undrained conditions, while the approach shown for the triaxial specimen was applied in order to simulate the swelling drained phase. In order to allow for undrained conditions during excavation, no flow was permitted in the model so that mechanical calculations only could take place. Realistic values were given to the water bulk modulus (2 GPa) and unit weight (10 kN/m3), so that pore pressure could be generated as a result of mechanical deformations. A water tension limit was set to be 10 GPa. The excavation of the adit was simulated by

400

velocity

Δu = -99 kPa

200 t [kPa]

70 mm

c o n fin in g p r e s s u r e

300

ESP

TSP

0 -100 -200 -300 -400 400

35 mm

TSP-uo

100

Δu = 99 kPa 600

800 s, s' [kPa]

1000

1200

Fig. 12. (left) Mesh and boundary conditions for the numerical model of the specimen. (right) TSP and ESP for numerical triaxial tests in the undrained phase (both in compression and in extension).

M. Barla / Tunnelling and Underground Space Technology 23 (2008) 508–521

519

400 m

Marmorino

0.2 m

3.4 m

800 m

σv = σh = 1 MPa

3.4 m u = 0.3 MPa

Caneva clay

Δu < 0

Caneva clay

decreasing the ground pressure to atmospheric pressure in five equal block increments (each block was run to equilibrium). As illustrated in Fig. 14, during the undrained excavation, the ground around the tunnel experiences a change in pore pressure distribution. A plastic zone develops as displacements occur at the tunnel perimeter with a 4.9 cm heave at the invert. The installation of a 20 cm thick lining was simulated before activating the swelling process in the Caneva clay. As a function of the excess pore pressure attained at the end of the undrained excavation (Fig. 14), the volumetric strain calculated by Eqs. (1) and (2) has been applied to the elements of the mesh in the Caneva clay and the model run to a new equilibrium. The limestone rock mass has no swelling potential, so that no volumetric strain is to be accounted for. Fig. 15 shows a comparison of the actual conditions of the exploratory adit, where failure of the concrete lining due to swelling of the clay is clearly visible, and the result of the numerical simulation. In the numerical model, additional vertical heave at the invert and convergence at the sidewalls, due to swelling of the clay, induce failure in the lining. Unfortunately, only a qualitative comparison between computed and observed behaviour is possible (no monitoring data being available). Based on the numer-

Marmorino

Fig. 13. (left) Sketch of the exploratory adit (not to scale). (right) Detail of the mesh used in model.

Δu < 0

Excess pore pressure contours in kPa -600.0 -300.0 0.0

Fig. 14. Plastic zone and area of negative excess pore pressure around the tunnel (before swelling).

ical analysis, the lining is shown to fail with a pattern of behaviour which is similar to what is known to have taken place in situ.

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Plastic zones in the lining

Fig. 15. (left) Exploratory adit. (right) Deformed lining from the numerical analysis (after swelling).

6. Conclusions A laboratory-based approach to predict the swelling behaviour around a tunnel was applied to the case study of the Caneva–Stevena` site, in Italy. Even though a detailed quantitative comparison of the results obtained with the numerical analyses and in situ observation was not possible, the method described in the paper has fulfilled the aim of capturing the phenomenological aspects of the problem under study and may represent an alternative to design analysis methods presently available. One advantage of the method proposed is that it is based on triaxial tests results which have been shown to be better representative of the ground stress behaviour. Another advantage is that it considers the role of ground water. Also, the application is straightforward for a tunnel engineer, being less computer demanding than a fully coupled numerical model based on advanced constitutive laws. In summary, the approach adopted is a combination of laboratory tests and numerical analyses consisting of the following steps: 1. Based on the information available for a particular case study, the typical stress path can be determined by means of numerical modelling and used as input for triaxial testing. 2. A number of triaxial tests can be performed for the desired stress level, with the undrained/drained procedure described. Depending on the stress path, the final state of the undrained phase will be characterised by a given value of the excess pore pressure and of the deviator stress. 3. Results of the laboratory tests may allow one to describe a evol–Du relationship, for the specific case study. 4. An effective stress numerical analysis can be performed to simulate the undrained response of the ground due to the excavation, accounting for the real geometry of the problem and the in situ state of stress.

5. By applying volumetric strain as a function of the excess pore pressure computed in undrained conditions, one can simulate the stress–strain behaviour at the end of the swelling process by iterating the analyses to equilibrium. At this stage it is possible to take into account the presence of a lining and to analyse the stresses induced in it by the swelling process.

Acknowledgements The work described in this paper was carried out with the financial support of the Italian Ministry for University and Technological Research (M.U.R.S.T.) as part of the Research Programme ‘‘Tunnelling in difficult conditions’’ (Responsible: Prof. G. Barla). The Author thankfully acknowledges the help of Mariacristina Bonini, Silvia Ferrero, Enrico Garibbo, and Carmelo Longo in various phases of the research. References Anagnostou, G., 1993. A model for swelling rock in tunnelling. Rock Mech. Rock Eng. 26/4, 307–331. Aristorenas, G.V., 1992. Time-dependent behaviour of tunnels excavated in shale. Ph.D. Thesis. Massachusetts Institute of Technology, Boston, USA. Barla, G., Arduino, G., Vai, L., 1997. Progetto di risistemazione del versante a monte della cava ‘‘Pare`’’ di Cordignano (Tv) e delle cave ‘‘Piai’’ e ‘‘Dal Cin’’ di Caneva (Pn). Relazione Tecnica No. 0086, Geodes S.r.l. Barla, M., 1999. Tunnels in Swelling Ground – Simulation of 3D stress paths by triaxial laboratory testing. Ph.D. Thesis in Geotechnical Engineering. Politecnico di Torino, 180 pp. Barla, M., Barla, G., Lo Presti, D.C.F., Pallara, O., Vandenbussche, N., 1999. Stiffness of soft rocks from laboratory tests. In: Proceedings of the IS Torino ‘99, 2nd International Symposium on Pre-failure deformation characteristics of geomatrials, Torino, Italy, pp. 43–50. Barla, M., 2000. Stress paths around a circular tunnel – Percorsi di sollecitazione attorno ad una galleria circolare. Rivista Italiana di Geotecnica (RIG) 1/2000. Pa`tron Editore, Bologna, pp. 53–58.

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