# Evaluation of Risk of Building Damage due to Deep Excavations via Numerical Modelling

Authors: Xingxing Zhang; Zhifeng Zhan
Journal: Advances in Civil Engineering
 (2021)

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## Abstract

In the densely populated urban environment, ground movements induced by deep excavations inevitably present a risk of damage to adjacent buildings and structures. An important and necessary aspect to justify the engineering design is to evaluate the degree of risk of such damage. This paper presents a specific procedure to evaluate the engineering design by assessing the risk level of building damage based on the deformation profiles along the ground surface which are calculated via numerical modelling and verified by empirical methods. This procedure is afterwards applied to justify the engineering design of the extension line construction of a metro project between PK0 + 344.00 and PK0 + 407.00 with the cut-and-cover excavation method. The results demonstrate that the damage risk levels of all the buildings adjacent to the excavations are within category level 0 indicating that the relevant design is acceptable while considering the risk of building damage induced by deep excavations.


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## Body

## 1. Introduction

The engineering design for deep excavations usually involves design factors such as the construction sequences, structure planning, drainage scheme, detailed structural design for supporting structures, and instrumentation system. Analyses of stress and deformation, internal and external stability, water flow, and piping are normally required in order to justify the relevant design strategy. One of the important considerations in this justification is to keep the displacements induced by deep excavations within acceptable limits because deep excavations in urban zones inevitably cause ground movements which may induce damages to adjacent buildings and structures. Supporting structures such as diaphragm walls and struts are usually set up in order to minimise possible building damage due to deep excavations in urban situations.Therefore, it is necessary, both for engineering design and for planning and consultation, to develop rational methods to assess the risks of damage. A rational approach to the assessment of risk of damage to buildings due to deep excavations was developed and adopted during the planning and enquiry stages of the London Underground Jubilee Line Extension project which involved tunnelling under densely developed areas of central London [1, 2]. This approach includes three stages of damage assessment: preliminary assessment, second stage assessment, and detailed evaluation.So as to avoid complex and unnecessary calculations, the preliminary phase uses a very simple and conservative method for the evaluation of damage level based on the contours of expected ground surface movements. In the second stage, the equivalent beam approach [3] is adopted to estimate the maximum tensile strain and establish a certain category of damage for the potentially affected buildings. The third stage of detailed evaluation is only performed for buildings that are classified as being at high risk of damage. This approach has been widely used internationally with minor variations. This paper mainly focuses on the second stage of this approach.A specific procedure to justify the engineering design is established in this paper as described in the following four steps: (1) prediction of the magnitude and distribution of ground movements behind diaphragm walls; (2) selection of appropriate damage criterion; (3) assessment of risk level of building damage under selected criterion based on known ground deformation profiles; (4) justification of engineering design according to the results of ground movements and risk assessment.The proposed engineering design of deep excavations is accepted only if the ground movements and risk level of damage are within the range of engineering safety. Otherwise, the design strategy should be modified and evaluated again through the 4 steps. This process should be repeated until the eventual design is judged to be acceptable.In step 1, the calculation of ground movements is not straight forward because of the complexity of the problem which is critically dependent both on the ground conditions (e.g., stratigraphy, groundwater conditions, deformation, and strength properties) and the method of construction (e.g., sequence of excavation, sequence of propping, rigidity of diaphragm wall, and supports). To estimate the likely damage, both the lateral ground movements and the settlement trough caused by the excavation must first be estimated. Recently, the development of advanced computational tools allows delicate calculation of these ground movements induced by deep excavations via numerical modelling. In this paper, both empirical and advanced numerical methods are presented. The latter method is preferred in consideration that it has been widely used for prediction of ground movements around deep excavations and can simulate the construction process, modelling the various stages of excavation and support conditions. Meanwhile, the comparison of numerical results with those obtained through empirical method is made to verify mutually the respective results from both methods.As for the damage criterion, different theories are reviewed and analysed to select the damage criterion. The details will be described later in this paper. This specific procedure is then applied to justify the engineering design of the extension line construction of a metro project from PK0 + 344.00 to PK0 + 407.00 with the cut-and-cover excavation method by assessing the risk of building damage via numerical modelling.


## 2. Estimation and Calculation of Ground Movement Induced by Excavation

The response of buildings adjacent to deep excavations refers to the translation and rotation of building structure in reaction to lateral ground movements and surface settlement. Proper assessment of risk of building damage requires an accurate prediction of the magnitude and distribution of ground movements adjacent to an excavation via empirical and advanced numerical methods.


### 2.1. Empirical Methods for Estimating Ground Movements

The research of Peck [4] accounting for varying soil types and depths provided the first rational basis for estimating general ground movements resulting from an adjacent excavation. Clough and O’Rourke [5] developed well-defined excavation-induced settlement profiles by plotting the various settlement data as fractions of the maximum settlement for sand, stiff to very hard clays, and soft to medium clays.Hsieh and Ou [6] developed a semiempirical method to predict the distribution of ground movements based upon previous research including Peck [4] and Clough and O’Rourke [5]. Two types of settlement profiles due to excavations were suggested: (1) the spandrel type with maximum settlement distributed very close to the wall and (2) the concave type with maximum settlement located at some distance away from the diaphragm wall. At the first stage of excavation, the spandrel type of settlement profile occurs if a large amount of wall deflection takes place under cantilever conditions. After the initial stages of excavation, additional cantilever wall deflection is restrained by installation of support as the excavation proceeds to deeper elevations and the concave type dominates the settlement profile with the maximum lateral deformation occurring near the bottom of the excavation.Figure1 presents the graphical methods for predicting settlement profiles of both the spandrel and concave conditions developed by Hsieh and Ou [6]. This figure was based on case history data compiled by Clough and O’Rourke [5] and the evaluation of case history data from Taipei, Taiwan.Figure 1
Empirical methods for predicting both spandrel and concave settlement profiles [6].
(a)(b)The “mean estimate” curve shown in Figure1(a) was adopted for the settlement profile prediction. Figure 1(a) plots the square root of the distance from the edge of the excavation (d) normalized by the excavation depth He versus the normalized settlement δv/δvm. δv represents the settlement at some location while δvm represents the maximum ground surface settlement.Figure1(b) plots the normalized distance from the edge of the wall versus the normalized settlement. Hsieh and Ou [6] concluded that the distance from the support wall to the point where the maximum ground surface settlement occurred was approximately equal to half of the excavated depth He/2. The settlement at the diaphragm wall location was half of the maximum settlement (δvm). The point on the settlement profile curve marked by d/He=2 corresponds to the extent of the primary influence zone. The settlement was practically negligible at a distance from the support wall equal to four times the depth of the excavation 4He.


### 2.2. Numerical Methods for Calculating Ground Movements

The building response due to deep excavations is dependent upon factors such as the stiffness of the excavation support system, the installation procedures of the system, the soil conditions, the excavation procedures, the type of building, the distance of the building from the excavation, the orientation of the building with respect to the excavation, and the size of the building with respect to the excavation. A purely theoretical approach to estimate building response due to excavation-related deformations is not possible due to the variability of these factors that contribute to the response. However, with the rapid innovation of computer technology, the numerical methods and relevant computer programs are available to take the mentioned factors into account.Numerical simulations using the finite element method and finite difference method with the aforementioned advantages are progressively replacing simplified traditional calculation methods—limit equilibrium method and Winkler’s theory. Software applications such as PLAXIS, ABAQUS, CRISP, ICFEP, MIDAS GTS, Z-SOIL (finite element method), and FLAC (finite difference method) are widely utilized to perform such numerical simulations. Schweiger [7–13] presented in detail the results from a numerical benchmark exercise addressing the design of a diaphragm wall for a deep excavation problem by using PLAXIS. Comprehensive study was performed to analyse the influence of various modelling parameters including domain analysed, stiffness of structural elements, soil-structure interface, constitutive model, etc. As stated by Schweiger [7–13], one of the critical factors is the constitutive model adopted to simulate the soil behavior. It has been confirmed that the generally used elastic-perfectly plastic constitutive model (Mohr–Coulomb model) or any other that incorporates a linear elastic component is not well suited for predicting realistic deformations for deep excavation problems. The main defects lie in the following: (1) although reasonable wall lateral movements can be obtained by using the Mohr–Coulomb model, computed settlements are often in error; (2) excavation bottom heave is considerably overestimated; and (3) the location of the lower boundary of the calculation domain has a decisive influence on computed displacements. It was also demonstrated by comparison with field data that constitutive models allowing for nonlinearity of the stress-strain curve can give both reasonable wall deflection and realistic ground movements. The hardening soil model is one such model which is being applied widely in recent years to deal with similar problems. It is accordingly adopted in the subsequent case study.In this paper, FLAC3D [14] is chosen as the numerical tool to carry out the calculations of ground movements. The detailed creation of numerical models involving all the model parameters via FLAC3D is beyond the scope of this paper and can be referred to Itasca [14].


