Behavior of a Deep Excavation and Damages on Adjacent Buildings: a Case Study in Vietnam

Abstract

This paper investigates the behavior of deep excavations and damages on adjacent buildings based on an excavation in a thick sand layer in Vietnam. Firstly, measured horizontal displacements of diaphragm walls were used to calibrate soil stiffness parameters for finite element analysis (FEA). Then, the behavior of diaphragm walls, groundwater, ground surface deformation, and an adjacent building was analyzed. The analysis results and damages observed in the field were used to review the validity of the criteria for evaluating the damage potential of excavation to adjacent buildings. It can be concluded from the study that the damage potential of adjacent buildings as evaluated from FEA through the strain state chart proposed by Boscardin and Cording (1989) or the damage potential index (DPI) proposed by Schuster et al. (2009) is fairly accurate with field observations.

1 Introduction

Construction of deep basements in narrow spaces is inevitable in urbanized areas. The design and construction of deep excavations under such situations require great attention to ensure stability and to minimize the impact on adjacent buildings. During the initial design and preparation stage, it is convenient to assess the damage potential of adjacent buildings by some simple rules. For this purpose, the damage potentials may be evaluated from the angular distortion β and the tensile strain ε_L (Skempton and MacDonald 1956; Burland et al. 1978; Boscardin and Cording 1989; Son and Cording 2005). Schuster et al. (2009) performed a regression analysis on collected field observations and proposed simple equations for predicting the β and ε_L values. Sabzi and Fakher (2015) applied the criteria proposed by Schuster et al. (2009) to a shallow excavation next to a low-rise building with inclined struts. Halim and Wong (2011) discussed the damage assessments of adjacent buildings by considering the influence zone of excavations and current structural conditions from visual inspection surveys. In general, these studies considered the performance of retaining wall, ground surface, and an adjacent building in separate models or only used measured field data to assess damage levels of adjacent buildings. Lin et al. (2016) assumed a simple artificial case study to estimate the damage potential of an adjacent building by employing finite element analysis (FEA).

The objective of this study is to investigate behaviors of deep excavations and damages on adjacent buildings based on both field observations and FEA results. A new approach for evaluating the damage level of the adjacent building is proposed based on deformations obtained from calibrated FEA.

2 A Case Study

2.1 Project Descriptions and Soil Conditions

A deep excavation project, namely Madison, located at 15 Thi Sach street, District 1, Ho Chi Minh City, Vietnam, as shown in Fig. 1, is adopted in the numerical simulation in this study. The project consisted of 17 stories and 3 basements placed in an area of 2360 m². The excavation was 65 m long and 37 m wide. The excavation was carried out by the semi top-down construction method and retained by reinforced concrete diaphragm wall (D-wall) which is 0.8 m thick and 37 m deep. It underwent 4 excavation stages with four-level slabs in conjunction with steel struts. The maximum excavation depth was 15.5 m from the ground level (GL). Figure 2 shows the cross-section, surcharge load, geological conditions, construction sequences, strutting systems, and excavation levels. More details on the excavation sequences can be found in Table 1. Besides, the SPT-N values from four boreholes of the project are shown in Fig. 3.

Fig. 1

Project location in Vietnam

Fig. 2

Construction section and soil profile

Table 1 Construction sequences of Madison project

Fig. 3

The variation of SPT-N values with the depth z in 3rd layer (the thick sand layer)

The ground consists of two sandy and three clayey soil layers. The 3rd layer is a thick medium dense sand layer with SPT-N values ranging from 8 to 25 blows/ft from the depth of 5 to 35 m, respectively. It has a significant influence on the behavior of the retaining system because most excavation works were conducted in this layer. The first two layers (1st and 2nd clay layers) are located at depths of 1.5–4.5 m and 4.5–5.5 m below the ground surface, respectively. The 1st and 2nd layers are very soft clay with SPT-N values of 0–1 blows/ft and medium-stiff clay with SPT-N values of 6–9 blows/ft in which the undrained shear strength of both clay layers are about 17–23 kPa and 34–47 kPa, respectively. The thicknesses of those layers are relatively thin (only approximately 2 m for each layer) comparing to the 3rd sand layer. The 4th clay layer is encountered between the depths of 35 m and 50 m. This clay layer is impermeable, very stiff. Its undrained shear strength is about 170–270 kPa. Since the toe of the D-wall was embedded in this layer, it plays a vital role in keeping the stability and limiting the movement of the D-wall. The 5th layer is a very dense sand layer. The sand is found at the depth of 50 m, with the SPT-N value in the range of 25–52 blows/ft. This layer has a negligible impact on the excavation since the final depth of the excavation did not reach this layer.

2.2 Instrumentations and Observed Behaviors of the Deep Excavation

Observation of retaining structures and adjacent buildings during excavations is vital for mitigating problems such as the instability and the excessive lateral movement of retaining walls, collapse and underground erosion of adjacent buildings, etc. For this purpose, seven inclinometers were installed inside the D-wall (ID01 to ID07), fourteen settlement points were installed on the ground surface (G1 to G14), twenty-one settlement points were installed on the adjacent building (B1 to B21), and six monitoring points (MW1 to MW6) were installed around the excavation area. The locations of these measurement points are shown in Fig. 4.

