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Response analysis of nearby structures to tunneling-induced ground movements in sandy soils
Tunnelling and Underground Space Technology 48 (2015) 156–169
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Response analysis of nearby structures to tunneling-induced ground movements in sandy soils Moorak Son Dept. of Civil Engineering, Daegu University, Jillyang, Gyeongsan, Gyeongbuk 712-714, South Korea
a r t i c l e
i n f o
Article history: Received 14 February 2014 Received in revised form 7 February 2015 Accepted 17 March 2015
Keywords: Tunneling Ground movement Structural damage Damage estimation Design frame Engineering practice Soil–structure interaction
a b s t r a c t This study examined the effects of tunneling-induced ground movements on the nearby structures in sandy soils considering the soil–structure interactions of different tunnels, structures, ground, and construction conditions. The investigation relates the level of structural distortion and damage to different tunnel field conditions. For this purpose, extensive numerical parametric studies were conducted and the results were compared with some field cases. The discrete element method (DEM) has been used to model structural cracking when the shear and tensile stress exceeds the maximum shear and tensile strength. Two different structures, brick-bearing and brick-infilled frame structures, were considered, and the distortion and cracking induced in the structures was related to different tunnel field conditions. A relationship that correlates the tunnel depth to diameter (Z/D) ratios and ground loss conditions with a level of structural damage with different ground and structure conditions was developed to integrate the study results into a design frame in engineering practice. The relationship developed can be used practically to assess the structural damage in the design stage of tunnel constructions under a range of tunnel field conditions. These results will provide a background for a better understanding of how to control and minimize the damage of the structure to tunneling-induced ground movements in sandy soils under different tunnel, structure, ground, and construction conditions. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction The number of tunnel constructions in congested urban spaces are increasing for many reasons, such as the development of underground transit systems and installing a range of utilities. At the same time, there has been increasing public concern regarding the effects of tunneling-induced ground movements on the adjacent structures. Tunneling-induced ground movement can distort and damage the adjacent structures, causing several problems, such as the loss of property, construction delay, and increase in project cost. To minimize these problems, it is important to have a reliable damage assessment of the adjacent structures as well as an appropriate protection measure prior to tunnel excavation. Reasonable damage assessments require a better understanding of the complex soil–structure interactions among the tunnel, structure, ground, and construction conditions. A failure to understand these interactions can lead to the implementation of unnecessary protection measures, unnecessary cost and unsatisfactory results.
E-mail address: [email protected] http://dx.doi.org/10.1016/j.tust.2015.03.008 0886-7798/Ó 2015 Elsevier Ltd. All rights reserved.
The response of the adjacent structures to excavation-induced ground movements has been investigated. Notable studies include Breth and Chambosse (1974), Attewell (1977), Boscardin and Cording (1989), Burland (1995), Boone et al. (1999), Finno et al. (2005), Schuster et al. (2009), Son and Yun (2009), Son et al. (2008), and Son and Cording (2005, 2011). Compared to previous studies, the present paper reports the results of a systematic integration of various tunnel conditions into a design frame, which guides the relationship between the different tunnel conditions and structural damage. In general, a structural response depends on a range of factors including the tunnel and structure conditions as well as the ground and construction conditions. Although field observations are of major importance in assessing the structural response to a nearby tunnel excavation, numerical model tests have the ability to add unique perspectives to an evaluation of the structural response. This study examined the structural response to tunneling-induced ground movements in sandy soils based on extensive numerical model tests. The structural distortion and damage were examined under a controlled variation of the tunnel (tunnel depth and diameter), structure (brick-bearing structure and brick-infilled frame structure), ground (looser and denser soil), and construction (ground loss) conditions. The results are expected to provide a
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background for a better understanding of how to control and minimize the building damage to the nearby structures due to tunneling-induced ground movement in sandy soils under many different field conditions.
Tunnel construction in urban areas can cause damage to the adjacent structures due to tunneling-induced ground movements. Ground movement is largely affected by the tunnel condition (depth and diameter), ground condition (loose sand and dense sand) and construction condition (ground loss in a tunnel caused by over excavation, delayed support and grouting installation, support deflection, and face instability, such as raveling or flowing). The ground loss is defined as the volume lost into a tunnel divided by the theoretical tunnel volume. Tunneling-induced ground movements differ from building self-weight-induced settlements in that the former generally have much larger horizontal displacements, which can cause more severe structural damage. Therefore, to assess the structural damage reasonably, it is essential to estimate the horizontal ground movement as well as the vertical ground settlement, where a structure is located. Peck (1969) assembled empirical information of the tunnel case histories in different types of ground and suggested an error function or normal probability curve for the shape of the settlement trough as follows. 2
S ¼ Smax e
x2 2i
where S is the settlement at a distance x from the center of the settlement trough, Smax is the settlement at the center of the trough, i is the point of inflection of the curve, and x is the distance from the center of the trough (refer to Fig. 1). The volume (Vs) of the settlement trough is equal to 2.5 i Smax. The points of inflection of the curve are located at a distance, i, on either side of the center line of the trough. The location of the inflection points (i) were determined from the relationship between the tunnel depth (Z) and radius (R), as shown in Fig. 2. Therefore, the ordinate of the normal probability curve can be determined at any distance from the tunnel center line in the transverse direction, provided that the inflection point and maximum settlement can be determined. The horizontal surface displacement can have a significant effect on the damage to the structures. On the other hand, it has not been commonly measured in the field and there is insufficient field data and information to estimate the horizontal surface displacement profile with the same degree as the settlement profile. Nevertheless, O’Reilly and New (1982) provided an equation to estimate the tunneling-induced horizontal displacements as follows:
x x2 Sh ¼ Smax 1:65 e 2i2 i W=2.5i
Inflection Point
Fig. 1. Error function or normal probability curve to represent a settlement trough above the tunnel (after Peck, 1969).
z/2R
2. Tunneling-induced ground movements and structure responses
Rock, Hard Clays, Sands Above Groundwater Level Soft to Stiff Clays
Sands Below Groundwater Level
i/R Fig. 2. Relationship among tunnel depth, tunnel radius, and inflection point (after Peck, 1969).
where Sh is the horizontal displacement at a distance x from the tunnel center line, Shmax is the maximum horizontal displacement at the inflection point, and i is the point of inflection of the settlement trough. The maximum horizontal displacement occurs at the inflection point, and in the Washington D.C Metro, it was one third of the maximum vertical displacement. Cording (1991) reported that the ratio of the maximum horizontal displacement to the maximum vertical displacement varies with the width of the trough and showed that the estimated horizontal displacement at the edge of the settlement profile can be smaller than the real displacement if the equation for estimating the horizontal displacement is used. Field studies by Cording and Hansmire (1975), Attewell (1977), and Cording (1991) revealed the ratios in the range of 0.25–0.4. From the many numerical tests, Son and Yun (2009) also reported that the maximum lateral displacements are approximately 0.35 times the maximum vertical displacements, which are consistent with field observations. Extensive studies related to ground movements during tunneling in soil have been conducted by many investigators including Attewell (1977), Ward and Pender (1981), Attewell and Yeates (1984), Fujita (1989), and Mair and Taylor (1997). 3. Numerical analysis The advantages of numerical analysis are that a range of conditions can be considered easily with limited time, cost and space, and reproducible analyses. This characteristic allows examinations of the response of structures to tunneling-induced ground movements under a range of conditions. The numerical approach used in this study is similar to that of previous studies (Son and Cording, 2011) but is described again briefly. The 2-D Universal Distinct Element Code (UDEC 3.1, 2000) was used to conduct the numerical tests. Each brick was modeled as a separate elastic unit and the brick/mortar contact was modeled using the Coulomb slip model, in which the contact loses strength and a crack is formed when the contact normal stress exceeds the maximum tensile strength of the contact or the contact shear stress exceeds the contact shear strength, which
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is the combination of cohesive (c) and frictional strength (/). Further extension across the contact causes separation of the adjacent bricks that leads to a larger opening of the crack. The contact does not simulate the crush in compression, which is reasonable, because compressive strength is generally higher than tensile strength, and cracks form mostly due to tensile stress. Prior to cracking, the brick/mortar contact model has a linear stress–displacement relationship with the slope of the contact normal stiffness for the normal stress condition and with the slope of the contact shear stiffness for the shear stress condition. After the cracks form, the contact has only frictional shear resistance. This model can easily simulate the large crack opening and post-crack inelastic behavior than continuum based numerical methods, such as the finite element method (FEM), which has difficulty in simulating the many large crack openings and propagation. The approach in this study was validated from a previous study (Son and Cording, 2005) comparing the results of physical model test with the numerical simulation using the same approach. The soil was modeled as an elastic mass and the elastic soil stiffness in the numerical tests (2D) was determined to provide the same normal pressure/displacement relationship at the base of the footing as the three-dimensional (3D) condition in the field using Boussinesq’s relationships. The structure/soil interface model was similar to the brick/mortar contact but the properties were different. Therefore, the interface allowed the structure to separate from the soil or slide between the structure and the soil. The frames in the brick-infilled frame structures were modeled elastically. The analyses were performed under plane stress conditions for both the soil and structure. The entire tunnel excavation sequence with a structure was not simulated because of the numerical limitations of modeling a large number of discrete bricks forming the structure. Instead, a freefield ground displacement profile determined from the empirical field observations (Peck, 1969; O’Reilly and New, 1982) was imposed on the soil mass, which has a finite thickness (Fig. 3). Both the vertical and horizontal green-field ground movements were applied to the soil mass to allow the soil–structure interaction between the structure and soil mass. Vertical green-field ground settlement was applied to the base of the soil mass after confirming that for the green-field condition, the displacement profile induced at the surface of the soil mass was the result of applying the profile to the base of the soil mass. The horizontal displacement profile was applied to the surface of the soil mass interconnected with the building wall at the soil/structure interface. The horizontal displacement was applied to the surface of the soil mass, not the base, because for the green-field condition, the application of horizontal displacement to the base of the elastic soil mass would produce a distorted horizontal displacement at the surface. On the other hand, the soil–structure interaction for horizontal ground movement was still allowed because an equivalent soil shear stiffness was applied at the interface element. The shear stiffness at the interface was selected to provide the same horizontal pressure/horizontal displacement relationship for the 2-D model as that for the 3-D condition. Therefore, the soil–structure interaction between the building wall and the soil mass was allowed both for the vertical and horizontal ground displacements. The procedures were explained well by Son (2003), and were verified by a comparison between the large-scale physical model test (Laefer, 2001) and its numerical simulation (Son and Cording, 2005). The numerical tests were performed in several stages. At the initial stage, the initial equilibrium was obtained with the building self-weight and floor loads. At this stage, the boundary condition for the soil mass was the roller supports at each end of the two vertical boundaries of the soil mass and at the bottom boundary of the soil mass. After ensuring the initial equilibrium condition, all displacements were reset to zero and a free-field
ground displacement was imposed on the soil mass. After completing the analysis, the distortions and cracking in the structures were investigated from the results of each analysis. Modeling of the soil with an advanced constitutive model and the entire excavation sequence with a structure is desirable for a specific field condition. On the other hand, the aim of this study was to better understand the structural response under a range of tunnel field conditions. For this purpose, it would be less than ideal to model the entire excavation and structure with both excavation and structure complexities under a specific condition. Instead, it would be preferable to employ a simple and conceptual approach for this study provided the applied conditions are within the range of typical field characteristics.
