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Structural Performance of Bridge Approach Slabs
under Given Embankment Settlement
C. S. Cai1;X.M.Shi
2; G. Z. Voyiadjis3; and Z. J. Zhang4
Abstract: Soil embankment settlement causes concrete approach slabs of bridges to lose their contact and support from the soil. When
soil settlement occurs, the slab will bend in a concave manner that causes a sudden change in slope grade near its ends. Meanwhile, loads
on the slab will also redistribute to the ends of the slab, which may result in faulting across the roadway at the ends of the approach slab.
Eventually, the rideability of the bridge approach slab will deteriorate. The current AmericanAssociation of State Highway Transportation
Officials code specifications do not provide clear guidelines to design approach slabs considering the embankment settlements. State
Departments of Transportation are spending millions of dollars each year to deal with problems near the ends of approach slabs. To
investigate the effect of embankment settlements on the performance of the approach slab, a three-dimensional finite element analysis was
conducted in the present study, considering the interaction between the approach slab and the embankment soil, and consequently the
separation of the slab and soil. The predicted internal moments of the approach slab provide design engineers with a scientific basis to
properly design the approach slab considering different levels of embankment settlements. Aproper design of the approach slab will help
mitigate the rideability problems of the slab.
DOI: 10.1061/共ASCE兲1084-0702共2005兲10:4共482兲
CE Database subject headings: Concrete slabs; Differential settlement; Finite element method; Embankments; Structural design.
Introduction
Bridge approaches in Louisiana are normally constructed with
reinforced concrete slabs that connect the bridge deck with the
adjacent paved roadway. Their function is to provide a smooth
transition between the bridge deck and the roadway pavement.
However, complaints about the ride quality of bridge approach
slabs still need to be resolved. The complaints usually involve a
“bump” that motorists feel when they approach or leave bridges.
Field observations indicated that either faulting near the slab and
the pavement joint or a sudden change in the slope grade of the
approach slab causes this bump.
Concrete approach slabs can lose their contact and support
from soils due to the settlement of embankment soil on which the
slabs are built. When settlement occurs, load and the self-weight
of the slab will redistribute to the ends of the slab, resulting in
vertical faulting or a bump across the roadway. Eventually, the
rideability of the bridge approach slabs will deteriorate. Although
the bump-related problems have been commonly recognized and
the causes identified, no unified engineering solutions have
emerged, primarily because of the complexity of the problem.
Typically, the embankment settlement reflects an accumulated ef-
fect of many factors such as subsoil conditions, materials, con-
struction techniques, drainage provisions, and quality control
methods during construction.
Several comprehensive studies on the performance of ap-
proach slabs have been sponsored over the years by various state
DOTs. Stewart 共1985兲identified the original ground subsidence
and fill settlement as primary causes of approach maintenance
problems. Kramer and Sajer 共1991兲summarized findings from
various state DOTs and recommended guidelines for the use and
construction of approach slabs. Mahmood 共1990兲indicated that
the type of abutment affects the magnitude of approach settlement
and thus recommended the use of various ground improvement
techniques, including wick drains and surcharging, to mitigate the
soil settlement. The use of lightweight fill materials was also pro-
posed as a means of reducing the vertical loading exerted on the
soil. Chini et al. 共1992兲summarized critical items in the design
and construction of bridge approaches. Their recommendations
included removal and replacement of compressible foundation
soils, dynamic compaction, surcharging, use of selected borrow
fill materials, and minimum compaction requirements of 95% of
the Standard Proctor, along with increased construction inspec-
tions. A National Cooperative Highway Research Program
共NCHRP兲synthesis report on the settlement of approach slabs
共Briaud et al. 1997兲recommended more stringent requirements
for fill material specifications and inspection practice. The study
concluded that good cooperation among geotechnical, structural,
pavement, construction, and maintenance engineers reduces re-
ported incidences of excessive approach settlement. Other studies
were also carried out by different investigators 共Stark et al. 1995;
Tadros and Benak 1989; Wahls 1990; Zaman et al. 1991; Hoppe
1999; Ha et al. 2003; Seo et al. 2003兲.