Fig. 4

The layout of monitoring points and adjacent buildings

In this study, two-dimensional FEA was performed by commercial software, Plaxis 2D (2019). The inclinometers ID02 and ID06, located on the central sections of the longest side of the excavation, were chosen for calibrating FEA input parameters since they were less affected by the 3D corner. According to previous studies by Ou et al. (1996) and Hsiung et al. (2016), the 3D corner effect can be neglected if the plane strain ratio (PSR) is closely 1. The PSR is a ratio of the maximum wall deflection that can be used to transfer 2D FE results to 3D FE results. The PSR depends on the excavation aspect ratio B/L and the distance (d) from the evaluated section to the excavation corner. The PSR ratio was firstly proposed by Ou et al. (1996) for a typical excavation in clayey soils and then modified by Hsiung et al. (2016) for the one in sandy soils. According to the chart proposed by Hsiung et al. (2016), the PSR value of the ID02 point can be considered 1 because the B/L value is about 0.56 (excavation width B = 37 m and excavation length L = 65) and the d value is about 32 m. Meanwhile, other inclinometer points had the PSR value in the range of 0.60–0.85. Note that the PSR ratio of the ID06 point is about 0.85. Lateral displacement profiles of the D-wall at ID06 and ID02 are shown in Fig. 5a and b. The figure indicates the similarity of the shape aspect of the lateral deflections with the difference in the magnitudes. It is also found that the maximum lateral displacements of ID06 point are approximately 10% lower than those of ID02 point. This is due to that the PSR ratios between both points are 0.85 and 1, which are very close to each other. Thus, it is assumed that the D-wall displacement at ID02 point is almost in the plane strain condition. The maximum horizontal displacement at the final excavation stage is approximately 32.9 mm at − 15.5 mGL. The percentage of the D-wall displacement is 0.4% of the excavation depth (H). These results are consistent with the range of 0.2–0.5% of the excavation depth by the study of Ou et al. (1993) for general excavation cases and the range of 0.15–0.6% of the excavation depth by the study of Hung and Phienwej (2016) for historical excavation cases using D-wall in Ho Chi Minh City.

Fig. 5

Observed lateral displacement of D-wall at each excavation stages: a ID06 point; b ID02 point

Figure 6 shows the variation of groundwater inside and outside the excavation area during construction. In the pre-excavation stage, the average depth of initial groundwater was − 3.2 mGL below the ground surface. During construction, groundwater inside the excavation area was continuously kept to at least 1 m below the excavated level. Since the toe of the D-wall was embedded in an impermeable stiff clay layer, the level of monitoring groundwater outside the excavation was considerably unchanged until the end of the excavation. The condition of groundwater level inside and outside the excavation was considered in the FEA.

Fig. 6

Field observation of groundwater levels inside and outside the excavation during excavation stages

To measure the ground surface settlements, 14 monitoring points were installed at the outside perimeter of the excavation with a distance between 2 and 6 m from edges of the excavation. However, some monitoring points, such as G3 and G9, were failed during the monitoring campaign due to the heavy site traffic and incautious protection. Figure 7 presents recorded ground surface settlements during construction. The measurements indicate that the corners of the excavation zone, such as G1, G5, G6, G9, G13, and G14, settled less than other points by 20 to 50% (3 to 8 mm). The main reason is that the deformations of the ground surface were induced by the lateral displacement of the D-wall (Hsieh and Ou 1998; Ou and Hsien 2000), which were influenced by the 3D corner effect (Ou et al. 1996; Hsiung et al. 2016). The maximum ground surface settlement (δ_vm) reached approximately 14 mm at the G11 point, which is located at the center of the long side of the excavation zone. The minimum surface settlements belonged to points located near the corner of the excavation zone, which was only 0.34 mm, 1.70 mm, and 2.26 mm for G1, G6, and G14 points, respectively. The maximum ratio δ_v/H was about 0.09%, which was smaller than the proposed value by Clough (1990) in which the average value of the maximum surface settlement was about 0.15%H. The reason is that the monitoring points were not installed at the concave curve locations that have the maximum surface movement, which was at the location of 0.5H from the excavation edge according to the study by Hsieh and Ou (1998).

Fig. 7

Field measurement of ground surface settlement during the construction process

2.3 Adjacent Buildings

Low-rise and high-rise buildings adjacent to the excavation were surveyed during the pre-construction phase. The layout of adjacent buildings is shown in Fig. 4. The high-rise buildings, such as the King Start Hotel, Power Company No. 2, 15B, were supported by pile foundations. They were not significantly impacted by induced ground deformation during excavation. The low-rise buildings, such as the 74/10A, 74/10B, 72/7, and 74/7F buildings, are 1~3 story buildings supported by shallow foundations. The damage potential of the 74/10A building is the highest since the building is located on the center of the long side of the excavation zone. It can be seen from Fig. 8 that the settlements of buildings on piles were very small (less than 3 mm), for instance, at the observed points of B11 to B15. On the contrary, the maximum settlement at the 74/10A building located near ID02 point was approximately 20 mm. Several points at the corners of the excavation displayed the small settlement value of about 5 mm although the buildings with shallow foundations were located around those areas. Note that the damage on the 74/10A building was significantly influenced by the lateral deflection of the D-wall. The other adjacent buildings were not damaged or negligibly influenced by the lateral defection of the D-wall.