4. Extensive parametric studies Based on a verification of the used numerical methodology and approach in previous studies (Son et al., 2008; Son and Cording, 2005, 2011; Son, 2013), more extensive numerical parametric studies have been conducted to examine the effects of the tunnel, structure, ground, and construction conditions on the nearby structures. Fig. 4 describes the conditions considered for the parametric studies. The tunnel depth considered was 10 m, 20 m and 30 m, and the diameter was 3 m, 6 m and 9 m. Two structure types were considered, brick-bearing and brick-infilled frame structures. Two ground conditions (loose sand and dense sand) were considered and the construction condition (ground loss) was varied from 0.17% to 0.5%, 1%, and 2%. A total of 144 cases were examined and the results were analyzed and compared. A structure was assumed to be located with one side above the tunnel centerline (see Fig. 4) with the structure imposed to both sagging (concave shape) and hogging (spandrel shape) modes of the settlement profile including the point of inflection (i.e. the point of maximum slope of the settlement trough), which could be the most unfavorable condition in terms of the structure response. The ground displacement profiles (settlement and horizontal displacement) were determined using the empirical approach described in Section 2 of this paper for sandy soil, assuming that the surface settlement volume is same as the ground loss. The surface settlement volume can be different from the ground loss due to volume changes in the soil mass. The relationship between the surface settlement volume and the ground loss around the tunnel depends on the tunnel condition (depth and diameter) as well as the soil condition (Hong, 1984 and Cording, 1991). The aim of this study was not to provide a case analysis of a specific soil and tunnel condition, but instead provide information to improve the general understanding of the structural response to tunneling. Therefore, in this study, the surface settlement volume was assumed to be same as the ground loss. Despite this, the effects of the volume change in a soil mass can also be considered by adjusting the ground loss either by adding (for dilating soil) or subtracting (for compressible soil) the possible change in volume from the ground loss given in this study. Fig. 5 shows the determined displacement profiles. Although the assumed displacement profiles in this study might not represent all the complex conditions in the field, the displacement profiles were chosen to be in the range of typical field observations (Peck, 1969 and Clough and O’Rourke, 1990). In other words, the displacement profiles are not for a specific field and construction condition, but are one of the typical displacement profiles in the field. This study was limited to the in-plane distortion of a structure. The structures that are skewed with respect to a tunnel axis may undergo three dimensional responses to ground movements. Out-of-plane distortion, such as torsion, can result in structural damage even with a small amount of in-plane distortion. Therefore, when the structure response is evaluated, the out-of-
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(Elastic frame) (Elastic brick unit) (Inelastic brick/mortar joint)
18300
Wooden lintels (25 mm thick)
3048 1270
406 12497 (4-story structure)
406
(unit: mm) Soil Element
Horizontal displacement applied Vertical displacement imposed
28956 Fig. 3. Numerical model geometries and boundary conditions for brick-infilled frame structures (⁄ Brick-bearing structures are composed of only the brick units without the frames in this figure).
In assessing the response of the structures due to tunneling-induced ground movement, cracking in a structure is a significant factor that should be considered. In this study, the structural responses were examined by simulating the crack opening and post-crack inelastic behaviors of the structures using the discrete element method. Table 1 lists the soil and structure properties for the numerical investigation. The brick unit and brick/mortar contact properties were selected based on the literatures (Beranek, 1987 and Atkinson et al., 1989).
5. Comparison of the structural response 5.1. Structural response in loose sand
Fig. 4. Considered conditions for numerical parametric studies.
plane distortion should be investigated in addition to in-plane distortion. In addition, the results in this study should be understood in the limited range of structures and ground conditions, which were considered in the study because a structural response can vary considerably with different structural conditions, such as openings or stories and different ground conditions.
5.1.1. Effect of the tunnel depth Fig. 6 compares the responses of the four-story brick-bearing structures in loose sand varying the tunnel depth for a ground loss of 1% and a tunnel diameter of 6 m. As shown in the figure, the structures were distorted with more cracking as the tunnel depth became shallower. The angular distortions (b) in bay 1 of the structures were 5.1 103, 1.96 103 and 0.12 103 for a tunnel depth of 10 m, 20 m and 30 m, respectively and the lateral strains (eL) were 6.96 103, 2.37 103 and 0.05 103 for the tunnel depth, respectively. Using the damage criterion by Son and Cording (2005), the damage to the structures was quite severe
Fig. 5. Displacement profiles applied to numerical analysis (in case of a tunnel depth of 20 m and tunnel diameter of 6 m in dense sand).
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Table 1 Soil, structure and interface properties used for numerical analysis. Structure type
Brick-bearing structure
Volume loss (%)
0.17, 0.5, 1.0, 2.0
Soil properties
Structure properties
Es (MPa) (ts = 0.33)
Brick Units
17.2
E (GPa) 10.34
Interface properties Brick/Mortar Joints
t 0.2
c
/ (°)
rt
(kN/m3)
c (kPa)
19
344
35
(kPa)
Kn (MPa/mm)
Ks (MPa/mm)
344
78
7.8
c, rt (kPa)
/ (°)
Kn (MPa/mm)
Ks (MPa/mm)
0
35
78
0.0146
68.9 Brick-infilled frame strucure
0.17, 0.5, 1.0, 2.0
17.2 68.9
0.0584 a
B: 10.34 F: 20.67
B: 0.2 F: 0.15
B: 19 F: 24
344
35
344
78
7.8
0
35
78
0.0146 0.0584
Notes: Es = Young’s modulus for soil; E = Young’s modulus for brick units; t = Poisson’s ratio for brick units; c = total unit weight; c = joint or interface cohesive strength; / = joint or interface friction angle; rt = joint or interface tensile strength; Kn = joint or interface normal stiffness; Ks = joint or interface shear stiffness. a ‘‘B’’ represents brick units and ‘‘F’’ represents frames.
Fig. 6. Comparison of the structural responses according to tunnel depth in loose sand (Brick-bearing structure, ground loss, 1%, tunnel diameter, 6 m).
for a depth of 10 m, moderate to severe for a depth of 20 m, and negligible for a depth of 30 m. Fig. 7 compares the responses of the four-story brick-infilled frame structures in a loose sand varying tunnel depth for a ground loss and tunnel diameter of 1% and 6 m, respectively. As shown in the figure, the structures were distorted with relatively more cracking as the tunnel depth became shallower. The angular distortions (b) in bay 1 of the structures were 1.11 103, 0.32 103 and 0.21 103 for a tunnel depth of 10 m, 20 m and 30 m, respectively, and the lateral strains (eL) were 0.33 103, 0.02 103, and 0.01 103 for the tunnel depth, respectively. The damage to the structures was very slight for a depth of 10 m and negligible for the other two tunnel depths. A comparison of the behaviors of the two different structures revealed the brick-infilled frame structure to sustain less damage. In a brick-bearing structure, once cracking occurs, the subsequent cracks concentrate around the initial cracks and propagate. On the other hand, for a brick-infilled frame structure, the enclosed frame confines the crack propagation so that the structure undergoes relatively little distortion with a larger tilt. In addition, the
structures are damaged more when the tunnels are excavated at a shallower depth with the same magnitude of ground loss. 5.1.2. Effect of ground loss Fig. 8 compares the responses of the four-story brick-bearing structures in loose sand, varying the ground loss for a tunnel depth and tunnel diameter of 20 m and 6 m, respectively. As shown in the figure, the structures were distorted with more cracking as the ground loss increased. The angular distortions (b) in bay 1 of the structures were 0.22 103, 1.96 103 and 7.47 103 for the ground loss of 0.5%, 1% and 2%, respectively, and the corresponding lateral strains (eL) were 0.05 103, 2.37 103 and 9.73 103. Using the damage criterion, the damage in the structure was negligible for a ground loss of 0.5%, moderate to severe for a ground loss of 1%, and very severe for a ground loss of 2%. Fig. 9 shows the responses of the four-story brick-infilled frame structures in loose sand varying ground loss for a tunnel depth and tunnel diameter of 20 m and 6 m, respectively. As shown in the figure, the structures were distorted with more cracking as the ground loss became larger. The angular distortions (b) in bay 1 of
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Fig. 7. Comparison of the structural responses according to tunnel depth in loose sand (Brick-infilled frame structure, ground loss, 1%, tunnel diameter, 6 m).
Fig. 8. Comparison of the structure responses with ground loss in loose sand (Brick-bearing structure, tunnel depth, 20 m tunnel diameter, 6 m).
the structures were 0.11 103, 0.32 103, and 0.50 103 for a ground loss of 0.5%, 1% and 2%, respectively and the corresponding lateral strains (eL) were 0.01 103, 0.02 103, and 0.09 103. The damage to the structures was negligible for all the ground losses, even though small cracks were distributed more with a larger ground loss. A comparison of the behaviors of the two different structures showed that for a small ground loss, both the brick-bearing and brick-infilled frame structures behaved like an elastic structure and there was a slight difference in the structural response. On the other hand, as the ground loss increased, the brick-bearing structure was damaged severely with large crack openings,
whereas the brick-infilled frame structure was distorted with a small difference due to the confining effect of the enclosed frame. 5.2. Structural response in dense sand 5.2.1. Effect of the tunnel depth Fig. 10 compares the responses of the four-story brick-bearing structures in dense sand with varying tunnel depths for a ground loss and a tunnel diameter of 1% and 6 m, respectively. As shown in the figure, with decreasing tunnel depth, the structure became increasingly distorted with more cracking. The angular distortions (b) in bay 1 of the structures were 8.71 103, 4.31 103 and
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Fig. 9. Comparison of the structure responses with ground loss in loose sand (Brick-infilled frame structure, tunnel depth, 20 m tunnel diameter, 6 m).