## 2.1. Empirical Methods for Estimating Ground Movements

The research of Peck [4] accounting for varying soil types and depths provided the first rational basis for estimating general ground movements resulting from an adjacent excavation. Clough and O’Rourke [5] developed well-defined excavation-induced settlement profiles by plotting the various settlement data as fractions of the maximum settlement for sand, stiff to very hard clays, and soft to medium clays.Hsieh and Ou [6] developed a semiempirical method to predict the distribution of ground movements based upon previous research including Peck [4] and Clough and O’Rourke [5]. Two types of settlement profiles due to excavations were suggested: (1) the spandrel type with maximum settlement distributed very close to the wall and (2) the concave type with maximum settlement located at some distance away from the diaphragm wall. At the first stage of excavation, the spandrel type of settlement profile occurs if a large amount of wall deflection takes place under cantilever conditions. After the initial stages of excavation, additional cantilever wall deflection is restrained by installation of support as the excavation proceeds to deeper elevations and the concave type dominates the settlement profile with the maximum lateral deformation occurring near the bottom of the excavation.Figure1 presents the graphical methods for predicting settlement profiles of both the spandrel and concave conditions developed by Hsieh and Ou [6]. This figure was based on case history data compiled by Clough and O’Rourke [5] and the evaluation of case history data from Taipei, Taiwan.Figure 1
Empirical methods for predicting both spandrel and concave settlement profiles [6].
(a)(b)The “mean estimate” curve shown in Figure1(a) was adopted for the settlement profile prediction. Figure 1(a) plots the square root of the distance from the edge of the excavation (d) normalized by the excavation depth He versus the normalized settlement δv/δvm. δv represents the settlement at some location while δvm represents the maximum ground surface settlement.Figure1(b) plots the normalized distance from the edge of the wall versus the normalized settlement. Hsieh and Ou [6] concluded that the distance from the support wall to the point where the maximum ground surface settlement occurred was approximately equal to half of the excavated depth He/2. The settlement at the diaphragm wall location was half of the maximum settlement (δvm). The point on the settlement profile curve marked by d/He=2 corresponds to the extent of the primary influence zone. The settlement was practically negligible at a distance from the support wall equal to four times the depth of the excavation 4He.


## 2.2. Numerical Methods for Calculating Ground Movements

The building response due to deep excavations is dependent upon factors such as the stiffness of the excavation support system, the installation procedures of the system, the soil conditions, the excavation procedures, the type of building, the distance of the building from the excavation, the orientation of the building with respect to the excavation, and the size of the building with respect to the excavation. A purely theoretical approach to estimate building response due to excavation-related deformations is not possible due to the variability of these factors that contribute to the response. However, with the rapid innovation of computer technology, the numerical methods and relevant computer programs are available to take the mentioned factors into account.Numerical simulations using the finite element method and finite difference method with the aforementioned advantages are progressively replacing simplified traditional calculation methods—limit equilibrium method and Winkler’s theory. Software applications such as PLAXIS, ABAQUS, CRISP, ICFEP, MIDAS GTS, Z-SOIL (finite element method), and FLAC (finite difference method) are widely utilized to perform such numerical simulations. Schweiger [7–13] presented in detail the results from a numerical benchmark exercise addressing the design of a diaphragm wall for a deep excavation problem by using PLAXIS. Comprehensive study was performed to analyse the influence of various modelling parameters including domain analysed, stiffness of structural elements, soil-structure interface, constitutive model, etc. As stated by Schweiger [7–13], one of the critical factors is the constitutive model adopted to simulate the soil behavior. It has been confirmed that the generally used elastic-perfectly plastic constitutive model (Mohr–Coulomb model) or any other that incorporates a linear elastic component is not well suited for predicting realistic deformations for deep excavation problems. The main defects lie in the following: (1) although reasonable wall lateral movements can be obtained by using the Mohr–Coulomb model, computed settlements are often in error; (2) excavation bottom heave is considerably overestimated; and (3) the location of the lower boundary of the calculation domain has a decisive influence on computed displacements. It was also demonstrated by comparison with field data that constitutive models allowing for nonlinearity of the stress-strain curve can give both reasonable wall deflection and realistic ground movements. The hardening soil model is one such model which is being applied widely in recent years to deal with similar problems. It is accordingly adopted in the subsequent case study.In this paper, FLAC3D [14] is chosen as the numerical tool to carry out the calculations of ground movements. The detailed creation of numerical models involving all the model parameters via FLAC3D is beyond the scope of this paper and can be referred to Itasca [14].


## 3. Criteria for Assessing Building Damage

### 3.1. Definitions of Excavation-Induced Deformations Related to Building Response

The translations and rotations of building adjacent to excavations result in direct tensile strains, bending strains, and diagonal tensile strains in building structures. A consistent set of definitions describing types of ground movements and building responses based on the displacements (either measured or calculated) of a number of discrete points on the foundations of a building was proposed by Burland and Wroth [3] and summarized by Finno and Alvello [15]. These definitions (illustrated in Figure 2) have been widely accepted and are described as follows:(a)
Settlement (downward displacement) or heave (upward displacement) is denoted asS.(b)
Relative settlement (differential settlement or differential heave) is denoted asδS.(c)
Rotation or slope is the change in gradient of a line joining two reference points (e.g., AB in Figure2). Rotation is typically used to describe the slope of the settlement trough.(d)
The angular strainα is defined in Figure 2. It is positive for upward concavity (sagging seen in Figure 3) and negative for downward concavity (hogging seen in Figure 3).(e)
Relative deflectionΔ is the displacement of a point relative to the line connecting two reference points on either side (see Figure 2). The sign convention is the same as (d).(f)
Deflection ratio (sagging ratio or hogging ratio) is denoted byΔ/L where L is the distance between the two reference points defining Δ. The sign convention is the same as (d) and (e). The deflection ratio is an approximate measure of curvature of the settlement curve and is often correlated with bending related distortions in a structure.(g)
Tiltω describes the rigid body rotation of the structure or a well-defined part of it (see Figure 2).(h)
Relative rotation (angular distortion)β is the rotation of the line joining two points, relative to the tilt ω (see Figure 2).(i)
Average horizontal strainεh is defined as the change of length δL over the length L and is used to describe the direct lateral movement of building structures. It is customary to take a reduction of length (compression) as positive in soil mechanics.Figure 2
Definitions of ground and foundation movement [3].Figure 3
Deflection mode of building in response to deformation [3].The above definitions only apply to in-plane deformations and no attempt has been made to define three-dimensional behavior.


### 3.2. Damage Criteria Based on Angular Distortion

Damage criteria based on angular distortion have been developed by Skempton and MacDonald [16], Polshin and Tokar [17], Bjerrum [18], O’Rourke et al. [19], and Attewell et al. [20]. Bjerrum [18] took the angular distortion as the governing variable in the assessment of permissible deformations. Typical limiting values of angular distortion for buildings where only building settlement is assessed are shown in Figure 4.Figure 4
Limiting angular distortion [18].Damage criteria based on angular distortion do not consider the horizontal displacement. But ground movements related to deep excavations can include a substantial component of horizontal strain except vertical deformation. Therefore, the traditional criteria based on differential settlement or angular distortion alone is inadequate for assessment of building response due to deep excavations.


### 3.3. Damage Criteria Proposed by Boscardin and Cording [21] and Burland et al. [22]

#### 3.3.1. Concept of Limiting Tensile Strainεlim and Classification of Building Damage

Cracking in masonry walls and finishes usually, but not always, results from tensile strain. Burland and Wroth [3] firstly defined critical tensile strain εcrit with which the onset of visible cracking in building is associated. Burland and Wroth [3] also showed how the concept of critical tensile strain could be used in conjunction with simple elastic beams to develop deflection criteria for the onset of visible damage. Burland et al. [23] introduced the concept of limiting tensile strain εlim to replace critical tensile strain εcrit as a serviceability parameter which can be varied to take account of differing material and serviceability limit states. Boscardin and Cording [21] developed this concept by assessing 17 case records of damage due to excavation-induced subsidence. They related the ranges of εlim to the likely severity of damage. Burland [24] summarized the categories of building damage as shown in Table 1 which provides the link between estimated building deformations and the possible severity of damage.Table 1
Building damage classification [22].
Category levelNormal degree of severityDescription of typical damageApproximate crack width (mm)Limiting tensile strainεlim (%)0NegligibleHairline cracks0–0.10–0.051Very slightFine cracks easily treated during normal decoration0.1–10.05–0.0752SlightCracks easily filled. Several slight fractures inside building. Exterior cracks visible.1–50.075–0.153ModerateCracks may require cutting out and patching. Door and windows sticking.5–15 (or several closely spaced cracks > 3 mm)0.15–0.34SevereExtensive repair involving removal and replacement of walls, especially over doors and windows. Windows and door frames distorted. Floor slopes noticeably.15–25 (but also depends on number of cracks)>0.35Very severeMajor repair required involving partial or complete reconstruction. Danger of instability.>25 (but also depends on number of cracks)>0.3Burland et al. [22] introduced the term “the level of risk” of damage to refer to the possible degree of damage as defined in Table 1. Most buildings with degree of damage within the first three categories 0 to 2 (i.e., negligible to slight) are considered to be at “low risk” and can be readily and economically repaired. A major objective of design and construction is to maintain the level of risk below the threshold between categories 2 and 3 for all buildings.