Fig. 8

Observation of adjacent building settlement during construction process

With the identification of the negative impact on adjacent buildings in the initial design stage, a careful investigation of the main structure and damage status of the 74/10A building was carried out in the pre-construction stage. In this stage, the building was in normal serviceability without any visible cracks on the external brickwork, masonry, or plaster ceiling. Figure 9 demonstrates the geometric dimension of the building plan in which there is a 3-story building with a height of 3.3 m per story. Investigated geometric dimensions of main building structures were 100 mm of floor thickness, 200 × 300 mm of beam width and height, 200 × 200mm of column width and height, 12.0 × 1.2 m of shallow foundation width, and length, and the spacing of 4.0 m (L_spacing = 4.0 m). Unfortunately, visible cracks appeared on the external brickwork and plaster ceiling as well as at the corner of windows of the building when excavation was advanced to − 15.5 mGL in the 4th excavation stage. The building was carefully re-surveyed and measured for evaluating the damage level. The investigation showed that there were 18 new visible cracks with the width varying from 0.2 to 0.7 mm and the length varying from 25 to 149 cm. The damage level of the 74/10A building is presented in Fig. 10. With full observation, the 74/10A building was chosen for analyzing and assessing the damage potential by FEA.

Fig. 9

The structural plan and geometric dimension of the adjacent building 74A/10

Fig. 10

Observed field cracking on the adjacent building 74A/10

3 Numerical Model and Verification

3.1 Soil Parameters

In this study, soil stiffness parameters were calibrated with field measurements by the back-analysis technique using the hardening soil (HS) model. The soil parameter calibration by the back-analysis technique is not uncommon in the geotechnical field, for example, tunnel excavations (Sakurai and Takeuchi 1983; Gens et al. 1996; Sakurai et al. 2003), consolidation and testing embankments on soft clay (Arai et al. 1986), deep excavation (Finno and Calvello 2005; Zhang et al. 2015; Zhang et al. 2018a), and the stiffness parameters of different soils (Tan and Chow 2008; Teo and Wong 2012; Khoiri and Ou 2013; Likitlersuang et al. 2013; Hsiung and Dao 2014).

HS model is an advanced soil model based on the isotropic hardening (Schanz et al. 1999) with basic characteristics as follows: the stress-dependent stiffness according to the power law as expressed in Eq. 1, the plastic straining due to both primary deviatoric loading (shear hardening) and the primary compression (compression hardening and cap yield), the elastic un/reloading, the dilatancy effect, and the Mohr-Coulomb failure criterion. The HS model is commonly used in deep excavation analyses; it gives more realistic predictions of the lateral displacement of retaining wall and surface ground settlement than the Mohr-Coulomb or soft soil model (Teo and Wong 2012; Khoiri and Ou 2013; Likitlersuang et al. 2013). In the HS model, the soil stiffness is described much more accurately by the triaxial loading stiffness E₅₀, the triaxial unloading stiffness E_ur, and the oedometer loading stiffness E_oed. Almost parameters in the HS model are commonly defined from laboratory tests such as the consolidated-drained triaxial test (CD) and the oedometer test (OED). The E₅₀ and E₅₀^ref represent the secant stiffnesses at pressure level σ′₃ and the reference pressure level P_ref, respectively. E₅₀^ref is commonly used as the input parameter while E₅₀ is automatically calculated from Eq. 1.

$$ {E}_{50}={E}_{50}^{\mathrm{ref}}{\left(\frac{c^{\prime}\cos {\upvarphi}^{\prime }+{\upsigma}_3^{\prime}\sin {\upvarphi}^{\prime }}{c^{\prime}\cos {\upvarphi}^{\prime }+{P}_{\mathrm{ref}}\sin \upvarphi}\right)}^{\mathrm{m}} $$

(1)

In the above equation, σ′₃ denotes the minor effective principal stress, m is the law power, and P_ref denotes the preference pressure corresponding to E₅₀^ref (Plaxis 2019).

The clay layers were adopted in total stress undrained analysis with a friction angle φ_u = 0 and undrained shear strength c_u = S_u. In that case, the E₅₀ is equal to the E₅₀^ref according to Eq. 1. The secant modulus for clay soils can be determined by empirical equations (Lim et al. 2010; Hsiung et al. 2016; Yong and Oh 2016). The E₅₀^ref equals to 300S_u in the case of soft soil and 500S_u for stiff clay.