1Assistant Professor, Dept. of Civil and Environmental Engineering,
Louisiana State Univ., Baton Rouge, LA 70803.
2PhD Candidate, Dept. of Civil and Environmental Engineering,
Louisiana State Univ., Baton Rouge, LA 70803.
3Boyd Professor, Dept. of Civil and Environmental Engineering,
Louisiana State Univ., Baton Rouge, LA 70803.
4Senior Research Engineer, LTRC, 4101 Gourrier Ave., Baton Rouge,
LA 70808.
Note. Discussion open until December 1, 2005. Separate discussions
must be submitted for individual papers. To extend the closing date by
one month, a written request must be filed with the ASCE Managing
Editor. The manuscript for this paper was submitted for review and pos-
sible publication on March 17, 2004; approved on July 20, 2004. This
paper is part of the Journal of Bridge Engineering, Vol. 10, No. 4, July
1, 2005. ©ASCE, ISSN 1084-0702/2005/4-482–489/$25.00.
482 / JOURNAL OF BRIDGE ENGINEERING © ASCE / JULY/AUGUST 2005
The majority of the previous studies can be categorized as 共1兲
syntheses of practice, 共2兲identification of the sources of differen-
tial settlements, and 共3兲soil improvement. Numerical studies on
approach slab and embankment settlement interaction have been
rare. There are no guidelines in the AASHTO code specifications
共AASHTO 1998, 2002兲regarding the structural design of ap-
proach slabs considering the effects of embankment settlements.
Similarly, the Louisiana Department of Transportation and Devel-
opment 共LaDOTD兲design manual 共LaDOTD 2002兲specifies
minimum reinforcement requirements but provide no specifica-
tions for the structural design of the approach slabs.
Objective and Research Approach
LaDOTD has launched a major effort under the Louisiana Quality
Initiative 共LQI兲program to solve the bump problem. The objec-
tive is to find a feasible solution that allows the approach slabs to
be stiff enough to lose a portion of their contact support without
detrimental deflection. This solution requires a thorough under-
standing of the interaction between the bridge approach slab and
the embankment settlement.
One extreme case assumes that the slab fully contacts the em-
bankment soil and that the slab’s performance is the same as that
of the concrete floors on the ground. This assumption is not real-
istic in many cases due to the embankment settlement discussed
above, and it may result in an unconservative design. At the other
extreme case, an approach slab can be designed as a simple beam
spanning the bridge end and the pavement end, assuming no soil
supports the beam between the two ends. This assumption, while
conservative, will definitely result in an uneconomical design. In
the majority of these cases, the slab is both partially separating
from and partially contacting the soil. The support provided to the
concrete slab by the embankment soil will reduce the internal
force in the slab. The extent of this support and reduction depends
on the slab and soil interaction for a given embankment settle-
ment.
This paper presents the strategies and results from a three-
dimensional finite element analysis that investigated the approach
slab performance under a given embankment settlement. These
results were used to check the structural design of the approach
slab currently used by LaDOTD, and will eventually be used to
systematically evaluate the effectiveness of approach slabs and to
develop guidelines for their structural design. This information
will also help determine when settlement controls are necessary
for an economical approach slab design.
Fig. 1 shows a sketch of a typical approach slab. Since the left
end of the slab sits on the pile-supported abutment whereas the
right end is on embankment soil, a differential movement occurs
between the two ends of the slab, resulting in a gap between the
slab and the embankment soil. The amplitude and distribution of
soil settlements can be very complicated and will be determined
in another ongoing research project supported by the LaDOTD
LQI program. Therefore, in the present finite element analysis, the
embankment settlement was given and a linear settlement was
assumed, as shown in Fig. 1. When the self-weight of the slab and
live loads were applied, the slab deformed and interacted with the
soil, resulting in partial contact of the slab with the soil. The
present research will provide essential information needed for the
structural design of the approach slab considering embankment
settlements.
