| 487 |
| 67/4 |
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES
V
G 2023
GEODETSKI VESTNIK | letn. / Vol. 67 | št. / No. 4 |
SI  |  EN
ABSTRACT IZVLEČEK 
KLJUČNE BESEDE KEY WORDS
deformation analysis, robust IWST method, Pelzer method, 
bridge, total station
deformacijska analiza, robustna metoda IWST, Pelzerjeva 
metoda, most, elektronski tahimeter
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |
UDK: 528.482 
Klasifikacija prispevka po COBISS.SI: 1.02
Prispelo: 9. 6. 2023
Sprejeto: 25. 9. 2023
DOI: 10.15292/geodetski-vestnik.2023.04.487-504
REVIEW ARTICLE
Received: 9. 6. 2023
Accepted: 25. 9. 2023
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović
DEFORMACIJSKA ANALIZA 
MOSTU RATKOV LAZ PO 
PELZERJEVI METODI IN 
METODI IWST
DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING 
PELZER AND IWST METHOD
The paper discusses the application of geodetic methods 
of deformation analysis of reinforced concrete structures 
made of prestressed concrete. In the paper, two independent 
methods of deformation analysis are applied on the example 
of the Ratkov Laz bridge in Montenegro, based on two 
epochs of geodetic measurements in a 3D geodetic network, 
which consists of the reference part of the network and 
points on the bridge. The results of the Pelzer’s method 
and the robust IWST method were analyzed. Although 
similar displacement vectors are obtained using the two 
methods, there are some differences in the identification of 
unstable points on the bridge. The IWST method identified 
significantly fewer points as unstable compared to the Pelzer’s 
method. The aforementioned methods of deformation 
analysis are of great importance in the geodetic observation 
of all types of engineering facilities.
V prispevku je obravnavana uporaba geodetskih metod 
deformacijske analize armiranobetonskih konstrukcij iz 
prednapetega betona. Na primeru mostu Ratkov Laz v Črni 
gori sta uporabljeni dve neodvisni metodi deformacijske 
analize na podlagi dveh epoh geodetskih meritev v 
3D-geodetski mreži, ki je sestavljena iz referenčnega dela 
mreže in točk na mostu. Analizirani so bili rezultati 
Pelzerjeve metode (postopka Hannover) in robustne 
metode IWST. Čeprav so z obema metodama izračunani 
podobni vektorji pomikov, obstajajo nekatere razlike pri 
identifikaciji nestabilnih točk na mostu. Z metodo IWST 
je bilo kot nestabilnih identificiranih precej manj točk kot 
s Pelzerjevo metodo. Opisani metodi deformacijske analize 
sta zelo pomembni pri geodetskem opazovanju vseh vrst 
inženirskih objektov.

| 488 |
| 67/4 | GEODETSKI VESTNIK  
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES
SI | EN
1 INTRODUCTION 
The characteristic phases of the construction of concrete bridges refer to the construction of foundations, 
abutments, coastal and river piers, as well as supporting and roadway construction structures. In addition 
to the preparatory works, all the mentioned phases must be monitored by geodetic support. A special 
geodetic micro-network, which consists of the reference part of the network and points on the bridge, is 
being designed for monitoring the construction of bridges. Bridges represent complex engineering facilities 
from the geodetic aspect of monitoring their construction. Although geotechnical special sensors, such 
as precise inclinometers (Xingmin et al., 2005), accelerometers (Olaszek et al., 2020), fiber-optic sensors 
(Marković et al., 2019), can be used for monitoring purposes, the traditional geodetic method to observing 
these structures is based on repeated geodetic measurements of horizontal directions, zenith angles and 
slope distances in geodetic network using conventional or robotic total stations with high performance.
The traditional concept of geodetic deformation measurements of bridges is based on a large number of 
repeated geodetic measurements, from which quality indicators such as accuracy, reliability, precision and 
sensitivity of the geodetic micro-network are obtained. The specified parameters can also be obtained in 
the process of designing geodetic micro-networks for the purposes of monitoring the specified categories 
of objects, through the procedure of previous estimation of the accuracy and reliability analysis of geodetic 
measurements and unknown parameters, in the case of 3D point coordinates of the geodetic network. 
The main task of deformation analysis is the investigation of displacements of an objects in relation 
to space and time. According to the hierarchy of deformation analysis models, there are congruence 
and kinematic as descriptive models and static and dynamic, as cause-response models (Heunecke and 
Welsh, 1999). Although the cause-and-response relationship of the appearance of deformation is often 
examined nowadays, congruence models are still most often used in deformation analysis procedures 
in engineering practice (Savšek and Ambrožić, 2023). Congruence models are based on the analysis of 
two independent measurement epochs. 
