7/18/2019 1-s2.0-S0141029614002703-main

http://slidepdf.com/reader/full/1-s20-s0141029614002703-main 1/11

Numerical investigation of H-shaped short steel piles with localized

severe corrosion

Cheng Shi a, Hossein Karagah a, Mina Dawood a,⇑, Abdeldjelil Belarbi b

a N107 Engineering Building 1, Department of Civil and Environmental Engineering, University of Houston, Houston, TX 77204-4003, United Statesb N108 Engineering Building 1, Department of Civil and Environmental Engineering, University of Houston, Houston, TX 77204-4003, United States

a r t i c l e i n f o

 Article history:

Received 20 September 2013

Revised 29 April 2014

Accepted 30 April 2014

Available online 24 May 2014

Keywords:

Inelastic buckling

Deteriorated H-shaped steel pile

Numerical analysis

Parametric study

Damage classification

a b s t r a c t

Evaluation of the capacity of steel bridge piles with localized severe corrosion is an important task for

maintenance and retrofit activities. To facilitate maintenance and rehabilitation activities for deteriorated

H-piles, numerical simulation for inelastic buckling of small-scale piles was conducted. The non-linear

finite element model included the effect of initial geometric imperfection, residual stresses, material

non-linearity, and geometric non-linearity at various levels of deterioration. The model was validated

using experimental results of small-scale piles. A parametric study was conducted to analyze different

factors that affect the axial capacity and failure mode of these piles. The parameters that were considered

include the magnitude of initial imperfections, residual stresses, slenderness of the pile, location and

extent of the corroded region, and severity of corrosion. Different pile slendernesses were considered

ranging from 32 to 64. Different levels of corrosion were simulated by reducing the thickness of the

flanges and web by 20–100%. The corroded length was varied from 15.2 cm, 30.5 cm and 61.0 cm. Differ-

ent deterioration locations, namely mid-height and third-height of the pile, were considered. Numerical

analysis results were compared to three design methods from current AASHTO (2012) [1], AISC (2011)

[2], and AISI (2007) [3] specifications. A damage classification system is proposed based on the remaining

capacity of the corroded pile and rehabilitation guidelines are suggested.

  2014 Elsevier Ltd. All rights reserved.

1. Introduction

Steel H-piles have been widely used in bridges crossing rivers or

seasonal streams in the United States. Due to repeated wetting and

drying throughout their service lives, these structural elements

suffer from severe but localized corrosion at the water level (inter-

face of water and air). To effectively retrofit these piles, an accurate

evaluation of the failure mode and remaining axial capacity is

necessary.

The AASHTO LRFD Bridge Design Specification [1] and AISC Steel

Construction Manual [2] recommend the same design equations to

predict the axial capacity of compression members with or without

slender elements. Alternatively, the AISI Specification [3]   recom-

mends two different methods for calculating the axial capacity of 

thin-walled compression members: the direct strength method

(DSM) and the effective width method (EWM). However, the axial

capacity of non-prismatic members is not discussed in any of these

specifications. To predict the capacity of steel piles with localized

corrosion using any of the methods of these specifications, it is nec-

essary to assume that the degradation is uniformly distributed

along the entire length of the member rather than being localized.

However, field investigations clearly indicate that for steel piles in

moist environments corrosion can cause nearly total deterioration

of the member in a localized region while the rest of the pile

remains essentially unaffected.

Several researchers have investigated the behavior of steel com-

pression members with different section shapes with localized

degradation. Paik et al.  [4]   developed a simple design formula to

predict the ultimate compressive capacity of a plate with pit corro-

sion based on experiments and numerical analysis. Similarly, Ok

et al. [5]   ran several non-linear finite element analyses on panels

with various locations and sizes of pitting corrosion to investigate

the effects of localized corrosion on the axial capacity of unstiff-

ened plates. The results indicated that increasing the length, width,

or depth of pit corrosion reduced the capacity of the plates

although the plate slenderness did not significantly influence the

capacity. The depth, width, and transverse location (distribution

along the short side) were identified as the critical factors that

affect the remaining capacity of the plate.

http://dx.doi.org/10.1016/j.engstruct.2014.04.048

0141-0296/  2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +1 713 743 2983.

E-mail addresses:   cshi@uh.edu  (C. Shi),  hkaragah@central.uh.edu (H. Karagah),

mmdawood@uh.edu (M. Dawood),  belarbi@uh.edu (A. Belarbi).