#### 3.3.2. Equivalent Beam Approach to Evaluate Building Damage

Burland and Wroth [3] introduced the equivalent beam approach in the evaluation of damage to buildings due to ground movements where the building is represented by an elastic rectangular deep beam of length L and height H (Figure 5). This approach is to calculate the tensile strains in the beam for a given deflected shape of the building foundations and hence obtain the deflection ratio Δ/L at which cracking is initiated. Burland and Wroth [3] considered two extreme modes: bending only about a neutral axis at the center and shearing only. In the case of bending only, the cracks are related to the bending strain εb occurring in the top fibre, whereas in the case of shearing only the diagonal cracks are due to the shear strain εd caused by shear deformations. In general, both modes of deformation will occur simultaneously and it is necessary to calculate both bending and shear strains to ascertain which type is limiting.Figure 5
The equivalent beam approach [22]. (a) Actual building. (b) Bending deformation with cracking due to direct tensile strain. (c) Beam: simple idealisation of building. (d) Shear deformation with cracking due to diagonal tensile strain. (e) Deflected shape of soffit of beam.
(a)(b)(c)(d)(e)Timoshenko [25] put up the expression for the total midspan deflection Δ/L of a central point loaded beam with the maximum bending strain εbmax and the maximum shear strain εdmax as follows:(1)ΔL=L12h+3I2hLHEGεbmax,(2)ΔL=1+HL218IGEεdmax,where h is the distance of the neutral axis from the edge of the beam in tension (h=H for hogging and h=H/2 for sagging); E is Young’s modulus; G is the shear modulus; and I is the second moment of area (I=H3/3 for hogging and I=H3/12 for sagging).By settingεmax=εlim, equations (1) and (2) define the limiting values of Δ/L for the deflection of simple beams. For a given deflection ratio Δ/L, an estimation of the maximum tensile strain in the building can be obtained as the maximum of the values of εbmax and εdmax provided by equations (1) and (2).Burland and Wroth [3] showed that generally hogging is much more damaging than sagging—a result that is well borne out in practice. Figure 6 presents the limiting relationships between Δ/L normalized by εlim and L/H for an isotropic beam undergoing hogging (E/G=2.6 and I=H3/3) with its neutral axis at the bottom edge h=H/2 and undergoing sagging (E/G=2.6 and I=H3/12) with its neutral axis at the middle h=H/2. It can be seen that the shear strains dominate if L/H<1.3, whereas for L/H>1.3, the bending strains dominate.Figure 6
Relationship betweenΔ/L/εlim and L/H for rectangular isotropic beams (hogging).Boscardin and Cording [21] incorporated horizontal extension strain εh, which excavations can induce, in the above analysis through simple superposition of this effect to Burland and Wroth’s [3] bending and shear strains.For the case of bending, the resultant extreme fibre strainεbr is given by(3)εbr=εbmax+εh.In the shearing region, the resultant shear strainεdr can be evaluated using Mohr’s circle of strain and is given by(4)εdr=εh1−v2+εh21+v22+εdmax2,where v is Poisson’s ratio.The maximum tensile strain is greater thanεbr and εdr and can be used in conjunction with Table 1 to assess the potential associated damage.


#### 3.3.3. Damage Criterion Proposed by Burland et al. [22]

By adopting the values ofεlim associated with the various categories of damage given in Table 1 and by using equations (1)–(4), a building damage interaction diagram can be developed showing the relationship between Δ/L and εh for appropriate values of h, L/H, E/G, v, and I selected for the structure being assessed. The physical implications of equations (1)–(4) can be illustrated by considering an isotropic beam with v=0.3 (E/G=2.6 and I=H3/12) undergoing hogging (h=H). For bending case, manipulation of equations (1) and (3) with εbr=εlim gives(5)Δ/Lεlim=0.083LH+1.3HL1−εhεlim.For shearing, manipulation of equations (2) and (4) with εdmax=εlim yields(6)Δ/Lεlim=1+0.064LH21−0.7εhεlim−0.3εhεlim2.The relationships betweenΔ/L and εh normalized by εlim given by equations (5) and (6) are shown in Figure 7. It is evident from Figure 7 that L/H determines the shape of the damage interaction diagram for isotropic beams undergoing hogging. The damage interaction diagram corresponding to L/H=1 is presented in Figure 8.Figure 7
Relationship betweenΔ/L/εlim and εh/εlim for rectangular isotropic beams (hogging). (a) Bending limit. (b) Shearing limit. (c) Limiting combinations.
(a)(b)(c)Figure 8
Damage interaction diagram forL/H=1 and hogging [22].


#### 3.3.4. Damage Criterion Proposed by Boscardin and Cording [21]

Boscardin and Cording [21] produced similar diagrams relating category of damage to horizontal strain εh and angular distortion β (instead of deflection ratio Δ/L). They expressed the relationship between angular distortion β and deflection ratio Δ/L as(7)β=3ΔL1+4E/GH/L21+6E/GH/L2.Substitution of equation (7) into equation (6) yields(8)βεlim=3⋅1+10.4H/L21+15.6H/L2⋅1+0.064L/H2⋅1−0.7εhεlim−0.3εhεlim2.The damage interaction diagram corresponding toL/H=1 for isotropic beams (E/G=2.6) undergoing hogging plotted according to equations (8) is shown in Figure 9. There are similarities between Figures 8 and 9. However, the maximum bending strain εbmax is ignored in Boscardin and Cording’s [21] method. Burland et al. [22] have shown that the relationship between angular distortion β and deflection ratio Δ/L is in fact very sensitive to the load distribution and to the value of E/G. Moreover, the precise evaluation of β is not always straight forward and can be uncertain on occasions. The damage interaction diagrams for sagging after Burland and after Boscardin and Cording [21] can be deduced similarly by setting h=H/2 and I=H3/12.Figure 9
Damage interaction diagram forL/H=1 and hogging [21].


### 3.4. Selection of Appropriate Damage Criteria

As stated by Burland [24], it is not always straight forward to identify the tilt and the evaluation of angular distortion can sometimes be difficult. It is also very important not to confuse relative rotation β with angular strain α. For these reasons, Burland and Wroth [3] preferred the use of deflection ratio as a measure of building distortion. Therefore, in this paper, the damage criterion proposed by Burland et al. [22] is adopted. However, both the damage criteria proposed by Boscardin and Cording [21] and Burland et al. [22] are the most common ones and their selection shall be dependent on the convenience to obtain the relevant parameters.


### 3.5. Comments on the Application of Damage Criteria

A building can be considered separately as per its deflection mode to deformation on each side of the inflection point of the settlement profile (seen in Figure3), which is used to partition the building. In a calculation of building strain, the building span length is required and is defined as the length of building in a hogging or sagging zone (shown as Lh or Ls in Figure 3). And it is advisable to treat the parts of the building under hogging and under sagging as separated beam segments by calculating the respective deflection ratio Δ/L and the average horizontal strain εh. The level of risk of damage can then be determined by categorizing the point plotted in terms of the Δ/L−εh pair according to the category boundaries of the interaction diagram of damage.


## 3.1. Definitions of Excavation-Induced Deformations Related to Building Response

The translations and rotations of building adjacent to excavations result in direct tensile strains, bending strains, and diagonal tensile strains in building structures. A consistent set of definitions describing types of ground movements and building responses based on the displacements (either measured or calculated) of a number of discrete points on the foundations of a building was proposed by Burland and Wroth [3] and summarized by Finno and Alvello [15]. These definitions (illustrated in Figure 2) have been widely accepted and are described as follows:(a)
Settlement (downward displacement) or heave (upward displacement) is denoted asS.(b)
Relative settlement (differential settlement or differential heave) is denoted asδS.(c)
Rotation or slope is the change in gradient of a line joining two reference points (e.g., AB in Figure2). Rotation is typically used to describe the slope of the settlement trough.(d)
The angular strainα is defined in Figure 2. It is positive for upward concavity (sagging seen in Figure 3) and negative for downward concavity (hogging seen in Figure 3).(e)
Relative deflectionΔ is the displacement of a point relative to the line connecting two reference points on either side (see Figure 2). The sign convention is the same as (d).(f)
Deflection ratio (sagging ratio or hogging ratio) is denoted byΔ/L where L is the distance between the two reference points defining Δ. The sign convention is the same as (d) and (e). The deflection ratio is an approximate measure of curvature of the settlement curve and is often correlated with bending related distortions in a structure.(g)
Tiltω describes the rigid body rotation of the structure or a well-defined part of it (see Figure 2).(h)
Relative rotation (angular distortion)β is the rotation of the line joining two points, relative to the tilt ω (see Figure 2).(i)
Average horizontal strainεh is defined as the change of length δL over the length L and is used to describe the direct lateral movement of building structures. It is customary to take a reduction of length (compression) as positive in soil mechanics.Figure 2
Definitions of ground and foundation movement [3].Figure 3
Deflection mode of building in response to deformation [3].The above definitions only apply to in-plane deformations and no attempt has been made to define three-dimensional behavior.


