Bridge Pier Collision Forces

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 6, Issue 9, Sep 2015, pp. 205-217, Article ID: IJCIET_06_09_018
Available online at
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=6&IType=9
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
VESSEL COLLISIONS ON BRIDGE PIERS:
SIMULATION STUDY FOR DYNAMIC
AMPLIFICATION FACTORS
Dr. Avinash S. Joshi
Research scholar, Department of Applied Mechanics,
Visveswaraya National Institute of Technology, Nagpur, India
Dr. Namdeo A. Hedaoo
Research scholar, Department of Applied Mechanics,
Visveswaraya National Institute of Technology, Nagpur, India
Dr. Laxmikant M. Gupta
Professor, Department of Applied Mechanics,
Visvesvaraya National Institute of Technology, Nagpur, INDIA
ABSTRACT
In conventional analysis and design of bridges, piers are analyzed for
dead, vehicular, and earthquake forces. As a special case, an unfendered
Bridge pier may experience a vessel collision. This collision (impact) of a
barge or a ship commonly known as vessel may adversely damage the
structure. This paper presents an estimate of the Dynamic Amplification
Factor (DAF) for impact due to such vessel collisions on unfendered bridge
piers. Various geometries of piers are analyzed for forces arising from such a
collision scene considering the Indian navigational conditions. Static and
dynamic analysis of RCC wall type solid and the hollow circular piers using
the finite element method is carried out. Specially made computer programs in
MATLAB software are used for this purpose. The Dynamic Amplification
Factors for various geometries of piers with impact force applied at different
heights and angles are calculated and the results are presented in the form of
graphs.
Key words: Bridge pier, Collision, Dynamic amplification factor, Slenderness
ratio
Cite this Article: Dr. Avinash S. Joshi, Dr. Namdeo A. Hedaoo and Dr.
Laxmikant M. Gupta. Vessel Collisions on Bridge Piers: Simulation Study for
Dynamic Amplification Factors. International Journal of Civil Engineering
and Technology, 6(9), 2015, pp. 205-217.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=6&IType=9

Avinash S. Joshi, Namdeo A. Hedaoo and Laxmikant M. Gupta
1. INTRODUCTION
Impact force due to collision of vessels (ships or barges) is a reality and may
adversely damage the piers of a bridge in rivers or creeks which have navigational
channels. It has been observed, that the annual rate of ship/barge collisions with
bridges has increased from 0.5 to 1.5 bridges [1] in the period 1960 to 1980. Such a
hit results in heavy damage to the pier causing disruption to road traffic, resulting in
loss of economy in millions besides inordinate delays.
The pier is modeled using FEM techniques and is exposed to a force-time relation.
The maximum dynamic and static deflections are calculated. A dynamic amplification
factor is estimated. An equivalent static force could then be obtained by multiplying
the maximum force by the dynamic amplification factor. This will enable faster, less
cumbersome design process and at the same time ensure that the dynamic effects are
taken care off. The shape and size of the piers, the impacting vessel and the load from
the superstructure is varied to get an overall spectrum of the dynamic amplification
factors. The DAFs are presented in the form of graphs and equations.
2. PROBLEM FORMULATION
2.1. Vessel size
In Western countries like the US and some European nations, the magnitudes of the
ships plying navigational channels vary from 25,000 Dead Weight Tonnage (DWT)
upwards to 400,000 DWT. Such huge liners or ships may not enter the Inland
waterways. Present work is restricted to the IS 4561-Part III, for characteristics of the
vessel and other required details. IS 4561 tabulates the DWT and dimensions of small
ships, boats or barges from 600 T down to 125 T [2].
2.2. Vessel characteristics
The characteristics of vessels plying inland waterways as stated in IS 4651 are
reproduced here. The collision force due to a 600 T and a 400 T vessel are
investigated and marked ‘*’ in Table 1.
Table 1 Characteristics of vessels plying inland waterways
Capacity (T)
Overall
Length (m)
Overall
Breadth (m)
Overall
Depth (m)
Draught
Light (m)
Draught
Loaded (m)
600 * 57 11.58 3.05 0.91 2.29
500 49.1 8.75 2.50 0.40 1.85
400 * 41 8.76 1.94 0.76 1.85
300 37.3 7.60 2.44 0.91 2.13
300 42 7.80 2.70 0.57 1.82
200 35.2 7.05 2.25 1.63 0.75
125 22 5.85 2.20 0.76 1.83
2.3. Geometry of the Pier
Piers of different shapes and heights as per navigation and other requirements are
considered. Two types of piers viz., solid wall type and hollow circular tapering pier
are analyzed. Geometrical inputs are as mentioned in Tables 2 to 5. The geometries
are selected considering the present codes and recent design practices [3]. The
slenderness ratios ( are same for each type of pier ranging from 11 to 20. The height

