Time-dependent behaviour of Italian clay shales

Time-dependent behaviour of Italian clay shales M. Bonini, D. Debernardi, G. Barla, M. Barla Dept. of Structural and Geotechnical Engineering, Politecnico di Torino, Italy Keywords: clay shales, triaxial tests, time-dependence, constitutive laws. ABSTRACT: This paper describes the studies carried out on the time-dependent behaviour of clay shales. The interest arises in connection with tunnelling works in Italy through structurally complex formations. Triaxial tests are performed in order to describe the undrained behaviour and the constant deviatoric phase. The clay shales are shown to exhibit significant time-dependence, which is the cause of both the radial and longitudinal displacements taking place at the tunnel face. An advanced visco-plastic constitutive law is used in order to calibrate the material parameters with respect to the laboratory data and to study the tunnel face stability during excavation. 1 Introduction Tunnelling through the Apennines is presently under way in Italy, in connection with the construction of the high speed railway line between Bologna and Firenze. A significant length of large size tunnels is being excavated under difficult conditions, within the Tectonised Clay Shales of the Chaotic Complex (CCTCS), which are shown to exhibit squeezing and swelling behaviour. One of such tunnels is the Raticosa tunnel (Lunardi and Focaracci, 1999). Landslide (b) 1 m dowels PASSO FRA DUE RINFORZI DEL FRONTE SUCCESSIVI BARRE IN VETRORESINA 45-6 inclined BARRE INCLINATE dowels (n. 45 ~ 6) 35-8 (a) horizontal BARRE CENTRALI dowels (n. 35 ~ 8) N S crown CALOTTA invert ARCO ROVESCIO + PIEDRITTI H 12 = 12 m 2 4 6 8 1 km D 14 = 14 m m 2 CENTINE ACCOPPIATE 2 IPN I 22 mm/m 18-3/m Figure 1. Raticosa tunnel longitudinal profile (left) and details of longitudinal and transversal cross sections (right). 265

From North to South (Figure 1 left), the 1.45 m long Raticosa tunnel crosses respectively the CCTCS formation (through a 5.5 km length), marly and arenaceous formations. A landslide, involves approximately 5 m of the tunnel length from the northern portal. The landslide is active with rates of displacement ranging from more than 4 mm/year to -1.5 mm/year. Here the formation has undergone softening and/or weathering processes which have modified both its structure and properties. The recent geological history and the variable structure of the material are likely to have originated a very different mechanical behaviour in terms of time dependence. The Raticosa tunnel has been excavated by the full face method as shown schematically in Figure 1 right. Observation and performance monitoring concurrent with excavation were carried out systematically, comprising convergence and extrusion measurements. Due to the difficult conditions, the cross section of the Raticosa tunnel requires a primary lining (2 cm thick shotcrete layer and steel sets 2IPN18/m, locally 2IPN22/m or HEA3/m) including an arched invert. The final lining is made of reinforced (invert and sidewalls) and plain concrete (crown). The face is reinforced by fiber-glass dowels (2 m long) installed every 1 m of face advance (Figure 1 right). A thin layer of shotcrete is applied to the face during excavation standstills, when installing the fiber-glass dowels. 2 Geotechnical characterisation of the Chaotic Complex Tectonised Clay Shales A detailed description of the geotechnical characterization of the CCTCS is given in Bonini (23) and Bonini et al. (23). Here, only the properties which may be considered useful for the understanding of the following are discussed. The cubic samples obtained at Raticosa tunnel face (chainage 3+116 m) were taken to the laboratory, where cylindrical specimens (to be adopted for triaxial tests) were cut with great difficulty, also because of the presence of inclusions. The material in excess was used for the determination of physical properties, mineralogical content and for oedometer tests. The CCTCS, classified as inorganic clays of low to average plasticity, are turbidites, with scaly structure heavily modified by tectonic events. Irregular striping is often present while sometimes a chaotic mix of clayey materials is found. The natural water content (5-15%) decreases with the overburden, as the degree of saturation (8-98%) increases with it, indicating a nearly absent water circulation at the rock mass scale. The high swelling potential of the CCTCS was detected by means of X-ray diffraction analyses which proved that the clay fraction (smectite, illite and chlorite) represents more than half of the total, the remaining part being constituted by quartz, calcite and albite (traces). Several oedometer tests (on natural and reconstituted soil, with and without change of pore fluid chemical composition) were performed. Four Huder-Amberg tests allowed for the determination of the swelling coefficient K (Figure 2). The swelling potential of the CCTCS is found to compare well with that exhibited by the S. Donato clay-shales (Barla et al., 1986). Swelling strain [%] 2 15 1 5 K EDO2 - K = 3.2 EDO3 - K = 7.5 EDO4 - K = 5.3 EDO5 - K = 9.9 S. Donato - K = 5.8-9.5.1.1 1 1 Vertical effective stress [MPa] Figure 2. Huder-Amberg tests and swelling coefficient K: the CCTCS compared with S. Donato clay shales (Barla et al., 1986). 266

