Research Paper

Journal of Engineering and Technological Sciences

The Risk of Failure Assessment in Bina Marga Standard Designed
Prestressed Concrete Girder Bridges under B-WIM Load
Measurement
\\\\\\\\

Widi Nugraha1,2,*, Indra Djati Sidi1, Made Suarjana1 & Ediansjah Zulkifli1
1

Department of Civil Engineering, Institut Teknologi Bandung, Jalan Ganesha No. 10, Bandung 40132, Indonesia
Directorate General of Highway, Ministry of Public Works and Housing, Jalan AH Nasution No. 264, Bandung
40294, Indonesia

2

Corresponding author: widi.nugraha@pu.go.id

Abstract
The use of precast prestressed concrete girder bridges in Indonesia has been increasing rapidly due to their high quality,
reliability, and faster construction on site. The girder components are typically designed for a specific bridge span and can
be prefabricated. The Directorate General of Highways of the Ministry of PUPR (Bina Marga) has released a standard design
for prestressed concrete girder bridges with a typical span of up to 40 m. This design is based on the bridge loading standard
SNI 1725 2016, which determines the live traffic load through consensus due to limited data on actual traffic load
measurement results. However, the Ministry of PUPR has been implementing actual traffic load measurements using weighin-motion (WIM) technology to directly measure the load of passing vehicles. In this study, a risk assessment of the failure
risk of a standard Bina Marga bridge with a 40-m span prestressed concrete girder type was conducted based on B-WIM load
measurements. The results of this assessment indicate that the standard Bina Marga bridge has a failure risk of 1.48 x 10-4,
which is smaller than the acceptable risk of failure according to the AASHTO LRFD Bridge Design Specification as referenced
in SNI 1725 2016.
Keywords: B-WIM; failure risk assessment; live traffic load; precast prestressed concrete girder bridges, reliability.

Introduction
Bridges are essential structures that connect different regions and facilitate transportation and mobility. They
are designed to support and carry traffic loads using various materials, such as wood, masonry, reinforced
concrete, steel, and prestressed concrete. Among these materials, prestressed concrete has become
increasingly popular in bridge construction due to its advantages over conventional reinforced concrete.
Prestressed concrete structures optimize the use of high concrete strength against compressive forces by
applying a pre-tensioning force to steel cables embedded in the lower part of the cross section. This creates a
compressive stress that counteracts the tensile stress induced by bending forces from traffic loads, allowing for
smaller cross sections and longer spans than ordinary reinforced concrete structures. Notably, this prestress
force also exerts a positive influence on critical structural aspects like the fundamental frequency and static
deflection shape of girders, ultimately enhancing performance when compared to their reinforced concrete
counterparts [1]. Moreover, prestressed concrete girders can be prefabricated off-site with a typical design for
the same span length, leading to faster construction compared to reinforced concrete girders that are cast on
site [2]. Prestressed concrete girder bridges have been widely used around the world for various types of bridges,
such as box girder bridges (e.g., Shibanpo Yangtze Bridge in China), T-girder bridges (e.g., Stolma Bridge in
Norway), or I-girder bridges (e.g., Natchez Trace Parkway Arches in USA).
However, despite their benefits, prestressed concrete girder bridges also face challenges, with deterioration
being a primary concern [3]. The degradation of these structures is attributed to a combination of factors,
including prestressing losses, tendon relaxation, concrete cracking, concrete creep and shrinkage, and the
influence of environmental factors [4]. A particularly noteworthy concern is the occurrence of cracking, which