Vessel Collisions On Bridge Piers: Simulation Study For Dynamic Amplification Factors
of the pier considered here is distance of pier top to pier base. The pier is assumed to
be fixed at the base. The inertial effects of the superstructure at the top are considered.
Table 2 Type 1 (wall type pier)
Length (m) Breadth (m) Height (m) Slenderness ratio
8.00 4.00 25.00 11
8.00 4.00 30.00 13
8.00 4.00 35.00 15
8.00 4.00 39.00 17
8.00 4.00 46.00 20
Table 3 Type 2 (wall type pier)
Table 4 Type 3 (hollow circular pier)
Table 5 Type 4 (hollow circular pier)
OD at
bottom
(m)
ID at bottom
(m)
OD at
top
(m)
ID at
top
(m)
Height
(m)
Slenderness ratio
5.550 4.35 2.500 1.300 19.00 11
5.550 4.35 2.500 1.300 22.00 13
5.550 4.35 2.500 1.300 25.00 15
5.550 4.35 2.500 1.300 30.00 17
5.550 4.35 2.500 1.300 35.00 20
2.4. Approach velocities
The vessels are assumed to be in midstream and hence velocities are higher taken as
0.5 Hs [4], where ‘Hs’ is the average wave height, generally 4 m. Thus velocity is
greater than or equal to 2 m/s. A barge collision with a bridge pier is primarily an
accident; generally in such cases the navigator of the vessel looses control because of
a storm or an engine shut off and drifts freely in the stream. Considering this, the
stream velocity is 4.0 m/s adopted as the velocity of the vessel.
Length (m) Breadth (m) Height (m) Slenderness ratio
6.00 3.00 19.00 11
6.00 3.00 22.00 13
6.00 3.00 25.00 15
6.00 3.00 30.00 17
6.00 3.00 35.00 20
OD at
bottom
(m)
ID at
bottom
(m)
OD at
top
(m)
ID at
top
(m)
Height
(m)
Slenderness ratio
7.000 5.800 3.500 2.300 25.00 11
7.000 5.800 3.500 2.300 30.00 13
7.000 5.800 3.500 2.300 35.00 15
7.000 5.800 3.500 2.300 38.00 17
7.000 5.800 3.500 2.300 45.00 20