## 3.2. Damage Criteria Based on Angular Distortion

Damage criteria based on angular distortion have been developed by Skempton and MacDonald [16], Polshin and Tokar [17], Bjerrum [18], O’Rourke et al. [19], and Attewell et al. [20]. Bjerrum [18] took the angular distortion as the governing variable in the assessment of permissible deformations. Typical limiting values of angular distortion for buildings where only building settlement is assessed are shown in Figure 4.Figure 4
Limiting angular distortion [18].Damage criteria based on angular distortion do not consider the horizontal displacement. But ground movements related to deep excavations can include a substantial component of horizontal strain except vertical deformation. Therefore, the traditional criteria based on differential settlement or angular distortion alone is inadequate for assessment of building response due to deep excavations.


## 3.3. Damage Criteria Proposed by Boscardin and Cording [21] and Burland et al. [22]

### 3.3.1. Concept of Limiting Tensile Strainεlim and Classification of Building Damage

Cracking in masonry walls and finishes usually, but not always, results from tensile strain. Burland and Wroth [3] firstly defined critical tensile strain εcrit with which the onset of visible cracking in building is associated. Burland and Wroth [3] also showed how the concept of critical tensile strain could be used in conjunction with simple elastic beams to develop deflection criteria for the onset of visible damage. Burland et al. [23] introduced the concept of limiting tensile strain εlim to replace critical tensile strain εcrit as a serviceability parameter which can be varied to take account of differing material and serviceability limit states. Boscardin and Cording [21] developed this concept by assessing 17 case records of damage due to excavation-induced subsidence. They related the ranges of εlim to the likely severity of damage. Burland [24] summarized the categories of building damage as shown in Table 1 which provides the link between estimated building deformations and the possible severity of damage.Table 1
Building damage classification [22].
Category levelNormal degree of severityDescription of typical damageApproximate crack width (mm)Limiting tensile strainεlim (%)0NegligibleHairline cracks0–0.10–0.051Very slightFine cracks easily treated during normal decoration0.1–10.05–0.0752SlightCracks easily filled. Several slight fractures inside building. Exterior cracks visible.1–50.075–0.153ModerateCracks may require cutting out and patching. Door and windows sticking.5–15 (or several closely spaced cracks > 3 mm)0.15–0.34SevereExtensive repair involving removal and replacement of walls, especially over doors and windows. Windows and door frames distorted. Floor slopes noticeably.15–25 (but also depends on number of cracks)>0.35Very severeMajor repair required involving partial or complete reconstruction. Danger of instability.>25 (but also depends on number of cracks)>0.3Burland et al. [22] introduced the term “the level of risk” of damage to refer to the possible degree of damage as defined in Table 1. Most buildings with degree of damage within the first three categories 0 to 2 (i.e., negligible to slight) are considered to be at “low risk” and can be readily and economically repaired. A major objective of design and construction is to maintain the level of risk below the threshold between categories 2 and 3 for all buildings.


### 3.3.2. Equivalent Beam Approach to Evaluate Building Damage

Burland and Wroth [3] introduced the equivalent beam approach in the evaluation of damage to buildings due to ground movements where the building is represented by an elastic rectangular deep beam of length L and height H (Figure 5). This approach is to calculate the tensile strains in the beam for a given deflected shape of the building foundations and hence obtain the deflection ratio Δ/L at which cracking is initiated. Burland and Wroth [3] considered two extreme modes: bending only about a neutral axis at the center and shearing only. In the case of bending only, the cracks are related to the bending strain εb occurring in the top fibre, whereas in the case of shearing only the diagonal cracks are due to the shear strain εd caused by shear deformations. In general, both modes of deformation will occur simultaneously and it is necessary to calculate both bending and shear strains to ascertain which type is limiting.Figure 5
The equivalent beam approach [22]. (a) Actual building. (b) Bending deformation with cracking due to direct tensile strain. (c) Beam: simple idealisation of building. (d) Shear deformation with cracking due to diagonal tensile strain. (e) Deflected shape of soffit of beam.
(a)(b)(c)(d)(e)Timoshenko [25] put up the expression for the total midspan deflection Δ/L of a central point loaded beam with the maximum bending strain εbmax and the maximum shear strain εdmax as follows:(1)ΔL=L12h+3I2hLHEGεbmax,(2)ΔL=1+HL218IGEεdmax,where h is the distance of the neutral axis from the edge of the beam in tension (h=H for hogging and h=H/2 for sagging); E is Young’s modulus; G is the shear modulus; and I is the second moment of area (I=H3/3 for hogging and I=H3/12 for sagging).By settingεmax=εlim, equations (1) and (2) define the limiting values of Δ/L for the deflection of simple beams. For a given deflection ratio Δ/L, an estimation of the maximum tensile strain in the building can be obtained as the maximum of the values of εbmax and εdmax provided by equations (1) and (2).Burland and Wroth [3] showed that generally hogging is much more damaging than sagging—a result that is well borne out in practice. Figure 6 presents the limiting relationships between Δ/L normalized by εlim and L/H for an isotropic beam undergoing hogging (E/G=2.6 and I=H3/3) with its neutral axis at the bottom edge h=H/2 and undergoing sagging (E/G=2.6 and I=H3/12) with its neutral axis at the middle h=H/2. It can be seen that the shear strains dominate if L/H<1.3, whereas for L/H>1.3, the bending strains dominate.Figure 6
Relationship betweenΔ/L/εlim and L/H for rectangular isotropic beams (hogging).Boscardin and Cording [21] incorporated horizontal extension strain εh, which excavations can induce, in the above analysis through simple superposition of this effect to Burland and Wroth’s [3] bending and shear strains.For the case of bending, the resultant extreme fibre strainεbr is given by(3)εbr=εbmax+εh.In the shearing region, the resultant shear strainεdr can be evaluated using Mohr’s circle of strain and is given by(4)εdr=εh1−v2+εh21+v22+εdmax2,where v is Poisson’s ratio.The maximum tensile strain is greater thanεbr and εdr and can be used in conjunction with Table 1 to assess the potential associated damage.


### 3.3.3. Damage Criterion Proposed by Burland et al. [22]

By adopting the values ofεlim associated with the various categories of damage given in Table 1 and by using equations (1)–(4), a building damage interaction diagram can be developed showing the relationship between Δ/L and εh for appropriate values of h, L/H, E/G, v, and I selected for the structure being assessed. The physical implications of equations (1)–(4) can be illustrated by considering an isotropic beam with v=0.3 (E/G=2.6 and I=H3/12) undergoing hogging (h=H). For bending case, manipulation of equations (1) and (3) with εbr=εlim gives(5)Δ/Lεlim=0.083LH+1.3HL1−εhεlim.For shearing, manipulation of equations (2) and (4) with εdmax=εlim yields(6)Δ/Lεlim=1+0.064LH21−0.7εhεlim−0.3εhεlim2.The relationships betweenΔ/L and εh normalized by εlim given by equations (5) and (6) are shown in Figure 7. It is evident from Figure 7 that L/H determines the shape of the damage interaction diagram for isotropic beams undergoing hogging. The damage interaction diagram corresponding to L/H=1 is presented in Figure 8.Figure 7
Relationship betweenΔ/L/εlim and εh/εlim for rectangular isotropic beams (hogging). (a) Bending limit. (b) Shearing limit. (c) Limiting combinations.
(a)(b)(c)Figure 8
Damage interaction diagram forL/H=1 and hogging [22].