Engineering Structures 73 (2014) 114–124

Contents lists available at  ScienceDirect

Engineering Structures

j o u r n a l h o m e p a g e :   w w w . e l s e v i e r . c o m / l o c a t e / e n g s t r u c t

7/18/2019 1-s2.0-S0141029614002703-main

http://slidepdf.com/reader/full/1-s20-s0141029614002703-main 2/11

Beaulieu et al. [6] tested sixteen corroded steel angles with var-

ious degrees of deterioration under axial load and provided recom-

mendations for the evaluation of the compressive capacity of the

corroded members. In their study, the corrosion was achieved by

an accelerated galvanic corrosion process; hence, the corrosion

pattern was uncontrolled and occurred along the entire length of 

the members rather than being localized. In another study   [7],

seven 304.8 cm long S4 9.5 H-shaped steel columns were tested

to investigate their axial capacities. The effect of corrosion was

simulated by cutting a 30.5 cm long by 1.6 cm wide notch at the

mid-height of the member. This approach simulated the decrease

of area caused by corrosion, but not the associated increase of 

the slenderness of the flange. In fact, the flange slenderness was

decreased by reducing the flange width. Consequently, flange and

web local buckling of corroded members was not investigated in

this study. Karagah and Dawood  [8]  tested thirteen 81.3 cm long

steel piles (US designation W4 13) with different degrees of sec-

tional deterioration under axial compression to evaluate their

remaining axial capacities. To simulate localized corrosion, the

thicknesses of the webs and flanges were reduced near the mid-

height of the specimens within a length of 30.5 cm. The thickness

reduction varied from 0% to 75%. Severe corrosion was represented

by additionally reducing the width of the flanges by 50% and by

machining a 5.1 cm void in the web. The results of these tests were

used to validate the numerical model that was developed in this

paper.

2. Research significance

The assessment of the remaining capacity of bridge piles that

are subjected to severe corrosion is an important task to facilitate

the repair and/or replacement decisions for the safe use of these

bridges. A non-linear finite element analysis was conducted to

investigate the remaining axial capacity of H-shaped steel piles

with localized severe corrosion. Furthermore, three design meth-

ods, including the design method recommended by both AASHTO

and AISC and two methods recommended by AISI, were compared

with the numerical predictions to evaluate the suitability of differ-

ent design approaches to predict the capacity of non-prismatic

members. Based on these results damage classification and reha-

bilitation guidelines for the remaining capacity of corroded piles

are proposed.

3. Development and validation of the finite element model

 3.1. Finite element modeling 

The commercial finite element package ABAQUS v6.12 was used

in the simulation of the steel piles under axial compression. An

81.3 cm long, simply supported W4

13 steel pile was loadedunder axial compression using displacement control. The cross-

section dimensions were determined from measurements of simi-

lar test specimens  [8]. Two consecutive steps were considered in

the numerical analysis: first, an eigenvalue analysis was conducted

to obtain the elastic buckling loads and failure modes. Subse-

quently, the elastic buckling shapes were used to impose an initial

imperfection in the piles and an inelastic buckling analysis was

conducted which incorporated the effect of residual stresses and

large displacements [10–14].

 3.1.1. Element and mesh

The steel piles were modeled using the four-node fully inte-

grated shell element S4 as recommended by Seif and Schafer

[15]. The element size was taken as 2.54 cm by 2.54 cm. A preli-minary mesh sensitivity study indicated satisfactory convergence

of the results with this mesh density for four representative cases

of the corroded piles in the validation.

 3.1.2. Material properties

The constitutive model for the compressive member was

defined using a bi-linear curve as shown in Fig. 1a. The elastic por-

tion of the curve, including the elastic modulus, yield strength, and

yield strain, was obtained from a stub column test while the ulti-mate stress and corresponding strain were obtained from tension

coupon tests. The strain-hardening branch of the curve was pri-

marily incorporated to ensure stability of the model after yielding.

The yielding and ultimate stresses were measured to be 370 MPa

and 480 MPa, respectively. The corresponding strains were 0.002

and 0.1 mm/mm, respectively. The elastic modulus was obtained

experimentally as 210 GPa.

Residual stresses were incorporated using the distribution sug-

gested by Ziemian [9] as shown in Fig. 1b. The stress–strain curve

obtained from stub column tests indicated that the magnitude of 

the residual stresses in the tested piles was relatively small. There-

fore, the maximum magnitude of the residual stresses was taken as

10% of the measured yield strength of the steel for the basic case

considered in the analysis.