Finite Element Modeling
Louisiana is currently using approach slabs with a length of either
6,096 mm 共20 ft兲or 12,195 mm 共40 ft兲depending on whether it
is a cut or filled embankment 共LaDOTD 2002兲. For the demon-
stration purpose of analysis, an approach slab with 12,195 mm
共40 ft兲in span length, 305 mm 共12 in.兲in thickness and the other
dimensions shown in Fig. 2 was chosen with a 1,220 mm 共4ft兲
wide sleeper slab. A 3D finite element model was established, as
shown in Fig. 3, where eight-node hexahedron elements 共ANSYS,
Canonsburg, Pa., Solid 45兲were used to form the finite element
mesh. In addition to the dead load of the slab, two AASHTO
Fig. 1. Illustration of slab interaction with soil
Fig. 2. Sketch of bridge abutment
Fig. 3. Typical finite element mesh with 8 node cubic element
JOURNAL OF BRIDGE ENGINEERING © ASCE / JULY/AUGUST 2005 / 483
共2002兲HS20 truck loads were applied on the slab. The two HS20
truck loads were moved along the slab length to produce the
worst loading scenario for the slab deflection and internal bending
moments, the same way as in the bridge live load analysis. These
predicted internal moments provide information for the structural
evaluation and design of the approach slabs by selecting appro-
priate slab reinforcement, section dimensions and length. The cur-
rent LaDOTD bridge design manual 共LaDOTD 2002兲specifies
the same reinforcement for both 6,096 and 12,195 mm span
length approach slabs.
The soil profile under the approach slab consisted of com-
pacted embankment and silty clay subgrade soil that are very
common in Louisiana. A contact and target pair surface element
available in the ANSYS element library was used to simulate the
interaction between the soil and the slab. This surface element is
compressive only and can thus model the contacting and separat-
ing process between the slab and soil. When the soil is in tension,
the slab and soil separate automatically. The Drucker–Prager
model was used to define the yield criteria for both embankment
soil and subgrade soil. Table 1 lists the material parameters used
in the finite element analysis of the present study.
Determination of Boundary Conditions
The soil underneath the approach span is theoretically semiinfi-
nite. Sensitivity analysis was conducted to determine how much
soil, laterally, vertically, and longitudinally, should be included in
the finite element model. Three parameters, W,L, and Hshown in
Fig. 2 were investigated in the sensitivity study as follows:
1. Wwas varied from 1,524, 3,049, 4,573, 6,098, 7,622, 9,146,
to 13,720 mm 共5, 10, 15, 20, 25, 30, to 45 ft兲for the fixed
L=9,146 mm 共30 ft兲and H=9,146 mm 共30 ft兲;
2. Lwas varied from 3,049, 6,098, 9,146, 12,195, 15,244, to
36,585 mm 共10, 20, 30, 40, 50, to 120 ft兲for the fixed H
=9,146 mm 共30 ft兲and W=7,622 mm 共25 ft兲;
3. Hwas varied from 1,524, 3,049, 6,098, 9,146, 10,671,
12,195, 15,244, 18,293, 30,488, to 60,976 mm 共5, 10, 20, 30,
35, 40, 50, 60, 100, to 200 ft兲for the fixed W=7,622 mm
共25 ft兲and L=9,146 mm 共30 ft兲.
For each case, two truck loads 共HS20兲on two lanes and the
slab’s self-weight were applied to the approach slab. The deflec-
tion of the approach slab and the vertical stress in the embank-
ment soil under the sleeper slab for the three conditions were
examined. It was found that Whas insignificant effects on the
results. When Lis larger than 12,195 mm 共40 ft兲, it insignificantly
affects the results of both the deflection and the soil stress. When
His larger than 15,244 mm 共50 ft兲, its effect on deflection re-
duces, but still makes some impact on the soil stress. Based on
this sensitivity study, the soil dimensions for the slab–soil inter-
action analysis were determined as: W=4,573 mm 共15 ft兲;L
=12,195 mm 共40 ft兲; and H=15,244 mm 共50 ft兲.