Fig. 10. Comparison of the structural responses according to tunnel depth in dense sand (Brick-bearing structure, ground loss, 1%, tunnel diameter, 6 m).
2.41 103 for tunnel depths of 10 m, 20 m and 30 m, respectively, and the corresponding lateral strains (eL) were 13.54 103, 6.25 103 and 2.34 103 for the tunnel depth, respectively. The damage to the structure was quite severe for depths of 10 m and 20 m, and moderate to severe at 30 m. Fig. 11 shows the responses of the four-story brick-infilled frame structures under the same conditions. As the tunnel depth decreased, the structure became increasingly distorted with more cracking. The angular distortions (b) in bay 1 of the structures were 1.23 103, 1.18 103 and 0.94 103 for tunnel depths of 10 m, 20 m and 30 m, respectively, and the corresponding lateral
strains (eL) were 0.48 103, 0.41 103, and 0.24 103. The damage to the structure was slight for depths of 10 m and 20 m, and very slight for a depth of 30 m. A comparison of the behaviors of the two different structures showed that the brick-infilled frame structure sustained much less damage. Regardless of the different levels of distortion, both structures were considerably more distorted and damaged than the structures on loose sand. This was attributed to a soil–structure interaction, where the ground displacement of loose sand is modified significantly by a structure inducing less distortion and damage. The effects of the soil stiffness on the structural damage was
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Fig. 11. Comparison of the structural responses according to tunnel depth in dense sand (Brick-infilled frame structure, ground loss, 1%, tunnel diameter, 6 m).
much more significant in the brick-bearing structure than in the brick-infilled frame structure. 5.2.2. Effect of ground loss Fig. 12 presents the responses of four-story brick-bearing structures in dense sand with varying ground losses for a tunnel depth and tunnel diameter of 20 m and 6 m, respectively. As shown in the figure, as the ground loss increased, the structure became increasingly distorted with more cracking. The angular distortions (b) in bay 1 of the structures were 1.65 103, 4.31 103 and 9.99 103 for the ground loss of 0.5%, 1% and 2%, respectively, and the corresponding lateral strains (eL) were 1.94 103, 6.25 103 and 11.07 103. The damage to the structure was moderate for a ground loss of 0.5% and very severe for ground losses of 1% and 2%. Fig. 13 shows the responses of the four-story brick-infilled frame structures under the same conditions. The structure became increasingly distorted with more cracking as the ground loss increased. The angular distortions (b) in bay 1 of the structures were 0.4 103, 1.18 103 and 1.19 103 for the ground loss of 0.5%, 1% and 2%, respectively, and the corresponding lateral strains (eL) were 0.07 103, 0.41 103, and 0.46 103. The damage to the structure was negligible, very slight and slight for a ground loss of 0.5%, 1% and 2%, respectively. A comparison of the behaviors of the two different structures revealed the brick-infilled frame structure to have sustained much less damage than the brick-bearing structure. The brick-bearing structure was considerably more dependent on the ground loss than the brick-infilled frame structure. Both structures showed more distortion and damage than the structures on loose sand, but the effects of the soil stiffness were more evident in the brick-bearing structure. 5.3. Integration of various tunnel field conditions into a design frame 5.3.1. Structural response in loose sand Fig. 14 shows the relationship among the maximum principal strain induced in a structure unit (Bay 1), tunnel depth to diameter (Z/D) ratio, and ground loss for all analyses of the brick-bearing
structure in loose sand. The maximum principal strain is the maximum average principal strain across the distorting portion (a structure unit, such as Bay 1) of a structure, not at a specific point in a structure. A structure unit can be a section between two columns or cross walls, two different geometries or stiffness. This is usually the portion of a structure closest to the excavation and subject to the largest distortions. Because vertical and horizontal ground displacements are imposed at the base of a structure, the angular distortion (b) and lateral strain (eL) are induced in a structure. A structure is deformed by a combination of the angular distortion and lateral strain, and the maximum average principal strain (ep) across a structure unit (such as Bay 1) can be determined by the state of strain theory using both the angular distortion (b) and lateral strain (eL) as follows.
ep ¼ eL cos h2max þ b sin hmax cos hmax ; tanð2hmax Þ ¼
b
eL
The angular distortion and lateral strain in a structure unit (Bay 1) can be determined by measuring the vertical and horizontal displacements at the corners of a structure unit. The details were well explained by Son and Cording (2005). The principal strains to divide the different damage levels follow the criterion reported by the same reference. The figure indicates that the maximum principal strain decreases with increasing ratio (Z/D), and a structure can be damaged quite severely for a ground loss greater than 1% if the tunnel depth to diameter ratio is less than 2.5. This also suggests that a structure can be damaged quite severely up to a ratio of 5.0 if the ground loss is 2%. For a tunnel depth to diameter ratio of approximately 3.5, the structure can sustain moderate to severe damage with ground losses of 1% and 2%. The damage to a structure on loose sand might be negligible if the ground loss is less than 0.5% or the depth to diameter ratio is greater than 6.5 for a ground loss less than 2%. Fig. 15 shows the relationship among the maximum principal strain induced in a structure, tunnel depth to diameter (Z/D) ratio, and ground loss for all analyses of the brick-infilled frame structure in loose sand. The figure shows that the maximum principal strain decreases with increasing (Z/D) ratio, but the principal strain was much smaller and less dependent on the Z/D ratio compared to
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Fig. 12. Comparison of the structural responses according to ground loss in dense sand (Brick-bearing structure, tunnel depth, 20 m tunnel diameter, 6 m).
Fig. 13. Comparison of the structural responses according to ground loss in dense sand (Brick-infilled frame structure, tunnel depth, 20 m tunnel diameter, 6 m).
the brick-bearing structure. A structure can be damaged slightly for a ground loss of 2% if the tunnel depth to diameter ratio is less than 3.5. This also suggests that the damage to a structure is negligible if the ground loss is less than 0.5% or the depth to diameter ratio is greater than 4.5 for a ground loss less than 2%. A comparison of the structural response between the brick-bearing structure and the brick-infilled frame structure showed that the former structure was much more sensitive to ground movement, and the difference in damage severity increased with decreasing depth to diameter ratio. On the other hand, the difference becomes
negligible when the ratio is larger than approximately 6.0 for a ground loss of less than 2%. 5.3.2. Structural response in dense sand Fig. 16 shows the relationship among the maximum principal strain induced in a structure, tunnel depth to diameter (Z/D) ratio, and ground loss for all analyses of the brick-bearing structure in dense sand. A comparison with loose sand showed that the maximum principal strain increased significantly at the same ground loss and depth to diameter ratio. Similarly, in loose sand, the
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165
Fig. 14. Relationship between the maximum principal strain in a structure and the tunnel depth to diameter (Z/D) ratio (Brick-bearing structures in the loose sand).
Fig. 15. Relationship between the maximum principal strain in a structure and the tunnel depth to diameter (Z/D) ratio (Brick-infilled frame structures in the loose sand).
maximum principal strain decreased with increasing Z/D ratio and the level of the decrease was dependent on the magnitude of the ground loss. The figure indicates that a structure can be damaged
quite severely up to a tunnel depth to diameter ratio of 7 if the ground loss is 2%, but the ratio for the same damage decreases to approximately 3.5 if the ground loss is 1%. In addition, a structure
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Fig. 16. Relationship between the maximum principal strain in a structure and the tunnel depth to diameter (Z/D) ratio (Brick-bearing structures in the dense sand).
can be damaged severely, even for a ground loss of 0.5 if the tunnel depth to ratio is smaller than 2.5. For a ground loss of 2%, a structure can be damaged moderately to severely at a depth to diameter ratio of approximately 10, but the ratio for the same damage decreases to approximately 5 if the ground loss is 1%. As the ground loss decreased, Z/D becomes smaller for the same degree of damage. From the figure, the damage to a structure might be negligible for a ground loss of 0.5 if the tunnel depth to diameter ratio is greater than 3.5 and for a ground loss of 1%, the ratio increases up to approximately 10 for negligible damage in a structure. Fig. 17 shows the relationship among the maximum principal strain induced in a structure, tunnel depth to diameter (Z/D) ratio, and ground loss for all analyses of the brick-infilled frame structure in dense sand. The figure clearly shows that the maximum principal strain decreases with increasing Z/D ratio, but the principal strain is much smaller and less dependent on the Z/D ratio than the brick-bearing structure. In addition, the difference in the maximum principal strain between the looser and denser soils is much smaller than that of a brick-bearing structure. The structure can be damaged slightly for a ground loss of 2% if the tunnel depth to diameter ratio is less than approximately 5.5. This also suggests that the damage to a structure is negligible if the ground loss is less than 0.17% or the depth to diameter ratio is larger than approximately 7 for a ground loss less than 2%. A comparison of the sensitivity of the structures to the ground movement revealed a brick-bearing structure to be much more sensitive than the brick-infilled frame structure. In addition, the depth to diameter ratio, in which the difference between the two structural types is negligible, was larger than that in loose sand. 5.3.3. Comparison with field cases Some limited field cases were examined for a comparison of the study results and field cases. Although there is significant field data
of ground movement and ground loss for different ground and tunnel conditions, there is limited field data, in which the soil condition, tunnel condition, ground loss, and structure response had been observed simultaneously. Nevertheless, the following three field cases were collected and investigated from the published materials (Cording and Hansmire, 1975; Boscardin, 1980; Boscardin and Cording, 1989). All three cases (Fig. 18) were investigated in relation to the construction of Washington D.C. Metro. The first case (FIELD 1 in Figs. 18a and 19) is a 2-story brickbearing wall structure, which was located 1.5 m from the tunnel centerline. The structure, 6.4 m 18.3 m in plan, had a basement and 2 stories above the ground. The longitudinal axis of the structure was skewed approximately 22° from the tunnel axis. Because of their proximity to the tunnel excavations, the structure was vacated for the duration of mining. The bearing walls were parallel to the longitudinal axis of the structure and were composed of brick with lime mortar. A steel beam supported by the façade walls and three equally spaced interior columns extended along the length of the structure. The timber floor joints spanned between the center bean and the bearing walls. The bearing walls and columns were supported by spread footings. The structure was estimated to be 80–90 years old. The tunnel was approximately 6.4 m in diameter and the springline was approximately 14.2 m below the ground surface. The tunnel was excavated using a Robbins articulated shield and the temporary lining consisted of steel ribs (1.2 m spacing) and timber lagging. The soil profile suggested that the location was near a transition from dense sand and gravel in the river flood plain deposits to hard, clay Cretaceous soils. From the tunnel construction, the ground loss induced at the ground surface was approximately 0.2%. Extensive cracking was observed on the structure before tunnel excavation, and additional cracking and an increase in the size of pre-existing cracks were noted during and after the tunnel excavation. The door became jammed and difficult to open as a result of the tunnel-
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167
Fig. 17. Relationship between the maximum principal strain in a structure and the tunnel depth to diameter (Z/D) ratio (Brick-infilled frame structures in the dense sand).