 3.1.3. Initial imperfection

Both global and local imperfections were considered to repre-

sent the types of imperfections that are observed in real piles.

The patterns for the initial imperfections were obtained from the

eigenvalue analyses. The first global buckling mode was used to

represent the global imperfection while the first local buckling

mode was used to represent the local imperfections.

Fig. 1a.  Constitutive relationship for material.

Fig. 1b.  Residual stress distribution.

C. Shi et al. / Engineering Structures 73 (2014) 114–124   115

7/18/2019 1-s2.0-S0141029614002703-main

http://slidepdf.com/reader/full/1-s20-s0141029614002703-main 3/11

 3.1.3.1. Global imperfection.  According to AISC  [2], the maximum

permissible sweep of a hot-rolled, H-shaped steel member is

0.32 cm per 152.4 cm of length   [2]. In contrast, according to

AASHTO [1] and AISC [2] the limitations on out-of-straightness of 

an axially loaded member are L/1000 and L/1500, respectively. This

suggests that the actual initial out-of-straightness, D, (Fig. 2a) of a

deteriorated steel pile could lie within a wide range of values. A

sensitivity study was performed to investigate the effect of the

magnitude of the initial imperfection on the capacity of corroded

steel piles. The magnitude of the initial imperfection,   D, ranged

from 0.05 cm (L/1500) to 0.18 cm (L/480). Fig. 2b shows the axial

load–shortening response of an 81.3 cm long W4 13 steel mem-

ber with different magnitudes of initial out-of-straightness. The

results demonstrate that out-of-straightness did not have a signif-

icant effect on the axial behavior of the compressive member.

Therefore, the peak value of the initial global imperfection was

taken as L/480 in the current study.

 3.1.3.2. Local imperfections.  To represent the effect of local imper-

fections on the local buckling capacity of the piles, a deformation

pattern matching the first local buckling mode of the pile was

imposed. Fig. 3 illustrates the first local buckling mode of an axiallyloaded steel pile as obtained from an eigenvalue analysis of a pile

with 60% localized reduction of the web thickness and 75% local-

ized reduction of the flange thickness. For each of the piles consid-

ered in the validation of the model, a separate eigenvalue analysis

was conducted to identify the corresponding local buckling mode.

This shape was imposed as the local geometric imperfection. The

peak magnitude of the local imperfections was taken as 10% of 

the element thickness as suggested by Chan and Gardner  [10].

 3.2. Comparison of finite element analyses (FEA) and experimental

results

To validate the accuracy of the non-linear analyses, the model-

ing results were compared to the experimental results based on

four parameters: failure mode, axial load–shortening relationship,

buckling load, and peak load.  Fig. 4 shows the details of the simu-

lated corrosion patterns. Each specimen that was used in the vali-

dation was designated a unique identifier  [8]. The first two parts

indicate the percentage reduction of the flange thickness and

web thickness, respectively. The third part, ‘‘V’’ or ‘‘NV’’, refers to

the presence or absence of a void in the web at mid-height of the

pile. The fourth part illustrates whether the area reduction on a

pile was symmetrical or unsymmetrical, denoted by ‘‘S’’ or ‘‘US,’’

respectively. The unsymmetrical condition was obtained by shift-

ing the milled portion of one flange 51 mm towards the top of 

the pile while shifting the milled portion of the other flange

51 mm towards the bottom of the pile as illustrated in   Fig. 4b.

The fifth part, ‘‘WR’’, indicates that there is a reduction of the width

of the flanges. Thirteen W4 13 piles were simply supported

about their weak axes and fixed at the base-pinned at the topabout their strong axes. They were loaded using a constant dis-

placement rate in a servo-hydraulic universal testing machine.

Additional details of the tested piles that were used to validate this

numerical study are given elsewhere  [8].

Table 1 shows the deformed shape of the tested piles and the

corresponding deformed shape obtained from the non-linear FEA.

