Communications and Network, 2013, 5, 641-648 Published Online September 2013 (
Copyright © 2013 SciRes. CN
RSS Based Bridge Scour Measurement Using Underwater
Acoustic S ensor N etworks
Prabhat Dahal, Dongming Peng, Yaoqing (Lamar) Yang, Hamid Sharif
Department of Computer and Electronics Engineering, University of Nebraska-Lincoln, Lincoln, USA
Received July 2013
Bridge Scour is one of the major causes of bridge failures all around the world and there have been significant efforts
for its detection and measurement using different acoustic approaches. In this paper, we propose and investigate an ef-
fective method to utilize Received Signal Strength (RSS) for measuring scour depth where acoustic sensors are dep-
loyed. We also extend a statistical testing to determine the difference in signal levels at the sensor nodes prior to and
after scour formation and subsequently determine the actual depth of scour. Additionally, we make an attempt to eva-
luate underwater distance and depth using signal strength perceived at the receiver which makes it free from the re-
quirement of accurate receiver-sender synchronization in contrast to Time of Flight (ToF) or Time of Arrival (ToA)
techniques. The scour depths are eventually compared for the conditions when the bottom is composed of a single or
multiple layers. The simulation results clearly show that different depths are calculated for the case of multilayered bo t-
tom (0.8 to 3.9 meters for instance) as compared to a constant depth of 2 meters for the case of a single layered bottom.
Keywords: Bridge Scour; Received Signal Strength; Acoustic Wave Propagation; Underwater Acoustic Sensor
Network s
1. Introduction
Bridge scour is considered to be one of the main causes
of bridge failures all over the world. For instance, tenta-
tively 60% of more than 1000 bridge collapses in the
United States in the past 30 years are linked to the scour
of bridge founda tions [1]. The problem of such gravity is
further aggravated by the fact that the annual cost for
scour-related bridge failures only, was estimated to be
around $30 million, according to a study by the Trans-
portation Research Board in 1997 [2].
The process of formation of a bridge scour can be cre-
dited to the erosive action of flowing water. Flowing
water tends to excavate and carry with it sediment mate-
rials from the water bed and from around the bridge col-
umns, piers and abutments. Formation of bridge scour is
a complex and dynamic process that depends on factors
such as the water depth, pier and abutment shape and
width, the velocity of flow, composition and material
properties of the sediments underneath the water body,
and many more. Normally, three different types of scours
are considered-local scour, contraction scour and degra-
dational scour. Local scour is the type that we are dealing
with in this paper, which is the washing away of sedi-
ments from around piers and abutments creating scour
Several means have been tried for the measurement of
scour depth in the field. Early on, radar and sonar were
employed to successfully measure t he sco ur dep th. R adar
sends out electromagnetic waves to the water bottom,
which then reflects off the bottom interface and reaches
the transmitter. Similarly, sonar is a technique that uses
sound propagation in the same way as a radar does. So-
nar is specifically used for underwater purposes. The time
taken by the radar and sonar waves to travel from trans-
mitter to the receiver after undergoing reflection off the
bottom is used to compute the range and hence the depth.
Despite being successful in measuring scour depth, the
use of radar and sonar is limited by the fact that they are
usually only used to determine the final stage of the se-
diment distribution around the pier and there is no conti-
nuous monitoring. In recent years, techniques employing
Time-Domain Reflectometry (TDR) [3] and Fiber Bragg
Grating (FBG) sensors [4] have emerged to facilitate
real-time monitoring of bridge scour. It is to be noted that
several mechanical systems also exist for the measure-
ment of bridge scour, with one of them being sliding
magnetic collar [5]. However, the major issue with this
system is that it suffers from the problem of jamming and
cannot be reversed for reuse.
Recently, water bottom sensor nodes have been consi-
Copyright © 2013 SciRes. CN
dered to extend applications beyond underwater environ-
ment monitoring like pollution monitoring, oceanographic
data collection and offshore exploration, and used for
bridge monitoring and tactical surveillance. In order to
achieve this, we need to establish communication be-
tween underwater devices. Underwater Acoustic Sensor
Networks (Underwater-ASN) consist of a variable num-
ber of sensors that are deployed to conduct the task of
collaborative monitoring over a particular area of interest.