Fig. 18. Schematic views of three field cases (not scaled).
induced distortions. The angular distortion (b) and lateral strain (eL), which had been investigated in the structure, were 1.3 103 and 0.3 103, respectively. The structure was damaged slightly. The second case (FIELD 2 in Figs. 18b and 19) is a 3-story brickbearing structure that was located 9 m from the tunnel centerline. The structure, 62 m by 82 m in plan, had a basement and 3 stories above ground. The long dimension of the structure paralleled the tunnel axis. The walls were formed from brick masonry and the plaster covered the barrel and groined vaults. Spread footings provided the foundation support for the walls. The tunnel was approximately 6.4 m in diameter and the springline approximately 19 m below the ground surface. Excavation of the tunnel was accomplished with a shield and support provided by steel ribs. The steel sets were installed after each 1.2 m shove of the shield.
The soil profile at the location consisted primarily of dense silt sand and gravel. During tunnel construction, dewatering problems were encountered and many runs occurred in the sandy soil. This resulted in relatively large ground loss and the induced ground loss at the ground surface was approximately 3%. Structure sustained extensive damage and cracking appeared on all floor levels in both walls and ceilings. Large continuous cracks appeared in the crown of the corridor barrel vaults due to a horizontal extension on all three floors. The angular distortion (b) and lateral strain (eL), which was investigated in the structure, were 7.2 103 and (3.6– 7.2) 103, respectively. The structure was damaged severely. The third case (FIELD 3 in Figs. 18c and 19) is a 4-story brickbearing structure that was located approximately 6.7 m from the tunnel centerline. The structure, 18 m by 6.7 m in plan, was in the order of 50–80 years old. The foundation for the structure
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FIELD 3 FIELD 2
FIELD 1
FIELD 1
Fig. 19. Comparison of the structural responses with limited field cases.
was provided by a rubble strip footing of a 304 mm-thick brick wall clad with a veneer of architectural stonework. The tunnel was approximately 6.4 m in diameter and the springline was approximately 14.6 m below the ground surface. The tunnel was driven using a shield, and steel ribs and timber lagging were placed to provide the initial support. The steel sets were located at 1.2 m intervals, corresponding to the length of shove used. The soil profile at the location consisted primarily of a medium dense sand and gravel. From the tunnel construction, large and localized runs occurred at the face of the tunnel excavation. The ground loss induced at the ground surface was approximately 4.3%. The structure was damaged extensively, which resulted in it being declared structurally unsound. Both bending cracks and diagonal cracks were readily visible in an exposed bearing wall. Diagonal cracking occurred approximately near the front of the structure, within a distance from the excavation equal to the height of the structure. The bending cracks occurred approximately at a distance of the height of the structure from the front of the structure and near the top of the bearing wall. The windows in the bearing wall were also distorted severely. From the exterior, the façade wall cladding appeared to be on the verge of buckling and separating from its support. The angular distortion (b) and lateral strain (eL) of the structure were (8.5–12) 103 and (7.5–12) 103, respectively. The structure was damaged severely. Although the three field cases were not precisely under the same conditions as the cases in this study, the structural type, tunnel conditions (diameter and depth) and ground conditions (sandy soil) were under similar conditions as those in this study. A comparison of the field cases and this study revealed the study results to be largely within a similar range in the structural response as the field cases, which had similar soil, ground loss and structure conditions. Nevertheless, more field data will be needed in the future to better understand the structural response under a range of tunnel construction conditions.
6. Conclusions The effects of tunneling-induced ground movements on the nearby structures in sandy soils were investigated numerically, considering the soil–structure interactions of different tunnel, structure, ground, and construction conditions. The study results were also compared with some limited field cases. From the investigations, the following conclusions were made. 1. The response of a building is strongly dependent on the tunnel, structure, ground, and construction conditions with the effect of soil–structure interaction. Accordingly, a building damage estimate should include the effects of the tunnel, structure, ground, and construction conditions together by considering the soil– structure interactions. 2. For small ground loss, the structural response was less dependent on the tunnel, structure, and ground conditions, but these factors had a much larger effect as the level of ground loss increased. When the ground loss became sufficiently large, the effects of the tunnel and ground conditions decreased, but the effect of the structure type was significant. 3. For a typical range of ground loss in the field, if the magnitude of ground movements is the same, the structure on denser soil is distorted much more than a structure on looser soil. This is due to the soil–structure interaction where the ground displacement of looser soil is modified significantly by a structure, causing less distortion and damage to the structure. 4. A comparison of the structural response between the brickbearing structure and brick-infilled frame structure revealed the former structure to be much more sensitive to the ground movements, and the difference in damage severity increased with decreasing tunnel depth to diameter ratio. The enclosed frame confined the crack propagation significantly so that the
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structure underwent a relatively small distortion. On the other hand, the difference in response between the two structural types decreased with increasing tunnel depth to diameter ratio. 5. A relationship between the tunnel depth to diameter (Z/D) ratios and ground loss conditions regarding the level of structural damage under different ground and structure conditions was developed to integrate the various tunnel field conditions into a design frame in engineering practice. Some limited field cases were compared with the relationship, and the comparison showed that the developed relationship can be used to assess a structural damage in the design stage of tunnel constructions in sandy soils. 6. These findings will help better understand the structural response to tunneling-induced ground movements in sandy soils, and the developed relationship can be used to control and minimize structure damage by assessing the possible structural damage in the design stage and making a decision if an action, such as ground improvement or structure reinforcement, needs to be taken to protect a structure. Nevertheless, more field data will be needed to better understand the structural response under a range of tunnel construction conditions.
References Atkinson, R.H., Amadei, B.P., Saeb, S., Sture, S., 1989. Response of masonry bed joints in direct shear. J. Struct. Eng. 115 (9), 2276–2296. Attewell, P.B., 1977. Ground movements caused by tunnelling in soil. In: Proc. Conf. on Large Ground Movements and Structures. Halstead Press, New York, NY, pp. 812–948. Attewell, P.B., Yeates, J., 1984. Tunnelling in soil. Ground Movements Effects Struct., 132–215 (Blackie & Son Ltd). Beranek, W.J., 1987. The prediction of damage to masonry buildings caused by subsoil settlements. Heron 32 (4), 55–93. Boone, S.J., Westland, J., Nusink, R., 1999. Comparative evaluation of building response to an adjacent braced excavation. Canadian J. Geotech. Eng. 36, 210– 223. Boscardin, M., 1980. Building Response to Excavation-Induced Ground Movements. Ph.D. Thesis, University of Illinois at Urbana-Champaign. Boscardin, M.D., Cording, E.J., 1989. Building response to excavation-induced settlement. J. Geotech. Geoenviron. Eng. 115 (1), 1–21. Breth, H., Chambosse, G., 1974. Settlement behavior of buildings above subway tunnels in Frankfurt clay. In: Proceedings of the Conference on Settlement of Structures, London, pp. 329–336.
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Burland, J.B., 1995. Assessment of risk of damage to buildings due to tunneling and excavation. In: Proceedings of the First International Conference on Earthquake Geotechnical Engineering, Tokyo. Cording, E.J., 1991. Control of ground movements around tunnels in soil. In: Ninth Pan American Conference, Vina del Mar, Chile. Sociedad Chilena de Geotechina, vol. 4, pp. 2195–2244. Cording, E.J., Hansmire, W.H., 1975. Displacements around soft ground tunnels. In: General Report, Session 4, 5th Panamerican Cong. on Soil Mech. and Foun. Engr. Buenos Aires, November. Finno, R.J., Voss Jr., F.T., Rossow, E., Blackburn, J.T., 2005. Evaluating damage potential in buildings affected by excavation. J. Geotech. Geoenviron. Eng. 131 (10), 1199–1210. Fujita, K., 1989. Special lecture B: underground construction, tunnel, underground transportation. In: Proceedings of the 12th International Conference on Soil Mechanics and Foundation Engineering, Rid de Janeiro, pp. 2159–2176. Hong, S.W., 1984. Ground Movements Around Model Tunnels in Sand. Ph.D. Thesis, University of Illinois at Urbana-Champaign, Urbana, Ill. Laefer, D.F., 2001. Prediction and Assessment of Ground Movement and Building Damage Induced by Adjacent Excavation. Ph.D. Thesis, Univ. of Illinois at Urbana-Champaign, Urbana, Ill. Mair, R.J., Taylor, R.N., 1997. Theme lecture: bored tunneling in the urban environment. In: Proceeding of the 14th International Conference on Soil Mechanics and Foundation Engineering, Hamburg, pp. 2353–2385. O’Reilly, M.P., New, B.M., 1982. Settlements above tunnels in the United Kingdom – their magnitude and effects. In: Jones, M.J. (Ed.), Tunnelling ’82, London, England, pp. 173–181. Peck, R.B., 1969. Deep excavations and tunneling in soft ground. In: Proc. 7th Int’l. Conf. on Soil Mech. and Foun. Engr., Mexico City, State-of-the-Art, pp. 225–290. Schuster, M., Kung, G.T.C., Juang, C.H., Hashash, Y.M.A., 2009. Simplified model for evaluating damage potential of buildings adjacent to a braced excavation. J. Geotech. Geoenviron. Eng. 135 (12), 1823–1835. Son, M., 2003. The Response of Buildings to Excavation-Induced Ground Movements, Ph.D. Dissertation, University of Illinois at Urbana-Champaign. Son, M., 2013. Analysis of response change of block structures due to tunnel excavation condition in sand ground. J. Korean Soc. Civ. Eng. 33 (4), 1541–1549. Son, M., Cording, E.J., 2005. Estimation of building damage due to excavationinduced ground movements. J. Geotech. Geoenviron. Eng. 131 (2), 162–177. Son, M., Cording, E.J., 2011. Response of buildings with different structural types to excavation-induced ground movements. J. Geotech. Geoenviron. Eng. 137 (4), 323–333. Son, M., Yun, J., 2009. Numerical analysis of tunnelling-induced ground movements. Tunn. Technol. 11 (3), 229–243 (Korea). Son, M., Laefer, D., Cording, E.J., 2008. Numerical model tests of building response to excavation-induced ground movements. Canadian Geotech. J. 45 (11), 1611– 1621. UDEC 3.1., 2000. UDEC 3.1 theory and manual. Itasca Consulting Group, Minn. Ward, W.H., Pender, M.J., 1981. Tunnelling in soft ground – general report. In: Proceedings of the 10th International Conference on Soil Mechanics and Foundation Engineering, Stockholm, pp. 261–275.