Effects of Embankment Settlements on Slab
Performance
With the dimensions 共i.e., boundaries兲of the finite element model
determined above, a parametric study was conducted to examine
the mechanism of interaction between the embankment soils and
the approach slab under different embankment settlements. The
maximum deflections and internal moments of the approach slab
under different settlements were obtained by moving the truck
loads along the slab. In the finite element analysis for a given
embankment settlement, the dead load 共DL兲was applied first;
then the dead load and live loads 共DL+LL兲were applied together.
The live load effects 共LL兲were then calculated from the total load
effect minus the dead load effect, i.e., 共DL+LL兲− DL. This pro-
cedure was necessary since the loading sequence affects the con-
tacting and separating process between the slab and the soil.
Therefore, the live load could not be applied independently with-
out including the dead load for a proper solution.
As shown in Figs. 4 and 5, the magnitude of the slab maxi-
mum deflections and internal moments increases with the increase
of embankment settlements. When the differential settlement in-
creases from 152 mm 共6.0 in.兲to a larger value, there is almost no
change in the deflection and internal moment of the approach
Table 1. Material Parameters
Soil type
Elastic
modulus
E
MPa 共psi兲
Poisson
ratio
Cohesion
c
kPa 共psi兲
Friction
angle
共degrees兲
Density
␥
kg/m3共pcf兲
Embankment 260 共37,700兲0.3 80 共11.6兲30 2,000 共127.4兲
Natural 30 共4,360兲0.3 50 共7.25兲30 1,500 共95.6兲
Fig. 4. Deflection of approach slab versus settlement 共slab length
=12,195 mm and thickness=305 mm兲
Fig. 5. Internal moment of approach slab versus settlement 共slab
length=12,195 mm and thickness=305 mm兲
484 / JOURNAL OF BRIDGE ENGINEERING © ASCE / JULY/AUGUST 2005
slab. This is because the settlement no longer affects the slab
performance since the approach slab loses almost all contact with
the soil and then performs as a simple beam.
Similarly, as shown in Fig. 6, the maximum vertical stress of
the embankment soil under the sleeper slab continued to increase
with the increase of the differential settlement. Since the slab lost
more support from the soil as the settlement increased, a larger
portion of the slab self-weight and truck loads was distributed to
the sleeper slab and then to the soil under the sleeper slab. In
contrast to slab deflection and internal moments 共Figs. 4 and 5兲,
the stress in the soil kept increasing 共but with a reduced rate兲even
when the settlement exceeded 152 mm 共6.0 in.兲. Even after the
complete loss of contact between the slab and the soil, the in-
crease of settlement changed the geometry of the soil around the
sleeper slab so that the stress in the soil underneath the sleeper
slab was slightly affected.
As discussed earlier, the differential settlement between the
two ends of the approach slab formed a gap between the approach
slab and the embankment. Due to the action of the truck loads and
slab self-weight, the approach slab deformed downward and was
supported by the embankment soil at the contacting points. Fig. 7
shows the assumed linear settlement lines of the embankment and
the predicted deflection shape of the slab under different differ-
ential settlements. The figure clearly exhibits the contact area be-
tween the slab and the embankment soil near the sleeper slab and
the gap near the abutment. As the settlement increased, the gap
became deeper and longer, and the contact area decreased. If the
settlement is large enough as the case with 244 mm, the slab and
embankment will have no contact, and the slab will lose the sup-
port from the embankment, except near the sleeper slab. Thus, the
deflection and internal moment of the approach slab will not
change with the increase of the embankment settlement as indi-
cated in Figs. 4 and 5.
Effects of Embankment Settlements on Slab Design
As the increase of the embankment settlement results in the sepa-
ration of the slab from the soil and subsequent increase of the
internal moment in the approach slab, the slab must be designed
to provide enough strength for an expected embankment settle-
ment. To this end, the results from the finite element analysis
were used to evaluate the structural design of the approach slabs
that are used by the LaDOTD. Currently, the LaDOTD standard
drawing 共LaDOTD 2002兲calls for #20 at 150 mm 共#6 at 6 in.兲for
the bottom reinforcement of the approach slab.