In terms of sandy soils, good-quality samples are comparatively difficult to obtain. The strength parameter of sandy soil named φ′ (effective stress friction angle) can be directly determined from the laboratory tests such as the direct shear test, and trial shear test. The φ′ value is dependent on the surface roughness and the shape of sand particles and is independent of the stress state (Alshibli and Alsaleh 2004; Altun et al. 2011; Sadrekarimi and Olson 2011). However, the stiffness parameter E′ is significantly influenced by physical properties, field sample density, and interactive force of the sand grains, which are mainly impacted by the sample disturbance. The stiffness parameters are commonly estimated from the SPT-N value in practice. Some empirical correlations of SPT-N value with soil stiffness and shear strength were proposed by Stroud (1989) from the collected data of different soil types. The correlation between E and N for sand soil is in the range of 2000N and 4000N (e.g., Stroud 1989; Tan and Chow 2008; Hsiung 2009; Shukor 2009; Hsiung et al. 2016; Yong and Oh 2016). Hsiung (2009) and Hsiung et al. (2016) proposed E₅₀ to be 2000N by conducting a series of back-analyses of monitoring data in Taiwan. The E value of 2000N was suggested for deep basement designs in Malaysia by Tan and Chow (2008). Stroud (1989) suggested that E decreases as the soil strain increases. The E can be equal to 4000N within the strain range of a retaining wall (0.1%) (Yong and Oh 2016). AIJ (2001) recommends the E value of 2800 N in common geotechnical practice. The E value of 3500 N was proposed by Shukor (2009) based on a back-analysis of lateral displacement of the cantilever diaphragm wall. From the above review results, the E values in the range of 2000–4000N were selected for back-analysis in this study. It is noted that SPT values had considered to measure shear strength reflected by shear wave velocity in some cases (Mase 2017; Misliniyati et al. 2019; Likitlersuang et al. 2020).

Note that it is not easy to set up the preferred value of E₅₀ in the HS model because of the considerable increases of the SPT-N value with depth z. The variation of E₅₀ according to N(SPT) values for a thick sand layer over 30 m cannot be reproduced in a single sand layer by Eq. 1. To avoid this difficulty, the thick sand layer (3rd layer) was divided into several sub-layers. The p^ref value of each sub-layer is assumed to be the σ′₃ at the middle of the layer, and the E₅₀^ref is calculated from the average SPT-N value of the layer. Figure 11 demonstrates comparisons of targeted E₅₀ and the actual calculated E₅₀ in the HS model. In this figure, the solid lines and unfilled markers represent the targeted E₅₀, E₅₀(Target), and actual calculated E₅₀, E₅₀(Plaxis), respectively. For the other stiffness parameters, the E_ur and E_oed values are assumed to be 3E₅₀ and E₅₀, respectively (Schanz et al. 1999; Schweiger 2009; Teo and Wong 2012). All soil parameters were summarized in Table 2.

Fig. 11

The secant stiffness E₅₀ according to SPT-N value and the reference pressure P_ref at depths (z)

Table 2 Input parameters for soil layers

3.2 Structural Parameters

The D-wall was simulated by plate elements equipped with zero-thickness interface elements (Khoiri and Ou 2013; Plaxis 2019). The reduction factor of the interface element ranges between 0.5 ~ 1.0 depending on soil and retaining wall materials as well as the degree of soil disturbance during constructions. The basement slabs and the steel struts were simulated by fixed-end anchor elements. The linear elastic model was adopted for the D-wall, basement slabs, and steel struts (Ou et al. 1996; Lin et al. 2016; Zhang et al. 2019; Huynh et al. 2020a; Zhang et al. 2020). The axial stiffness (EA) of the basement slabs shown in Table 3 was determined by a structural software considering the percentage of openings in the slabs. The axial stiffness (EA) is based on the elastic relationship between unit force P(kN) and corresponding displacement Δy(m) as Eq. 2. In which L is the length of fixed-end anchor in the model Plaxis,

$$ \mathrm{EA}=\frac{\mathrm{PL}}{\Delta \mathrm{y}} $$

(2)

Table 3 Input parameters of structures for Plaxis 2D model

In the 2D FEA, the adjacent building was simulated as a flat framed structure including floors, beams, columns, and foundations. This adoption has been successfully applied in several previous studies (Cording et al. 2010; Sabzi and Fakher 2015; Zhang et al. 2018b; Huynh et al. 2020b). The structures in this study were modeled by plate elements with flexural stiffness EI (kN/m²/m) and axial stiffness EA (kN/m). The actual dimensions of the 74/10A building structures were mentioned earlier in Section 2.3. The 2D framed stiffness was computed per 1 m unit in the plane strain model. The total stiffness of the floor and the beams was divided by corresponding spacings as expressed by Eq. 3. Dead and live loads of the building were directly added to the weight of the plate element (w). Table 4 presents the input parameters of the structural element for FE modeling.

$$ {\mathrm{EI}}_{1\mathrm{m}}=\frac{{\mathrm{EI}}_{\mathrm{floor}}+{\mathrm{EI}}_{\mathrm{beams}}}{{\mathrm{L}}_{\mathrm{spacing}}} $$

(3)

$$ {\mathrm{EA}}_{1\mathrm{m}}=\frac{{\mathrm{EA}}_{\mathrm{floor}}+{\mathrm{EA}}_{\mathrm{beams}}}{{\mathrm{L}}_{\mathrm{spacing}}} $$