Copyright ©2023 Published by IRCS - ITB
ISSN: 2337-5779

J. Eng. Technol. Sci. Vol. 55, No. 5, 2023, 558-568
DOI: 10.5614/j.eng.technol.sci.2023.55.5.5

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has the potential to significantly erode the flexural stiffness of the girder [5]. This, in turn, can lead to a reduction
in both static and dynamic performance, adversely affecting the bridge’s capacity to bear various loads.
Therefore, it is important to evaluate their performance and safety using reliable methods that account for their
structural characteristics and loading conditions, including live traffic loads, seismic forces, wind pressures, and
more. Through a comprehensive evaluation of the risk of failure, proactive measures can be implemented to
ensure that the risk aligns with established safety thresholds. This may entail updates to the loading regulations
in Indonesia’s bridge design code (SNI) [6]. The existing Indonesia bridge design code (SNI) operates in
accordance with the principles of Load and Resistance Factor Design (LRFD), employing a risk-based and
probabilistic approach to define crucial provisions, including nominal loading and load factors [7].
In this paper, we focus on prestressed concrete girder bridges in Indonesia and their loading conditions. In
Indonesia, the Bina Marga standard design for prestressed bridges with spans ranging from 22 m to 40 m [8] is
based on the bridge loading code SNI 1725 2016 [9]. However, the SNI 1725 2016 determines the amount of live
traffic load through consensus by referencing foreign bridge loading standards, such as those from the United
States (AASHTO LRFD Bridge Design Specifications [10]) and Australia (Bridge Management System [11]), rather
than actual vehicle measurement data. Using actual vehicle measurement data can provide more realistic and
accurate estimates of the load effects and risk of failure of bridges under different traffic scenarios. One option
is to use weigh-in-motion (WIM) technology to measure the actual vehicle loads on Indonesian bridges. WIM
technology is constantly evolving, with various types of pavement-based WIM and bridge WIM (B-WIM) sensors
currently available [12]. In Indonesia, the Ministry of PUPR has started measuring actual vehicle loads with BWIM in recent years. B-WIM measurement stations have been operating on the North Coast of Central Java
national road section since 2017 and have also been installed at several other locations on national roads and
toll roads [13]. The data generated from B-WIM measurements includes the total vehicle load, the weight of
individual axles, the distance between the axles, the vehicle speed, the axle configuration, and the time the
vehicle passes [14]. However, B-WIM data also pose some challenges for bridge analysis, such as data quality
issues, calibration errors, environmental influences, or sensor failure [15]. These challenges need to be
addressed in order to use B-WIM data effectively for risk assessment of prestressed concrete girder bridges.
The objective of this study was to develop a comprehensive risk assessment method for prestressed concrete
girder bridges utilizing data from bridge weigh-in-motion (B-WIM) systems to enhance structural analysis
models. To achieve this, we utilized B-WIM data obtained from a measurement station situated along a national
road in Central Java, which has been in operation since 2017, as illustrated in Figure 1.

Figure 1

B-WIM instrumentation on the PCI girder bridge.

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To align with best practices, we adopted a standard B-WIM system sensor layout designed for both girder and
slab bridges, depicted in Figure 2. Within this layout, strategically positioned strain transducers were affixed at
the mid span of each girder’s bottom flange, denoted by the red rectangles. These strain gauges played a crucial
role in capturing the maximum strain induced by vehicles passing over the bridge, effectively functioning as
weighing sensors for the B-WIM measurement system. Additionally, the strain transducers also served as speed
and axle detection sensors, installed at the bottom part of the slab in each vehicle lane, as indicated by the black
rectangles. All these sensors were interconnected with a data processing unit, depicted by the gray rectangle,
dedicated to processing the bridge response data from the sensors and calculating essential B-WIM output
parameters such as vehicle gross vehicle weight (GVW), axle load, axle distance, speed, and classification, using
the Moses algorithm [16].

Figure 2

Typical B-WIM system installation [17].

We applied statistical methods to extract the characteristic values and distributions of the vehicle parameters
from the B-WIM data. We then selected a set of representative load cases that cover different combinations of
vehicle types, weights, speeds, and positions on the bridge. The simulation involved applying moving loads on a
standard Bina Marga prestressed concrete girder bridge model to determine the response of the prestressed
concrete girder elements to actual traffic loads. The response of the structure can vary due to different load and
vehicle configurations, resulting in a random variable response distribution. In addition to the response variable
due to load, the resistance of the prestressed concrete girder to external loads is also a random variable because
the forming materials, such as concrete, steel strands, and reinforcing steel, are themselves random variables.
Therefore, there is a risk of failure if the response of the structure to loading exceeds the bearing capacity of the
structure. This study analyzed and evaluated the risk of failure against an acceptable target risk of structural
failure based on the importance of the bridge infrastructure according to the SNI code in Indonesia [9]. We
expected our method to provide more realistic and accurate estimates of the load effects and risk of failure of
prestressed concrete girder bridges under actual traffic scenarios than conventional methods based on design
codes. Our method could also help to identify critical load cases and locations on the bridge that require more
attention. Furthermore, our method can be applied to other types of bridges or WIM data sources with minor
modifications.