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Response analysis of nearby structures to tunneling-induced ground movements in sandy soils Moorak Son Dept. of Civil Engineering, Daegu University, Jillyang, Gyeongsan, Gyeongbuk 712-714, South Korea
a r t i c l e
i n f o
Article history: Received 14 February 2014 Received in revised form 7 February 2015 Accepted 17 March 2015
Keywords: Tunneling Ground movement Structural damage Damage estimation Design frame Engineering practice Soil–structure interaction
a b s t r a c t This study examined the effects of tunneling-induced ground movements on the nearby structures in sandy soils considering the soil–structure interactions of different tunnels, structures, ground, and construction conditions. The investigation relates the level of structural distortion and damage to different tunnel field conditions. For this purpose, extensive numerical parametric studies were conducted and the results were compared with some field cases. The discrete element method (DEM) has been used to model structural cracking when the shear and tensile stress exceeds the maximum shear and tensile strength. Two different structures, brick-bearing and brick-infilled frame structures, were considered, and the distortion and cracking induced in the structures was related to different tunnel field conditions. A relationship that correlates the tunnel depth to diameter (Z/D) ratios and ground loss conditions with a level of structural damage with different ground and structure conditions was developed to integrate the study results into a design frame in engineering practice. The relationship developed can be used practically to assess the structural damage in the design stage of tunnel constructions under a range of tunnel field conditions. These results will provide a background for a better understanding of how to control and minimize the damage of the structure to tunneling-induced ground movements in sandy soils under different tunnel, structure, ground, and construction conditions. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction The number of tunnel constructions in congested urban spaces are increasing for many reasons, such as the development of underground transit systems and installing a range of utilities. At the same time, there has been increasing public concern regarding the effects of tunneling-induced ground movements on the adjacent structures. Tunneling-induced ground movement can distort and damage the adjacent structures, causing several problems, such as the loss of property, construction delay, and increase in project cost. To minimize these problems, it is important to have a reliable damage assessment of the adjacent structures as well as an appropriate protection measure prior to tunnel excavation. Reasonable damage assessments require a better understanding of the complex soil–structure interactions among the tunnel, structure, ground, and construction conditions. A failure to understand these interactions can lead to the implementation of unnecessary protection measures, unnecessary cost and unsatisfactory results.
E-mail address: [email protected] http://dx.doi.org/10.1016/j.tust.2015.03.008 0886-7798/Ó 2015 Elsevier Ltd. All rights reserved.
The response of the adjacent structures to excavation-induced ground movements has been investigated. Notable studies include Breth and Chambosse (1974), Attewell (1977), Boscardin and Cording (1989), Burland (1995), Boone et al. (1999), Finno et al. (2005), Schuster et al. (2009), Son and Yun (2009), Son et al. (2008), and Son and Cording (2005, 2011). Compared to previous studies, the present paper reports the results of a systematic integration of various tunnel conditions into a design frame, which guides the relationship between the different tunnel conditions and structural damage. In general, a structural response depends on a range of factors including the tunnel and structure conditions as well as the ground and construction conditions. Although field observations are of major importance in assessing the structural response to a nearby tunnel excavation, numerical model tests have the ability to add unique perspectives to an evaluation of the structural response. This study examined the structural response to tunneling-induced ground movements in sandy soils based on extensive numerical model tests. The structural distortion and damage were examined under a controlled variation of the tunnel (tunnel depth and diameter), structure (brick-bearing structure and brick-infilled frame structure), ground (looser and denser soil), and construction (ground loss) conditions. The results are expected to provide a
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background for a better understanding of how to control and minimize the building damage to the nearby structures due to tunneling-induced ground movement in sandy soils under many different field conditions.
Tunnel construction in urban areas can cause damage to the adjacent structures due to tunneling-induced ground movements. Ground movement is largely affected by the tunnel condition (depth and diameter), ground condition (loose sand and dense sand) and construction condition (ground loss in a tunnel caused by over excavation, delayed support and grouting installation, support deflection, and face instability, such as raveling or flowing). The ground loss is defined as the volume lost into a tunnel divided by the theoretical tunnel volume. Tunneling-induced ground movements differ from building self-weight-induced settlements in that the former generally have much larger horizontal displacements, which can cause more severe structural damage. Therefore, to assess the structural damage reasonably, it is essential to estimate the horizontal ground movement as well as the vertical ground settlement, where a structure is located. Peck (1969) assembled empirical information of the tunnel case histories in different types of ground and suggested an error function or normal probability curve for the shape of the settlement trough as follows. 2
S ¼ Smax e
x2 2i
where S is the settlement at a distance x from the center of the settlement trough, Smax is the settlement at the center of the trough, i is the point of inflection of the curve, and x is the distance from the center of the trough (refer to Fig. 1). The volume (Vs) of the settlement trough is equal to 2.5 i Smax. The points of inflection of the curve are located at a distance, i, on either side of the center line of the trough. The location of the inflection points (i) were determined from the relationship between the tunnel depth (Z) and radius (R), as shown in Fig. 2. Therefore, the ordinate of the normal probability curve can be determined at any distance from the tunnel center line in the transverse direction, provided that the inflection point and maximum settlement can be determined. The horizontal surface displacement can have a significant effect on the damage to the structures. On the other hand, it has not been commonly measured in the field and there is insufficient field data and information to estimate the horizontal surface displacement profile with the same degree as the settlement profile. Nevertheless, O’Reilly and New (1982) provided an equation to estimate the tunneling-induced horizontal displacements as follows:
x x2 Sh ¼ Smax 1:65 e 2i2 i W=2.5i
Inflection Point
Fig. 1. Error function or normal probability curve to represent a settlement trough above the tunnel (after Peck, 1969).
z/2R
2. Tunneling-induced ground movements and structure responses
Rock, Hard Clays, Sands Above Groundwater Level Soft to Stiff Clays
Sands Below Groundwater Level
i/R Fig. 2. Relationship among tunnel depth, tunnel radius, and inflection point (after Peck, 1969).
where Sh is the horizontal displacement at a distance x from the tunnel center line, Shmax is the maximum horizontal displacement at the inflection point, and i is the point of inflection of the settlement trough. The maximum horizontal displacement occurs at the inflection point, and in the Washington D.C Metro, it was one third of the maximum vertical displacement. Cording (1991) reported that the ratio of the maximum horizontal displacement to the maximum vertical displacement varies with the width of the trough and showed that the estimated horizontal displacement at the edge of the settlement profile can be smaller than the real displacement if the equation for estimating the horizontal displacement is used. Field studies by Cording and Hansmire (1975), Attewell (1977), and Cording (1991) revealed the ratios in the range of 0.25–0.4. From the many numerical tests, Son and Yun (2009) also reported that the maximum lateral displacements are approximately 0.35 times the maximum vertical displacements, which are consistent with field observations. Extensive studies related to ground movements during tunneling in soil have been conducted by many investigators including Attewell (1977), Ward and Pender (1981), Attewell and Yeates (1984), Fujita (1989), and Mair and Taylor (1997). 3. Numerical analysis The advantages of numerical analysis are that a range of conditions can be considered easily with limited time, cost and space, and reproducible analyses. This characteristic allows examinations of the response of structures to tunneling-induced ground movements under a range of conditions. The numerical approach used in this study is similar to that of previous studies (Son and Cording, 2011) but is described again briefly. The 2-D Universal Distinct Element Code (UDEC 3.1, 2000) was used to conduct the numerical tests. Each brick was modeled as a separate elastic unit and the brick/mortar contact was modeled using the Coulomb slip model, in which the contact loses strength and a crack is formed when the contact normal stress exceeds the maximum tensile strength of the contact or the contact shear stress exceeds the contact shear strength, which
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is the combination of cohesive (c) and frictional strength (/). Further extension across the contact causes separation of the adjacent bricks that leads to a larger opening of the crack. The contact does not simulate the crush in compression, which is reasonable, because compressive strength is generally higher than tensile strength, and cracks form mostly due to tensile stress. Prior to cracking, the brick/mortar contact model has a linear stress–displacement relationship with the slope of the contact normal stiffness for the normal stress condition and with the slope of the contact shear stiffness for the shear stress condition. After the cracks form, the contact has only frictional shear resistance. This model can easily simulate the large crack opening and post-crack inelastic behavior than continuum based numerical methods, such as the finite element method (FEM), which has difficulty in simulating the many large crack openings and propagation. The approach in this study was validated from a previous study (Son and Cording, 2005) comparing the results of physical model test with the numerical simulation using the same approach. The soil was modeled as an elastic mass and the elastic soil stiffness in the numerical tests (2D) was determined to provide the same normal pressure/displacement relationship at the base of the footing as the three-dimensional (3D) condition in the field using Boussinesq’s relationships. The structure/soil interface model was similar to the brick/mortar contact but the properties were different. Therefore, the interface allowed the structure to separate from the soil or slide between the structure and the soil. The frames in the brick-infilled frame structures were modeled elastically. The analyses were performed under plane stress conditions for both the soil and structure. The entire tunnel excavation sequence with a structure was not simulated because of the numerical limitations of modeling a large number of discrete bricks forming the structure. Instead, a freefield ground displacement profile determined from the empirical field observations (Peck, 1969; O’Reilly and New, 1982) was imposed on the soil mass, which has a finite thickness (Fig. 3). Both the vertical and horizontal green-field ground movements were applied to the soil mass to allow the soil–structure interaction between the structure and soil mass. Vertical green-field ground settlement was applied to the base of the soil mass after confirming that for the green-field condition, the displacement profile induced at the surface of the soil mass was the result of applying the profile to the base of the soil mass. The horizontal displacement profile was applied to the surface of the soil mass interconnected with the building wall at the soil/structure interface. The horizontal displacement was applied to the surface of the soil mass, not the base, because for the green-field condition, the application of horizontal displacement to the base of the elastic soil mass would produce a distorted horizontal displacement at the surface. On the other hand, the soil–structure interaction for horizontal ground movement was still allowed because an equivalent soil shear stiffness was applied at the interface element. The shear stiffness at the interface was selected to provide the same horizontal pressure/horizontal displacement relationship for the 2-D model as that for the 3-D condition. Therefore, the soil–structure interaction between the building wall and the soil mass was allowed both for the vertical and horizontal ground displacements. The procedures were explained well by Son (2003), and were verified by a comparison between the large-scale physical model test (Laefer, 2001) and its numerical simulation (Son and Cording, 2005). The numerical tests were performed in several stages. At the initial stage, the initial equilibrium was obtained with the building self-weight and floor loads. At this stage, the boundary condition for the soil mass was the roller supports at each end of the two vertical boundaries of the soil mass and at the bottom boundary of the soil mass. After ensuring the initial equilibrium condition, all displacements were reset to zero and a free-field
ground displacement was imposed on the soil mass. After completing the analysis, the distortions and cracking in the structures were investigated from the results of each analysis. Modeling of the soil with an advanced constitutive model and the entire excavation sequence with a structure is desirable for a specific field condition. On the other hand, the aim of this study was to better understand the structural response under a range of tunnel field conditions. For this purpose, it would be less than ideal to model the entire excavation and structure with both excavation and structure complexities under a specific condition. Instead, it would be preferable to employ a simple and conceptual approach for this study provided the applied conditions are within the range of typical field characteristics.