2.5. Eccentricity of impact
The actual collision may be at some angle, which cannot be easily estimated
beforehand. The collision angle is of 10o
, 15o
, 20o
, 25o
and 30o
is considered.
2.6. Water depth
The collision force is applied at 5 m, 10 m and 15 m from the base of the pier. The
application of the force, which depends on the depth of water, is selected so as to take
into consideration quite a large number of channels. Depth of inland waterways
having navigation with depths greater than 15 m is of rare occurrence.
2.7. The Dead load reaction on the pier
Navigable channels require a minimum horizontal clearance for the ship/barge to pass
comfortably below the bridge. The navigable spans are longer than normal hence dead
load reactions on the pier are larger, say of the magnitude (1500 T to 2000 T). 2000 T
is placed over different geometries of piers as mentioned above.
2.8. Material Properties
The Piers are considered to be of Reinforced Cement Concrete with E = 5000 ckf in
MPa, and poisons ratio ν = 0.15.
3. ESTIMATION OF THE IMPACT LOAD
3.1. Estimation of impact force
The present study is carried out for a head-on bow impact on the pier along the flow
of water [5]. The determination of the impact load on a bridge structure subjected to
vessel collision accident is complex. It depends on the characteristics of the vessel and
the bridge structure as well as the circumstances of the collision accident. Some
important parameters on which the present study is based on vessel characteristics i.e
type, size, shape and speed; geometry of pier i.e size, shape and mass and for the
collision circumstances i.e approach velocity, eccentricity of impact and water depth.
The following equation is used to assess the maximum impact force [6].
   2.61/22.62
0 for5.0 LELLELPPBOW  (1)
  2.61/2
0 for5 LEELPPBOW  (2)
where
PBOW = maximum bow collision (MN)
P0 = reference collision load equal to 210 MN
L = Lpp /275 m
E = Eimp /1425 MNm
Lpp = Length of the vessel in (m)
E imp = Kinetic energy of vessel (MNm)
Using this equation the maximum or peak impact force has been established for
vessels between 500 DWT to 300,000 DWT. The formula used is based on
investigations carried out at the Great Belt Project. Using this method the impact
forces are tabulated in Table 6.

Table 6 Impact force
Mass + 5%
added
mass
L=Len/275
Velocity
m/s
K.E. imp
MNm
1/2 m.v2
E=KE/1425
Force in
MN
Force in
(T)
Depth
of
Vessel
630 0.207 4 5.138 0.004 12.837 1284 3
420 0.149 4 3.425 0.002 8.889 889 2
3.2. Mass coefficient or added mass
When the motion of a vessel is suddenly checked the force of impact which the vessel
imparts comprises of the weight of vessel and an effect from the water moving along
with the vessel. Such an effect, expressed in terms of weight of water moving with the
vessel, is called added mass. The following order of magnitude of the hydrodynamic
added mass is normally recommended [7].
Mh = 0.05 DWT to 0.10 DWT : For Bow impacts
Mh = 0.4 DWT to 0.5 DWT : For sideways impact.
Work is restricted to only bow impacts and hence the mass has been increased by
5% to take into account the effect of the surrounding water during collision.
3.3. The force-time relationship
The impact force is dynamic in nature. The time history as established by Woisin. G
[7] is used. The maximum load Pmax occurs at the very beginning of the collision and
only for a very short duration (0.1 second to 0.2 second) as shown in Figure 1 and
then drops to a mean of value of Pmean ≈ 0.5Pmax. The total collision may last for 1
second to 2 seconds. The forcing function is suitably simplified without introducing
much error. The force–time relationship used is as shown in Figure 2.
ImpactForce(P)
0
Time (t)
Pmax = Maximum Impact Force
P(t)= Average Impact Force
Figure 1 Typical vessel impact force time history

Pmax = Maximum Impact Force
0
ImpactForce(P)
Pavg = Pmax / 2
1 sec.
Time (t)
0.2 0.3
Figure 2 Simplified force – time history
4. MODELING OF PIER
To cover all the cases of static and dynamic loads, the choice of finite element has to
be made carefully. The force is applied over an area on the selected geometry of the
pier. The 3D-8 Noded, Isoparametric formulation is used for both, the wall type of
pier and the circular pier. The hollow piers have a very thick staining (0.6 m) and
hence the use of a thin shell element is not found to be suitable. Figure 3 and 4
indicate the finite element model of the piers along with the orientation.
Figure 3 Discretisation of wall type pier Figure 4 Discretisation of hollow pier
5. CALCULATING THE DYNAMIC AMPLIFICATION FACTOR
(DAF)
5.1. Static domain
The force due to collision is applied as a static force to the descritised pier at the
predefined height and angle. Using the Finite element technique the static deflections
are calculated. The force applied here is the Pmax as shown in Figure 2.
5.2. Dynamic domain
The problem in the dynamic domain can be best described as a case of forced
vibration of a multiple degree freedom system. For the dynamic analysis, the