The table indicates that the model accurately predicted the failure

mode and deformation pattern of all of the tested piles.  Fig. 5 pro-

vides the comparison of the axial load–shortening behavior of the

piles. It shows a good correlation between FEA predictions and test

results for stiffness, onset of non-linearity, and the post-peak

response. Note that the abnormal post-peak response exhibited

in Fig. 5c was attributed to electrical interference during testing

and is not believed to represent the actual behavior of the pile.Table 2 presents the measured andpredicted buckling loads and

peak loads for all of the tested piles. The buckling load of each pile

was defined as the load corresponding to the onset of non-linearity

of the axial load–shortening curves. The peak load was typically

within 2–15% larger than the buckling load of the piles. This was

attributed partially to the progression of yielding through the sec-

tion and partially to the post-buckling strength of the slender ele-

ments. Comparison of the values in   Table 2   indicates good

correlation between the measured and predicted buckling and

peak loads. For piles with nominal flange thickness reductions up

to 50%, the differences between experimental and numerical

results were generally less than 10%. For the tested piles with

flange thickness reductions of 75%, the differences between the

measured and predicted peak capacities were up to 50%. However,for these piles the FEA predictions were conservative.Fig. 2a.  Initial global imperfection.

Fig. 2b.   Axial load–shortening for members with different initial global

imperfections.

116   C. Shi et al. / Engineering Structures 73 (2014) 114–124

7/18/2019 1-s2.0-S0141029614002703-main

http://slidepdf.com/reader/full/1-s20-s0141029614002703-main 4/11

Comparison of the measured and predicted capacities and over-

all pile behavior indicates excellent correlation and provides confi-dence in the modeling approach.

4. Parametric study 

4.1. Analyses parameters

A parametric study was performed to investigate six factors

influencing the compressive capacity of the corroded piles. The

parameters considered include flange slenderness, web slender-

ness, pile slenderness, the location of the corroded region along

the height of the pile, the extent of the corroded region, and the

magnitude of the residual stresses. Each study was carried out byvarying one particular parameter while keeping the other parame-

ters constant.

In the following analyses, the dimensions for the W4 13 col-

umns and the constitutive relationship of the steel were adopted

from AISC   [2]  instead of the values from the model validation.

For practical purposes the precise material properties and member

geometry may not be easily determined for each member. There-

fore, design values for steel strength and member dimensions were

considered in the parametric study. The yield strength was taken

as 345 MPa and the elastic modulus was 200 GPa. The magnitudes

of initial global and local imperfections were L/480 cm and 10% of 

the element thickness, respectively. For the baseline configuration,

the magnitude of residual stresses at the tips of the flanges was

103 MPa; the extent of corrosion was 30.5 cm at mid-height of the member.

4.2. Effect of individual parameters

4.2.1. Effect of flange and web slenderness

From the observation of the behavior of the thirteen piles used

for validation, and by inspection of  Table 2, two main conclusions

were drawn: (i) flange corrosion has a greater effect on the axial

capacity of a pile than web corrosion, and (ii) reduction of the

width of the flanges does not significantly decrease the axial capac-

ity. However, the cases investigated experimentally focused on

specific cases with 50% and 75% loss of flange thickness and 30%,

60%, and 100% loss of web thickness. To study the effect of flange

corrosion comprehensively, numerical simulations within the

range of 0–80% deterioration of the flanges and 0–100% deteriora-

tion of the web were performed.

Figs. 6a and 6b show the effect of flange corrosion and web cor-

rosion on the buckling load and peak load of corroded piles of dif-

ferent slendernesses of 32, 48, and 64 as determined from finite

element analyses. Each point in the figure indicates the result of 

a unique numerical simulation. The points are connected by differ-

ent styles of lines for clarity. The three line styles indicate the three

different slendernesses of the piles. Different groups of lines indi-

cate different degrees of flange reduction of 0%, 20%, 60% and

80%. The horizontal axis shows the degree of web reduction from

0% to 100% (a 5.1 cm void at mid-height).The points along the right edges of the plots in Fig. 6 indicate

piles with different degrees of flange corrosion and different slen-

dernesses but all with a 5.1 cm void in the web to simulate through

corrosion of the web. In these cases, the failure is due to buckling of 

the flanges on either side of the void. In this range, the capacity

Fig. 3.  Local geometric imperfections.

Fig. 4a.  Test specimens 1–7 [8].

Fig. 4b.  Test specimens 8–13 [8].

C. Shi et al. / Engineering Structures 73 (2014) 114–124   117

7/18/2019 1-s2.0-S0141029614002703-main

http://slidepdf.com/reader/full/1-s20-s0141029614002703-main 5/11

depends primarily on the flange slenderness. However, due to the

initial global imperfection, the flanges are not subject to equal com-

pression. Therefore, the onset of buckling occurs in one flange first.