Standard Design for Prestressed Concrete Girder Bridge
In 2008, the Directorate General of Highways released a standard design for prestressed concrete girder bridges
with a cross section in the shape of type I beams and spans ranging from 22 m to 40 m. The bridge analyzed in
this study has a 40 m span with a traffic width of 7 m and sidewalks 1 m wide on both sides. Figure 3 provides
an in-depth view of the dimensions and section specifics of this standardized design. The girders used are 2300

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mm x 850 mm with a total of five girders arranged with a distance of 1750 mm between them. These girders are
connected with locally cast diaphragms measuring 200 mm x 1850 mm at intervals of 10 m, 20 m, and 30 m from
the initial supports. The structural components utilize a mix of materials, including concrete girders with a
compressive strength, fc', of 40 MPa, concrete diaphragms, and slabs with a compressive strength fc' of 30 MPa.
Reinforcement comprises BJTD40 steel and prestressed PC strands measuring 12.7 mm in diameter, adhering to
ASTM-416 Low Relaxation specifications. These detailed specifications were instrumental in modeling the bridge
using the 3D finite element method (FEM) and accurately calculating the bridge’s resistance or capacity. It is
noteworthy that the material strength values presented herein are nominal and they were further converted to
mean values using bias factors, subsequently facilitating precise girder resistance calculations essential for
reliability analysis.

(a) Longitudinal cut of the bridge

(b) Cross section of the bridge

(c) Cross section of the girder at support and
at mid span

(d) Plan view of the bridge
Figure 3

Design drawing of 40 m PCI girder bridge.

In the calculation of the resistance variable, we adopted a calculation approach for the PCI girder bending
moment capacity under ultimate conditions. This calculation method involves utilizing the principles of force
and moment equilibrium, taking into consideration the concrete compressive strength, the tensile strength of
the reinforcement bars, and the effect of the prestress force acting on the girder. By integrating these factors,
we were able to derive a comprehensive understanding of the girder’s capacity to withstand bending moments.

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Notably, throughout these calculations, the mean values of material strength and dimensions were employed
to ensure accuracy and reliability in the determination of the resistance variable.
To analyze the load effect variable of the standard design for prestressed concrete girder bridges due to bridge
WIM live load, a 3D FEM was created using the CSI Bridge Software [18] based on the bridge design drawing and
material specification. The FE model was used to simulate traffic loads and calculate the load effect generated
by the traffic load simulation. This load effect variable assessment was based on real-world B-WIM vehicle load
measurement data, encompassing comprehensive vehicle specifics such as total weight, individual axle weights,
axle distances, and axle configurations. The FE model, utilized for the traffic load simulation, is visually presented
in Figure 4.
The FE model of the PCI girder bridge consisted of several components, as listed in Table 1. The girder, the
primary load-bearing element, was represented using beam/frame elements made of precast concrete with a
mesh size of 5 m. Notably, the girder exhibits a non-prismatic geometric characteristic, transitioning from a
nearly full section at the support points (measuring 800 x 2300 mm) to a more I-shaped section at mid-span,
with an end section length of 2100 mm and a 500-mm transition zone towards the mid-span section, as
illustrated in Figure 3(d). Tendons, essential for prestressing, were simulated as tendon elements comprising
steel strand material. The prestressing force is applied through pre-tensioning, a process where prestressing
tendons, modeled as tendon elements with a curved geometry, are perfectly bonded to the concrete beam. The
simulation accurately transfers the prestressing force from the tendon to the concrete reference axis, allowing
for the effects of prestressing in the FE model. The slab, supporting the road surface, was simulated using shellthin elements made of reinforced concrete, with a mesh size of 5 by 0.25 m. Diaphragms, enhancing the
structural stability, were represented with reinforced concrete beam/frame elements and a mesh size of 1.75
meters. The boundary conditions applied were of a simple support nature, where one end was designed as a
rolled support, and the other as a pin support. Importantly, this study did not delve into geometric nonlinear
analyses; it assumes the bridge operates within typical traffic load conditions. These elements, along with their
specific mesh sizes, collectively constitute the FE model, enabling a comprehensive analysis of the PCI girder
bridge’s structural behavior under varying vehicular loads based on B-WIM measurements.