When the approach slab is subjected to bending, the stresses
induced by the concentrated loads may not uniformly distribute
over the whole width of the slab. If the width of the slab is large,
only part of the slab is effective in resisting a given bending load.
The non-uniform distribution of the stresses in the slab means that
a simple beam theory cannot directly be applied for the slab
analysis without some modifications. Therefore it is convenient,
for design purposes, to consider a certain width of the slab 共an
effective width兲, which, if uniformly stressed, would represent the
same amount of flexural resistance as the real slab.
For the simply supported slab, the case of the two trucks ap-
plied at the mid-span was chosen as the basic loading type and a
uniformly distributed dead load was considered. By moving the
trucks along the transverse direction of the slab, the critical sce-
nario was observed when the trucks move to one side of the slab.
The effective width weis defined as
we=兰0
wydx
ymax
共1兲
where y=bending stress in section; ymax=maximum bending
stress in section; and w=width of the slab.
For an approach slab with the span length of 12,195 mm
共40 ft兲, width of 12,195 mm 共40 ft兲, and thickness of 305 mm
共12 in.兲, the effective width, we, for the truck loads on the side of
the slab were calculated by varying the differential settlement
from 15 mm 共0.6 in.兲to 183 mm 共7.2 in.兲. The effective width
per one truck load is plotted in Fig. 8. As expected, the dead load
is much more uniformly distributed across the bridge width and
thus the effective width is larger than that of the live load. The
effective width per truck was also determined to be 3,600 mm
共11.8 ft兲per AASHTO code 共1998兲, which agrees reasonably
well with the present finite element prediction. Therefore, when
no more accurate information is available, the effective width
specified in the AASHTO specifications can be used for the de-
sign of approach slabs. As shown in Fig. 8, when the differential
settlement is small, then the predicted effective width for live
loads is smaller than that specified in the codes, implying that
using the code effective width is not conservative for design.
Fig. 6. Vertical stress of soil under sleeper slab versus settlement
共slab length=12,195 mm and thickness= 305 mm兲
Fig. 7. Interface between approach slab and embankment soil 共slab
length=12,195 mm and thickness=305 mm兲
JOURNAL OF BRIDGE ENGINEERING © ASCE / JULY/AUGUST 2005 / 485
However, small settlement is usually not the critical condition.
For larger settlement 共about 90 mm or 3.5 in. in this case兲, the
code effective width is more conservative.
Checking the strength of the approach slab was conducted
according to the AASHTO standard specifications 共AASHTO
2002兲, namely, with load factors of 1.3 for dead load, 2.17 for live
load, and 1.3 for impact factor, and with an equivalent slab width
of 3,600 mm. The results of the reinforcement design considering
the effects of different differential settlements are shown in Table
2. It is interesting to observe in Table 2 that when the settlement
is zero, the required reinforcement at the bottom of slab is
1.27 mm2/mm 共0.6 in.2/ft兲and it increases to 3.175 mm2/mm
共1.5 in.2/ft兲when the settlement increases to 15 mm 共0.6 in.兲.
