Simulations of tunnel excavation in 2D and 3D conditions considering building loads

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1 Simulations of tunnel excavation in D and 3D conditions considering building loads T. Nakai, E. Sung, H.M. Shahin & M. Yamamoto Nagoya Institute of Technology, Nagoya, Japan ABSTRACT: Two-dimensional model tests of group and d raft using trap door apparatus are carried out to investigate the effects of the building loads during tunnel D and 3D finite element analyses using elastoplastic subloading tij model are also conducted in this research. The deformation mechanism and the earth pressure distribution during the tunnel excavation in the by the building loads are different from those of the situation. Surface settlement trough for tunnel excavation in the disturbed by existing buildings does not follow the usual pattern of a Gaussian distribution curve, as generally observed for the condition. Due to the building loads, unsymmetrical earth pressure distribution is seen at the level of tunnel, even after completion of tunnel The settlements of the cap are unequal for sequential excavation in 3D condition. The numerical results show very good agreement with the results of the model tests. INTRODUCTION As a lot of structure exist alongside the road where tunnel is usually excavated, the interaction of existing structure and tunneling should properly be considered during tunnel construction. This interaction could be thought in two cases. One is the influence of tunnel construction on existing s, and the other is the influence of construction and loading on existing tunnels. Especially, the effect of tunneling to the foundation not yet fully understood. Recently, several studies on this interaction problem have been published. Among them Jacobsz et al., (4) published the study about the behavior of single driven due to tunneling. They discussed about the changes of settlement, base load and shaft friction in dense sand using Centrifuge test. And they also presented the affected area for settlement due to tunneling. Shahin et al., (4) presented the numerical analysis and plane strain trap door test for tunnel earth pressure and settlement considering footing as a foundation of existing building. This paper reports D model test and numerical analyses to investigate the effects of tunneling near group and d raft. Firstly, earth pressure and settlement are investigated. Then, the change of load of the is presented with excavation step. Some topics are also studied using 3D finite element method to investigate the effects of 3 dimensional condition in the tunnel All the model tests and numerical analyses were carried out assuming that the initial stress in the and s is induced with the existing building load. DESCRIPTION OF D MODEL TEST Figure represents the D trap door apparatuses for d raft used in the model tests. The apparatus consists of brass blocks (blocks A to J) of 8 cm in width each, and set along the centerline of an iron table. Ground is made with the mass of aluminum rods, having diameters of.6 mm and 3. mm mixed in a ratio of 3: in weight. The unit weight of the aluminum rod mass is.4 kn/m 3, and the length is 5 mm. After the installation of the in the, tunnel excavation is performed descending block F until 4 mm. In every excavation step, earth pressure is measured by 3 load cell blocks, each of which consists of Supersonic Transducer Figure.. B=8cm Laser type Displacement Transducer Lp Dp A AB B C D E F FG G H I J J Imposing Dead Load Mass of aluminum rods Load cells D Block Handle D trap door apparatus for d raft and group 637 Copyright 6 Taylor & Francis Group plc, London, UK

Table. D Model tests. Case D/B D p /B L p /B Case... Case 3... Case 3 3... 8 load cells. And, the surface settlement is measured using a laser type displacement transducer.