Figure 4

FE Model of 40 m PCI girder bridge.

Table 1
Element Name
Girder
Tendon
Slab
Diaphragm

FE model element information.

Element type
Beam/frame
Tendon
Shell – thin
Beam/frame

Material
Precast Concrete
Steel Strand
Reinforced Concrete
Reinforced Concrete

Mesh Size
5m
5 m x 0.25 m
1.75 m

B-WIM Vehicle Live Load Measurement Data
The data used in this study were based on the results of measuring vehicle loads with B-WIM on the national
road along the north coast of Central Java within one year, 2018. Detailed vehicle data, including the time the

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vehicle passed, the total weight of the vehicle, the weight of each vehicle axle, the distance between vehicle
axles, and vehicle axle configurations, could be obtained from B-WIM measurements. In this study, the data was
used to construct a vehicle load sequence for simulating traffic loading on the bridge model. One of the vehicle
load sequences with the largest vehicle load effect for a 40-m bridge span was recorded on 2 December 2018,
as shown in Figure 5 below. The vehicle sequence was used as a moving load in the bridge structure model to
then carry out a loading simulation. Simulations were carried out for other vehicle sequences according to the
results of the vehicle load measurements with B-WIM in this study, namely for one year. The output of the model
structure analysis were the internal forces in the form of the bending moments and shear of the girder. The
maximum internal force value for each daily data from vehicle load measurement results with B-WIM was then
recapitulated and the type of variable distribution was sought for the purpose of reliability analysis.

Figure 5

Heaviest 40-m vehicle sequence of 2 December 2018.

The distribution of daily maximum load effects was used to estimate the maximum load effects for a bridge
lifespan of 75 years. Since the daily maximum value represents the highest value for that day, it can be assumed
that the distribution of daily maximum values follows an extreme value distribution. This study assumed that
the daily maximum value follows a Gumbel Type I distribution. Figure 6 shows the projection of the maximum
load effects for a 75-year return period.
Cumulative Distribution Function
1
0,9
0,8
0,7

F(x)

0,6
0,5

Data

0,4
0,3

Gumbel

0,2
0,1

Fx 75 years

0
0
Figure 6

100
200
300
400
Maximum bending moment, x (tonf-m)
CDF of 75 years maximum bending moment.

500

Reliability Analysis
Reliability analysis is a method that plays a vital role in determining the risk of failure of a structure. It provides
a precise estimate of the probability that the structure will be able to resist the loads it is subjected to over its
service life. The primary objective of reliability analysis is to ensure that the structure meets the safety
requirements and complies with the codes and standards set by regulatory bodies. The reliability index is the