Newmark method of direct integration has been used. The forcing function is divided
into discrete time intervals Δt apart.
5.3. The Dynamic Amplification Factor (DAF)
DAF is calculated from the results of the above two steps that is the ratio of the
dynamic displacement to the static displacement ( staticdynamicDAF  ). The DAF is
calculated considering all the nodal displacements of the pier just above the height of
collision. The maximum ratio is considered for plotting the graphs. It was also
observed that this ratio is greatest for the nodes at the top of the pier.
6. THE NEWMARK SCHEME AND FORMATION OF THE MASS
AND DAMPING MATRICES
The pier is represented as a multiple degree of freedom system and is subjected to the
dynamic load. The equations of equilibrium for a finite element system of motion are:
-
          tPyKyCyM 

(3)
where [M], [C] and [K] are the mass, damping and stiffness matrices and {Pt} is the
external load vector i.e. the collision force. {

y }, {

y } and {y} are the acceleration,
velocity and displacement vectors of the finite element assemblage.
6.1. Newmark method of direct Integration
The equations in the Newmark Integration scheme are [7]
Δt]yδyδ)[(yy ΔttttΔtt  



1 (4)
2
½ Δt]yαyα)[(yyy ΔtttΔtttΔtt  



 (5)
where  >= 0.5;  >= 0.25(0.5+) 2
6.2. Forming the Mass Matrix [M]
There are two ways of forming the mass matrix; one is the consistent mass matrix,
which is related to the volume of element through the shape function. The other is
lumped matrix, which can be taken in proportion to the area or volume of the element
at a given node. Herein the consistent mass matrix has been used. For generation of
the element mass matrix of a 3D solid element with 3 degrees of freedom for each
node mass is placed in each direction (u, v, w) for each node. Global mass matrix is
assembled from the element mass matrix.
6.3. Contribution of the dead weight of the superstructure
In the mass matrix, at the topmost nodes of the given pier configuration the dead
weight of the superstructure received (say 2000 T) is converted to mass. This enters
the pier system only at the topmost nodes. This Dead weight of the superstructure
plays a significant role in the Eigen values.

6.4. Damping
The Raleigh Damping method has been used to consider 5% damping which is the
normal practice for concrete structures. The Raleigh Damping method is found to be
suitable for the Newmark method. The two equations used are as follows –
C= M + K (6)
iii ξωβωα 22
 (7)
where
ωi frequency for ith
mode.
ξi damping ratio for ith
mode
Damping increases as the vibration mode transgresses from the 1st
mode to higher
modes. In applying this procedure to a practical problem the modes i and j with
specified damping ratios are to be chosen to ensure reasonable values for damping
ratios in all the modes contributing significantly to the response. In the present work
the damping ratio is considered to be 5% in the first mode of vibration which is
considered to increase to 7% in the 5th
mode of vibration. Thus using these values the
Raleigh damping coefficients by substituting in equation 7; two equations for  and 
are obtained. Substituting these values along with the already established [K]
(stiffness matrix) and [M] (mass matrix) we obtain the Raleigh damping matrix [7].
The Raleigh damping matrix is evaluated with = 5% and 5 = 7% these are well
known factors for concrete.
7. PROGRAMMING
The programming for finite element method is done in MATLAB. The programs
created specially for the present work were validated before use. The Algorithm for
the program is as under:-
Main program: - Calls all subroutines. Input data.
1. Subroutine for shape functions and isoparametric formulation.
2. Subroutine for nodal co-ordinates.
3. Subroutine for support specifications.
4. Formation of the element stiffness matrix [Ke] and element mass matrix [Me].
5. Assembly of the global stiffness matrix.
6. Assembly of the global Mass matrix.
7. Subroutine for eigen values and data input for dynamic analysis.
8. Formation of the force vector for static analysis.
9. Solving F=Kxto get static displacements
10. Formation of the force vector for dynamic analysis.
11. Solving [M]{y’’} + [K]{y} = {P(t)} to get undamped dynamic displacements using
Newmark method.
12. Solving [M] {y’’} + [C] {y’} + [K] {y} = {P (t)} to get damped dynamic
displacements using Newmark method.
13. Store results and calculate the DAF.