However, there are several hindrances when it comes to
the deployment of underwater acoustic sensors. Under-
water acoustic communications are mainly influenced by
path loss, noise, multi-path, Doppler spread and high and
variable propagation delay. All these factors combine to
affect the temporal and spatial variability of the under-
water acoustic channel and make the available bandwidth
of the Underwater Acoustic (UWA) channel limited and
dramatically dependent on both range and frequency. Pro-
vided that underwater acoustic channel has several com-
plexities as such, long-range systems may have a band-
width of only a few KHz, while short-range systems may
have a more than a hundr e d KHz bandwidth.
The rest of the paper is organized as follows: Section
II describes how distances or depths can be estimated by
Received Signal Strength (RSS) method. Section III pro-
vides a detail of the proposed architecture explaining how
the sensors are positioned and the signals are received to
make estimations. Section IV includes the simulation
results that point out the deviation in scour depth from
normal when multilayered bottom is taken into account.
Finally, Section V presents our co nc lusion s.
2. RSS Based Range Estimation
There are different techniques that exist for distance mea-
surement in terrestrial wireless communications such as
Time Difference of Arrival (TDoA), T i me of Arrival (ToA),
Received Signal and Strength Indication (RSSI), and An-
gle of Arrival (AoA), to name a few. TDoA uses two
different transmission-media, e.g. Radio Frequency (RF)
and acoustic wave, to estimate the distance between two
nodes. This estimation is based on different arrival times
due to the difference in propagation speeds through the
same medium [6]. But RF is not quite applicable for un-
derwater usage because of its limited propagation in wa-
ter medium caused by high attenuation [7], and therefore,
TDoA is not used in aquatic environment. In contrast,
AoA method is dependent on a direct line-of-sight (LOS)
path from a transmitter to a receiver. This means that
mul t i -path components of the same signal may appear as
signals arriving from different (unwanted) directions and
can lead to erroneous results in AoA measurements [8].
ToA is extensively used for range measurement in short-
range Underwater Acoustic Sensor Networks (UASNs)
[9,10]. As its name refers, it utilizes the time taken by an
acoustic wave to travel from the transmitter to the re-
ceiver [8]. The time taken for travel is used to calculate
the distance according to the underwater sound velocity.
It is worth mentioning that for accurate results using ToA,
the sender and receiver must be accurately synchronized.
For this work, we attempt to make use of a new dis-
tance measurement technique (here, depth) based on Re-
ceived Signal Strength (RSS) for short range underwater
acoustic communications. Unlike ToA, in RSS, wireless
devices use the received signal power to measure the
distance between the sender and the receiver. Seen this
way, synchronization is not a problem as in ToA, but
simplifying the distance/transmission-loss relationship
can be quite complex. The work in [11] shows that the
function to express distance in terms of transmission loss
required by RSS for distance calculation uses the Lam-
bert W function. The distance function is derived after
sufficient iteration functions. The authors claim that a
very accurate calculation of distance can be made in less
than four iterations. We utilize the RSS based range es-
timation approach as proposed by [11] for our research.
Sound loss in water is classified as spreading loss and
attenuation loss. Spr eading loss includes spherical 1) and
cylindrical 2) losses, which is caused by the expansion of
an acoustic wave as it propagates through a medium, and
attenuation includes absorption, scattering and diffrac tion
[12]. Accurate values for attenuation can be measured by
considering the effects of transmission medium (salinity,
pressure, temperature and many others) and environment
parameters like air bubbles within water volume, absorp-
tion by the sediments, reflection off the surfaces and
scattering. Here, only transmission medium parameters
are considered for the ease of calculation. Transmission
losses can be mathematically expressed as
20log( )TLsph Dist=
10log( )TLcyl Dist=
where the first equation gives an expression for the trans-
mission loss with respect to spherical propagation of the
wave and the second equation is that with respect to cy-
lindrical propagation. So the general expression for trans-
mission loss in sea water [12] is given by
10TLtotalTLsph TLcylDist
= ++
( 3)
where α is the absorption coefficient in sea water as ex-
pressed in (4), given by the Thorps absorption coeffi-
cient [13], which depends only on frequency f below 50
0.1 40
1 4100
= +
Here, the factor 1.0936 is used to change the unit of
the coefficient from dB/kyd to dB/km. The authors in [11]
Copyright © 2013 SciRes. CN
consider spherical spreading to be good enough to model
a wide range of available data. Hence, (3) reduces to a
total transmission loss given by
20log() 10TLtotalDist Dist
= +
Equation (5) means that the total transmission loss can
be expressed in terms of the path loss due to spherical
spreading and absorption. Now, the distance can be cal-
culated using the following rela t ion as expre s s e d in [11],
(6 )
where W is the Lambert function.