### 3.3.4. Damage Criterion Proposed by Boscardin and Cording [21]

Boscardin and Cording [21] produced similar diagrams relating category of damage to horizontal strain εh and angular distortion β (instead of deflection ratio Δ/L). They expressed the relationship between angular distortion β and deflection ratio Δ/L as(7)β=3ΔL1+4E/GH/L21+6E/GH/L2.Substitution of equation (7) into equation (6) yields(8)βεlim=3⋅1+10.4H/L21+15.6H/L2⋅1+0.064L/H2⋅1−0.7εhεlim−0.3εhεlim2.The damage interaction diagram corresponding toL/H=1 for isotropic beams (E/G=2.6) undergoing hogging plotted according to equations (8) is shown in Figure 9. There are similarities between Figures 8 and 9. However, the maximum bending strain εbmax is ignored in Boscardin and Cording’s [21] method. Burland et al. [22] have shown that the relationship between angular distortion β and deflection ratio Δ/L is in fact very sensitive to the load distribution and to the value of E/G. Moreover, the precise evaluation of β is not always straight forward and can be uncertain on occasions. The damage interaction diagrams for sagging after Burland and after Boscardin and Cording [21] can be deduced similarly by setting h=H/2 and I=H3/12.Figure 9
Damage interaction diagram forL/H=1 and hogging [21].


## 3.3.1. Concept of Limiting Tensile Strainεlim and Classification of Building Damage

Cracking in masonry walls and finishes usually, but not always, results from tensile strain. Burland and Wroth [3] firstly defined critical tensile strain εcrit with which the onset of visible cracking in building is associated. Burland and Wroth [3] also showed how the concept of critical tensile strain could be used in conjunction with simple elastic beams to develop deflection criteria for the onset of visible damage. Burland et al. [23] introduced the concept of limiting tensile strain εlim to replace critical tensile strain εcrit as a serviceability parameter which can be varied to take account of differing material and serviceability limit states. Boscardin and Cording [21] developed this concept by assessing 17 case records of damage due to excavation-induced subsidence. They related the ranges of εlim to the likely severity of damage. Burland [24] summarized the categories of building damage as shown in Table 1 which provides the link between estimated building deformations and the possible severity of damage.Table 1
Building damage classification [22].
Category levelNormal degree of severityDescription of typical damageApproximate crack width (mm)Limiting tensile strainεlim (%)0NegligibleHairline cracks0–0.10–0.051Very slightFine cracks easily treated during normal decoration0.1–10.05–0.0752SlightCracks easily filled. Several slight fractures inside building. Exterior cracks visible.1–50.075–0.153ModerateCracks may require cutting out and patching. Door and windows sticking.5–15 (or several closely spaced cracks > 3 mm)0.15–0.34SevereExtensive repair involving removal and replacement of walls, especially over doors and windows. Windows and door frames distorted. Floor slopes noticeably.15–25 (but also depends on number of cracks)>0.35Very severeMajor repair required involving partial or complete reconstruction. Danger of instability.>25 (but also depends on number of cracks)>0.3Burland et al. [22] introduced the term “the level of risk” of damage to refer to the possible degree of damage as defined in Table 1. Most buildings with degree of damage within the first three categories 0 to 2 (i.e., negligible to slight) are considered to be at “low risk” and can be readily and economically repaired. A major objective of design and construction is to maintain the level of risk below the threshold between categories 2 and 3 for all buildings.


## 3.3.2. Equivalent Beam Approach to Evaluate Building Damage

Burland and Wroth [3] introduced the equivalent beam approach in the evaluation of damage to buildings due to ground movements where the building is represented by an elastic rectangular deep beam of length L and height H (Figure 5). This approach is to calculate the tensile strains in the beam for a given deflected shape of the building foundations and hence obtain the deflection ratio Δ/L at which cracking is initiated. Burland and Wroth [3] considered two extreme modes: bending only about a neutral axis at the center and shearing only. In the case of bending only, the cracks are related to the bending strain εb occurring in the top fibre, whereas in the case of shearing only the diagonal cracks are due to the shear strain εd caused by shear deformations. In general, both modes of deformation will occur simultaneously and it is necessary to calculate both bending and shear strains to ascertain which type is limiting.Figure 5
The equivalent beam approach [22]. (a) Actual building. (b) Bending deformation with cracking due to direct tensile strain. (c) Beam: simple idealisation of building. (d) Shear deformation with cracking due to diagonal tensile strain. (e) Deflected shape of soffit of beam.
(a)(b)(c)(d)(e)Timoshenko [25] put up the expression for the total midspan deflection Δ/L of a central point loaded beam with the maximum bending strain εbmax and the maximum shear strain εdmax as follows:(1)ΔL=L12h+3I2hLHEGεbmax,(2)ΔL=1+HL218IGEεdmax,where h is the distance of the neutral axis from the edge of the beam in tension (h=H for hogging and h=H/2 for sagging); E is Young’s modulus; G is the shear modulus; and I is the second moment of area (I=H3/3 for hogging and I=H3/12 for sagging).By settingεmax=εlim, equations (1) and (2) define the limiting values of Δ/L for the deflection of simple beams. For a given deflection ratio Δ/L, an estimation of the maximum tensile strain in the building can be obtained as the maximum of the values of εbmax and εdmax provided by equations (1) and (2).Burland and Wroth [3] showed that generally hogging is much more damaging than sagging—a result that is well borne out in practice. Figure 6 presents the limiting relationships between Δ/L normalized by εlim and L/H for an isotropic beam undergoing hogging (E/G=2.6 and I=H3/3) with its neutral axis at the bottom edge h=H/2 and undergoing sagging (E/G=2.6 and I=H3/12) with its neutral axis at the middle h=H/2. It can be seen that the shear strains dominate if L/H<1.3, whereas for L/H>1.3, the bending strains dominate.Figure 6
Relationship betweenΔ/L/εlim and L/H for rectangular isotropic beams (hogging).Boscardin and Cording [21] incorporated horizontal extension strain εh, which excavations can induce, in the above analysis through simple superposition of this effect to Burland and Wroth’s [3] bending and shear strains.For the case of bending, the resultant extreme fibre strainεbr is given by(3)εbr=εbmax+εh.In the shearing region, the resultant shear strainεdr can be evaluated using Mohr’s circle of strain and is given by(4)εdr=εh1−v2+εh21+v22+εdmax2,where v is Poisson’s ratio.The maximum tensile strain is greater thanεbr and εdr and can be used in conjunction with Table 1 to assess the potential associated damage.


## 3.3.3. Damage Criterion Proposed by Burland et al. [22]

By adopting the values ofεlim associated with the various categories of damage given in Table 1 and by using equations (1)–(4), a building damage interaction diagram can be developed showing the relationship between Δ/L and εh for appropriate values of h, L/H, E/G, v, and I selected for the structure being assessed. The physical implications of equations (1)–(4) can be illustrated by considering an isotropic beam with v=0.3 (E/G=2.6 and I=H3/12) undergoing hogging (h=H). For bending case, manipulation of equations (1) and (3) with εbr=εlim gives(5)Δ/Lεlim=0.083LH+1.3HL1−εhεlim.For shearing, manipulation of equations (2) and (4) with εdmax=εlim yields(6)Δ/Lεlim=1+0.064LH21−0.7εhεlim−0.3εhεlim2.The relationships betweenΔ/L and εh normalized by εlim given by equations (5) and (6) are shown in Figure 7. It is evident from Figure 7 that L/H determines the shape of the damage interaction diagram for isotropic beams undergoing hogging. The damage interaction diagram corresponding to L/H=1 is presented in Figure 8.Figure 7
Relationship betweenΔ/L/εlim and εh/εlim for rectangular isotropic beams (hogging). (a) Bending limit. (b) Shearing limit. (c) Limiting combinations.
(a)(b)(c)Figure 8
Damage interaction diagram forL/H=1 and hogging [22].


## 3.3.4. Damage Criterion Proposed by Boscardin and Cording [21]

Boscardin and Cording [21] produced similar diagrams relating category of damage to horizontal strain εh and angular distortion β (instead of deflection ratio Δ/L). They expressed the relationship between angular distortion β and deflection ratio Δ/L as(7)β=3ΔL1+4E/GH/L21+6E/GH/L2.Substitution of equation (7) into equation (6) yields(8)βεlim=3⋅1+10.4H/L21+15.6H/L2⋅1+0.064L/H2⋅1−0.7εhεlim−0.3εhεlim2.The damage interaction diagram corresponding toL/H=1 for isotropic beams (E/G=2.6) undergoing hogging plotted according to equations (8) is shown in Figure 9. There are similarities between Figures 8 and 9. However, the maximum bending strain εbmax is ignored in Boscardin and Cording’s [21] method. Burland et al. [22] have shown that the relationship between angular distortion β and deflection ratio Δ/L is in fact very sensitive to the load distribution and to the value of E/G. Moreover, the precise evaluation of β is not always straight forward and can be uncertain on occasions. The damage interaction diagrams for sagging after Burland and after Boscardin and Cording [21] can be deduced similarly by setting h=H/2 and I=H3/12.Figure 9
Damage interaction diagram forL/H=1 and hogging [21].