This indicates that the current design 共LaDOTD 2002兲,
1.86 mm2/mm 共0.88 in.2/ft兲, is good only for the case of zero
settlement and is not adequate for a settlement larger than 15 mm
共0.6 in.兲. When the embankment settlement increases, more rein-
forcement is required. When the settlement exceeds 76 mm
共3.0 in.兲, then the required reinforcement ratio, , will exceed the
allowed maximum reinforcement ratio, max, namely 75% of the
balanced reinforcement ratio 共AASHTO 2002兲. In this case, either
Table 2. Design of Approach Slab
Settlement
mm
共in.兲
DL
M
kN m
共ft kips兲
LL
M
kN m
共ft kips兲
1.3DL
+2.17共LL+IM兲
M
kN m
共ft kips兲
max
As
mm2/mm
共in.2/ft兲Reinforcementa
0
共0兲
270.9
共195.8兲
37.5
共27.1兲
458.0
共331.0兲
0.0050 0.0214 1.27
共0.60兲
#16 at 150 mm
共#5 at 6.0 in.兲
15
共0.6兲
423.7
共306.2兲
180.6
共130.5兲
1,060.4
共766.3兲
0.0125 0.0214 3.18
共1.50兲
#19 at 90 mm
共#6 at 3.5 in.兲
30
共1.2兲
466.3
共337.0兲
222.7
共160.9兲
1,234.5
共892.1兲
0.0149 0.0214 3.77
共1.78兲
#22 at 100 mm
共#7 at 4.0 in.兲
46
共1.8兲
498.2
共360.0兲
244.9
共177.0兲
1,346.2
共972.8兲
0.0165 0.0214 4.19
共1.98兲
#25 at 110 mm
共#8 at 4.5 in.兲
61
共2.4兲
510.1
共368.6兲
277.6
共200.6兲
1,446.1
共1,045.0兲
0.0180 0.0214 4.57
共2.16兲
#29 at 140 mm
共#9 at 5.5 in.兲
76
共3.0兲
526.1
共380.2兲
321.0
共232.0兲
1,589.7
共1,148.8兲
0.0202 0.0214 5.14
共2.43兲
#32 at 150 mm
共#10 at 6.0 in.兲
91
共3.6兲
526.1
共380.2兲
389.3
共281.3兲
1,782.0
共1,287.8兲
0.0235 0.0214 NAbNA
106.7
共4.2兲
531.4
共384.0兲
469.7
共339.4兲
2,015.8
共1,456.7兲
0.0280 0.0214 NA NA
122
共4.8兲
531.4
共384.0兲
535.4
共386.9兲
2,201.1
共1,590.6兲
0.0321 0.0214 NA NA
137
共5.4兲
530.0
共383.0兲
572.2
共413.5兲
2,303.2
共1,664.4兲
0.0347 0.0214 NA NA
152
共6.0兲
530.0
共383.0兲
579.4
共418.7兲
2,323.5
共1,679.1兲
0.0353 0.0214 NA NA
183
共7.2兲
530.0
共383.0兲
581.1
共419.9兲
2,328.2
共1,682.5兲
0.0354 0.0214 NA NA
213
共8.4兲
530.0
共383.0兲
581.2
共420.0兲
2,328.5
共1,682.7兲
0.0354 0.0214 NA NA
244
共9.6兲
526.1
共380.2兲
580.5
共419.5兲
2,321.3
共1,677.5兲
0.0352 0.0214 NA NA
305
共12.0兲
526.1
共380.2兲
582.6
共421.0兲
2,327.5
共1,682.0兲
0.0354 0.0214 NA NA
aSome rebar size listed in the table is for demonstration only; they may not be practical for a slab with a thickness of 305 mm 共12 in.兲.
bThe required reinforcement ratio exceeds the allowed maximum reinforcement of flexure, i.e., ⬎max=0.75b, meaning that section dimension needs
to be increased.
Fig. 8. Effective width of slab versus differential settlement 共slab
length=12,195 mm and thickness=305 mm兲
486 / JOURNAL OF BRIDGE ENGINEERING © ASCE / JULY/AUGUST 2005
the slab thickness should be increased or the soil should be im-
proved to control the embankment settlement within the allow-
able limit.
Development of Design Aids
A parametric study was conducted by changing the slab thickness
and length to establish the relationship between the slab re-
sponses, parameters, and the corresponding differential settle-
ments, which can be used in routine design. The slab parameters,
length 共L兲and thickness 共h兲, were investigated in the parametric
study for the following cases: 共1兲hwas varied from 305, 457, to
610 mm 共1, 1.5, to 2 ft兲for the fixed L=12,195 mm 共40 ft兲; and
共2兲hwas varied from 457, 686, to 915 mm 共1.5, 2.25, to 3 ft兲for
the fixed L=18,288 mm 共60 ft兲.