Three oedometer tests were carried out on reconstituted specimens with the aim of obtaining both the intrinsic properties and the sensitivity of the double diffuse layer to the pore fluid type. The compressibility and swelling index proved to be affected by the cation concentration. The indirect determination of hydraulic conductivity showed that it is strictly dependent on the void index, for both the natural and reconstituted conditions, even if the structure of the CCTCS is essentially different. The hydraulic conductivity proved to be so low that it is likely that swelling behaviour could not develop, at least in the short-term conditions. This is confirmed by the almost total absence of underground water circulation. A total of five triaxial tests (RTC) were performed by means of the Soft Rock Triaxial Apparatus (SRTA) available at the Politecnico di Torino, specifically designed for testing soft rocks in controlled conditions. The testing procedure is complex and involves six different phases dedicated to the simulation of the tunnel behaviour in short and long term conditions (Barla M., 1999). Here only the shearing phase and the undrained creep phase are considered. In fact, due to the low hydraulic conductivity and to the rates of advancement and lining installation, the high displacements developing around the tunnel face are likely to occur in undrained conditions. Deviator stress [kpa] 4 3 2 1 RTC2.1 mm/min RTC4.5 mm/min RTC3.5 mm/min RTC5.1 mm/min RTC1.1 mm/min 1 2 3 4 5 External axial strain [%] t [kpa] 2 15 1 5 RTC3.77 RTC4.8 RTC2.75 RTC5.65-.83 RTC1.81.8.9 1. 1.1 1.2 s'/s'o [-] Figure 3. Stress-strain behaviour, showing different axial strain rate values (left) and effective stress paths, giving the B value of each specimen (right). Axial strain rate [%/min / 1] 1 q/q f =.55 1 q/q f =.78 q/q f =.87 1 q/q f = 1..1.1.1.1 1 1 1 1 Time [min x 1] Figure 4. Axial strain (left) and axial strain rate (right) versus time during undrained creep phase of RTC tests (q/q f = stress level). The specimens were subjected to an s = constant stress path (s o = 5 kpa), typical of an 267

element of ground located at the tunnel sidewall. The consolidation isotropic effective stress and the initial back pressure adopted were considered to be representative of the site conditions. The stress-strain curves illustrated in Figure 3 (left) show an elasto-plastic hyperbolic behaviour, clearly influenced by the rate of imposed axial displacement and the saturation degree. The same considerations apply to the effective stress-paths, which are shown in Figure 3 (right), together with the Mohr-Coulomb failure envelope holding true for the CCTCS of the paleo-landslide zone (c = 2.3 kpa and = 16.6 ). The undrained creep phase performed at the end of the shearing undrained phase, when the desired mobilised strength was attained, allowed one to determine the behaviour of specimens under undrained constant loading conditions (Figure 4 left). It is shown that time-dependent strains develop for a mobilised strength (q/q f ) nearly equal to 5% of the failure value (Figure 4 right). The strain rate is shown not to increase significantly as the stress increases, even if the failure stress deviator is attained. These results demonstrate that the CCTCS may exhibit a significant time dependent behaviour even for a small deviatoric stress. 3 The time-dependent constitutive law In order to represent the mechanical time-dependent behaviour of the CCTCS, Lemaitre s constitutive law was adopted. This law, based on the Perzyna s elasto-viscoplastic theory (Perzyna, 1966; Lemaitre & Chaboche, 1996; Boidy, 22), was developed into the finite difference code Flac (Itasca, 21) and afterwards validated. In the general theory of elasto-viscoplasticity, the strain rate tensor can be split into elastic el and viscoplastic components, to give: el (1) The viscoplastic strain rate tensor can be calculated by the flow rule: G F (2) where is a viscous constitutive parameter, F is the so-called viscous nucleus, F is the yield function, G is the viscoplastic potential function and is the stress tensor. The time-dependency is introduced by modifying the flow rule and by discarding the consistency rule ( df, F ), allowing thus the yield function F to be positive or negative. The viscoplastic potential G defines the direction of the viscoplastic strain rate tensor, while the yield function F influences its modulus by means of the viscous nucleus. The choice of the viscous nucleus is very important to describe the mechanical time-dependent behaviour of soil. It is generally assumed to be a monotonous function of F and to be equal to zero inside the yield surface ( F ) and positive otherwise. A linear, a power law or an exponential function can be used. According to Lemaitre s formulation, the viscous nucleus is assumed to be a power law: F F F n (3) where F is the stress reference unit and n is a viscoplastic constitutive parameter ( n 1). The yield function F is supposed to be divisible into a part f, which depends only on the stress state, and into a part, which depends only on the viscoplastic strain state, according to: f F (4) f coincides with the classic yield function of elasto-plasticy. A Von Mises s yield criterion is assumed: The function 268