Given that we have A1 = 10000/(λα), A2 = 1/A1 and A3
= λTL, we can wri t e ,
( )
DistAW Ae=××
(7 )
where Dist refers to the distance from the sensor to the
point of reflection and back. The scour depth that we
seek to measure will be half the distance measured.
3. Communication Architecture
Underwater Wireless Acoustic Sensor Networks (Under-
water-ASN) are equipped with a number of acoustic sen-
sors that work collectively to achieve the monitoring
requirement imposed upon the network. The deployment
of the sensors depends on various dynamic underwater
environments. However, the overall Un derwater-ASN can
be broadly categorized into two basic communication ar-
chitectures: tw o di mensional arch itectur e, wher e the nodes
are attached near to the bottom, and three dimensional
architecture, where the nodes float at different depths
inside t he wa ter body [14].
3.1. Architecture for Depth Measurement
Despite the fact that there are three dimensional and two
dimensional architectures for underwater-ASN, the for-
mer is generally used to provide a complete sampling of
the 3D underwater environment, whereas for underwater
depth measurements, the latter is preferred. In a three
dimensional architecture, the sensors float at different
depths within the water volume by means of floating
buoys using wires or winches. In contrast, the two di-
mensional architecture is the one in which the sensor
nodes are organized in a cluster fashion and remain stat-
ically anchored at or near the water bottom as shown in
Figure 1.
The sensor nodes make use of acoustic means to com-
municate with each other. A central hub exists for each
cluster of the sensor nodes and is known as the underwa-
ter gateways (underwater-gateways). These hubs act as
means to transfer the data collected from the anchored
nodes to the surface station and to achieve this, they use
a set of vertical and horizontal transceivers. While the
horizontal transceivers are used for establishing commu-
nication with the sensor nodes to collect monitored data
and send some commands, the vertical ones are used to
relay the collected data to the surface station. Since the
surface station is required to handle multiple communi-
cations with the underwater-gateways, it is equipped with
a transceiver designed specifically for this purpose. In
addition, it also has a long range radio transmitter for the
final transmission of collected data to the onshore sink.
Figu re 1. Two dimensional unde rw ate r -ASN Architecture.
Copyright © 2013 SciRes. CN
3.2. Proposed Architecture
The architecture proposed in this paper for the case of
bridge-pier scour depth measurement is essentially a two
dimensional static architecture as shown in Figure 2. A
number of sensor nodes are fixed in each bridge pier near
to the water bottom. The nodes in each pier form a clus-
ter and have their own underwater-gateway. The nodes
are oriented to direct acoustic waves to the bottom and
receive the reflected waves. The collected data (signal
strength in this case) is sent through acoustic links to the
gateway located in the same pier as the sensor nodes. The
underwater-gateway sends the data to the surface station
(which can be located in the bridge structure near the
water surface) for final relay to the onshore sink.
3.3. Signal Analysis
The underwater acoustic channel is complex, exhibiting
different behaviors under different conditions. The speed
of sound that varies with dep th cau ses propaga tion dela ys.
In addition, scattering, multipath interference are exam-
ples of phenomena that make the UWA channel complex.
Different research suggests different ideas. Rayleigh fad-
ing was assumed in [15]. As research in UWA progressed,
it was proposed that several distinct paths called eigen-
paths exist in an UWA channel [16]. The signals exist
over all these paths. Moreover, each path contains sub
paths called eigen-rays, comprising of a dominant path
and other smaller paths. The number of eigen-rays reach-
ing the receiver is a Poissons distribution. Saleh-Valen-
zula model [17] has been proposed for UWA networks in
[18]. According to S-V model, usually, multipath signals
of the same pulse arrive at the receiver in clusters and
two Poisson models are employed to model the path ar-
rivals, one for the first path of different clusters and the
other for the rays within each cluster. In an Ultra-Wide
Band-SV (UWB-SV) model, the k-th path within the l-th
cluster is denoted by αkl(u) whose magnitude, |αkl(u)|,
follows a Rayleigh distribution.
According to [18], the reflected signal from the bottom
received by senso r m is give n by
( )( )
m kl
Z uunu
(8 )
which is received by summing all the received signals in
a pulse duration an d γ is the received signal strength.
For M sensor nodes, y= [ y1, y2, y3, ..., yM], then,
( )
fy fy
and the unique solution of the maximum- likelihood es-
timate of the signal poweris g iven by
= −
where, ym = |Zm(u)| follows Rayleigh distribution, σ2 is
the variance of noise n(u) with zero mean complex Gaus-
sian distribution and M is the number of sensor nodes.