Therefore, the observed peak load is higher than the initial buckling

load. This effect becomes less pronounced as the degree of corrosion

of the flanges increases and as the pile slenderness increases. Inspec-

tion of the figure highlights several important trends. First, the

remaining capacity of the corroded piles is highly sensitive to the

degree of the flange corrosion. Further, as the degree of flange corro-

sion increases, the buckling strength and peak load of the piles

become less sensitive to the pile slenderness. This is due to the tran-sition from a global buckling failure mode to a flange local buckling

failure mode. Therefore, an effective retrofit technique should miti-

gate the effect of flange local buckling by bracingthe flanges and also

possibly by adding additional material to the section. Fig. 6 also indi-

cate that while web corrosion affects the capacity of the piles, the

effect is less significant than the influence of flange corrosion.

4.2.2. Effect of pile slenderness

Fig. 6   also illustrates the effect of pile slenderness on the

remaining capacity of the corroded piles.  Fig. 6a   shows that the

maximum increment of axial buckling load by reducing pile slen-

derness from 64 to 32 is only 20%. The difference becomes negligi-ble when either the web or flanges become slender since local

 Table 1

Comparison of failure modes from FEA and test results.

0/0a 0/30 0/60 50/0 75/0

GBb GB GB GB GB GB FLBc FLB FLB FLB

50/30 75/60 75/60/NV/US 75/60/V/S

FLB&WLBd FLB&WLB FLB&WLB FLB&WLB FLB&WLB FLB&WLB FLB FLB

75/60/V/US 75/60/NV/US/WR 75/60/V/S/WR 75/60/V/US/WR  

FLB FLB FLB&WLB FLB&WLB FLB FLB FLB FLB

a Flange thickness reduction/web thickness reduction.b GB = global buckling.c FLB = flange local buckling.

d WLB= web local buckling.

118   C. Shi et al. / Engineering Structures 73 (2014) 114–124

7/18/2019 1-s2.0-S0141029614002703-main

http://slidepdf.com/reader/full/1-s20-s0141029614002703-main 6/11

buckling of the slender elements governs the pile capacity in those

cases. Similarly decreasing the pile slenderness from 64 to 32 only

increases the peak load by up to 48% for piles without any slender

elements. For retrofit purpose bracing the piles to reduce their glo-

bal slenderness would moderately increase the pile strength. Fur-

ther, geometric constraints may make such an intervention

impractical or unfeasible. Therefore, other retrofit options should

also be considered.

4.2.3. Effect of location of the corroded region

To evaluate the effect of the location of deterioration on the pile

capacity representative cases were modeled and investigated. The

location of degradation was shifted to the third-height of the

162.6 cm piles instead of the mid-height. The results in   Table 3

indicate that the location of the corroded region has essentially

no effect on the pile peak load regardless of the observed failure

modes.

Fig. 5.  (a–m) Comparison of axial load–shortening behavior from FEA and test results.

C. Shi et al. / Engineering Structures 73 (2014) 114–124   119

7/18/2019 1-s2.0-S0141029614002703-main

http://slidepdf.com/reader/full/1-s20-s0141029614002703-main 7/11

Fig. 5  (continued)

 Table 2

Comparison of axial loads from FEA and test results.

Buckling strength (kN) Peak strength (kN)

Test FEA   P test/P FEA   Test FEA   P test/P FEA

0/0 934 867 1.08 956 925 1.03

0/30 859 801 1.07 894 823 1.09

0/60 703 734 0.96 792 756 1.05

50/0 507 494 1.03 520 552 0.94

75/0 391 316 1.24 409 325 1.26

50/30 498 480 1.04 578 516 1.12

75/60 307 249 1.23 311 258 1.21

75/60/V/S 173 151 1.15 173 151 1.15

75/60/NV/US 245 191 1.28 254 191 1.33

75/60/V/US 173 160 1.08 178 160 1.11

75/60/NV/US/WR 276 205 1.35 311 231 1.35

75/60/V/S/WR 156 107 1.46 160 107 1.50

75/60/V/US/WR 165 125 1.32 173 151 1.15

Mean 1.18 Mean 1.18

Stdev 0.15 Stdev 0.15

CoV 12.7% CoV 12.7%   Fig. 6a.   Axial buckling loads of members with varying reduction on flange and web

thickness.