4. Extensive parametric studies Based on a verification of the used numerical methodology and approach in previous studies (Son et al., 2008; Son and Cording, 2005, 2011; Son, 2013), more extensive numerical parametric studies have been conducted to examine the effects of the tunnel, structure, ground, and construction conditions on the nearby structures. Fig. 4 describes the conditions considered for the parametric studies. The tunnel depth considered was 10 m, 20 m and 30 m, and the diameter was 3 m, 6 m and 9 m. Two structure types were considered, brick-bearing and brick-infilled frame structures. Two ground conditions (loose sand and dense sand) were considered and the construction condition (ground loss) was varied from 0.17% to 0.5%, 1%, and 2%. A total of 144 cases were examined and the results were analyzed and compared. A structure was assumed to be located with one side above the tunnel centerline (see Fig. 4) with the structure imposed to both sagging (concave shape) and hogging (spandrel shape) modes of the settlement profile including the point of inflection (i.e. the point of maximum slope of the settlement trough), which could be the most unfavorable condition in terms of the structure response. The ground displacement profiles (settlement and horizontal displacement) were determined using the empirical approach described in Section 2 of this paper for sandy soil, assuming that the surface settlement volume is same as the ground loss. The surface settlement volume can be different from the ground loss due to volume changes in the soil mass. The relationship between the surface settlement volume and the ground loss around the tunnel depends on the tunnel condition (depth and diameter) as well as the soil condition (Hong, 1984 and Cording, 1991). The aim of this study was not to provide a case analysis of a specific soil and tunnel condition, but instead provide information to improve the general understanding of the structural response to tunneling. Therefore, in this study, the surface settlement volume was assumed to be same as the ground loss. Despite this, the effects of the volume change in a soil mass can also be considered by adjusting the ground loss either by adding (for dilating soil) or subtracting (for compressible soil) the possible change in volume from the ground loss given in this study. Fig. 5 shows the determined displacement profiles. Although the assumed displacement profiles in this study might not represent all the complex conditions in the field, the displacement profiles were chosen to be in the range of typical field observations (Peck, 1969 and Clough and O’Rourke, 1990). In other words, the displacement profiles are not for a specific field and construction condition, but are one of the typical displacement profiles in the field. This study was limited to the in-plane distortion of a structure. The structures that are skewed with respect to a tunnel axis may undergo three dimensional responses to ground movements. Out-of-plane distortion, such as torsion, can result in structural damage even with a small amount of in-plane distortion. Therefore, when the structure response is evaluated, the out-of-
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(Elastic frame) (Elastic brick unit) (Inelastic brick/mortar joint)
18300
Wooden lintels (25 mm thick)
3048 1270
406 12497 (4-story structure)
406
(unit: mm) Soil Element
Horizontal displacement applied Vertical displacement imposed
28956 Fig. 3. Numerical model geometries and boundary conditions for brick-infilled frame structures (⁄ Brick-bearing structures are composed of only the brick units without the frames in this figure).
In assessing the response of the structures due to tunneling-induced ground movement, cracking in a structure is a significant factor that should be considered. In this study, the structural responses were examined by simulating the crack opening and post-crack inelastic behaviors of the structures using the discrete element method. Table 1 lists the soil and structure properties for the numerical investigation. The brick unit and brick/mortar contact properties were selected based on the literatures (Beranek, 1987 and Atkinson et al., 1989).
5. Comparison of the structural response 5.1. Structural response in loose sand
Fig. 4. Considered conditions for numerical parametric studies.
plane distortion should be investigated in addition to in-plane distortion. In addition, the results in this study should be understood in the limited range of structures and ground conditions, which were considered in the study because a structural response can vary considerably with different structural conditions, such as openings or stories and different ground conditions.
5.1.1. Effect of the tunnel depth Fig. 6 compares the responses of the four-story brick-bearing structures in loose sand varying the tunnel depth for a ground loss of 1% and a tunnel diameter of 6 m. As shown in the figure, the structures were distorted with more cracking as the tunnel depth became shallower. The angular distortions (b) in bay 1 of the structures were 5.1 103, 1.96 103 and 0.12 103 for a tunnel depth of 10 m, 20 m and 30 m, respectively and the lateral strains (eL) were 6.96 103, 2.37 103 and 0.05 103 for the tunnel depth, respectively. Using the damage criterion by Son and Cording (2005), the damage to the structures was quite severe
Fig. 5. Displacement profiles applied to numerical analysis (in case of a tunnel depth of 20 m and tunnel diameter of 6 m in dense sand).
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Table 1 Soil, structure and interface properties used for numerical analysis. Structure type
Brick-bearing structure
Volume loss (%)
0.17, 0.5, 1.0, 2.0
Soil properties
Structure properties
Es (MPa) (ts = 0.33)
Brick Units
17.2
E (GPa) 10.34
Interface properties Brick/Mortar Joints
t 0.2
c
/ (°)
rt
(kN/m3)
c (kPa)
19
344
35
(kPa)
Kn (MPa/mm)
Ks (MPa/mm)
344
78
7.8
c, rt (kPa)
/ (°)
Kn (MPa/mm)
Ks (MPa/mm)
0
35
78
0.0146
68.9 Brick-infilled frame strucure
0.17, 0.5, 1.0, 2.0
17.2 68.9
0.0584 a
B: 10.34 F: 20.67
B: 0.2 F: 0.15
B: 19 F: 24
344
35
344
78
7.8
0
35
78
0.0146 0.0584
Notes: Es = Young’s modulus for soil; E = Young’s modulus for brick units; t = Poisson’s ratio for brick units; c = total unit weight; c = joint or interface cohesive strength; / = joint or interface friction angle; rt = joint or interface tensile strength; Kn = joint or interface normal stiffness; Ks = joint or interface shear stiffness. a ‘‘B’’ represents brick units and ‘‘F’’ represents frames.
Fig. 6. Comparison of the structural responses according to tunnel depth in loose sand (Brick-bearing structure, ground loss, 1%, tunnel diameter, 6 m).
for a depth of 10 m, moderate to severe for a depth of 20 m, and negligible for a depth of 30 m. Fig. 7 compares the responses of the four-story brick-infilled frame structures in a loose sand varying tunnel depth for a ground loss and tunnel diameter of 1% and 6 m, respectively. As shown in the figure, the structures were distorted with relatively more cracking as the tunnel depth became shallower. The angular distortions (b) in bay 1 of the structures were 1.11 103, 0.32 103 and 0.21 103 for a tunnel depth of 10 m, 20 m and 30 m, respectively, and the lateral strains (eL) were 0.33 103, 0.02 103, and 0.01 103 for the tunnel depth, respectively. The damage to the structures was very slight for a depth of 10 m and negligible for the other two tunnel depths. A comparison of the behaviors of the two different structures revealed the brick-infilled frame structure to sustain less damage. In a brick-bearing structure, once cracking occurs, the subsequent cracks concentrate around the initial cracks and propagate. On the other hand, for a brick-infilled frame structure, the enclosed frame confines the crack propagation so that the structure undergoes relatively little distortion with a larger tilt. In addition, the
structures are damaged more when the tunnels are excavated at a shallower depth with the same magnitude of ground loss. 5.1.2. Effect of ground loss Fig. 8 compares the responses of the four-story brick-bearing structures in loose sand, varying the ground loss for a tunnel depth and tunnel diameter of 20 m and 6 m, respectively. As shown in the figure, the structures were distorted with more cracking as the ground loss increased. The angular distortions (b) in bay 1 of the structures were 0.22 103, 1.96 103 and 7.47 103 for the ground loss of 0.5%, 1% and 2%, respectively, and the corresponding lateral strains (eL) were 0.05 103, 2.37 103 and 9.73 103. Using the damage criterion, the damage in the structure was negligible for a ground loss of 0.5%, moderate to severe for a ground loss of 1%, and very severe for a ground loss of 2%. Fig. 9 shows the responses of the four-story brick-infilled frame structures in loose sand varying ground loss for a tunnel depth and tunnel diameter of 20 m and 6 m, respectively. As shown in the figure, the structures were distorted with more cracking as the ground loss became larger. The angular distortions (b) in bay 1 of
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Fig. 7. Comparison of the structural responses according to tunnel depth in loose sand (Brick-infilled frame structure, ground loss, 1%, tunnel diameter, 6 m).