where q is the so-called equivalent deviatoric stress, q 3 J 2,, where J 2, is the second invariant of the stress deviator. A potential hardening rule is introduced for the yield function F : m n (6) where m is a viscoplastic constitutive parameter ( 1n m ) and is the so-called equivalent viscoplastic strain, 43J, where J is the second invariant of the viscoplastic strain 2, 2, deviator. The yield surface ( F ) is reduced to the hydrostatic axis and it does not change with time. The viscoplastic potential function G is supposed to be equal to f (i.e. the flow rule is associated). With these assumptions, the viscoplastic strains depend on the deviatoric stress state only and do not induce volumetric strains. Therefore equation (2) becomes: 3 n1 m q s (7) 2 where s is the stress deviator. The constitutive parameters n and m define respectively the dependence of viscoplastic strain rate tensor on the equivalent deviatoric stress and on the equivalent viscoplastic strain. The differential equation (7) results in a closed-form solution only when q is constant; otherwise, a numerical method is required. f q (5) 4 Determination of parameters at laboratory scale The viscoplastic constitutive parameters of Lemaitre s law were determined for the CCTCS on the basis of three triaxial undrained creep tests performed at different deviatoric stress levels (required to separate the contribution of the parameters and n ). Assuming that a and r are the axial and radial stresses and that a and r are the axial and radial viscoplastic strains, during a triaxial creep test q a r cost and a 12r. Therefore, equation (7) can be integrated in the time t, to give: 1 n aq t with: ; n ; a 1m 1m Writing equation (8) in logarithmic notation allows one to obtain a linear relationship between ln, as follows: and ln ln ln t with: aq and: ln ln ln (8) ln t a q (9) Figure 5. Procedure for the determination of the parameters (left) and (right) for the Lemaitre s law. 269

In each test, the parameter i is defined as the slope of the linear interpolation of the experimental data on the ln ln t plane (Figure 5 left). The parameter is chosen as the arithmetical mean of the three parameters i. Then, for each test, the experimental curve t is normalized with respect to t (Figure 5 right) and the parameter i is assumed as the arithmetical mean of the obtained curve. The parameters and (Figure 6 left) were chosen as the slope and the natural exponential of the intercept with the y axis of the linear interpolation of the three experimental data i - q i calculated for each test, on the plane lni - lnq i. Finally, the parameters, m and n were derived according to equation (8). The constitutive viscoplastic parameters obtained are summarized in Table 1. A comparison between the experimental data and the results of numerical computations is shown in Figure 6 right. The agreement is very good. Table 1. Constitutive parameters of Lemaitre s law (time in years and stresses in kpa)..2 1.13E-28 1.45 n 7.14 a 2.85E-6 m -3.91 Figure 6. Procedure for the determination of the parameters (left) and comparison between the experimental data and numerical computations (right). 5 Application to Raticosa tunnel Numerical analyses were carried out in order to reproduce the tunnel response during excavation, which was performed with the full face method. Particular attention was posed on the chronological sequence of excavation (face advancement, lining installation, ground reinforcement) which is considered to influence significantly the deformational response. For the purpose of representing correctly the three-dimensional effects, an axis-symmetric condition is adopted (Figure 7 left). The tunnel cross section is assumed to be circular, with an equivalent radius of 7 m. The mesh is composed of square elements, with size increasing gradually from.5 m to 4 m when moving from the near vicinity of the tunnel outwards. The primary lining is represented as a.3 m-thick circular ring. The final lining is not considered. The initial state of stress is assumed constant and equal to 1.25 MPa (5 m overburden); the initial pore pressure distribution is constant and equal to 4 kpa. The rock mass is assumed to behave according Lemaitre s law. Referring to the mechanical properties of the rock mass, the viscoplastic constitutive parameters are those determined for the laboratory creep tests (Table 1). The Young modulus E =1 MPa is inferred from the ground 27