120   C. Shi et al. / Engineering Structures 73 (2014) 114–124

7/18/2019 1-s2.0-S0141029614002703-main

http://slidepdf.com/reader/full/1-s20-s0141029614002703-main 8/11

4.2.4. Effect of extent of the reductionThe influence of the extent of corrosion, defined as the length of 

the corroded region, was also studied. Table 4  provides the axial

peak loads of piles with degradation of 15.2 cm, 30.5 cm and

61.0 cm at mid-height for piles with a total length of 162.6 cm,

which corresponds to corrosion along 9%, 19% and 38% of the pile

length, respectively. These correspond to 152%, 305% and 610% of 

the nominal depth of the pile cross-section, respectively.

According to   Table 4   doubling the extent of corrosion only

slightly reduced the axial capacities of the piles when the degree

of corrosion was minor. The most significant reductions were

observed for cases when flange or web corrosion was severe. In

these cases the failure was governed by local buckling which is

affected by the aspect ratio of the element. Increasing the extent

of corrosion increased the aspect ratio of the slender element

and therefore reduced its local buckling capacity.

4.2.5. Effect of residual stresses

The effect of the magnitude of residual stresses on the capacity

of corroded piles is presented in Fig. 7. Two different residual stress

levels are considered: 0.1F y (34.5 MPa) and 0.3F y (103 MPa). Fig. 7b

indicates that the peak load of the buckled piles is relatively insen-

sitive to the magnitude of the residual stresses. Increasing the

residual stress level by three times reduces the pile capacity by a

maximum of 7%. In contrast, the initial buckling load decreases sig-

nificantly as the residual stress level increases. This is most notable

for piles with minor corrosion for which inelastic global buckling is

the predominant failure mode. In these cases, increasing the resid-

ual stress level can decrease the pile capacity by up to 47%. How-

ever, when the degree of corrosion is severe, and when local

buckling dominates the failure, the magnitude of the residual

stresses does not significantly affect capacity.

5. Comparison of numerical results and predictions using 

design guidelines

Three different design models were evaluated to predict the

capacity of piles with severe but localized corrosion: the design

model adopted by AASHTO and AISC (which is based on the Struc-

tural Stability Research Council (SSRC) column curve) and the two

methods used in the AISI specifications, namely the DSM and

EWM. The approach recommended by AASHTO and AISC conserva-

tively predicts the axial capacity based on the onset of buckling of 

steel members (although the post-buckling strength of slender

webs is considered), while AISI takes the post-buckling strengthof slender elements fully into consideration. In repair applications,

consideration of the peak load rather than the initial buckling load

of the corroded members could yield a more economical repair in

some cases. Also, based on the parametric study, axial peak load is

insensitive to the magnitude of residual stresses which can be very

challenging to accurately quantify for structures that have been in

service for extended periods. Therefore, in the following discus-

sion, the axial peak loads predicted by the FEA are taken as the

compressive capacity of the partially corroded piles.

Fig. 6b.  Axial peak loads of members with varying reduction on flange and web

thicknesses.

 Table 3

Comparison of axial strength for different locations of reduction.

Failure mode Axial peak load (kN) Difference

Mid-height One third height

20/0 GB 441 445 1%

20/40 GB 427 432 1%

60/40 FLB&WLB 294 289 1%

60/80 FLB&WLB 231 223 2%

80/80 FLB&WLB 98 102 1%

Mean 1%

Stdev 0.004

 Table 4

Comparison of axial strength for different lengths of reduction.

Extent of corrosion Axial peak load (kN) Load difference (%) Axial peak load (kN) Load difference (%)15.2 cm 30.5 cm 30.5 cm 61.0 cm

0/0 476 476 0 476 476 0

0/40 472 467 1 467 463 1

0/60 467 458 2 458 449 2

0/80 458 449 2 449 432 4

20/0 454 441 3 441 423 4

20/40 445 427 4 427 396 7

20/60 436 414 5 414 383 8

20/80 423 401 5 401 365 9

60/0 356 334 7 334 254 24

60/40 320 294 9 294 231 21

60/60 267 267 0 267 218 18

60/80 249 231 8 231 191 17

80/0 205 182 12 182 120 34

80/40 178 160 11 160 107 33

80/60 165 134 23 134 98 27

80/80 138 98 41 98 85 14

C. Shi et al. / Engineering Structures 73 (2014) 114–124   121

7/18/2019 1-s2.0-S0141029614002703-main

http://slidepdf.com/reader/full/1-s20-s0141029614002703-main 9/11

Since none of the current design rules investigate the axial

capacity of non-prismatic members, predictions from the three

design methods were compared to the axial peak load obtained

from FEA to evaluate their suitability for predicting the capacity

of non-prismatic piles. The comparison is shown in Fig. 8. The hor-

izontal and vertical axes represent the axial peak loads obtained

from numerical simulation and design guidelines, respectively.