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metric used to determine the safety of the structure, and it is calculated by comparing the strength of the
structure to the load it is expected to carry. If the reliability index is less than a certain target reliability, the
structure may be at risk of failure, and appropriate measures may need to be taken to improve its safety. In this
study, the reliability analysis was performed using the first-order reliability method (FORM), a widely accepted
and accurate approach for estimating the probability of failure of a structure [19]. FORM is a computational
approach utilized to assess the probability of failure within a structure. This probability is typically depicted
graphically through a reliability index curve, as illustrated in Figure 7. The figure showcases a probability density
function (PDF) of a performance function g, a function influenced by random variables, representing the
relationship between resistance R and total loads Q acting on the structure. In essence, the structure is
considered safe when the total load Q is less than the resistance R (R > Q), resulting in a positive g value.
Conversely, failure occurs if the total load Q surpasses the resistance R (R < Q), leading to a negative g value. The
probability of failure (pf) is calculated based on the area where the distribution of g falls to the left of the y = 0
axis, while the probability of safety (ps) is computed as 1 - pf. Additionally, the reliability index β is the inverse of
the normal distribution of ps. These parameters collectively help in comprehensively evaluating the structural
safety and failure probability, aiding in effective risk assessment and mitigation strategies.
The load placed on a bridge by vehicles is a random variable, meaning it can vary greatly from one moment to
the next. At times, this load may be so large that it exceeds the designed capacity or resistance of the bridge,
putting it at risk of failure. This is a concern, because the strength of a bridge must be able to withstand the loads
it is subjected to in order to remain safe and functional. If the load on the bridge is consistently too high, the
structure may eventually become overloaded and fail, leading to costly repairs or even collapse. To mitigate this
risk, it is important to carefully consider the expected loads on a bridge during the design process and ensure
that the structure is capable of handling them. Reliability analysis can be used to evaluate the risk of failure of a
bridge due to vehicle loads and identify any potential weaknesses or vulnerabilities in the structure.
PD
F
Saf
e

Failur
e

g = R-Q
Probability
of failure

0
Figure 7

g
Probability of failure concept.

The risk of failure assessment method used in this study followed the flowchart depicted in Figure 8. The
methodology involved utilizing the FE model of the bridge, incorporating Bridge Data to accurately calculate load
effects resulting from vehicle loading based on B-WIM measurements. The daily vehicle data was used to
construct a vehicle load model, representing one or several vehicles as moving loads on the FE model.
Subsequently, the maximum load effect, specifically the maximum bending moment, was computed for each
date of the B-WIM measurements data. This process was repeated for each date over a year, allowing statistical
data on the daily maximum load effect to be collected. These statistics are pivotal in calculating the 75-year
return period of the maximum load effect, a crucial component for the subsequent reliability analysis.

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Loads

WIM data
Resistance
Bina Marga Standard
Designed PCI Girder Bridge

Daily maximum observed
vehicle sequences

Daily maximum load
effect

FEM Model
Bridge Data

Bridge live load model SNI 1725 2016
D Lane Load & T Truck Load

Resistance SNI 1725 2016
≥

75 years load effect:
Extreme value theory

Dead Load & statistical
parameters

+

+

({ } ×

Resistance statistical
parameters

Risk of Failure Analyisis

Figure 8

Flowchart for risk of failure analysis.

The mean and standard deviation of the maximum live load effect over a 75-year period were determined using
the scale and location parameters, the daily maximum value followed a Gumbel Type I distribution based on
distribution fitting. The dead load effect was assumed to follow a normal distribution [20], and the resistance
was calculated using the bias factor and coefficient of variation. The reliability index was determined utilizing
the First Order Reliability Method (FORM), a widely acknowledged approach represented by Eq. (1). Additionally,
the Rosenblatt transformation [21], was applied due to the non-normal distribution of the variables. In this
study, the probability distributions for various factors were determined to facilitate reliability analysis. The
maximum load effect, representing bending moments, was found to follow a Gumbel Type I distribution through
fitting the data, illustrated in Figure 6. Conversely, the dead load effect was assumed to conform to a normal
distribution, a standard assumption [22]. To assess the resistance, representing the structure’s capacity, careful
consideration of its bias factor and coefficient of variation was made. The resistance was modeled using a
lognormal distribution, a choice also grounded in previous work [22]. To ensure the reliability analysis was
conducted effectively, the Rosenblatt transformation was employed. This transformation allowed for the
conversion of input variables into standard normal variables, preserving their correlation and ensuring suitability
for the subsequent FORM analysis aimed at estimating the probability of structural failure.
=

µ

µ
(

µ

(1)

)

The variables involved in these calculations encompassed essential parameters such as
(mean value of the
resistance normal equivalent variable), (mean value of the dead load effect variable), (mean value of the
live load effect normal equivalent variable), σ (standard variation of the resistance normal equivalent variable),
σ (standard variation of the dead load effect variable), and σ (standard variation of the live load effect normal
equivalent variable).
=

(− )