14. Repeat steps 9 to 13 for 600 t and 400 t vessels
15. Repeat steps 9 to 14 for varying angle of Impact i.e. 30o
, 25o
, 20o
, 15o
and 10o
.
16. Repeat steps 9 to 15 for varying height of location of Impact i.e. 5 m, 10 m and 15 m
from base.
Steps 1 to 16 are repeated for different geometries of pier considered for this work.
8. DESCRIPTION OF THE ANALYTICAL WORK
Twenty different geometries as tabulated in Tables 2 to 5 were selected for analyzing
for the collision. The slenderness ratio (λ=l / r) is used as a measure representing all
the three dimensions of the pier. Graphs of DAF versus slenderness ratio are plotted.
Each of the above piers is subjected to the collision force at three different
predefined heights from the base of pier. The collision force is applied at 5 m, 10 m
and 15 m from the base of the pier. In addition to the above two variations another
parameter has been introduced, that is the angle of impact. The bow collision force is
applied at an angle of 10o
to 30o
in steps of 5o
. The angle is measured with respect to
the direction of flow of water. For a particular geometry, variation of DAF is studied
with respect to the angle of impact θ.
9. RESULTS
The Dynamic amplification factors versus the slenderness ratio for impact at different
heights, wall type piers and hollow circular piers with varying angles of impact are
plotted in Figures 5 to 9. The maximum values of DAF i.e. for an impact angle of 30o
presented in the form of a polynomial equation are given in Table 8 for use in
equation 6 below
32
2
1 CλCλCDAF  (8)
where, C1, C2 and C3 are given in Table 7 and are to be used as the case may be.
Table 7 Constants to obtain DAF
Applicable to C1 C2 C3
Wall pier with impact at 5 m 0.0017 0.1096 2.7393
Hollow Circular pier with impact at 5 m 0.0024 0.0966 1.9964

Figure 5 Dynamic amplification Vs λ with 5% damping & impact angle=30o
1.7204
1.6323
1.4745
1.3377
1.2316
1.6074
1.5202
1.3775
1.2844
1.1824
1.5559
1.4699
1.3342
1.2605
1.1718
1.146
1.0804
1.0459
1.018
1.222
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
10 11 12 13 14 15 16 17 18 19 20 21 22
Slenderness ratio
DynamicAmplificationFactordyn/static
Wall pier, Impact at 5 m from base
Wall Pier, Impact at 10 m from base
Hollow Cicrular Pier, Impact at 5 m from base
Hollow Circular Pier, Impact at 10 m from base
Hollow Circular Pier, Imapct at 15 m from base
1.6611
1.5751
1.4265
1.3127
1.2084
1.5733
1.4875
1.3502
1.2703
1.1805
1.5317
1.4471
1.3152
1.2507
1.1707
1.2111
1.1357
1.0735
1.0388
1.0131
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
10 11 12 13 14 15 16 17 18 19 20 21 22
Slenderness ratio 
DynamicAmplificationFactordyn/static
Hollow Circular Pier,Impact at 5 m from base
1.6105
1.5257
1.3847
1.2909
1.1941
1.5433
1.4586
1.3259
1.2576
1.1791
1.5101
1.4266
1.3043
1.2418
1.1697
1.2014
1.1264
1.0673
1.0324
1.00861
1.1
1.2
1.3
1.4
1.5
1.6
1.7
10 11 12 13 14 15 16 17 18 19 20 21 22
DynamicAmplificationFactordyn/static
Hollow Circular pier, Impact at 5 m from base

