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Paper accepted for publication in the Journal of Geotechnical and Geoenvironmental Journal

Evaluating Damage Potential in Buildings Affected by Excavations

Richard J. Finno

, M. ASCE, Frank T. Voss. Jr.

, M. ASCE, Edwin Rossow

and J. Tanner

Blackburn,

Abstract

Predicting building damage due to ground movements caused by excavations is an important

design consideration when building in a congested urban environment. Current predictive

approaches range from empirical methods to detailed finite element calculations. Limitations

inherent in the simpler of these models preclude them from accurately predicting damage in

cases where important assumptions are invalid. A new simple model for representing buildings

is presented to allow a designer to make realistic simplifications to a building system that is

consistent with major features of the structure so that the response to ground movements can be

adequately represented. This model assumes that the floors restrain bending deformations and

the walls, whether load bearing or in-fill between columns, resist shear deformations. Closed-

form equations are presented that relate bending and shear stiffness to normalized deflection

ratios. The proposed model is shown to adequately represent the response of a three-story

framed structure which was affected by an adjacent deep excavation. The proposed model

represents a reasonable compromise between overly simplistic empirical methods and complex,

burdensome detailed analyses.

INTRODUCTION

Damage to buildings adjacent to excavations can be a major design consideration when

constructing facilities in congested urban areas. As new buildings are constructed, the

excavations required for basements affect nearby existing buildings, especially those founded on

shallow foundations. Often excavation support system design must prevent any damage to

adjacent structures or balance the cost of a stiffer support system with the cost of repairing

damage to the affected structures. In either case, it is necessary to predict the level of ground

movements that will induce damage to a structure. Practically speaking, a designer is attempting

to limit/prevent damage to the architectural details of a building, which occurs prior to structural

damage.

Professor, Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208, r-

finno@northwestern.edu

Structural Engineer, GRC Engineering, Inc., 5544 w. 147

St., Tinley Park, IL

Professor Emeritus, Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL

Research Assistant, Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL

A number of methods found in literature relate building damage to associated ground

movements. Several of these methods are based on movements caused by settlements of a

structure due to its own weight, and do not consider the deformations that may occur as a result

of a nearby excavation. Other methods do attempt to account for the additional modes of

deformation, but are limited in their ability to adequately represent the affected structure. The

purpose of this paper is to present a laminate beam method of evaluating potential building

damage due to excavation-induced ground movements. This method avoids oversimplification

common in current empirical methods, yet is not as computationally burdensome as a detailed

finite element analysis. Published criteria applicable to excavation-induced building damage are

reviewed and compared to the laminate beam method. In addition, assessments of damage

potential as determined by both the existing and proposed methods are compared to detailed

records of damage to a three-story framed structure.

BACKGROUND

Definition of terms

Figure 1 shows a sketch of a hypothetical settlement profile. The settlement of any point i is

denoted as ρ

. Differential settlement between two points, i and j, is given the symbol δ

. The

distance between two points i and j is denoted ℓ

. Distortion between two points, i and j, is

defined as δ

/ℓ

, and is not explicitly shown on the figure. A concave-up deformation is called

“sagging,” while a concave-down deformation is called “hogging.” An inflection point, D,

separates two modes of deformation. The length of a particular mode of deformation, bounded

by either the ends of a building or inflection points of the settlement profile, is denoted L. The

average slope, m, of a specific mode of deformation is defined as δ

kl,

where the subscripts k

and l are boundaries of the mode of deformation. This slope differs from the distortion, δ

/ℓ

which is the ratio for two adjacent points. The relative settlement of each mode, ∆, is the

maximum deviation from the average slope of a particular deformation mode. The deflection

ratio, ∆/L, not explicitly shown, is the ratio of the relative settlement to the length of the

deflected part. This term will be used herein as a measure of the ground deformation profile

when evaluating damage predictions.

Rigid body rotation of the building, ω, is the tilt of the building and causes no stresses or

strains in the building. Angular distortion, β, is the difference between distortion, δ

/ℓ

, and rigid

body rotation, ω. When multiple modes of deformation occur in a building, i.e., when the slope,

m, of each portion is not equal to ω, additional shearing strains, γ

add

, arise from the difference

between the rigid body rotation and the slope and must be considered when computing strains.

This point will be illustrated in more detail later.

The critical tensile strain, ε

crit.

, the strain at which cracking becomes evident, may vary

significantly from one material to another. Tensile strains, ε

, can be caused by bending, ε

diagonal tension due to shear, ε

, or horizontal extension, ε

, caused by lateral extension of the

building due to lateral movement in the soil mass below the footings. If multiple modes of

deformation are superposed, these components can be combined in a Mohr circle of strain to

determine the maximum principal tensile strain, ε

. Critical strains that cause failure in common

building materials vary widely as a function of material and mode of deformation, as

summarized by Boone (1996).