2 Table. D Model tests. Case D/B D p /B L p /B Case... Case 3... Case load cells. And, the surface settlement is measured using a laser type displacement transducer. The references (Nakai et al., 997 and Shahin et al., 4) described the details of the apparatus. Piled raft (or cap) is made by aluminum plate of 8 cm in length and cm in thick.the is made by polyurethane, and the Young s modulus of this material is kn/m. The material is chosen assuming a similarity ratio of : between the model test and prototype. The thickness of the is.5 cm and the length is varied according to the pattern of the test.the model tests and the numerical analyses are carried out for two types of deep foundation of the structure, one is for group and the other is for d raft. For both deep foundations, three patterns of tests are performed which is shown in Table. The model tests are conducted for two kinds of soil covers, D/B equals., 3., and D p /B equals.,.. Here, D is the depth of from the surface to the top of the tunnel, B is the width of trap door, and D p is the vertical distance between the tip and the tunnel block. And L p (=D D p )isthe length of s. 3 NUMERICAL ANALYSES Figure shows the D and 3D mesh used in the finite element analyses. Isoparametric 4-noded and 8- noded elements are used in the mesh for D and 3D, respectively. Both vertical sides of mesh are free in the vertical direction, and the bottom face is fixed. To simulate the tunnel excavation, vertical displacement is applied up to 4 mm to the nodes that correspond to the tunnel block. D analyses are carried out with the same conditions of D model test. To simulate 3D sequential excavation, vertical displacement is applied sequentially. 3D numerical analyses are also performed for two kinds of foundation. One is a square footing, and the other is a d raft. In the d raft D/B is.. And D p /B is.. The same amount of the dead load (Q v = 3. N/cm) is used for comparison between the group and d raft in the D model tests and numerical analyses. In case of 3D analyses the amount of applied dead load is 5.88 N/cm. The constitutive law used in this numerical analysis is the subloading t ij model (Nakai and Hinokio, 4). Figure 3 shows the results of the biaxial tests for the mass of aluminum rods used in the D model tests and numerical analyses. From these results, it is seen Figure. stress ratio σ /σ Figure 3. D and 3D FEM mesh. Biaxial Test. observed (σ=9.6kpa) calculated (σ=9.6kpa) calculated(σ=.kpa) εd (%) Stress strain dilatancy relation. εv (%) that the mass of aluminum rods has a property of the positive and negative dilatancy like dense sand. In this figure, the dotted line represents the numerical results for a confined pressure of times about the confined pressure of the experiments. From figure 3, it is noticed that the subloading t ij model can express the dependency of stiffness, strength and dilatancy on density and confining pressure. It can be also understood that the subloading t ij model can express softening behavior of the mass of aluminum rods very well. The model parameters for D and 3D numerical analyses are represented in Table. The parameters can easily be obtained from traditional laboratory tests. In the numerical analyses, the initial stress is calculated by the simulation of the self-weight consolidation. And then existing load is applied to the foundation. This state of is assumed as the initial condition of the tunnel In all numerical analyses, the elements of the and the raft (cap) are modeled as a linear elastic material. 638 Copyright 6 Taylor & Francis Group plc, London, UK

3 Table. Material parameters for aluminum rods. Q V =3.4(N/cm) Q V =3.4(N/cm) λ.8 κ.4 N (e NC at p =.3 Same parameters as 98 kpa & q = kpa) Cam-clay model R CS = (s /s 3 ) CS(comp.).8 ν e. β. Shape of yield surface (same as original Cam-clay at β = ) a 3 Influence of density and confining pressure) 4 RESULT AND DISCUSSION 4. Earth pressure and surface settlement of the D condition Figure 4 represents the earth pressure of the model tests and numerical analyses at the level of the lowering block of the group due to tunneling. Figure 5 represents the distribution of earth pressure for the d raft. The solid line without marks shows the result of the earth pressure for the conditions. From these figures, it can be seen that the distribution of earth pressure for the existing group or d raft is different from that for the condition. Especially, at the place of the installed the vertical stress distribution is very different from the condition due to the initial stress condition. Figures 6 and 7 represent the surface settlements for the model tests and numerical analyses both for the group and the d raft. It is revealed in these figures that the settlement profiles for the existing group or d raft are different from the condition. For both cases the maximum settlement occurs at the place of the existing structure. The maximum settlement is larger than the condition for this amount of applied load. It is also noticed that the inclination of the group or d raft depends on the distance between the tip and the excavation block (D p ). The closer the tip from the excavation block, the more inclination of the existing structure towards the excavation place is seen. Figure 8 is the distribution of the deviatoric strain for the d raft. It is seen in this figure that the deviatoric strain of the is developed during However, because of the disturbed initial stress, the development of the deformation is different between the left and the right side of the excavation block from the initial excavation step, which results the unsymmetrical distribution of earth pressure in case of the d raft. The deformation is formed from the excavation block to the position of the front in case of D p is equal to 8 cm, which is seen case in figures 8. /γ Ζ 4 3 Case Case.mm AL Case 3 Case Figure 4. /γ Ζ /γ Ζ D/B=. Dp/B=. D/B=3. Dp/B=. D/B=3. Dp/B=. Pile=6cm d=.mm Case Case D/B=. Dp/B=. D/B=3. Dp/B=. D/B=3. Dp/B=. Pile=6cm Distribution of earth pressure in the group. 4 4.mm AL d=.mm.5 D/B=. D/B= Dp/B=.. Dp/B= Case Case 4 D/B=3. D/B=3. D/B=3. D/B=3. Dp/B=. Dp/B=. Dp/B=. Dp/B= Case Case Figure 5. Settlement (cm) D/B=. Dp/B=. D/B=3. Dp/B=. Distribution of earth pressure in the d raft. d=mm 4mm D/B=3. Dp/B=. =6cm Figure 6. Q v =3.4 (N/cm) D/B=. Dp/B=. D/B=3. Dp/B=. D/B=3. Dp/B=. =6cm Q v =3.4 (N/cm) (*98 Pa) d=mm 4mm (*98 Pa) (*98 Pa) Surface settlement for the group. 639 Copyright 6 Taylor & Francis Group plc, London, UK

Settlement (cm)...3.4.5...3.4.5 D/B=. Dp/B=. D/B=3. Dp/B=. d=mm 4 D/B=. Dp/B=. D/B=3. Dp/B=. - - 4 8 6 - - 4 4 8 6 Figure 7. Surface settlement for the d raft. Case Case d=mm 4mm Figure 8.