10. OBSERVATIONS AND DISCUSSION
 Figures 10 and 11 show the vibrations of a wall type and a hollow circular pier of
special significance is the nature of punching into the hollow circular pier, when
collision occurs. This particular shape of distortion is noteworthy; the result of impact
or collision on a hollow circular pier is clearly visible in Figure 11.
 Figure 12 shows the response of a wall type pier and Figure 13 indicates the response
of a hollow circular pier. The undamped and damped responses can be seen. The peak
can be observed in the initial stages in the graph. As the force no longer exists the
vibrations can be seen to be about the zero deflection line. The time period of the wall
type pier is seen to be lesser than the circular pier suggesting the greater flexibility of
the circular pier over the wall type pier.
1.5662
1.4819
1.3473
1.2713
1.1917
1.5164
1.4325
1.3103
1.246
1.1778
1.4906
1.4079
1.2965
1.2336
1.1688
1.1924
1.1179
1.0615
1.0264
1.0044
1
1.1
1.2
1.3
1.4
1.5
1.6
10 11 12 13 14 15 16 17 18 19 20 21 22
Wall Pier, Imapct at 15 m from base
Hollow Circular Pier, imapct at 5 m from base
1.5265
1.4424
1.3194
1.2533
1.1895
1.4917
1.4083
1.3001
1.2353
1.1766
1.4725
1.3905
1.2893
1.2259
1.168
1.184
1.1099
1.0561
1.0213
1.0004
1
1.1
1.2
1.3
1.4
1.5
1.6
10 11 12 13 14 15 16 17 18 19 20 21 22
Wall Pier, Imapct at 15 m from base

Figure 10 Displacement of wall type pier Figure 11 Displacement of hollow circular
at each time interval at each time interval
 The graph of Slenderness ratio (X-axis) versus the DAF (Y-axis) (Figure 5 to 9)
shows that as the slenderness ratio goes beyond 17 the DAF is nearly 1.00 for circular
columns while it is higher for wall type of piers. Thus slender piers may prove to be
advantageous and dynamically sound. This consideration goes in line with the general
principles advocated by structural designers of reducing the stiffness of the structure.
Figure 12 Un-damped and damped response of wall type pier

Figure 13 Un-damped and damped Response of hollow circular pier
11. CONCLUSIONS
 The DAF obtained using equation 8 or from the graphs 5 to 9 will be useful to
reasonably cater for the dynamic effects of a ship collision on a bridge pier.
 The circular tapering piers fare better and are generally felt to be dynamically more
efficient over the rectangular wall type of piers provided the local deformation near
the hit area is addressed.
REFERENCES
[1] Frandsen, A.G., Accidents Involving Bridges, IABSE Colloquium, Copenhagen,
1983, pp 11-26.
[2] Indian Standard 4651 (Part III) –1974, “Code of practice for planning and Design
of ports and Harbors, Part III Loading
[3] Indian Roads Congress specifications for Foundations and Substructures No. 78-
2000.
[4] DNV Guidelines for structures exposed to ship collisions.
[5] Ole Damgard Larsen, Ship collisions with Bridges, IABSE –SED 4, pp 53-76
[6] Woisin.G and Gerlach, on estimation of forces developed in collisions between
ships and offshore lighthouses, Stockholm 1970.
[7] Bathe and Wilson, Numerical methods in FEM.
[8] Prof. P.T. Nimbalkar and Mr. Vipin Chandra. Estimation of Bridge Pier Scour for
Clear Water & Live Bed Scour Condition. International Journal of Civil
Engineering and Technology, 4(3), 2015, pp. 92 - 97.
[9] Dr. Avinash S. Joshi Dr. Namdeo A.Hedaoo and Dr. Laxmikant M. Gupta.
Transient Elasto-Plastic Response of Bridge Piers Subjected To Vehicle
Collision. International Journal of Civil Engineering and Technology, 6(10),
2015, pp. 147 - 162.
[10] Adnan Ismael, Mustafa Gunal and Hamid Hussein. Use of Downstream-Facing
Aerofoil-Shaped Bridge Piers to Reduce Local Scour. International Journal of
Civil Engineering and Technology, 5(11), 2014, pp. 44 - 56.

Bridge Pier Collision Forces

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