Figure 2. Proposed underwater-ASN architecture.
Copyright © 2013 SciRes. CN
Let us define the estimates of received signal power (θ
= γ2/2) before and after scour formation as
( )( )
11 11
ˆˆ and
ML mML m
The estimates are gamma distributed (parameter k and
θ). For sufficiently large number of sensor nodes, the
estimates tend to normal distribution with mean, µ =
and variance = 2. Then,
= −
= −
Given that a scour has been formed, the signal incident
at the bottom now has to undergo an additional path
through water and be reflected off the bottom comprising
of a dense layer of water and a solid half space. It is ob-
vious that the signal reaching the sensor in this case
weakens in strength, owing to the additional transmission
loss and the reflection loss. We seek to calculate the dif-
ference in the estimate at the receiver and difference in
mean of the two estimates is employed for this. In order
to take into account, the effect of the entire distribution
of the estimates, a 95% Confidence Interval (C.I.) is
created that will provide us with a range [a, b], as given
in (15) and (16) between which the difference of mean of
the estimates is likely to exist. We have proven this
through the simulations that the higher the number of
sensors, the more accurate the confidence interval is. For
a 95% significance level (two tailed), the C.I. is given by,
( )
1 212
. .1.96CI
µµ σ
= ±−
(14 )
such that,
( )
1 212
µµ σ
( )
1 212
µµ σ
(1 6)
where a and b are the lower and upper limits of the con-
fidence interval respec tively and 1.96 is the z-value from
the z-table correspo nding to the 95% significance level.
If a and b are both positive in C.I. = [a, b], we are 95%
confident that there has been a decrement in received
signal power. Assuming similar conditions of water and
the environment, the signal has probably travelled addi-
tional path (depth) and there could be a probable scour
forma tion which can be checked for.
The difference in signal power (γ2/2) thus estimated is
due to the additional Transmission Loss and Reflection
Loss (RL). From Figure 3(a), for the condition prior to
scour formati on, we have,
1 011SLSLTL RL= −−
where SL1 = 20log (
) is the received signal level at the
Similarly, after the scour has been formed, as shown in
Figure 3(c), we have the expression for received signal
level at the sensors as,
2 0112 2SLSLTLRL TLRL=−−− −
where SL2 = 20 log (
) is the received signal level, TL2
is the transmission loss in water with depth d0 and RL2 is
the reflection loss from the layered bottom, with the
depth of se di ment lay e r be i ng d1.
From (17) and (18), we have,
20log2 2 1RL TLRL
= +−
where RL2 is the reflection loss from the layered bottom
expressed as RL2 = 20log (Rb).
Provided that we make an estimate of γ1 and γ2, we can
calculate RL1, TL2 for a particular depth d1 and this
would lead us to estimate the depth d0 using (7). The total
depth would then be D = d0 + d1. Despite the fact that d1
is the depth of the sediment layer, it should be noted that
this layer is unconsolidated, which is considered liquid
and would n ot provide s upport require d f o r the pier.
In contrast, when the bottom after scour formation is
considered to be a single layered half space, (19) be-
20log 2TL
with TL2 being accountable for the entire depth D = d0
and d1 = 0.
Figure 3. Reflection and Transmission Losses when (a) no
scour has been formed (b) the bottom is a single layer half-
space and (c) the bottom is composed of unconsolidated
sediment layer over solid half-space.
Copyright © 2013 SciRes. CN
4. Simulation Results
The simulation results presented in this section are based
on assumed values as given in Table 1 and were imple-
mented in MATLAB on a Intel(R) Core(TM)2Duo 2.00
GHz processor. The frequency of acoustic wave chosen
is 10 KHz which gives a Thorps absorption coefficient,
α, equal to 1.1498.
For a significance level of 95%, we have the Confi-
dence Interval (C.I.) as
1 212
. .()1.96CI
µµ σ
(21 )
where, the z-value 1.96 corresponds to 95% significance
level from the z-table.
Different values of received signal strengths at the sen-
sor nodes are assumed for two different conditions- the
initial one, where the acoustic signals reflect off the solid
half layered bottom, which is taken as a reference; and
the second one, where a scour has been formed and the
bottom has shifted to a certain depth from the reference
level. For the second case, as per our assumption, the
bottom consists of a dense liquid layer atop a solid half
layered bottom, thereby causing the reflected signals
reaching the sensors to be of lesser strength than in the
initial condition.