Criteria to evaluate excavation-induced damage

Selected criteria that are applicable to evaluate excavation-induced damage are summarized in

Table 1, wherein the relevant parameter and its limiting value are shown. Note that the

parameter used to relate structural movements at the foundation level to damage depends on the

method. Deep beam methods are more general than empirical methods (e.g., Skempton and

McDonald 1956 and Polshin and Tolkar 1957) which were limited to damage of structures based

on settlements arising from the weight of the structure.

Burland and Wroth (1975) modeled a building as a deep isotropic beam to relate strains in the

building to the imposed deformations. Tensile strain served as the limiting criterion for visible

crack development when used with an elastic analysis of the building. They suggested that for

sagging type deformations, the neutral axis is located at the middle of the beam. For hogging

type deformations, the foundation and soil provide significant restraint to deformations. In the

limit, the bottom of the beam does not deform, in effect moving the neutral axis to its bottom.

Equations for limiting ∆/L were written in terms of maximum bending strain and maximum

diagonal tensile strain for a linear elastic beam with a Poisson’s ratio, ν, of 0.3 subjected to a

point load with the neutral axis at either the center or bottom of the beam. The effects of a

building that is not adequately represented by an isotropic elastic beam are accounted for by

varying the ratio of Young’s modulus, E, to shear modulus, G, for the beam, depending on the

type of structure. They postulated that for buildings with significant tensile restraint, or very

flexible in shear (i.e. frame buildings), an E/G ratio greater than the theoretical value of 2.6

would be appropriate, and recommended that the value be taken as 12.5. However, for buildings

that have little or no tensile restraint (i.e. traditional masonry buildings), they recommended that

the E/G ratio should be reduced to 0.5.

Voss (2002) extended the Burland and Wroth (1975) equations to allow explicit input of E/G

and location of the neutral axis, resulting in the following equations that relate limiting ∆/L to

bending strain at the top, ε

b(top)

, and bottom of a beam, ε

b(bottom)

and the maximum diagonal

tensile strain, ε

d(average)

() ()

()

111

12 1 1 12 2

btop

LH LG

λε

λλ

⎛⎞

∆

⎛⎞

=++−

⎜⎟

−−

⎝⎠

(1)

(

111

12 12 2

bbottom

LH LG

λε

λλ

⎛⎞

∆

⎛⎞

=++−

⎜

⎜⎟

⎜

⎝⎠

)

⎟

(2)

(

12 2

d average

αε

⎛⎞

⎜⎟

∆

⎜

⎛⎞

⎜⎟

+−

⎜⎟

⎝⎠

)

⎟

(3)

where H and L are the height and length of a beam, respectively, λ is the ratio of the distance

from the neutral axis to the bottom on the beam to its height, and α is the ratio of the of

maximum shear stress to average shear stress – equal to 3/2 for a rectangular beam.

Based on eqs. (1)-(3), Figure 2 shows the effects of different E/G ratios and neutral axis

locations on the conditions required for initial cracking. In this figure, the kink in a curve

represents the limit between shear critical and bending critical geometries of a beam. With the

exception of flexible structures (E/G ≥ 12.5) and structures with small L/H ratios, bending strains

are more critical. These results also show that the limiting deflection ratio that causes cracks

varies over wide limits, implying that structural details must be considered when establishing

criteria. However, it is difficult to provide guidance on the selection of the beam characteristic

parameter E/G and the neutral axis location, especially when developing a deep beam model for

a multi-story structure.

Boscardin and Cording (1989) extended this deep beam model to include horizontal extension

strains, ε

, caused by lateral ground movements induced by adjacent excavation and tunneling

activities. A chart relating β and ε

to levels of damage was developed for buildings with brick,

load-bearing walls and an L/H ratio of 1 undergoing a hogging deformation with the neutral axis

at the bottom. Similar to Burland and Wroth (1975), the building is idealized as a linear elastic

beam with υ equal to 0.3. Direct transfer of horizontal ground strain to the structure is assumed

in this approach. However, when the ground displaces laterally, relative slip will occur at the

foundation level, and the horizontal displacement in the building will be less than that in the

ground (Geddes 1977, 1991). Thus, this approach represents an upper bound of the effects of

horizontal ground strain. Many modern buildings are well-reinforced laterally by stiff floor

systems, which essentially eliminate lateral movements at the foundation level in presence of

lateral ground movements (e.g., Finno and Bryson 2002).

Boone (1996) presented a more detailed approach to evaluate building damage due to

differential ground movement caused by adjacent construction. This method considers structure

geometry and design, strain superposition and critical strains of building materials. Load bearing

walls are modeled as uniformly-loaded, simple-supported beams. Damage to frame buildings is

assumed to occur from differential vertical movements of columns, depending on the column’s

tilt and degree of fixity. Damage to infill walls is presumed to occur as a result of the deformed

shape of the surrounding beams and columns. If a structure is subjected to horizontal extension,

then these strains are superposed on the ones caused by bending and shear.

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