elastoplastic modeling of the chimney failure potential at

Elastoplastic Modeling of the Chimney Failure Potential at the Face of Underground Openings Z. Agioutantis1, P. Viopoulos1, S. Maurigiannakis1

1 Department of Mineral Resources Engineering, Technical University of Crete, 73100 Hania ABSTRACT Chimney failures in the overburden may occur as a result of urban tunnelling or mining activities. Propagation of these failures has undesirable effects both underground and on the surface. These failures may be attributed to a number of distinct mechanisms, each associated with different geological environments. These mechanisms are usually connected with shallow cover, weakness in the crown of an opening, insufficient cover to overlaying permeable water bearing strata, etc. Furthermore, they can also be due to vertical fissures, pipes and man made features, such as wells or sewer constructions. At the underground level a range of effects may be evident such as instability of the sides of the opening, popping of the face, or explosive failure of the soil / rock mass. When such failures propagate to the surface, consequences there may also be severe depending on the specific conditions. In this paper, soil / rock mass parameters that may lead to chimney failure of the face of shallow underground openings are investigated using the finite element method. Both elastic and elastoplastic solutions are presented with a measure of the expected deformations. 1. INTRODUCTION Tunneling in soft clayey soils has become very popular in recent years because it is one of the best construction methods for building mass rapid transit systems and sewage collection systems in densely populated cities. As the face of a tunnel is advanced, a means of supporting the ground close to the face may be needed; without such support, collapse might occur due to gross plastic deformation of the soil (Lee et al, 2006). If this collapse propagates to the surface, then chimney caving occurs, and consequences there may also be severe depending on the specific conditions (Fig. 1).

Fig. 1. Typical caving mechanisms under shallow cover (HSE, 1996). Three distinct chimney caving mechanisms are identified by Brady and Brown (1985), each associated with different geological environments. These mechanisms are usually connected with shallow cover of overlaying materials, weakness in the crown of an opening, insufficient cover to overlaying permeable water bearing strata, etc. Furthermore, they can also be due to vertical fissures, pipes and

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11th ACUUS Conference: “Underground Space: Expanding the Frontiers”, September 10-13 2007, Athens - Greece

man made features, such as wells or sewer constructions. When such conditions occur, either as a result of urban tunnelling or mining activities, effects are undesirable both underground and on the surface. At the underground level a range of effects may be evident such as instability of the sides of the opening, popping of the face, explosive failure of the soil / rock mass. The first mechanism occurs in weathered or weak rock, or in previously caved rock. The second mechanism involves unravelling of a discontinuous rock mass, while the third mechanism relates to adverse structural features (Brady and Brown, 1985). The presence of weak lenses (i.e. sand lenses) raise the possibility of ravelling or running sand conditions leading either to local or global instability. For example, during construction of the Toulouse metro extension (Langmaack and Feng, 2005) an EPB tunnel boring machine was affected by sand lenses. This progressive mechanism starts with failure of the roof or the face. If a stable, self-supporting arch cannot be formed, the failure may progressively propagate towards the surface. As materials falls from the roof or from the propagating cave, it will bulk and will tend to fill the stope void. Unless the stope is initially large and open, or unless sufficient material is progressively drawn from it, the stope will eventually become filled with caved material, which will provide support for the upper surface and so arrest the development of the cave. This progressive failure mechanism has been well established in model studies of the failure of shallow tunnels in sand and clay and in model studies of the mining of steeply dipping, tabular orebodies (Seidenfub, 2006). It is most likely to occur when the mechanical properties of the weak material are similar to those of a soil. Once initiated, propagation of the failure to surface can be very rapid, above all in regions of insufficient cover (Fig. 1). This can give the impression that the cave reaches the surface instantaneously and that the mechanism is that of sudden plug subsidence rather than a progressive one (Seidenfub, 2006). In this paper, the potential of chimney failure as described by the first mechanism is investigated through a parametric analysis. The parametric analysis with respect to geometry of the geological formations in front of the face, involves the development of a number of 2D longitudinal section models. 2. MODEL DESCRIPTION The models were developed in the MSC.Marc 2005 R3 platform, which is a non-linear Finite Element package. Thus the tunnel crown was located 10m below the surface, tunnel diameter was 6m and tunnel length from the right border to the face was 10m. The overall dimensions of the model were selected in order to avoid edge effects, i.e. the influence of the borders on the solution around the tunnel face (Fig. 2). Each model describes the same geometrical model, but with varying material models and properties. Thus, a “soft” soil material lens was introduced via a parametric analysis. The lens was rectangular with side equal to 0.5D, 1D, 1.5, 2D, 2.5D, 3D, 3.5D and 4D, where D was the tunnel diameter (Fig. 3). The surrounding material (termed “soil1”) was always considered as an elastic, homogeneous and isotropic material with properties shown in Table 1. The material in the lens (termed “soil2”) was considered an elastoplastic material with properties also shown in Table 1. The elastoplastic material follows the linear Mohr-Coulomb criterion, i.e. the material behaves as elastic up to the yield point. Elastic beam elements were introduced to support the tunnel with spacing equal to 1m. Each model was descretized using eight node plane strain quadrilateral elements (element type 27), which are considered more appropriate when modelling soil-like materials. Each model comprised 2695 elements and 8177 nodes. Boundary conditions were as follows: rolling nodes on the horizontal (x) direction at the base of the model and rolling nodes on the vertical (y) direction (left side of the model) as shown in Figure 1. Loading was accomplished through gravity, where the unit weight of all geomaterials is set to 24kN/m3

.