(2)

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Widi Nugraha et al.

where:
is the failure probability,
is the standard normal cumulative distribution function, and
is the reliability index.
Upon conducting the FORM calculation, as illustrated in Table 2, it appears that the reliability indexes for the
Bina Marga standard design for prestressed concrete girder bridges are 3.63. This value falls short of the desired
target reliability index of 3.72 [22]. The probability of failure (pf) was determined using Equation 2, involving the
standard normal cumulative distribution function of (– β). The obtained pf amounted to 1.36 x 10-4. This result
indicates that the current SNI Bridge Loading Code may result in an under-designed bridge superstructure.
Table 2
Iteration
No.
1
2
3
4
5
6
7
8
9
10

Failure points
l*
r*
336.60 1418.06
336.89 842.73
337.15 875.22
337.13 873.22
337.13 873.34
337.13 873.34
337.13 873.34
337.13 873.34
337.13 873.34
337.13 873.34

Iteration on risk of failure assessment analysis.
σ LN

σRN

µLN

µRN

4.51
4.51
4.52
4.52
4.52
4.52
4.52
4.52
4.52
4.52

198.49
117.96
122.51
122.23
122.25
122.24
122.24
122.24
122.24
122.24

336.57
336.57
336.57
336.57
336.57
336.57
336.57
336.57
336.57
336.57

1404.17
1273.03
1289.00
1288.05
1288.11
1288.11
1288.11
1288.11
1288.11
1288.11

Reliability
index (β)
2.91
3.64
3.64
3.64
3.64
3.64
3.64
3.64
3.64
3.64

Probability of
failure (pf)
1.81E-03
1.38E-04
1.36E-04
1.36E-04
1.36E-04
1.36E-04
1.36E-04
1.36E-04
1.36E-04
1.36E-04

The acceptable risk of failure for structures is generally higher for buildings compared to bridges, with a target
of 10-3 for buildings [23] and 10-4 for bridges [24]. This is because bridges are considered more important and
critical infrastructure. The results of this study indicate that a standard high-level bridge with a precast
prestressed concrete I girder type span of 40 m has a higher risk of failure than the expected target. This is likely
due to a variety of influencing factors, including the random and variable nature of the load, which may be
different from the loads experienced by bridges in other countries. As such, it is important to carefully consider
the unique characteristics of the load on a bridge and ensure that the structure is capable of handling it in order
to minimize the risk of failure.

Conclusion
In conclusion, this risk assessment of the standard design for prestressed concrete girder bridges showed that
the risk of failure due to live load based on bridge WIM measurements is 1.48 x 10-4. While this value is lower
than the acceptable risk of failure for bridges according to the AASHTO LRFD Bridge Design Specification and SNI
1725 2016 (10-4), it is still higher than the expected target for building (10-3). This indicates that there are
potentially influencing factors that may increase the risk of failure for this type of bridge. It is important to
continue monitoring the performance of this standard designed bridge and consider any necessary measures to
improve its reliability and reduce the risk of failure in the future.
In future research, we aim to apply the proposed methodology to a range of standard designed bridges, including
various types and span lengths. This expansion is intended to provide a comprehensive understanding of the
reliability of existing bridges across Indonesia, considering actual vehicle loading based on B-WIM
measurements. By evaluating different bridge designs, our goal is to gain insight into how these structures
perform under various traffic conditions. Furthermore, we seek to identify suitable load and resistance factors
in line with the Indonesia bridge design code to ensure that the target reliability levels are achieved. This
research will play a crucial role in enhancing the safety and reliability of bridge infrastructure throughout the
country, adapting to changes in traffic patterns and load distributions.

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Acknowledgement
We would like to express our gratitude to the Indonesia Endowment Funds for Education (LPDP) for funding this
study and to the Ministry of Public Works and Housing Republic of Indonesia for their support. Without their
generosity and support, this research would not have been possible. We are grateful for their commitment to
improving infrastructure and ensuring the safety of bridges in Indonesia.

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Manuscript Received: 7 March 2023
Revised Manuscript Received: 25 September 2023
Accepted Manuscript: 14 November 2023