reaction curve while the Poisson s ratio =.3 is determined from triaxial tests. For the reinforced ground an elastic modulus E increased to 2 MPa is postulated. In the first phase the lining follows a linear elastic law, with the equivalent elastic properties E = 2899 MPa and =.2. The complex excavation sequence requires 254 computational steps, in order to truly follow the real chronological sequence (Figure 7 right) with particular attention paid to: (a) the face advance; (b) the first phase lining installation and (c) the ground reinforcement. According to the low permeability of the clay shales, determined during laboratory tests, the analysis were performed in hydraulic completely-undrained coupled conditions. Figure 7. Sketch of the numerical model of Raticosa tunnel (left) and chronological sequence of excavation (right). 5.1 Numerical results and comparison with monitoring data Figure 8 left shows the comparison of computed and measured values in terms of tunnel convergence for the section at chainage 3+113. The agreement of the numerical results with the mean measurement is excellent. The lining installation stops rapidly and completely the transversal displacements. Figure 8. Comparisons between numerical results and monitoring data: convergences in section 3+113 m (left) and longitudinal displacements (extrusion) in section 3+12 m (right). 271

Figure 8 right shows the comparison in terms of longitudinal displacements (extrusion) for the sliding micrometer installed in section at chainage 3+12. As the agreement is very good for the first two measurements (July, 4 and 5), it becomes less satisfactory for the latter ones (July, 6, 15 and 16). From this point of view, it is worth remembering that on July, 16 an important face instability occurred. 6 Conclusions The studies carried out on Italian clay shales in order to describe the time dependent behaviour at laboratory and tunnel scale have been described in this paper. The interest was posed on the triaxial tests of laboratory specimens taken at the face of the Raticosa tunnel, along the Apennines, during the undrained and subsequent constant deviatoric phase. The viscoplastic constitutive parameters of the Lemaitre s law were determined to fit the experimental data successfully. It has been shown that the ground response at the tunnel face and in its surrounding can be described in detail. An axis-symmetric finite difference model was implemented by using the Flac code and the advanced viscoplastic constitutive law above, with parameters based on laboratory testing. The role of time-dependent constitutive laws in the analysis of tunnels in squeezing rock conditions and full face excavation has been underlined. 7 References Barla G., Pazzagli G., Rabagliati U. 1986. The San Donato tunnel (Florence). Proc. Int. Congress on Large Caverns. Florence, Italy, 61-69. Barla M. 1999. Tunnels in swelling ground Simulation of 3D stress paths by triaxial laboratory testing. Ph. D. Thesis, Politecnico di Torino, Italy. Bonini M. 23. Mechanical behaviour of Clay-Shales (Argille Scagliose) and implications on the design of tunnels. Ph. D. Thesis, Politecnico di Torino, Italy. Bonini M., Barla G., Barla M. 23. Characterisation studies of Tectonised Clay Shales and implications in the excavation of large size tunnels. 1 th International Congress on Rock Mechanics ISRM 23, Johannesburg. Boidy E. 22. Modélisation numérique du comportement différé des cavités souterraines. Ph. D. Thesis, Université Joseph Fourier, Grenoble, France. Itasca, 2. FLAC, Fast Lagrangian Analysis of Continua, Version 4.. Itasca Consulting Group Inc. Lemaitre J., Chaboche J.L. 1996. Mécanique des matériaux solides. Dunod, 253-341. Lunardi, P. and Focaracci, A. 1999. The Bologna to Florence high speed railway line: Progress of underground. In Alten et al. (ed.), Challenges of the 21 st Century, Rotterdam: Balkema. Perzyna P. 1966. Fundamental Problems in Viscoplasticity. Advances in Applied Mechanics, Academic Press, 9, 243-377. 272