Fig. 8. Comparison of the structure responses with ground loss in loose sand (Brick-bearing structure, tunnel depth, 20 m tunnel diameter, 6 m).
the structures were 0.11 103, 0.32 103, and 0.50 103 for a ground loss of 0.5%, 1% and 2%, respectively and the corresponding lateral strains (eL) were 0.01 103, 0.02 103, and 0.09 103. The damage to the structures was negligible for all the ground losses, even though small cracks were distributed more with a larger ground loss. A comparison of the behaviors of the two different structures showed that for a small ground loss, both the brick-bearing and brick-infilled frame structures behaved like an elastic structure and there was a slight difference in the structural response. On the other hand, as the ground loss increased, the brick-bearing structure was damaged severely with large crack openings,
whereas the brick-infilled frame structure was distorted with a small difference due to the confining effect of the enclosed frame. 5.2. Structural response in dense sand 5.2.1. Effect of the tunnel depth Fig. 10 compares the responses of the four-story brick-bearing structures in dense sand with varying tunnel depths for a ground loss and a tunnel diameter of 1% and 6 m, respectively. As shown in the figure, with decreasing tunnel depth, the structure became increasingly distorted with more cracking. The angular distortions (b) in bay 1 of the structures were 8.71 103, 4.31 103 and
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Fig. 9. Comparison of the structure responses with ground loss in loose sand (Brick-infilled frame structure, tunnel depth, 20 m tunnel diameter, 6 m).
Fig. 10. Comparison of the structural responses according to tunnel depth in dense sand (Brick-bearing structure, ground loss, 1%, tunnel diameter, 6 m).
2.41 103 for tunnel depths of 10 m, 20 m and 30 m, respectively, and the corresponding lateral strains (eL) were 13.54 103, 6.25 103 and 2.34 103 for the tunnel depth, respectively. The damage to the structure was quite severe for depths of 10 m and 20 m, and moderate to severe at 30 m. Fig. 11 shows the responses of the four-story brick-infilled frame structures under the same conditions. As the tunnel depth decreased, the structure became increasingly distorted with more cracking. The angular distortions (b) in bay 1 of the structures were 1.23 103, 1.18 103 and 0.94 103 for tunnel depths of 10 m, 20 m and 30 m, respectively, and the corresponding lateral
strains (eL) were 0.48 103, 0.41 103, and 0.24 103. The damage to the structure was slight for depths of 10 m and 20 m, and very slight for a depth of 30 m. A comparison of the behaviors of the two different structures showed that the brick-infilled frame structure sustained much less damage. Regardless of the different levels of distortion, both structures were considerably more distorted and damaged than the structures on loose sand. This was attributed to a soil–structure interaction, where the ground displacement of loose sand is modified significantly by a structure inducing less distortion and damage. The effects of the soil stiffness on the structural damage was
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Fig. 11. Comparison of the structural responses according to tunnel depth in dense sand (Brick-infilled frame structure, ground loss, 1%, tunnel diameter, 6 m).
much more significant in the brick-bearing structure than in the brick-infilled frame structure. 5.2.2. Effect of ground loss Fig. 12 presents the responses of four-story brick-bearing structures in dense sand with varying ground losses for a tunnel depth and tunnel diameter of 20 m and 6 m, respectively. As shown in the figure, as the ground loss increased, the structure became increasingly distorted with more cracking. The angular distortions (b) in bay 1 of the structures were 1.65 103, 4.31 103 and 9.99 103 for the ground loss of 0.5%, 1% and 2%, respectively, and the corresponding lateral strains (eL) were 1.94 103, 6.25 103 and 11.07 103. The damage to the structure was moderate for a ground loss of 0.5% and very severe for ground losses of 1% and 2%. Fig. 13 shows the responses of the four-story brick-infilled frame structures under the same conditions. The structure became increasingly distorted with more cracking as the ground loss increased. The angular distortions (b) in bay 1 of the structures were 0.4 103, 1.18 103 and 1.19 103 for the ground loss of 0.5%, 1% and 2%, respectively, and the corresponding lateral strains (eL) were 0.07 103, 0.41 103, and 0.46 103. The damage to the structure was negligible, very slight and slight for a ground loss of 0.5%, 1% and 2%, respectively. A comparison of the behaviors of the two different structures revealed the brick-infilled frame structure to have sustained much less damage than the brick-bearing structure. The brick-bearing structure was considerably more dependent on the ground loss than the brick-infilled frame structure. Both structures showed more distortion and damage than the structures on loose sand, but the effects of the soil stiffness were more evident in the brick-bearing structure. 5.3. Integration of various tunnel field conditions into a design frame 5.3.1. Structural response in loose sand Fig. 14 shows the relationship among the maximum principal strain induced in a structure unit (Bay 1), tunnel depth to diameter (Z/D) ratio, and ground loss for all analyses of the brick-bearing
structure in loose sand. The maximum principal strain is the maximum average principal strain across the distorting portion (a structure unit, such as Bay 1) of a structure, not at a specific point in a structure. A structure unit can be a section between two columns or cross walls, two different geometries or stiffness. This is usually the portion of a structure closest to the excavation and subject to the largest distortions. Because vertical and horizontal ground displacements are imposed at the base of a structure, the angular distortion (b) and lateral strain (eL) are induced in a structure. A structure is deformed by a combination of the angular distortion and lateral strain, and the maximum average principal strain (ep) across a structure unit (such as Bay 1) can be determined by the state of strain theory using both the angular distortion (b) and lateral strain (eL) as follows.
ep ¼ eL cos h2max þ b sin hmax cos hmax ; tanð2hmax Þ ¼
b
eL
The angular distortion and lateral strain in a structure unit (Bay 1) can be determined by measuring the vertical and horizontal displacements at the corners of a structure unit. The details were well explained by Son and Cording (2005). The principal strains to divide the different damage levels follow the criterion reported by the same reference. The figure indicates that the maximum principal strain decreases with increasing ratio (Z/D), and a structure can be damaged quite severely for a ground loss greater than 1% if the tunnel depth to diameter ratio is less than 2.5. This also suggests that a structure can be damaged quite severely up to a ratio of 5.0 if the ground loss is 2%. For a tunnel depth to diameter ratio of approximately 3.5, the structure can sustain moderate to severe damage with ground losses of 1% and 2%. The damage to a structure on loose sand might be negligible if the ground loss is less than 0.5% or the depth to diameter ratio is greater than 6.5 for a ground loss less than 2%. Fig. 15 shows the relationship among the maximum principal strain induced in a structure, tunnel depth to diameter (Z/D) ratio, and ground loss for all analyses of the brick-infilled frame structure in loose sand. The figure shows that the maximum principal strain decreases with increasing (Z/D) ratio, but the principal strain was much smaller and less dependent on the Z/D ratio compared to
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Fig. 12. Comparison of the structural responses according to ground loss in dense sand (Brick-bearing structure, tunnel depth, 20 m tunnel diameter, 6 m).
Fig. 13. Comparison of the structural responses according to ground loss in dense sand (Brick-infilled frame structure, tunnel depth, 20 m tunnel diameter, 6 m).
the brick-bearing structure. A structure can be damaged slightly for a ground loss of 2% if the tunnel depth to diameter ratio is less than 3.5. This also suggests that the damage to a structure is negligible if the ground loss is less than 0.5% or the depth to diameter ratio is greater than 4.5 for a ground loss less than 2%. A comparison of the structural response between the brick-bearing structure and the brick-infilled frame structure showed that the former structure was much more sensitive to ground movement, and the difference in damage severity increased with decreasing depth to diameter ratio. On the other hand, the difference becomes
negligible when the ratio is larger than approximately 6.0 for a ground loss of less than 2%. 5.3.2. Structural response in dense sand Fig. 16 shows the relationship among the maximum principal strain induced in a structure, tunnel depth to diameter (Z/D) ratio, and ground loss for all analyses of the brick-bearing structure in dense sand. A comparison with loose sand showed that the maximum principal strain increased significantly at the same ground loss and depth to diameter ratio. Similarly, in loose sand, the
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Fig. 14. Relationship between the maximum principal strain in a structure and the tunnel depth to diameter (Z/D) ratio (Brick-bearing structures in the loose sand).
Fig. 15. Relationship between the maximum principal strain in a structure and the tunnel depth to diameter (Z/D) ratio (Brick-infilled frame structures in the loose sand).
maximum principal strain decreased with increasing Z/D ratio and the level of the decrease was dependent on the magnitude of the ground loss. The figure indicates that a structure can be damaged
quite severely up to a tunnel depth to diameter ratio of 7 if the ground loss is 2%, but the ratio for the same damage decreases to approximately 3.5 if the ground loss is 1%. In addition, a structure
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Fig. 16. Relationship between the maximum principal strain in a structure and the tunnel depth to diameter (Z/D) ratio (Brick-bearing structures in the dense sand).
can be damaged severely, even for a ground loss of 0.5 if the tunnel depth to ratio is smaller than 2.5. For a ground loss of 2%, a structure can be damaged moderately to severely at a depth to diameter ratio of approximately 10, but the ratio for the same damage decreases to approximately 5 if the ground loss is 1%. As the ground loss decreased, Z/D becomes smaller for the same degree of damage. From the figure, the damage to a structure might be negligible for a ground loss of 0.5 if the tunnel depth to diameter ratio is greater than 3.5 and for a ground loss of 1%, the ratio increases up to approximately 10 for negligible damage in a structure. Fig. 17 shows the relationship among the maximum principal strain induced in a structure, tunnel depth to diameter (Z/D) ratio, and ground loss for all analyses of the brick-infilled frame structure in dense sand. The figure clearly shows that the maximum principal strain decreases with increasing Z/D ratio, but the principal strain is much smaller and less dependent on the Z/D ratio than the brick-bearing structure. In addition, the difference in the maximum principal strain between the looser and denser soils is much smaller than that of a brick-bearing structure. The structure can be damaged slightly for a ground loss of 2% if the tunnel depth to diameter ratio is less than approximately 5.5. This also suggests that the damage to a structure is negligible if the ground loss is less than 0.17% or the depth to diameter ratio is larger than approximately 7 for a ground loss less than 2%. A comparison of the sensitivity of the structures to the ground movement revealed a brick-bearing structure to be much more sensitive than the brick-infilled frame structure. In addition, the depth to diameter ratio, in which the difference between the two structural types is negligible, was larger than that in loose sand. 5.3.3. Comparison with field cases Some limited field cases were examined for a comparison of the study results and field cases. Although there is significant field data
of ground movement and ground loss for different ground and tunnel conditions, there is limited field data, in which the soil condition, tunnel condition, ground loss, and structure response had been observed simultaneously. Nevertheless, the following three field cases were collected and investigated from the published materials (Cording and Hansmire, 1975; Boscardin, 1980; Boscardin and Cording, 1989). All three cases (Fig. 18) were investigated in relation to the construction of Washington D.C. Metro. The first case (FIELD 1 in Figs. 18a and 19) is a 2-story brickbearing wall structure, which was located 1.5 m from the tunnel centerline. The structure, 6.4 m 18.3 m in plan, had a basement and 2 stories above the ground. The longitudinal axis of the structure was skewed approximately 22° from the tunnel axis. Because of their proximity to the tunnel excavations, the structure was vacated for the duration of mining. The bearing walls were parallel to the longitudinal axis of the structure and were composed of brick with lime mortar. A steel beam supported by the façade walls and three equally spaced interior columns extended along the length of the structure. The timber floor joints spanned between the center bean and the bearing walls. The bearing walls and columns were supported by spread footings. The structure was estimated to be 80–90 years old. The tunnel was approximately 6.4 m in diameter and the springline was approximately 14.2 m below the ground surface. The tunnel was excavated using a Robbins articulated shield and the temporary lining consisted of steel ribs (1.2 m spacing) and timber lagging. The soil profile suggested that the location was near a transition from dense sand and gravel in the river flood plain deposits to hard, clay Cretaceous soils. From the tunnel construction, the ground loss induced at the ground surface was approximately 0.2%. Extensive cracking was observed on the structure before tunnel excavation, and additional cracking and an increase in the size of pre-existing cracks were noted during and after the tunnel excavation. The door became jammed and difficult to open as a result of the tunnel-
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Fig. 17. Relationship between the maximum principal strain in a structure and the tunnel depth to diameter (Z/D) ratio (Brick-infilled frame structures in the dense sand).