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Fig. 2. Typical 2D model.

Fig. 3. Series of 2D models developed for the parametric analysis.

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Table 1. Material models used in the analysis. Material Elastic

modulus Poisson’s

ratio Angle of Internal

Friction Cohesion Model

soil 1 150 MPa 0.3 - - elastic

soil 2 1.5 MPa 0.3 5 deg 10 kPa elastoplastic

beam 210 GPa 0.25 - - elastic

3. RESULTS AND DISCUSSION The purpose of this parametric analysis was to determine the changes in the stress, strain and displacement regime around the tunnel face, when ground conditions suddenly change, i.e. from good to poor, either due to water presence or to weak soil lenses, which result in conditions that can promote chimney formations. Results are shown in diagrams for horizontal (Fig. 4) and vertical displacements (Fig. 5) on the face of the tunnel for each of the aforementioned models. Results indicate, that the larger the lens of the weak material, the larger the calculated horizontal and vertical displacements at the face. The orders of magnitude shown i.e. around 100cm indicate that immediate collapse at the face is expected. Figure 6 demonstrates material movement using the concept of total displacements, i.e. the algebraic sum of vertical and horizontal displacements. Chimney formation is evident as the relative volume of the week material increases. Figure 7 shows this movement in detail for the 4D case. Results similar to those obtained for the face movements were obtained for the vertical and horizontal displacements at the surface. The maximum vertical displacement for the 3.5D case was in the order of 150cm while for the 4D case it was in the order of 550cm.

-100

0

100

200

300

400

500

0 100 200 300 400 500 600 700

Face Location (cm)

Hor

izon

tal D

ispl

acem

ents

(cm

)

0 D0.5 D1 D1.5 D2 D2.5 D3 D3.5 D4 D

Fig. 4. Horizontal displacements on the face line (the zero point is at the top of the face).

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-180-160-140-120-100

-80-60-40-20

00 100 200 300 400 500 600 700

Face Location (cm)

Ver

tical

Dis

plac

emen

ts (c

m)

0 D0.5 D1 D1.5 D2 D2.5 D3 D3.5 D4 D

Fig. 5. Vertical displacements on the face line (the zero point is at the top of the face).

Fig. 6. Total displacement contours for all models. 4. SUMMARY AND CONCLUSIONS Simple models were developed for the estimation of displacements (and therefore, strains and stresses) on a free tunnel face and the surface for a potential chimney failure mechanism for the case of weak rock at the face.

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Fig. 7: Total displacements for the 4D case. Vertical movement at the surface is in the order of 500cm, while horizontal movement at the face is in the order of 450cm.

Although plain strain conditions are not very representative of the actual geometry of a longitudinal tunnel section, model solution times are very good and elastoplastic (linear Mohr Coulomb) material modelling can give an estimation of material flow and magnitude of movement. A necessary step towards dependable utilization of this technique for potential chimney failure forecasting requires model calibration with actual measurements prior to such failures. Future work will involve incorporation of pore water pressure (either transient or stready state), as well as other soil strength criteria. Also modelling in three dimensions will overcome the problem of modelling longitudinal sections of circular openings in two dimensions. REFERENCES Brady, B.H.G., Brown, E.T., 1985. Rock Mechanics for Underground Mining. George Allen & Unwin

(Publishers) Ltd, London. Health and Safety Executive, 1996. Safety of New Austrian Tunnelling Method (NATM) Tunnels.

HSE Health & Safety Executive Books, London. Langmaack, L. ,Feng, Q., 2005. Soil Conditioning for EPB Machines – Balance of Functional and

Ecological Properties. In www.ugc.basf.com/NR/rdonlyres/2D00D73B-3DF0-4939-87AA-0E035839C388/0/ITA2005.pdf

Lee, C.J., Wu, B.R., Chen, H.T., Chiang, K.H. ,2006. Tunnel stability and arching effects during tunneling in soft clayey soil. Tunnelling and Underground Space Technology 21, 119 - 132.

MSC Marc 2005, Users Manuals. MSC Marc Mentat Volume B: Element Library. Seidenfub, T., 2006. Collapses in Tunnelling. Master thesis, Lausanne 2006. Master Degree,

Foundation Engineering and Tunnelling, Stuttgart, Germany.

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elastoplastic modeling of the chimney failure potential at

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