The graphs in Figure 4 present different instances of
calculated C.I. that indicate that we are 95% confident of
the difference in signal powers between the initial and
the latter condition being in between the lower limit (the
bar on the left) and the upper limit (the bar on the right),
for the case of 50 sensor nodes. The line between the
upper limit and the lower limit in each pair of bars indi-
cate the actual difference in signal levels.
Talbe 1. Assumed Data For Water Bottom Layers.
Layer Thickness cp ( m/s)a cs (m/s)b ρ (g/cm3)
1 1 1700 0 1.8
2 4700 1900 2.5
a Compre s si on wave velocity; bShear wave velocity.
Figure 4. Confidence Interval for difference in signal stren-
gth at the receiver (M = 50).
Figure 5 presents similar graphs for the cases of the
number of nodes being 5 and 80 respectively. It can clear-
ly be seen that, as the number nodes increases, the 95%
C.I. of the estimate of difference in signal powers nar-
rows and gets closer to the actual value. The result is the
opposite when the number of sensor nodes is decreased.
This shows that, for our C.I. to be a more accurate repre-
sentation of difference in signal powers, a greater number
of sensor nodes is preferred.
The second section of the simulation, as shown in Fig-
ure 6, comprises of the part where the effect of layered
bottom is compared to non-layered bottom with respect
to scour-depth measurement. For different data, as given
in Table 1, scour depths are measured for the condition
when the bottom is composed of a single layer, and the
condition when the bottom is composed of two layers (a
sediment layer of a certain thickness d1, treated as liquid
and a solid bottom). The graphs present the results for the
signal powers in case 1 of Figure 5, for the case of 80
sensor nodes.
Figure 6 expresses that the total scour depth, for the
same received signal strength, depends on the thickness
of the sediment layer. The bars represent the total depth
(including the additional water depth, d0, and the sedi-
ment layer depth, d1). For each depth, different thickness
Figure 5. Confidence Interval for difference in signal
strength at the receiver (M = 5, M = 80).
Figure 6. Comparison of scour depth with and without
layered bottom. Bars for the layered bottom show the vari-
ation in total depth with the depth of the sediment layer.
Copyright © 2013 SciRes. CN
of the sediment layer is considered and the water depth is
calculated to account for the total loss in signal strength
as compared to the reference level. As the sediment layer
depth increases (shown by the lower portion of the bars),
the corresponding water layer depth also increases, thus
increasing the total scour depth. For instance, for a 24.63
dB signal loss measured at the receiver (with respect to
the condition when no scour was formed), an assumption
of 0.5 meters sediment layer thickness leads to a total
scour depth of approximately 0.8 meters. Likewise, for
the same signal loss measured, assuming a sediment layer
depth of 2 meters gives a total scour depth of around 1.8
However, the scour depth without considering the
layered approach (when the bottom is a single layered
half space), as shown by the straight line in Figure 6, is
constant and seems to deviate from the depths calculated
for a layered bottom. This shows that the single layered
approach, which is inconsistent with the real underwater
scenario as pointed out in literature, gives misleading
values for scour depth and the effect of sediment layer
thickness on scour depth cannot be neglected. The for-
mation of dense sediment layer above solid water bottom
results in different val ue s of scour depth.
5. Conclusion
Scour holes that ten d to make bridge foundatio ns weaker
to collapses sh ould be accurately measured. W e have suc-
cessfully shown the RSS for acoustic sensor networks.
Unlike ToF or ToA methods for range measurement in
underwater environment, in this paper we provided RSS
approach to measuring bridge scour depth. Simulations
show that the estimation of scour depth tends to approach
the real depth as the number of acoustic sensors em-
ployed is increased. Also, since in real underwater condi-
tions, erosion of sediments leads to the formation of a
dense water layer over the water bottom due to the dis-
solved sediments, an effort is made to compare the effect
of layered nature of water bottom on scour depth to that
of non-layered approach- the layered approach giving
more accurate values for scour depth. For instance, as
seen in the simulations, a sediment layer depth of 1.5
meters results in a total scour depth of 2.8 meters and this
value increases with the thickness of the sediment layer.
In contrast, when the sing le layered bottom is considered,
the resultant scour depth is about 2 meters. However,
since a single layered bottom assumption is fairly unrea-
listic, the result obtained could be misleading.
6. Acknowledgments
This work was sponsored in part by an Interdisciplinary
Research Grant of the University of Nebraska-Lincoln.
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