4 Settlement (cm) D/B=. Dp/B=. D/B=3. Dp/B=. d=mm 4 D/B=. Dp/B=. D/B=3. Dp/B= Figure 7. Surface settlement for the d raft. Case Case d=mm 4mm Figure 8. Distribution of deviatoric strain contour (after excavation). In contrast, the deformation is extended from the right side of the excavation block to the position of the rear in case of D p is equal to 6 cm as seen in figure 8. From the initial step, the development of deviatoric strain in the right side of excavation block is faster than the left side. Figure 9 shows the computed displacement vectors for the group and d raft for lowering block F. It is revealed in this figure that the deformation zone in case of D/B =., 3. and D p /B =. spreads towards the tip of the front from the top of the lowering block, which is different from the result observed for the condition. The cap or raft is rotated to the direction of the excavation except D/B = 3. and Dp/B =.. In case of D/B = 3. and Dp/B =., deformation spreads towards the head of the rear both for the d raft and the group. Therefore, the cap of the group and the raft of the d raft do not rotate to the direction of the tunnel but do in the opposite direction. Although the foundations of the same length are located at the same place of the, the distance of tip and tunnel is most important to the behavior of foundation. 4. Effect of existing load on bearing capacity in the D condition Figures and represent the results of vertical load of the s and settlement of the s and around the for existing load Q v = 3.4 N/cm and Q v = 5.88 N/cm. Figure illustrates the shaft friction load. Here, the vertical load of the is calculated from the vertical stress of the element at every excavation step. The settlement of the presented Figure Piled raft (a) case (b) case D/B=. Dp/B=. (Front ) D/B=. Dp/B=. (Rear ) Displacement vector of the d raft. d=.mm d=.mm (a) load D/B=., Dp/B=., (Front ) d = 4. mm D/B=.,Dp/B=., (Rear ) d=4. mm.5..5 Settlement (cm) (b) settlement of and Figure. Computed vertical load and relative settlement for front and rear pil. (Q v = 3.4 N/cm). - - D/B=. Dp/B=. (Front ) D/B=. Dp/B=. (Rear ) d=.mm d=. mm (a) front and real D/B=., Dp/B=., (Front ) d=4. mm D/B=., Dp/B=., (Rear ) d=4. mm.5..5 Settlement (cm) (b) settlement of and Figure. Computed vertical load and relative settlement for front and rear (Q v = 5.88 N/cm). here is the vertical displacement of node after completion of the excavation (d = 4 mm). The shaft load capacity of the is calculated from the difference of the vertical load of the head and the 64 Copyright 6 Taylor & Francis Group plc, London, UK

5 Pile length (cm) Pile length (cm) Figure. D/B=., Dp/B=., (Front ) d =. mm D/B=., Dp/B=., (Front ) d =. mm (a) applied building load (Qv=3.4 N/cm).4. Head load Tip load Head load Tip load (b) applied building load (Qv=5.88 N/cm) D/B=., Dp/B=., (Rear ) d =. mm D/B=., Dp/B=. Pile=8c, (Rear ) d =. mm Computed change of shaft friction load. position along the depth of the at every excavation step. It is seen in these figures that the occurrence of the settlements is different between these load magnitudes. When exiting load is 3.4 N/cm, due to the tunnel excavation the settlement is larger than the settlement of the front, but the settlement of the rear is larger than the settlement. However, for Q v = 5.88 N/cm the settlement of the both s are larger than the settlement of the. For the larger settlement of the around the front in case of Q v = 3.4 N/cm, negative friction is developed on the face of the front. In contrast, the larger settlement of the produces positive friction on the face of the. The differential settlement is seen in the d raft, and it is also varied according to the magnitude of the existing load. It is seen that the vertical load at the head of the decreases more than the tip due to the development of the negative friction. It is also seen in Figure (a), the shaft friction load decreases significantly with the excavation step as negative friction is developed at the front of the d raft. However, for the settlement of the larger than the like figure (b) the reduction of the shaft friction is less compare to the negative friction. 4.3 Computed results of 3D condition Figure 3 is the computed vertical load of for 3D sequential excavation, where D/B is. and D p /B is.. It is seen in the figure that until the excavation front of the tunnel is reached the center of the cap, the vertical load of front decreases. However, after - y=4 y= y= initial load y=4cm y= y=4 tunneling complete front (a) front rear y= initial load y=4cm y= y=4 tunneling complete (b) rear Figure 3. Change of vertical load for 3D sequential / γζ Q v =. N D/B=. Footing (8*8 cm) Q v =9.4 N D/B=. Dp/B=. initial condition y= y= y= 4 final step Q v =9.4 N (*98 Pa) Figure 4. Change of computed earth pressure for sequential excavation in the middle section of the. the excavation front passes the center of the cap, the vertical load of the backs to the initial value. This is due to increase of the lateral initial value. This is due to increase of the lateral arching pressure in the as the excavation front goes away from d raft. These are different results between D and 3D analyses results. Figure 4 shows the distribution of earth pressure at the level of the applied displacement for sequential excavation in the middle transverse section of the. Same as the results of D, unsymmetrical earth pressure distribution is seen for existing load, and it is more severe in case of the d raft than the footing. 64 Copyright 6 Taylor & Francis Group plc, London, UK