The solid line indicates perfect correlation between the FEA andthe design guidelines; points that lie below the solid line indicate

that the design model is conservative, while points that lie above

the line indicate that the design model is unconservative.

Fig. 8 illustrates that the AISI EWM provides the most accurate

prediction of axial capacity for cases when flange corrosion is

greater than 60% and when failure is governed by flange local

buckling. The mean value of the ratio of axial capacity from FEA

to prediction by the EWM is 0.97, 0.93 and 0.92 for pile slender-

nesses of 32, 48 and 64, respectively, with coefficient of variations

of 5%, 5% and 9%, respectively. In contrast, for cases of mild corro-

sion the AISI EWM is quite unconservative. Predictions from

AASHTO and the AISI DSM are more accurate for cases of mild cor-

rosion but overly conservative for cases when corrosion is severe.

Generally, all three design methods are more unconservative forpiles with mild corrosion and higher global slenderness. This is

attributed to two factors: (1) the equations for calculating global

buckling strength are empirical and can yield higher or lower pre-

dictions for special cases; (2) the axial peak load from the FEA is

based on a model with the maximum permissible initial imperfec-tion and residual stress level, which could result in a more

Fig. 7a.   Axial buckling loads of members with different magnitudes of residual

stresses.

Fig. 7b.   Axial peak loads of memberswith differentmagnitudesof residual stresses.

Fig. 8a.  Comparison of  P FEA and P DSW/EWM/AASHTO  (kL/r  = 32).

Fig. 8b.  Comparison of  P FEA and P DSW/EWM/AASHTO  (kL/r  = 48).

Fig. 8c.  Comparison of  P FEA and P DSW/EWM/AASHTO  (kL/r  = 64).

122   C. Shi et al. / Engineering Structures 73 (2014) 114–124

7/18/2019 1-s2.0-S0141029614002703-main

http://slidepdf.com/reader/full/1-s20-s0141029614002703-main 10/11

conservative prediction. For more slender piles, the effect of initial

imperfection and residual stress level is more significant.

6. Damage classification and rehabilitation guidelines

Three damage classifications are proposed according to the

remaining capacity of a section: minor damage, moderate damage,

and major damage. Considering a pile of 162.6 cm length with 40%

reduction of the web thickness, the axial capacity obtained from

FEA for different levels of flange corrosion is shown in  Fig. 9. The

horizontal line indicates the design strength of the original pile cal-

culated by AASHTO, while the dashed line represents the remain-

ing yield strength of the section. It can be seen that, for the

specific case being considered, if the flange corrosion is less than

24%, the yield strength of the section is greater than the original

design strength of the pile. Therefore, if local buckling of the cross

section can be prevented and the weak axis moment of inertia of the section can be restored, the pile should be able to achieve its

design capacity. This range is defined as minor damage.

Moderate damage is a range of damage for which additional

material is required to resist part of the axial load, because

restraining buckling to achieve the yielding load of the section

would be insufficient to restore the design capacity of the member.

Therefore some of the axial load must be transferred from the

existing pile to the repair system by friction, bond, or shear inter-

lock. Major damage refers to severe cases of corrosion for which a

significant amount of additional material or replacement of the

severely corroded region may be necessary. This case is indicated

by the hatched region in the figure. The specific boundary between

moderate and major damage may be influenced by other non-tech-

nical considerations including economics, social requirements, orexpected remaining service life.

7. Conclusions

Inelastic buckling of partially deteriorated short steel piles was

studied using a non-linear finite element analysis. According to the

comparison of the FEA simulation and the test results the model

was demonstrated to be reliable and appropriate for detailed

investigation of the buckling behavior of corroded steel piles. A

parametric analysis was performed using the validated model

and factors that influence the axial capacity of a corroded pile were

discussed. Current design rules including the DSM and EWM from

AISI and the design procedure from AASHTO and AISC were com-pared to FEA predictions. Damage classification and rehabilitation

guidelines were proposed according to the residual strength of 

the corroded piles. The following conclusions are drawn:

(1) The degree of flange corrosion is the single factor which

most significantly affects the remaining capacity of steel

piles with localized corrosion.