## 3.4. Selection of Appropriate Damage Criteria

As stated by Burland [24], it is not always straight forward to identify the tilt and the evaluation of angular distortion can sometimes be difficult. It is also very important not to confuse relative rotation β with angular strain α. For these reasons, Burland and Wroth [3] preferred the use of deflection ratio as a measure of building distortion. Therefore, in this paper, the damage criterion proposed by Burland et al. [22] is adopted. However, both the damage criteria proposed by Boscardin and Cording [21] and Burland et al. [22] are the most common ones and their selection shall be dependent on the convenience to obtain the relevant parameters.


## 3.5. Comments on the Application of Damage Criteria

A building can be considered separately as per its deflection mode to deformation on each side of the inflection point of the settlement profile (seen in Figure3), which is used to partition the building. In a calculation of building strain, the building span length is required and is defined as the length of building in a hogging or sagging zone (shown as Lh or Ls in Figure 3). And it is advisable to treat the parts of the building under hogging and under sagging as separated beam segments by calculating the respective deflection ratio Δ/L and the average horizontal strain εh. The level of risk of damage can then be determined by categorizing the point plotted in terms of the Δ/L−εh pair according to the category boundaries of the interaction diagram of damage.


## 4. Case Study

The aforementioned global procedure is applied in this section to evaluate the engineering design of the extension line construction of a metro project from PK0 + 344.00 to PK0 + 407.00 (as seen in Figure10) with the cut-and-cover/top-down excavation method. Both the ground deformations and structural deformations and forces are calculated through numerical modelling via FLAC3D program which utilizes the finite difference method (FDM).Figure 10
Plan view of a metro project.


### 4.1. Case Introduction

Figure10 presents the plan view of a metro project including the studied zone. The following computational stages in numerical analysis are performed in order to simulate construction sequences:(1)
Stage 1: initial stress state (σv=γz and σh=K0∗σv)(2)
Stage 2: activation of diaphragm wall (wished-in-place)(3)
Stage 3: activation of surcharge loads(4)
Stage 4: excavation step 1 to level −2.9 m (note: level 0 refers to the ground surface)(5)
Stage 5: activation of roof slab with 0.9 m thickness(6)
Stage 6: backfill from roof slab till the ground surface (level 0)(7)
Stage 7: excavation step 2 to level −6.2 m(8)
Stage 8: activation of struts at level −5.7 m(9)
Stage 9: groundwater lowering inside excavation to level −15.2 m(10)
Stage 10: excavation step 3 to the bottom of invert with lowest point at level −13.7 m(11)
Stage 11: activation of invertFigure11 presents the three main buildings (1, 2, and 3) located, respectively, at PK0 + 380, PK0 + 364, and PK0 + 350 adjacent to the excavation zones. The three buildings have the same width L=48.0m and height H=27.45m. The distances of the three buildings from the excavation centerline are individually 10.2 m, 10.4 m, and 10.9 m. With the design strategy, the evaluation of the potential damage of these three building should be made according to Burland criterion. Meanwhile, Boscardin criterion is also adopted to make comparisons with Burland criterion.Figure 11
Buildings adjacent to the excavation.


### 4.2. Description of Numerical Model

The numerical model is shown in Figure12 including the mesh, soil profile, structural elements, and surcharges. The model is 63 m long along the longitudinal direction of metro line, and the right boundary is set to be at a distance of 100 m from the excavation centerline, which is sufficient because it is beyond the excavation influence zone (usually larger than 4 times the excavation depth, He=13.7m and the bottom at 43.7 m below the ground, and the bottom is set at a distance of 43.7 m below the ground surface. The model has totally 511296 nodes and 489510 zones.Figure 12
Numerical model in FLAC3D.In this model, the slightly curved metro line is simplified as a straight line and the diaphragm walls with little variable lengths are assumed to bear the same length (19.7 m)—the lowest value of wall length which theoretically produces conservative results.Only half of the whole excavation geometry is considered in the numerical model by assuming symmetry conditions on the centerline of the excavation. The assumption of symmetry condition is due to the following considerations: (a) this case study is mainly to present an example to show how to apply this method for real problem; (b) in reality, it is really difficult to have absolute symmetry condition. As a good practice, in many real projects, this kind of assumption may save time and encourage the engineers to adopt advanced analysis methods such as this one.The soil profile comprises backfill, silty clay, and silty clay with sand and gravel. In Figure11, backfill1 denotes the existent backfill before excavation while backfill2 refers to the newly added soil material above the roof slab. Backfill1 and backfill2 are supposed to have the same properties. Silty clay and silty clay with sand and gravel are divided individually into two groups: silty clay1/silty clay2 and silty clay with sand and gravel1/silty clay with sand and gravel2 by adopting two different values of elastic modulus which depends on the soil depth. All the soils are simulated with a hardening soil model—CYSoil model [14] in FLAC3D which has been proved to be capable of calculating realistic ground settlement profile. Table 2 presents the corresponding soil parameters for CYSoil model whose definitions can be referred to Itasca [14].Table 2
Soil parameters for CYSoil model.
PropertySoil typeBackfillSilty clay1Silty clay with sand and gravel1Silty clay2Silty clay with sand and gravel2γ (kN/m3)17.0021.0021.0021.0021.00Porosityn0.30.30.30.30.3Permeabilityk (m/s)2.0e − 51.2e − 87.7e − 21.2e − 87.7e − 2K00.50.5310.5150.5310.515Eurref (MPa)24.027.033.030.062.3Eoedref (MPa)8.09.011.010.020.8νur0.20.20.20.20.2Krefiso (MPa)8.09.011.010.020.8Grefe (MPa)10.011.313.812.526.0α11111c (MPa)00000ϕf (°)3028292829ϕini (°)19.517.818.717.818.7ψf (°)00000R0.670.670.670.670.67pref (MPa)0.10.10.10.10.1m11111Rf0.90.90.90.90.9The 0.9 m-thick roof slab and the 0.4 m-thick invert are modelled as volumetric elements via linear elastic model. Table3 gives the corresponding model parameters for roof slab and invert. Liner elements are applied to simulate the diaphragm walls whose parameters are given in Table 4 in which the liner interface properties are also presented. Struts are simulated via beam elements with the corresponding parameters shown in Table 5.Table 3
Model parameters of roof slab and invert.
Structural elementConstitutive modelE (GPa)νγ (kN/m3)Roof slab and invertLinear elastic29.800.1525.0Table 4
Model parameters of diaphragm walls.
Structural elementConstitutive modelThickness (m)Length (m)γ (kN/m3)νKn (Pa)Ks (Pa)ϕ (°)Cs (Pa)Cs−res (Pa)Diaphragm wallsLiner0.819.725.00.155e95e920.05e65e3Table 5
Model parameters of struts.
Structural elementConstitutive modelE (GPa)νγ (kN/m3)Area (m2)Ixx (m4)Iyy (m4)Spacing (m)StrutsBeam29.800.225.00.250.005210.005212.50The permanent surcharge of 10 kPa is set on the ground surface within 5.8 m distance from the diaphragm walls and between 54.5 m distance from the wall and the far side of the model. The variable surcharge of 60 kPa due to building weights is set on the ground surface between 5.8 m distance and 54.5 m distance from the wall. This combination of surcharges is a simplification of the real surcharge conditions.Symmetry boundary conditions are set on the left boundary, i.e., the excavation centerline. Horizontal displacements are fixed on the other three vertical boundaries (right, front, and behind). Both horizontal and vertical displacements are restrained on the bottom of the model.The initial stress state is calculated with theK0 method [14]. The initial phreatic surface is located at level −8.2 m. At stage 9, the groundwater inside excavation is lowered to level −15.2 m.


### 4.3. Results

Stage 10 is the most unfavorable. Therefore, the results including the ground movement profiles at stage 10 are used to make the evaluation.