Settlement (cm) -. Green field Footing Q v =9.4 N Piled raft -. - 4 Distance from tunneling centerline (cm) Figure 5.

6 Settlement (cm) -. Green field Footing Q v =9.4 N Piled raft Distance from tunneling centerline (cm) Figure 5. Surface settlement at the end of the tunnel In the 3D condition, when the excavation front passes the foundation, lateral earth stress is smaller than those of D plain strain condition due to the arching in the direction of tunnel However, if tunnel face goes away from the foundation, the effect of lateral arching increases and consequently lateral earth pressure increases. Figure 5 is results of surface settlement in the middle transverse section of the. Same as the earth pressure distribution, the shape of surface settlement trough for the footing and d raft is not symmetric. It can be seen that the maximum surface settlement of the d raft is a little than the footing. Figure 6 shows plan views of vertical settlement contours for the condition and footing. The figure represents the results where the excavation front at the middle transverse section and at the end of the. In the, the settlement is uniform along to the tunnel axis. However, the settlement with footing is asymmetric and concentrates around footing. Figure 7(a) is the settlements of four points on the footing for sequential The settlements of all points are different at every excavation step, and this difference increases when the excavation front goes away from the centerline. The footing rotates in the different direction at the four points as seen in Figure 7(b), which results the twisting of the foundation. 5 CONCLUSIONS To investigate the interaction problems of foundation and tunneling, D model test and elastoplastic finite element analyses are carried out. The influences of type, soil cover, length and intensity of existing loading size on the behavior of d raft are investigated. From the model tests and numerical analyses, the following points can be concluded: () For the group and the d raft, unsymmetrical earth pressure distribution is observed at the Figure 6. Footing edge point settlement (mm) 3 4 Contours of surface settlement. y= point point point 3 point 4-4 Position of tunnel face; y (cm) (a) settlement Rotation angle (degree).8 Footing Z.6 Y.4. X Y= Rotation about X Rotation about Y Rotation about Z Position of tunnel face; y (cm) (b) rotation angle Figure 7. Settlement and rotation of footing for sequential level to the tunnel due to the change of the initial stress of the. () Surface settlement troughs for tunnel excavation in case of existing group or d raft are different from condition. The deformation zone of the spreads towards the foundation from the tunnel crown. (3) The distance between the tip and the crown of the tunnel is more important than the length in the interaction problem of tunneling and foundation. (4) The vertical load of the front that is nearer to the excavation block decreases significantly with the tunnel excavation in the D condition. In contrast, the vertical load of the rear increases with the excavation of the tunnel. (5) Differential settlement and rotation of the footing are seen at every step of 3D sequential 64 Copyright 6 Taylor & Francis Group plc, London, UK

7 REFERENCES Jacobsz, S. W., Standing, J. R., Mair, R. J., Hagiwara, T., and Sugitama, T. 4. Centrifuge modeling of tunnelling near driven s. Soils and Foundation. 44(): Nakai, T., Xu, L., andyamazaki, H. (997): 3D and D model tests and numerical analyses of settlements and earth pressure due to tunnel excavation, Soils and Foundations, 37(3), 3 4. Nakai,T., and Hinokio, M. 4.A simple elastoplastic model for normally and over consolidated soils with unified material parameters. Soils and Foundation. 44(): Shahin, H. M., Nakai, T., Hinokio, M., Kurimoto, T., and Sada, T. (4): Influence of surface loads and construction sequence on response due to tunneling, Soils and Foundation, 44(), Copyright 6 Taylor & Francis Group plc, London, UK

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