(4)

Table 4 Input parameters for 2D frame structure

3.3 Boundary Conditions and Groundwater Calculations

Figure 12 illustrates the cross-section of deep excavation adopted for the simulation as well as the mesh generation of FEA. The length of the cross-section of the domain is 37 m obeying the actual design of the basement. The bottom of the FEA mesh was set at 80-m depth which is located in the very dense sand layer. The lateral boundary was set at about 80 m from the D-wall, which is more than four times of the final excavation depth (d > 4H) and over two times of the D-wall length (d > 2 L). It exceeds the zone of influence of the excavation deformation as suggested by Plaxis (2019) and the range of ground concave surface settlement (Clough 1990; Hsieh and Ou 1998). The horizontal movements are restrained at left and right boundaries while the fixed condition was applied to the bottom of the FEA mesh.

Fig. 12

2-dimensional FE simulation by Plaxis 2D 2019

For the hydraulic boundary condition of the FEA, water was allowed to permeate through lateral boundaries while the impermeable condition was assumed at the bottom boundary. To simulate dewatering inside the deep excavation, the initial groundwater level was set at 3.2 m below the ground surface based on data from monitoring wells, and the steady-state groundwater flow calculation was simulated as suggested by Plaxis (2019). The seepage from the outside to the inside of the deep excavation and the active pore-water pressure on the D-wall were maintained during excavation. Figure 13 demonstrates the comparisons of the groundwater level outside and inside the excavation from FEA and field observation. The outside groundwater level is almost stable during the excavation sequence, which agrees with the field observations. However, in the final stage, monitoring groundwater level outside the excavation increased very slightly, because it might be influenced by uncertain factors such as rain, flow, and river water level. The observed water table in the excavation area was lower than the excavation level between 1 and 3 m and well consistent with the FEA results.

Fig. 13

Hydraulic condition in FE analysis and field observation

3.4 Verification of FE Analysis

To obtain a good agreement between the predicted and observed D-wall displacement, the authors performed a parametric study by varying the stiffness E₅₀ in the range between 2000 and 4000N. Figure 14 illustrates the comparison between observations and simulations of lateral wall displacements at the final excavation stage. When the E₅₀ is equal to 2000N, the predicted lateral displacements at the toe of the D-wall and the middle part significantly overestimate the observed values. Only the top of the D-wall more or less fits with the observed value. The maximum difference between the measured and calculated displacement is about 30% indicating the underestimation of soil-related stiffness. When E₅₀ is adjusted to 4000N, the difference between the calculated lateral movements of the D-wall toe and the observed value is almost zero. The predicted movements are 4.4 mm and 2.9 mm less than the observed values at the middle and the top of the D-wall, respectively. The predicted movements are about 15% lower than the measured one indicating the overestimation of soil-related stiffness. Based on these analysis cases, the secant modulus of the thick sand layer should be varying with depth and in the range of 2000–4000N. The suitable value of E₅₀ was further explored by multiplying a constant value of 2000N by a modifier function, F(z), which varies with depth (z) as Eq. 4. Note that the depth z should be in the range between 5 and 40 m.

$$ F(z)=1+{\left(0.0286z-0.1429\right)}^{0.5}. $$

(5)

Fig. 14

Comparison of the predicted and observed horizontal D-wall displacement of various secant modulus at the final stage

As seen from Fig. 14, a good agreement between field measurements and FEA can be obtained when the E₅₀ was estimated by the proposed function. The predicted lateral displacements were 14.0 mm, 33.9 mm, and 7.2 mm at the top, the middle, and the toe of the D-wall, respectively (the corresponding observed values are 12.9 mm, 32.9 mm, and 6 mm, respectively). Comparing to the observed maximum lateral displacement in the middle part of the wall (32.9 mm), the total displacement errors at all wall parts between prediction and observation were about 5%. To confirm the validity of calibrated FEA, the predicted lateral displacements of the D-wall and the settlement of the adjacent building were compared with field measurements when the excavation depth was 3.8, 7.3, 11.8, and 15.5 mGL. As seen from Fig. 15 and Fig. 16, the prediction using E₅₀ = 2000N × f(z) agrees well with the measured displacements for all excavation stages.

Fig. 15

Comparison of the predicted and observed horizontal D-wall displacement at all excavation stages

Fig. 16

Comparison of the predicted and observed adjacent building settlements at various excavation stages

Figure 17 compares the calculated and measured ground settlement in the final stage. The settlement at G10, which is the nearest to the ID02 inclinometer, was closer to the FE result than other points. It should be noted that the observed settlement at other points was smaller than that at the G10 point and the predictions under plane strain condition because of the influence of the 3D corner effect. The FEA indicates that 20.1 mm of the maximum ground surface settlement occurs at 8 m (0.5H) away from the excavation edge. The obtained results agree with the findings by Hsieh and Ou (1998). The ratio of the maximum ground surface settlement to the maximum wall displacements according to the FEA (δ_vmax/δ_hmax) is about 0.6. The FEA results are also close to this value in which δ_vmax/δ_hmax is in the range of 0.5–0.75 as discussed in the works by Mana and Clough (1981) and Ou et al. (1993).