As shown in Figs. 9–11, with the increase of embankment
settlement, the magnitude of the maximum internal moments, de-
flections, and rotation angles in the slab increases to some con-
stant values. For example, with L=12,195 mm 共40 ft兲and h
=305 mm 共12 in.兲, when the settlement is increased from
152 mm 共6.0 in.兲to larger values, there is almost no change in the
internal moment, deflection, and rotation angle since the approach
slab had become a simply supported beam. For the same differ-
ential settlement, with the increase of approach slab thickness 共h兲,
the deflection in the slab decreases. Smaller deflections of the
approach slab reduce the contact area between the slab and em-
bankment soil. As a result, the value of the differential settlement
beyond which the settlement ceases to affect the slab behavior
decreases.
By analyzing the results from the finite element analysis, this
study established a correlation among the slab parameters, deflec-
tion and angle of the slab, internal moment of the slab, and the
differential settlement. The results were then normalized with re-
spect to the traditional simply supported 共pin and roller supports兲
beams, i.e., without considering the contact between the slab and
the soil, and without considering the settlement of the end sup-
ports. Engineers can conveniently obtain the slab response, such
as deflections and moments, by multiplying the slab response of
the simply-supported beam with a computed coefficient. These
coefficients are developed next.
The predicted maximum internal moments in approach slabs
due to total load 共dead load plus live load without considering
dynamic impact effect兲and dead load only were normalized and
represented in Fig. 12. They can be expressed by an exponential
function with a regression analysis as follows:
MT
MT0= 0.955 − 0.78e−5.49⫻109共␦h2/L4兲=KTM 共2兲
Fig. 9. Internal moment of approach slab versus differential
settlement
Fig. 10. Deflection of slab versus differential settlement
Fig. 11. Rotation angle of slab versus differential settlement
Fig. 12. KTM and KDM curve
JOURNAL OF BRIDGE ENGINEERING © ASCE / JULY/AUGUST 2005 / 487
MD
MD0= 0.95 − 0.8e−7.02⫻109共␦h2/L4兲=KDM 共3兲
where MT=maximum moment of approach slab due to total load;
MD=maximum moment of approach slab due to dead load; ␦
=differential settlement 共mm兲;h=thickness of approach slab
共mm兲;L=length of approach slab 共mm兲;KDM and KTM
=moment coefficients that are self-evidenced in the equations;
MT0=maximum moment of simply supported beam due to total
load; and MD0=maximum moment of simply supported beam due
to dead load.
The maximum internal moment in approach slab due to live
load is then calculated as
ML=MT−MD=KTMMT0−KDMMD0共4兲
Similarly, the maximum deflections 共⌬2in Fig. 1, including
both slab deflection and load-induced support deformation兲in the
approach slab due to the total load and dead load only are repre-
sented by the curves shown in Fig. 13 and can be expressed by
the an exponential function as
dT
dT0=共3.05 − 2.58e−4.88⫻109共␦h2/L4兲兲⫻
冉
h
L
冊
0.3 =KTd 共5兲
dD
dD0=共3.01 − 2.63e−6.10⫻109共␦h2/L4兲兲⫻
冉
h
L
冊
0.3 =KDd 共6兲
where dT=maximum deflection of approach slab due to total load;
dD=maximum deflection of approach slab due to dead load; KDd
and KTd=deflection coefficients that are self-evidenced in the
equations; dT0=maximum deflection of simply supported beam
due to total load; and dD0=maximum deflection of simply sup-
ported beam due to dead load.
The maximum deflection in approach slab due to live load is
then calculated as
dL=dT−dD=KTddT0−KDddD0共7兲
Finally, the end rotation angle also shown in Fig. 1 is repre-
sented in Fig. 14 and the formulas are obtained as
T
T0=共1.86 − 1.44e−5.9⫻109共␦h2/L4兲兲
冉
h
L
冊
0.2 =KT共8兲
D
D0=共1.84 − 1.45e−7.32⫻109共␦h2/L4兲兲
冉
h
L
冊
0.2 =KD共9兲
where T=maximum rotation of approach slab due to total load;
D=maximum rotation of approach slab due to dead load; KD
and KT=moment coefficients that are self-evidenced in the equa-
tions; T0=angle of simple beam due to total load; and D0
=angle of simple beam due to dead load.