Fig. 18. Schematic views of three field cases (not scaled).
induced distortions. The angular distortion (b) and lateral strain (eL), which had been investigated in the structure, were 1.3 103 and 0.3 103, respectively. The structure was damaged slightly. The second case (FIELD 2 in Figs. 18b and 19) is a 3-story brickbearing structure that was located 9 m from the tunnel centerline. The structure, 62 m by 82 m in plan, had a basement and 3 stories above ground. The long dimension of the structure paralleled the tunnel axis. The walls were formed from brick masonry and the plaster covered the barrel and groined vaults. Spread footings provided the foundation support for the walls. The tunnel was approximately 6.4 m in diameter and the springline approximately 19 m below the ground surface. Excavation of the tunnel was accomplished with a shield and support provided by steel ribs. The steel sets were installed after each 1.2 m shove of the shield.
The soil profile at the location consisted primarily of dense silt sand and gravel. During tunnel construction, dewatering problems were encountered and many runs occurred in the sandy soil. This resulted in relatively large ground loss and the induced ground loss at the ground surface was approximately 3%. Structure sustained extensive damage and cracking appeared on all floor levels in both walls and ceilings. Large continuous cracks appeared in the crown of the corridor barrel vaults due to a horizontal extension on all three floors. The angular distortion (b) and lateral strain (eL), which was investigated in the structure, were 7.2 103 and (3.6– 7.2) 103, respectively. The structure was damaged severely. The third case (FIELD 3 in Figs. 18c and 19) is a 4-story brickbearing structure that was located approximately 6.7 m from the tunnel centerline. The structure, 18 m by 6.7 m in plan, was in the order of 50–80 years old. The foundation for the structure
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FIELD 3 FIELD 2
FIELD 1
FIELD 1
Fig. 19. Comparison of the structural responses with limited field cases.
was provided by a rubble strip footing of a 304 mm-thick brick wall clad with a veneer of architectural stonework. The tunnel was approximately 6.4 m in diameter and the springline was approximately 14.6 m below the ground surface. The tunnel was driven using a shield, and steel ribs and timber lagging were placed to provide the initial support. The steel sets were located at 1.2 m intervals, corresponding to the length of shove used. The soil profile at the location consisted primarily of a medium dense sand and gravel. From the tunnel construction, large and localized runs occurred at the face of the tunnel excavation. The ground loss induced at the ground surface was approximately 4.3%. The structure was damaged extensively, which resulted in it being declared structurally unsound. Both bending cracks and diagonal cracks were readily visible in an exposed bearing wall. Diagonal cracking occurred approximately near the front of the structure, within a distance from the excavation equal to the height of the structure. The bending cracks occurred approximately at a distance of the height of the structure from the front of the structure and near the top of the bearing wall. The windows in the bearing wall were also distorted severely. From the exterior, the façade wall cladding appeared to be on the verge of buckling and separating from its support. The angular distortion (b) and lateral strain (eL) of the structure were (8.5–12) 103 and (7.5–12) 103, respectively. The structure was damaged severely. Although the three field cases were not precisely under the same conditions as the cases in this study, the structural type, tunnel conditions (diameter and depth) and ground conditions (sandy soil) were under similar conditions as those in this study. A comparison of the field cases and this study revealed the study results to be largely within a similar range in the structural response as the field cases, which had similar soil, ground loss and structure conditions. Nevertheless, more field data will be needed in the future to better understand the structural response under a range of tunnel construction conditions.
6. Conclusions The effects of tunneling-induced ground movements on the nearby structures in sandy soils were investigated numerically, considering the soil–structure interactions of different tunnel, structure, ground, and construction conditions. The study results were also compared with some limited field cases. From the investigations, the following conclusions were made. 1. The response of a building is strongly dependent on the tunnel, structure, ground, and construction conditions with the effect of soil–structure interaction. Accordingly, a building damage estimate should include the effects of the tunnel, structure, ground, and construction conditions together by considering the soil– structure interactions. 2. For small ground loss, the structural response was less dependent on the tunnel, structure, and ground conditions, but these factors had a much larger effect as the level of ground loss increased. When the ground loss became sufficiently large, the effects of the tunnel and ground conditions decreased, but the effect of the structure type was significant. 3. For a typical range of ground loss in the field, if the magnitude of ground movements is the same, the structure on denser soil is distorted much more than a structure on looser soil. This is due to the soil–structure interaction where the ground displacement of looser soil is modified significantly by a structure, causing less distortion and damage to the structure. 4. A comparison of the structural response between the brickbearing structure and brick-infilled frame structure revealed the former structure to be much more sensitive to the ground movements, and the difference in damage severity increased with decreasing tunnel depth to diameter ratio. The enclosed frame confined the crack propagation significantly so that the
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structure underwent a relatively small distortion. On the other hand, the difference in response between the two structural types decreased with increasing tunnel depth to diameter ratio. 5. A relationship between the tunnel depth to diameter (Z/D) ratios and ground loss conditions regarding the level of structural damage under different ground and structure conditions was developed to integrate the various tunnel field conditions into a design frame in engineering practice. Some limited field cases were compared with the relationship, and the comparison showed that the developed relationship can be used to assess a structural damage in the design stage of tunnel constructions in sandy soils. 6. These findings will help better understand the structural response to tunneling-induced ground movements in sandy soils, and the developed relationship can be used to control and minimize structure damage by assessing the possible structural damage in the design stage and making a decision if an action, such as ground improvement or structure reinforcement, needs to be taken to protect a structure. Nevertheless, more field data will be needed to better understand the structural response under a range of tunnel construction conditions.
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Burland, J.B., 1995. Assessment of risk of damage to buildings due to tunneling and excavation. In: Proceedings of the First International Conference on Earthquake Geotechnical Engineering, Tokyo. Cording, E.J., 1991. Control of ground movements around tunnels in soil. In: Ninth Pan American Conference, Vina del Mar, Chile. Sociedad Chilena de Geotechina, vol. 4, pp. 2195–2244. Cording, E.J., Hansmire, W.H., 1975. Displacements around soft ground tunnels. In: General Report, Session 4, 5th Panamerican Cong. on Soil Mech. and Foun. Engr. Buenos Aires, November. Finno, R.J., Voss Jr., F.T., Rossow, E., Blackburn, J.T., 2005. Evaluating damage potential in buildings affected by excavation. J. Geotech. Geoenviron. Eng. 131 (10), 1199–1210. Fujita, K., 1989. Special lecture B: underground construction, tunnel, underground transportation. In: Proceedings of the 12th International Conference on Soil Mechanics and Foundation Engineering, Rid de Janeiro, pp. 2159–2176. Hong, S.W., 1984. Ground Movements Around Model Tunnels in Sand. Ph.D. Thesis, University of Illinois at Urbana-Champaign, Urbana, Ill. Laefer, D.F., 2001. Prediction and Assessment of Ground Movement and Building Damage Induced by Adjacent Excavation. Ph.D. Thesis, Univ. of Illinois at Urbana-Champaign, Urbana, Ill. Mair, R.J., Taylor, R.N., 1997. Theme lecture: bored tunneling in the urban environment. In: Proceeding of the 14th International Conference on Soil Mechanics and Foundation Engineering, Hamburg, pp. 2353–2385. O’Reilly, M.P., New, B.M., 1982. Settlements above tunnels in the United Kingdom – their magnitude and effects. In: Jones, M.J. (Ed.), Tunnelling ’82, London, England, pp. 173–181. Peck, R.B., 1969. Deep excavations and tunneling in soft ground. In: Proc. 7th Int’l. Conf. on Soil Mech. and Foun. Engr., Mexico City, State-of-the-Art, pp. 225–290. Schuster, M., Kung, G.T.C., Juang, C.H., Hashash, Y.M.A., 2009. Simplified model for evaluating damage potential of buildings adjacent to a braced excavation. J. Geotech. Geoenviron. Eng. 135 (12), 1823–1835. Son, M., 2003. The Response of Buildings to Excavation-Induced Ground Movements, Ph.D. Dissertation, University of Illinois at Urbana-Champaign. Son, M., 2013. Analysis of response change of block structures due to tunnel excavation condition in sand ground. J. Korean Soc. Civ. Eng. 33 (4), 1541–1549. Son, M., Cording, E.J., 2005. Estimation of building damage due to excavationinduced ground movements. J. Geotech. Geoenviron. Eng. 131 (2), 162–177. Son, M., Cording, E.J., 2011. Response of buildings with different structural types to excavation-induced ground movements. J. Geotech. Geoenviron. Eng. 137 (4), 323–333. Son, M., Yun, J., 2009. Numerical analysis of tunnelling-induced ground movements. Tunn. Technol. 11 (3), 229–243 (Korea). Son, M., Laefer, D., Cording, E.J., 2008. Numerical model tests of building response to excavation-induced ground movements. Canadian Geotech. J. 45 (11), 1611– 1621. UDEC 3.1., 2000. UDEC 3.1 theory and manual. Itasca Consulting Group, Minn. Ward, W.H., Pender, M.J., 1981. Tunnelling in soft ground – general report. In: Proceedings of the 10th International Conference on Soil Mechanics and Foundation Engineering, Stockholm, pp. 261–275.