#### 4.3.1. Representative Profiles of Ground Movements

The transversal section is selected at the middle of the numerical model alongY axis so as to establish the representative profiles of ground movements adjacent to the excavation. Figure 13 presents the ground settlement profile, and Figure 14 shows the profile of horizontal ground displacement. In Figure 13, the ground settlement profile predicted from the empirical method proposed by Hsieh and Ou [6] is also exhibited by taking the maximum settlement the same as that calculated from FLAC3D. In this way, the distribution shape of the ground settlement obtained from FLAC3D could be checked by comparison with that predicted from the empirical method. It is evident that the ground settlement profile calculated via FLAC3D is similar to the predicted one which is constituted by linear segments and cannot capture the curvature of ground settlement profile and the inflection points. However, such ground settlement profile with curvature and inflection points can be acquired from FLAC3D.Figure 13
Profiles of ground settlement.Figure 14
Profiles of horizontal ground displacement.As seen in Figure13, the building is divided into three parts by points E, F, G, and H in line with the inflection points i1 where the derivative of the horizontal displacement is zero (as seen in Figure 15 at point N). The parts EF and FG are under sagging and the part GH is under hogging.Figure 15
Damage interaction diagrams with points ofΔ/L−εh pair.
(a)(b)(c)(d)(e)(f)(g)(h)(i)


#### 4.3.2. Evaluation of Risk of Building Damage

In Figure13, Lh1, Ls1, and Ls2 denote the lengths of the three parts of building. Δmax_h1, Δmax_s1, and Δmax_s2 are the corresponding maximum relative deflections. In addition, the horizontal displacements at points E–H are denoted by δxE, δxF, δxG, and δxH. Therefore, the risk of building damage of each part is then evaluated separately by calculating the respective deflection ratio Δ/L and average horizontal strain εh=δxj−δxk/L under the corresponding L/H where the superscripts j and k denote the division endpoints (E, F, F, and H) of the building.The results of damage risk evaluation for buildings 1–3 are shown in Table6. The point of Δ/L−εh pair is plotted in the relevant interaction diagram of damage for each division of each building (seen in Figure 15). It should be pointed out that the absolute values of Δ/L−εh pair are used to make these plots. The shape of damage interaction diagram for each L/H ratio is firstly determined by selecting the lowest bounding limits of the combination of bending limiting and shearing limiting as shown in Figure 7(c).Table 6
Evaluation of the risk of building damage.
No.P.K.H(m)Ls1(m)Ls2(m)Lh1(m)Ls1/HΔmax_s1(mm)Δ/Ls1εh_s1(%)Damage risk1Ls2/HΔmax_s2(mm)Δ/Ls2εh_s2(%)Damage risk2Lh1/HΔmax_h1(mm)Δ/Lh1εh_h1(%)Damage risk310 + 38027.453.864.9439.200.140.470.0120.03400.180.380.0080.02401.43−8.03−0.0200.019020 + 36427.453.664.9439.400.130.350.0090.03400.180.380.0080.02401.44−7.87−0.0200.019030 + 35027.453.164.9439.900.120.150.0050.03300.180.380.0080.02401.45−7.86−0.0200.0190It can be seen from Figure15 that all the points of Δ/L−εh pair for each part of the three buildings are within category level 0 implying the low risk of damage for all the three buildings induced by the excavations. Therefore, the engineering design of a metro project from PK0 + 344.00 to PK0 + 407.00 is acceptable while considering the risk of damage to buildings due to deep excavations.


## 4.1. Case Introduction

Figure10 presents the plan view of a metro project including the studied zone. The following computational stages in numerical analysis are performed in order to simulate construction sequences:(1)
Stage 1: initial stress state (σv=γz and σh=K0∗σv)(2)
Stage 2: activation of diaphragm wall (wished-in-place)(3)
Stage 3: activation of surcharge loads(4)
Stage 4: excavation step 1 to level −2.9 m (note: level 0 refers to the ground surface)(5)
Stage 5: activation of roof slab with 0.9 m thickness(6)
Stage 6: backfill from roof slab till the ground surface (level 0)(7)
Stage 7: excavation step 2 to level −6.2 m(8)
Stage 8: activation of struts at level −5.7 m(9)
Stage 9: groundwater lowering inside excavation to level −15.2 m(10)
Stage 10: excavation step 3 to the bottom of invert with lowest point at level −13.7 m(11)
Stage 11: activation of invertFigure11 presents the three main buildings (1, 2, and 3) located, respectively, at PK0 + 380, PK0 + 364, and PK0 + 350 adjacent to the excavation zones. The three buildings have the same width L=48.0m and height H=27.45m. The distances of the three buildings from the excavation centerline are individually 10.2 m, 10.4 m, and 10.9 m. With the design strategy, the evaluation of the potential damage of these three building should be made according to Burland criterion. Meanwhile, Boscardin criterion is also adopted to make comparisons with Burland criterion.Figure 11
Buildings adjacent to the excavation.


## 4.2. Description of Numerical Model

The numerical model is shown in Figure12 including the mesh, soil profile, structural elements, and surcharges. The model is 63 m long along the longitudinal direction of metro line, and the right boundary is set to be at a distance of 100 m from the excavation centerline, which is sufficient because it is beyond the excavation influence zone (usually larger than 4 times the excavation depth, He=13.7m and the bottom at 43.7 m below the ground, and the bottom is set at a distance of 43.7 m below the ground surface. The model has totally 511296 nodes and 489510 zones.Figure 12
Numerical model in FLAC3D.In this model, the slightly curved metro line is simplified as a straight line and the diaphragm walls with little variable lengths are assumed to bear the same length (19.7 m)—the lowest value of wall length which theoretically produces conservative results.Only half of the whole excavation geometry is considered in the numerical model by assuming symmetry conditions on the centerline of the excavation. The assumption of symmetry condition is due to the following considerations: (a) this case study is mainly to present an example to show how to apply this method for real problem; (b) in reality, it is really difficult to have absolute symmetry condition. As a good practice, in many real projects, this kind of assumption may save time and encourage the engineers to adopt advanced analysis methods such as this one.The soil profile comprises backfill, silty clay, and silty clay with sand and gravel. In Figure11, backfill1 denotes the existent backfill before excavation while backfill2 refers to the newly added soil material above the roof slab. Backfill1 and backfill2 are supposed to have the same properties. Silty clay and silty clay with sand and gravel are divided individually into two groups: silty clay1/silty clay2 and silty clay with sand and gravel1/silty clay with sand and gravel2 by adopting two different values of elastic modulus which depends on the soil depth. All the soils are simulated with a hardening soil model—CYSoil model [14] in FLAC3D which has been proved to be capable of calculating realistic ground settlement profile. Table 2 presents the corresponding soil parameters for CYSoil model whose definitions can be referred to Itasca [14].Table 2
Soil parameters for CYSoil model.
PropertySoil typeBackfillSilty clay1Silty clay with sand and gravel1Silty clay2Silty clay with sand and gravel2γ (kN/m3)17.0021.0021.0021.0021.00Porosityn0.30.30.30.30.3Permeabilityk (m/s)2.0e − 51.2e − 87.7e − 21.2e − 87.7e − 2K00.50.5310.5150.5310.515Eurref (MPa)24.027.033.030.062.3Eoedref (MPa)8.09.011.010.020.8νur0.20.20.20.20.2Krefiso (MPa)8.09.011.010.020.8Grefe (MPa)10.011.313.812.526.0α11111c (MPa)00000ϕf (°)3028292829ϕini (°)19.517.818.717.818.7ψf (°)00000R0.670.670.670.670.67pref (MPa)0.10.10.10.10.1m11111Rf0.90.90.90.90.9The 0.9 m-thick roof slab and the 0.4 m-thick invert are modelled as volumetric elements via linear elastic model. Table3 gives the corresponding model parameters for roof slab and invert. Liner elements are applied to simulate the diaphragm walls whose parameters are given in Table 4 in which the liner interface properties are also presented. Struts are simulated via beam elements with the corresponding parameters shown in Table 5.Table 3
Model parameters of roof slab and invert.
Structural elementConstitutive modelE (GPa)νγ (kN/m3)Roof slab and invertLinear elastic29.800.1525.0Table 4
Model parameters of diaphragm walls.
Structural elementConstitutive modelThickness (m)Length (m)γ (kN/m3)νKn (Pa)Ks (Pa)ϕ (°)Cs (Pa)Cs−res (Pa)Diaphragm wallsLiner0.819.725.00.155e95e920.05e65e3Table 5
Model parameters of struts.
Structural elementConstitutive modelE (GPa)νγ (kN/m3)Area (m2)Ixx (m4)Iyy (m4)Spacing (m)StrutsBeam29.800.225.00.250.005210.005212.50The permanent surcharge of 10 kPa is set on the ground surface within 5.8 m distance from the diaphragm walls and between 54.5 m distance from the wall and the far side of the model. The variable surcharge of 60 kPa due to building weights is set on the ground surface between 5.8 m distance and 54.5 m distance from the wall. This combination of surcharges is a simplification of the real surcharge conditions.Symmetry boundary conditions are set on the left boundary, i.e., the excavation centerline. Horizontal displacements are fixed on the other three vertical boundaries (right, front, and behind). Both horizontal and vertical displacements are restrained on the bottom of the model.The initial stress state is calculated with theK0 method [14]. The initial phreatic surface is located at level −8.2 m. At stage 9, the groundwater inside excavation is lowered to level −15.2 m.


## 4.3. Results

Stage 10 is the most unfavorable. Therefore, the results including the ground movement profiles at stage 10 are used to make the evaluation.