Fig. 17

Comparison of the predicted and observed surface ground settlement at the 4th excavation stage

The tilt of the adjacent building at each construction stage is presented in Fig. 18. The building tilted toward the excavation in the 1st and 2nd stages and was larger than that that occurred in other states. The change in the tilt is due to the different curve shapes of ground deformations in each stage. The changes in the tilt also depend on the lengths and the locations of the buildings in the influence zone of the ground surface settlement.

Fig. 18

The change in the tilt of the adjacent building according to excavation sequences. Note: θ = direction of crack formation and the angle of the plane on which ε_p acts, measured from vertical plane

4 Review of Evaluation Criteria of Building Damage Potential

Several criteria were proposed for assessing damage potential and damage levels of adjacent buildings caused by deep excavation. The main parameters for evaluation consist of the angular distortion β, the lateral extension strain ε_L, and the principal strain ε_p. Among these parameters, β is calculated from the average settlement slope minus the building tilt as presented in Eq. 5. This parameter, β, is relevant to diagonal cracks in affected buildings. The lateral extension strain ε_L is the deformation due to the lateral ground displacement, which is calculated by the lateral extension of a building base divided by its length as described in Eq. 6. This parameter, ε_L, is relevant to vertical cracks in affected buildings. The principal strain ε_p is assumed as the maximum strain on a building formed from the β and ε_L as shown in Eq. 7. Figure 19 demonstrates the details of this determination. Typically, the maximum principal strain ε_p is compared with the critical strain values of building damage classification to estimate damage levels. In some special cases, adjacent buildings with short lengths are mainly damaged by the angular distortion, where the influence of lateral strain is negligible.

$$ \upbeta =\frac{\updelta_{\mathrm{v}}}{\mathrm{L}}=\mathrm{Slope}\left(\mathrm{S}\right)\hbox{-} \mathrm{Tilt}\left(\mathrm{T}\right) $$

(6)

$$ {\upvarepsilon}_{\mathrm{L}}=\frac{\updelta_{\mathrm{L}}}{\mathrm{L}} $$

(7)

$$ {\upvarepsilon}_{\mathrm{p}}={\upvarepsilon}_{\mathrm{L}}{\mathrm{cos}\uptheta}_{\mathrm{max}}^2+\upbeta\ {\mathrm{sin}\uptheta}_{\mathrm{max}}{\mathrm{cos}\uptheta}_{\mathrm{max}} $$

(8)

Fig. 19

Define angular distortion β, lateral strain ε_L, and maximum principal strain ε_P

In which $\mathrm{Tan}\left(2{\uptheta}_{\mathrm{max}}\right)=\frac{\upbeta}{\upvarepsilon_{\mathrm{L}}}$.

In the above equations, L denotes the building length, δ_v denotes the forced distortion, δ_L denotes the forced lateral extension, β denotes the angular distortion, ε_L denotes the lateral strain, and θ_max denotes the direction of crack formation measured from the vertical plane.

Burland (1977), firstly, proposed the damage levels for adjacent buildings by collecting and analyzing the data of the building damages observed from construction sites. Table 5 defines six levels of building damages, numbered from 0 to 5 with increasing severity, based on the criteria of severity degree such as the width of cracks or the limiting tensile strain of buildings. For instance, with a measured width of cracks less than 5 mm or calculated result of ε_p in the range of 0.75–0.15%, the damage level of the adjacent building is classified as level 2. Besides, a simple chart of strain state to evaluate building damage potential was also proposed as described in Fig. 19(c).

Table 5 Damage classification established by Burland et al. (1977) and the relationship between the degree of damage and limiting tensile strain (after Boscardin and Cording 1989)

Boscardin and Cording (1989) extended the work of Burland (1977) and combined the previous building damage studies of Skempton and MacDonald (1956) and Bjerrum (1963). An updated practical chart of strain state for the estimation of building damage potential was proposed by Boscardin and Cording (1989) as indicated in Fig. 20. In Fig. 20, three categories of damage were classified by visible damage repairs, and six degrees of severity were classified by crack width. Three categories of damage are explained as follows;

• Aesthetic damages are related to slight cracks of building structures, affection mainly is easy to repair generally, and redecoration is sufficient to cover the light cracks.

• Functional damages are related to the loss of functionality or serviceability of parts of the building (e.g., doors and windows may be stuck and pipelines can be damaged) or of sensitive devices located inside the building (such as precision instruments that are sensitive to differential movements); the structural integrity of the building is not affected; however, the lack of serviceability can have commercial and economic impacts on the building and the host’s activities.

• Structural damages are related to excessive cracks or deformations of bearing structures and can lead to the partial or total collapse of the building. Structural damages can sometimes remain partially hidden beneath the finishes. However, whitewash and plaster are good indicators of the cracking propagation.