The maximum rotation angle in the approach slab due to live
load is then calculated as
L=T−D=KTT0−KDD0共10兲
These developed formulas provide information 共deflection, ro-
tation, and internal force兲for the structural evaluation and design
of approach slabs without conducting complicated finite element
analysis. For example, the predicted internal moments 共simply
using a coefficient times the corresponding simple beam mo-
ments兲can be used to design the slab reinforcement for a given
settlement. Engineers can also control the excessive settlement by
either improving embankment fills or foundations, or by selecting
a stiffer approach slab once the predicted deformation is known.
It should be noted that unless very minimal settlement is al-
lowed in the embankment 共both geotechnical and construction
related兲, there will always be a bump at the bridge approach slab.
Regardless of the efforts made to improve the structural rigidity
and long-term performance of the approach slab, the magnitude
of the bump will be a function of the total settlement. A more
rigid approach slab will decrease the change of slope angle 共1in
Fig 1兲, but may also increase the local soil pressure beneath the
contact area 共sleeper slab兲, thereby may increase the faulting de-
flection 共⌬1in Fig. 1兲. Therefore, a balanced/optimal approach
slab design is desirable and will be further studied.
Summary and Conclusions
An appropriate approach slab design directly affects the safety
and economy of the transportation infrastructure. A rational de-
sign is necessary not only for the serviceability requirement of the
transition approach slab, but also for the life expectancy of the
whole highway system including bridges and pavements. As the
bump problem has existed for years, the design of the approach
slab is still more an art than a science. Engineering calculations of
Fig. 13. KTd and KDd curve Fig. 14. KTand KDcurve
488 / JOURNAL OF BRIDGE ENGINEERING © ASCE / JULY/AUGUST 2005
the approach slab are typically not conducted or the approach slab
is simply designed as a simply-supported beam since the infor-
mation about the interaction of the approach slab and the embank-
ment settlement is unknown for a routine office design. There are
no AASHTO guidelines for designing approach slabs considering
a given embankment settlement.
The present study investigated the effect of embankment
settlement on the structural performance of the approach slab.
Deflections and internal moments of the slab and stresses of the
embankment soil were predicted with finite element modeling;
they increased with the increase of the embankment settlement.
For the particular example used in the present study, when the
settlement increased to 152 mm 共6.0 in.兲, the approach slab be-
came a simply-supported beam. Predicted results indicated that
LaDOTD’s current slab design is good for cases without embank-
ment settlement, but the ultimate strength is not adequate if settle-
ment greater than 15 mm is considered, implying that more rein-
forcement, thicker slab section, or settlement control are needed
to satisfy the AASHTO structural design requirement. Similar is-
sues may exist in other states and modifications of concrete slab
design may be warranted.
This research shows how finite element procedures can help
design approach slabs for a given embankment settlement. Para-
metric studies were then conducted to develop a simpler design
procedure so that engineers do not need to use complicated finite
element analysis in a routine design. Instead, the developed coef-
ficients can be multiplied with the corresponding simple beam
response to consider the interaction of the embankment soil and
slab under a given embankment settlement. The more rational
design considering a given settlement will eventually lead to a
more reliable practice in using approach slabs. LaDOTD has ini-
tiated a large effort under the Louisiana Quality Initiative pro-
gram to resolve the bump problems related to approach spans, and
this study is one of the components necessary to eventually re-
solve this issue.
Acknowledgments
The writers appreciate the Louisiana Department of Transporta-
tion and Development 共LaDOTD兲for financially supporting this
project 共Project No. 736-99-1149/03-4GT兲through the Louisiana
Transportation Research Center. The contents of this paper reflect
the views of the writers and do not necessarily reflect the views or
policies of the LaDOTD. In addition, the writers appreciate the
very constructive comments from the three reviewers.
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