### 4.3.1. Representative Profiles of Ground Movements

The transversal section is selected at the middle of the numerical model alongY axis so as to establish the representative profiles of ground movements adjacent to the excavation. Figure 13 presents the ground settlement profile, and Figure 14 shows the profile of horizontal ground displacement. In Figure 13, the ground settlement profile predicted from the empirical method proposed by Hsieh and Ou [6] is also exhibited by taking the maximum settlement the same as that calculated from FLAC3D. In this way, the distribution shape of the ground settlement obtained from FLAC3D could be checked by comparison with that predicted from the empirical method. It is evident that the ground settlement profile calculated via FLAC3D is similar to the predicted one which is constituted by linear segments and cannot capture the curvature of ground settlement profile and the inflection points. However, such ground settlement profile with curvature and inflection points can be acquired from FLAC3D.Figure 13
Profiles of ground settlement.Figure 14
Profiles of horizontal ground displacement.As seen in Figure13, the building is divided into three parts by points E, F, G, and H in line with the inflection points i1 where the derivative of the horizontal displacement is zero (as seen in Figure 15 at point N). The parts EF and FG are under sagging and the part GH is under hogging.Figure 15
Damage interaction diagrams with points ofΔ/L−εh pair.
(a)(b)(c)(d)(e)(f)(g)(h)(i)


### 4.3.2. Evaluation of Risk of Building Damage

In Figure13, Lh1, Ls1, and Ls2 denote the lengths of the three parts of building. Δmax_h1, Δmax_s1, and Δmax_s2 are the corresponding maximum relative deflections. In addition, the horizontal displacements at points E–H are denoted by δxE, δxF, δxG, and δxH. Therefore, the risk of building damage of each part is then evaluated separately by calculating the respective deflection ratio Δ/L and average horizontal strain εh=δxj−δxk/L under the corresponding L/H where the superscripts j and k denote the division endpoints (E, F, F, and H) of the building.The results of damage risk evaluation for buildings 1–3 are shown in Table6. The point of Δ/L−εh pair is plotted in the relevant interaction diagram of damage for each division of each building (seen in Figure 15). It should be pointed out that the absolute values of Δ/L−εh pair are used to make these plots. The shape of damage interaction diagram for each L/H ratio is firstly determined by selecting the lowest bounding limits of the combination of bending limiting and shearing limiting as shown in Figure 7(c).Table 6
Evaluation of the risk of building damage.
No.P.K.H(m)Ls1(m)Ls2(m)Lh1(m)Ls1/HΔmax_s1(mm)Δ/Ls1εh_s1(%)Damage risk1Ls2/HΔmax_s2(mm)Δ/Ls2εh_s2(%)Damage risk2Lh1/HΔmax_h1(mm)Δ/Lh1εh_h1(%)Damage risk310 + 38027.453.864.9439.200.140.470.0120.03400.180.380.0080.02401.43−8.03−0.0200.019020 + 36427.453.664.9439.400.130.350.0090.03400.180.380.0080.02401.44−7.87−0.0200.019030 + 35027.453.164.9439.900.120.150.0050.03300.180.380.0080.02401.45−7.86−0.0200.0190It can be seen from Figure15 that all the points of Δ/L−εh pair for each part of the three buildings are within category level 0 implying the low risk of damage for all the three buildings induced by the excavations. Therefore, the engineering design of a metro project from PK0 + 344.00 to PK0 + 407.00 is acceptable while considering the risk of damage to buildings due to deep excavations.


## 4.3.1. Representative Profiles of Ground Movements

The transversal section is selected at the middle of the numerical model alongY axis so as to establish the representative profiles of ground movements adjacent to the excavation. Figure 13 presents the ground settlement profile, and Figure 14 shows the profile of horizontal ground displacement. In Figure 13, the ground settlement profile predicted from the empirical method proposed by Hsieh and Ou [6] is also exhibited by taking the maximum settlement the same as that calculated from FLAC3D. In this way, the distribution shape of the ground settlement obtained from FLAC3D could be checked by comparison with that predicted from the empirical method. It is evident that the ground settlement profile calculated via FLAC3D is similar to the predicted one which is constituted by linear segments and cannot capture the curvature of ground settlement profile and the inflection points. However, such ground settlement profile with curvature and inflection points can be acquired from FLAC3D.Figure 13
Profiles of ground settlement.Figure 14
Profiles of horizontal ground displacement.As seen in Figure13, the building is divided into three parts by points E, F, G, and H in line with the inflection points i1 where the derivative of the horizontal displacement is zero (as seen in Figure 15 at point N). The parts EF and FG are under sagging and the part GH is under hogging.Figure 15
Damage interaction diagrams with points ofΔ/L−εh pair.
(a)(b)(c)(d)(e)(f)(g)(h)(i)


## 4.3.2. Evaluation of Risk of Building Damage

In Figure13, Lh1, Ls1, and Ls2 denote the lengths of the three parts of building. Δmax_h1, Δmax_s1, and Δmax_s2 are the corresponding maximum relative deflections. In addition, the horizontal displacements at points E–H are denoted by δxE, δxF, δxG, and δxH. Therefore, the risk of building damage of each part is then evaluated separately by calculating the respective deflection ratio Δ/L and average horizontal strain εh=δxj−δxk/L under the corresponding L/H where the superscripts j and k denote the division endpoints (E, F, F, and H) of the building.The results of damage risk evaluation for buildings 1–3 are shown in Table6. The point of Δ/L−εh pair is plotted in the relevant interaction diagram of damage for each division of each building (seen in Figure 15). It should be pointed out that the absolute values of Δ/L−εh pair are used to make these plots. The shape of damage interaction diagram for each L/H ratio is firstly determined by selecting the lowest bounding limits of the combination of bending limiting and shearing limiting as shown in Figure 7(c).Table 6
Evaluation of the risk of building damage.
No.P.K.H(m)Ls1(m)Ls2(m)Lh1(m)Ls1/HΔmax_s1(mm)Δ/Ls1εh_s1(%)Damage risk1Ls2/HΔmax_s2(mm)Δ/Ls2εh_s2(%)Damage risk2Lh1/HΔmax_h1(mm)Δ/Lh1εh_h1(%)Damage risk310 + 38027.453.864.9439.200.140.470.0120.03400.180.380.0080.02401.43−8.03−0.0200.019020 + 36427.453.664.9439.400.130.350.0090.03400.180.380.0080.02401.44−7.87−0.0200.019030 + 35027.453.164.9439.900.120.150.0050.03300.180.380.0080.02401.45−7.86−0.0200.0190It can be seen from Figure15 that all the points of Δ/L−εh pair for each part of the three buildings are within category level 0 implying the low risk of damage for all the three buildings induced by the excavations. Therefore, the engineering design of a metro project from PK0 + 344.00 to PK0 + 407.00 is acceptable while considering the risk of damage to buildings due to deep excavations.


## 5. Conclusions and Recommendations

This paper puts forward a 4-step procedure to justify the engineering design in view of the risk of damage to buildings due to deep excavations. Firstly, the ground movement profiles induced by excavations are obtained from numerical modelling via numerical software such as FLAC3D and at the same time verified by empirical results. Secondly, the appropriate damage criterion proposed by Burland et al. [22] is adopted. Thirdly, the buildings adjacent to the excavations are partitioned by building endpoints and inflection points. Meanwhile, for each division of each building, Δ/L and εh are calculated from the ground settlement and horizontal displacement profiles and plotted in the interaction diagram of damage. The risk level of building damage is then classified according to the domain of the point of Δ/L−εh pair. Fourthly, the corresponding engineering design is justified in line with the magnitude of ground movements and the risk level of building damage. The 4-step procedure should be cycled until the magnitude of ground movements and the risk level of building damage with the current engineering design are within the range of engineering safety.By adopting this procedure, the engineering design of a metro project between PK0 + 344.00 and PK0 + 407.00 is justified to be acceptable considering that the damage risk levels of all the buildings adjacent to the excavations are within category level 0 and the magnitude of ground movement is within the range of engineering safety.This procedure provides a way to estimate and evaluate quantitatively the damage risk of adjacent buildings due to deep excavation in the stage of engineering design. However, while applying it, attention shall be paid to the following considerations:(1)
The appropriate soil constitutive model shall be adopted based on the soil behavior.(2)
Proper model parameters, boundary conditions, and techniques shall be used.(3)
Hogging and sagging parts of the calculated ground profile shall be divided correctly.(4)
The parameters used in damage interaction diagram shall be understood clearly and calculated correctly consideringL/H ratio.(5)
Both Burland and Boscardin criteria are applicable and the use of which one is dependent on the convenience to acquire the relevant parameters.However, the field ground movement profiles observed in the construction stage should be compared with the calculated ground movement profiles in the design stage to verify its reasonableness.Finally, it shall be pointed out that the risk level assessment of building damage induced by deep excavations is only one aspect of justification of the engineering design. The other aspects such as analyses of stress and deformation, internal and external stability, water flow and piping, and analyses of structure safety should also be considered in order to justify the relevant design strategy.



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*Source: 6646094-2021-07-01.xml*