Fig. 20

Damage criterion based on the strain state of a point (after Boscardin and Cording 1989)

In the recent study by Schuster et al. (2009), a new notion, called the damage potential index (DPI), was introduced for the evaluation of the damage potential of adjacent buildings. The DPI is a modification of the maximum principal tensile strain ε_p, which can be calculated from Eq. 8.

$$ \mathrm{DPI}={\upvarepsilon}_{\mathrm{p}}/\left(1/200\right)\times 100 $$

(9)

Schuster et al. (2009) illustrated six damage levels of buildings associated with DPI values as presented in Table 6. In addition, to verify the damage classification according to DPI value, 75 historical excavation cases from the database of previous studies were evaluated in their study. The results indicated that the majority of the evaluated cases (approximately 80%) were correctly classified.

Table 6 Levels of building damage according to DPI

Comparing to previously proposed criteria, the advantage of the DPI concept is that it provides a relative measure of the maximum principal strain and a convenient approach of the damage potential evaluation. The damage levels of the building can be easily assessed in terms of relative DPI value. In this study, approaches proposed by Boscardin and Cording (1989) and Schuster et al. (2009) were employed to evaluate the damage potential of adjacent buildings.

5 Assessment of Damage Level on the Adjacent Building

To assess the damage levels of the adjacent building named 74/10A from the FE results, the simple chart of strain state proposed by Boscardin and Cording (1989) and the DPI value proposed by Schuster et al. (2009) were used in this part.

According to the field investigation, there are 18 new visible cracks with a width between 0.02 and 0.07 cm and the length from 25 to 149 cm as recorded in Fig. 10. These cracks were easily treated by normal decoration to cover the visible cracks. According to Burland (1977), visible cracks with the width being smaller than 5 mm are categorized as aesthetic damages with the degrees of severity from very slight to slight conditions.

In the 1st and 2nd stage, no cracks or damages were observed. Little fine cracks in the internal brickwork of the building were noticed when the excavation depth was 11.8 mGL. In the 4th stages of the excavation which the excavation depth was 15.50 mGL, visible cracks were readily observed in the internal and external brickwork, masonries, and plaster ceilings. Some cracks were at window corners. However, the adjacent building is still in a good serviceability condition. No visible crack was observed on main structural elements such as slabs, beams, and columns.

Based on the calculated displacements of structural elements of the adjacent building and the ground surface from the FEA, the angular distortion β and lateral strain ε_L of the adjacent building are determined according to Eq. 5 and Eq. 6, respectively. The movements of the ground surface and the adjacent building structures at the 4th excavation stage are shown in Fig. 21. This figure illustrates a cross-section of the adjacent building including height building (H), isolated bay length (L), distance to the excavation edge, and nodal points of the frame structure. In that, the x, y values (x,y) are the vertical and horizontal displacements of the nodal points obtained from the FEA. Besides, the lateral and vertical displacements of the ground surface and isolated column bases are described by dotted lines and filled markers, respectively, in the chart. The slope of Bay no. 1 is determined from the vertical movements of nodal points A, B, C, and D as expressed by Eq. 9. Equation 10 demonstrates the determination of the tilt of a bay from the horizontal displacements of nodal points and the building height. The lateral extension, ε_L, was calculated from the difference between lateral movements at two ends of a beam element by Eq. 11. The calculations for other bays are similar to that of Bay no. 1. Table 7 summarized the calculated results of all bays from all excavation stages.

$$ \mathrm{Slope}\left(\mathrm{S}\right)=\frac{\left({\mathrm{y}}_{\mathrm{A}}\hbox{-} {\mathrm{y}}_{\mathrm{B}}\right)+\left({\mathrm{y}}_{\mathrm{C}}\hbox{-} {\mathrm{y}}_{\mathrm{D}}\right)}{{\mathrm{L}}_{\mathrm{A}\mathrm{B}}+{\mathrm{L}}_{\mathrm{C}\mathrm{D}}} $$

(10)

$$ \mathrm{Tilt}\left(\mathrm{T}\right)=\frac{\left({\mathrm{x}}_{\mathrm{c}}\hbox{-} {\mathrm{x}}_{\mathrm{A}}\right)+\left({\mathrm{x}}_{\mathrm{D}}\hbox{-} {\mathrm{x}}_{\mathrm{B}}\right)}{{\mathrm{H}}_{\mathrm{A}\mathrm{C}}+{\mathrm{H}}_{\mathrm{B}\mathrm{D}}} $$

(11)

$$ {\upvarepsilon}_{\mathrm{L}}=\frac{\updelta_{\mathrm{L}}}{\mathrm{L}}=\frac{\left({\mathrm{x}}_{\mathrm{A}}\hbox{-} {\mathrm{x}}_{\mathrm{B}}\right)+\left({\mathrm{x}}_{\mathrm{C}}\hbox{-} {\mathrm{x}}_{\mathrm{D}}\right)}{{\mathrm{L}}_{\mathrm{A}\mathrm{B}}+{\mathrm{L}}_{\mathrm{C}\mathrm{D}}} $$

(12)

Fig. 21

Movement of the ground surface and adjacent building structures in the 4th excavation stage

Table 7 Calculation of ground slope, building tilt, lateral strain ε_L, angular distortion β, and damage potential index (DPI) at excavation stages

The calculated values of β and ε_L and the damage criteria proposed by Boscardin and Cording (1989) are shown in Fig. 22. The calculated results almost indicate negligible to slight damage potentials. Additionally, the DPI values are also determined by Eq. 4 and shown in Table 7. The maximum DPI values at each excavation stage varied from 5.7 to 24.1. It means that the damage potential varies from very slight to slight conditions. Table 8 demonstrates the comparison of estimated damages by two criteria using field observations and FEA predictions. The evaluated damages are completely consistent with the observed ones in the field as the comparisons are shown in Table 8.