(2) Varying the initial geometric imperfection within the limita-

tions from the AASHTO and AISC design specifications does

not significantly affect the axial capacity of corroded piles.

(3) Pile slenderness has a notable influence on the peak load of 

piles with mild corrosion. However, it has a relatively minor

effect on the capacity of piles with slender web or flanges.

This indicates that bracing to reduce the effective length

may only provide a limited increase of the capacity of piles.

(4) The location and extent of the corroded region along the

length of the pile does not have a significant impact on the

axial capacity.

(5) The magnitude of residual stress has a notable effect on the

buckling load of corroded piles with minor corrosion. How-

ever, this effect is small for piles with more severe corrosion.

The magnitude of residual stresses has little effect on the

predicted peak loads of the corroded piles within the range

considered in this study.

(6) Among the three design methods considered in this paper,

the EWM provides the most accurate prediction of axial

capacity for severely corroded piles while it is unconserva-

tive for piles with mild corrosion. The AASHTO and DSM

design methods are more accurate for mildly corroded piles

but overly conservative for severely corroded cases.

(7) Three damage classifications are proposed based on the

remaining capacity and failure mode of a corroded pile. Cor-

responding rehabilitation guidelines are suggested for each

level of damage. Rehabilitation decisions may also be influ-

enced by other non-technical considerations including eco-

nomics, social concerns, or expected remaining service life

of the structure.

 Acknowledgments

The authors would like to acknowledge the financial support

provided through TXDOT project 0-6731 ‘Repair Systems for Dete-

riorated Bridge Piles’. The financial support of the Department of 

Civil & Environmental Engineering at the University of Houston

is also gratefully acknowledged.

References

[1] AASHTO LRFD bridge design specification. American Association of State

Highway and Transportation Officials (AASHTO). Section 6; 2012. p. 77–93.[2] AISC steel construction manual. 14th ed.; 2011. p. 16.1-22–298.

[3] AISI S100-2007. North American specification for design of cold-formed steel

structure members: Appendix 1: 3–8; 2007. p. 57–62.

[4] Paik JK, Lee JM, Ko MJ. Ultimate compressive strength of plate elements with

pit corrosion wastage. Proc Inst Mech Eng, Part M. J Eng Marit Environ

2003;217:185–200.

[5] Ok D, Pu Y, Incecik A. Computation of ultimate strength of locally corroded

unstiffened plates under uniaxial compression. Mar Struct 2007;20:100–14.

[6] Beaulieu LV, Legeron F, Langlois S. Compression strength of corroded steel

angle members. J Constr Steel Res 2010;66:1366–73.

[7] Liu XD, Nanni A, Silva PF. Rehabilitation of compression steel members using

FRP pipes filled with non-expansive and expansive light-weight concrete. Adv

Struct Eng 2005:129–42.

[8] Karagah H, Dawood M. Axial capacity of partially corroded steel bridge piles.

In: Proceeding of the annual stability conference. St. Louis, Missouri, April 16–

20, 2013. p. 411–25.

[9] Ziemian RD. Guide to stability design criteria for metal structures; 2010. p.

651–3.

[10]  Chan TM, Gardner L. Compressive resistance of hot-rolled elliptical hollowsections. Eng Struct 2008;30:522–32.

Fig. 9.  Damage classification for member with 40% reduction on web thickness.

C. Shi et al. / Engineering Structures 73 (2014) 114–124   123

7/18/2019 1-s2.0-S0141029614002703-main

http://slidepdf.com/reader/full/1-s20-s0141029614002703-main 11/11

[11]  Sarawit AT, Kim Y, Bakker MCM, Pekoz T. The finite element method for thin-

walled members – applications. Thin Wall Struct 2003;41:191–206.

[12]  Yan J, Young B. Numerical investigation of channel columns with complex

stiffeners – Part I: Test verification. Thin Wall Struct 2004;42:883–93.

[13]   Zhu J, Young B. Aluminum alloy tubular columns – Part I: Finite element

modeling and test verification. Thin Wall Struct 2006;44:961–8.

[14]  Saad-Eldeen S, Garbatov Y, Guedes Soares C. Ultimate strength assessment of 

corroded box girders. Ocean Eng 2013;58:35–47.

[15] Seif M, Schafer BW. Design method for local-global interaction of locally

slender steel members. In: SSRC annual stability conference, Orlando, FL, May

12–15; 2010.

124   C. Shi et al. / Engineering Structures 73 (2014) 114–124