Fig. 22

Assessing the adjacent building damage potential according to the simple chart of Boscardin and Cording (1989)

Table 8 Comparisons of damage levels of adjacent building based on FE analysis and field observation

In the first stage, the highest DPI value of 5.7 occurs at the farthest bay from the excavation. However, the highest DPI of 24.1 was observed at the nearest bay in the final stage. The compelling reason is that the influence zone and the ground concave surface of the settlement expands as the excavation depth increases. According to Clough (1990) and Ou and Hsien (2000), the influence zone is the distance of two to three times of the excavation depth (H) from the excavation edge. The maximum ground surface settlement occurs approximately within half of the excavation depth from the edge of the D-wall (Hsieh and Ou 1998).

For more discussion, Table 7 also shows the values of lateral strain ε_L of the adjacent building in all excavation stages. The ε_L values are approximately equal to zero because the absolute lateral movement of isolated columns is similar, for example, in the final stage, this movement is approximately 7.3 mm as shown in Fig. 21. It means that the tensile strains in the beams and the floors were not developed in the adjacent building in this case.

6 Conclusions

This paper investigates the behavior of deep excavation and adjacent building including the lateral movements of the D-wall, the ground surface settlements, the adjacent building tilts, and the damage of adjacent buildings based on an excavation case in a sand thick layer in Vietnam. The findings from the study can be summarized as follows:

• 1. The percentages of the lateral displacements of the D-wall are 0.4% and 0.2% of excavation depth (H) for the cantilever and braced excavations, respectively. The FEA indicates that the maximum ground surface settlement occurs at the location of 0.5H from the excavation edge. In addition, the ratio of the maximum ground surface settlement to the maximum lateral D-wall displacement (δ_vmax/δ_hmax) is 0.6.

• 2. The ground surface and adjacent building settlements are influenced by the 3D corner effect. The settlements around the corner of the excavation zone are about 20–50% of that occurs in the central section.

• 3. For the thick sand layer in Ho Chi Minh City, Vietnam, stiffness parameters E₅₀ can be determined from the SPT-N value by the proposed formula E₅₀ = 2000N × [1 + (0.0286z − 0.1429)^0.5]. Note that the depth z should be in the range between 5 and 40 m.

• 4. The thick Ho Chi Minh sand layer should be divided into several layers for proper modeling by the HS soil model in FEA. The reference pressures P_ref is set to be equal to the minor effective principal stress σ′₃ at the middle of each layer while the E₅₀^ref should be determined from the average of SPT-N value in each layer.

• 5. The tilt of adjacent buildings is varied with the shape of ground deformation in each stage. The change of tilt depends on the length and the location of the adjacent building in the influence zone of the ground surface settlements.

• 6. The 2D simulations can be used to predict the damage degrees of the adjacent building at the initial design stages as well as the construction stages of the deep excavation work by determining the angular distortion β and the lateral strain ε_L from the FEA.

• 7. The damage potential of adjacent buildings as evaluated from FEA through the strain state chart proposed by Boscardin and Cording (1989) or the damage potential index (DPI) proposed by Schuster et al. (2009) is fairly accurate with field observations.

7 Notations

EA:

axial stiffness

b :

excavation width

c :

adhesion factor

c _u :

undrained adhesion factor

DPI:

damage potential index

EI:

flexural stiffness

E ₅₀ :

secant stiffness at pressure level σ₃

E ₅₀ ^ref :

oedometer loading stiffness at a reference stress level p_ref

E _oed ^ref :

oedometer loading stiffness at a reference stress level p_ref

E _ur ^ref :

triaxial unloading stiffness at a reference stress level p_ref

H :

excavation depth

L :

excavation length

L _a :

length of fixed-end anchor in the Plaxis model

L _spacing :

spacing of anchor in Plaxis 2D model

m :

power

SPT-N:

SPT value

P _ref :

preference pressure corresponding to E₅₀^ref

S _u :

undrained shear strength

w :

weight of the plate element

z :

depth

β:

angular distortion of the adjacent building

ε_L:

lateral strain of the adjacent building

ε_p:

principal strain of adjacent building

θ_max:

direction of crack formation measured from the vertical plan

Δ_y:

corresponding displacement of the fixed-end anchor of opening slabs

ν:

Poisson’s ratio

σ’₃:

minor effective principal stress of layer soil

δ_vm:

maximum settlement of ground surface

φ:

internal friction angle

φ_’:

drained internal friction angle

φ_u:

undrained internal friction angle