One of the pioneering methods of Conventional Deformation Analysis (CDA) refers to the Pelzer method 
or Hanover procedure (Pelzer, 1971).  Well-known methods of conventional deformation analysis are the 
Karlsruhe method (Heck, 1983), Caspary method (Caspary, 1987), Delft method (Heck et al., 1982), 
Fredericton (Chrzanowski, Chen and Secord, 1982) and others. Research based on these methods can be 
found in numerous professional and scientific papers (Ambrožič, 2001, 2004; Sušić et al., 2015; Sušić et 
al., 2017; Vrečko and Ambrožič, 2013). As opposed to CDA, robust deformation analysis methods are 
based on various robust displacement vector estimation approaches. One of the most well-known robust 
methods is IWST (Iterative Weighted Similarity T ransformation), which was published at the University 
of New Brunswick in Canada in 1983 (Chen, 1983). Of the recent methods of robust deformation analy-
sis, it is important to mention REDOD and GREDOD methods (Nowel and Kamiński, 2014; Nowel, 
2015), a method based of the Hodges–Lehmann estimates, which belong to the class of R-estimates 
(Duchnowski, 2013), the method based on M-split estimation (Duchnowski and Wyszkowska, 2022), 
a modified IWST and GREDOD method (Batilović et al., 2021, 2022a, 2022b). Testing the efficacy 
of the CDA method can be measured through the MSR (the mean success rate) factor (Hekimoglu et 
al., 2010). In the modified method according to the Munich approach, it is proposed to determine the 
congruence of all lengths and all angles in the network between two epochs of measurement as well as 
determine the congruence of all triangles between points in the network (Savšek and Ambrožić, 2023).
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 489 |
GEODETSKI VESTNIK | 67/4 |
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES SI | EN
2 MOTIVATION AND RESEARCH AREA
The subject of geodetic monitoring in this paper refers to the reinforced concrete bridge Ratkov Laz made 
of prestressed concrete in Montenegro. The bridge is located on the highway Podgorica - Mateševo, sec-
tion Smokovac - Uvač, in the locality Ratkov Laz (42°36'38.62" degrees north latitude and 19°23'57.83" 
degrees east longitude). The section from Smokovac to Mateševo is part of the Bar-Boljare Highway, 
which is part of the Trans-European Motorway (TEM) route through Montenegro. It connects the 
main route of the TEM (from Gdańsk to Athens and Istanbul) with the Adriatic Sea and it is part of the 
Belgrade-South Adriatic highway corridor via the TEM.
The bridge spans the valley with a length of about 352 metres and a maximum depth of about 35 me-
tres. The total length of the bridge in the left lane of the highway is 350 metres, and 325 metres in the 
right lane. The left structure is placed on 2 coastal and 12 central pillars and the right one is placed on 
2 coastal and 11 central pillars. The bridge is mostly in a circular curve (Figure 1). 
Figure 1: An example of stabilization of reference network points and points on the Ratkov Laz bridge piers
The characteristic phases of the observation of this bridge were related to the installation of founda -
tions, piers, supporting construction structure of the bridge, removal of scaffolding and laying the 
final layer of asphalt. The subject of this paper refers to the analysis of two epochs of measurement, 
the zero and the control epoch. The zero epoch was performed after removing the scaffolding from 
the bridge, while the control epoch was performed after placing the final layer of asphalt on the 
structure. The zero epoch was carried out during October 2020, while the control epoch was car -
ried out during December 2021. The locations where geodetic observation points are set up refer 
to the following:
 – two benchmarks at the top and at the bottom of central piers at opposite sides whose height is 
greater than 20 meters;
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 490 |
| 67/4 | GEODETSKI VESTNIK  
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES
SI | EN
 – two benchmarks at the top of central piers whose height is less than 20 meters;
 – two benchmarks in the middle of each span of the bridge;
 – two points at the top on abutments.
Figure 2: Sketch of the reference geodetic network for bridge monitoring with the disposition of observation points
The total number of points for geodetic monitoring of the Ratkov Laz bridge is 137 (71 for the left lane 
and 66 for the right lane), which is a sufficient number of points for the geometric interpretation of 
the bridge in a spatial sense, based on of which high-quality geodetic deformation measurements with 
deformation analysis can be performed.  The reference geodetic network is shown in Figure 2. The loca -
tions of the reference points are directly determined by the terrain and object configuration.
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 491 |
GEODETSKI VESTNIK | 67/4 |
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES SI | EN
3 DATA AND METHODS
The geodetic micro-network consists of a reference part, which is conditionally stable and is mostly placed 
outside the zone of influence of the bridge and the benhchmark points on the bridge that are subject of 
geodetic monitoring. The total number of points of the reference part of the geodetic network is 9. The 
geometry of the geodetic network is adapted to the bridge and depends on the terrain configuration.  All 
points on the bridge can be observed from at least two, and mostly three points of the reference part of 
the geodetic network. The measured quantities in the network are horizontal directions, zenith angles and 
slope distances. Measurements were performed by the gyrus method in two repetitions. Measurements 
were made with a total station Leica TS11 that has the following performance: standard deviation of 
horizontal directions is 1" and standard deviation of measured distances is 1 mm + 1 ppm [mm]. Dur-
ing the measurement, the temperature and atmospheric pressure were taken into account, after which 
the atmospheric correction was calculated in the postprocessing. The average distance from the points 
of the reference part of the geodetic micro-network and the points on the bridge is less than 70 meters. 
The observation plan was identical in both measurement epochs. Adjustment of measurement in both 
epochs was performed by Least Squares method with the datum definition of the minimum trace to the 
points of the reference part of the network. Table 1 shows average statistical indicators of the geodetic 
network in both measurement epochs. All the data listed in table 1 were calculated in the specially pro-
jected software package MatGeo in the framework of the Matlab programme, which has been developed 
in the internal surroundings of the Faculty of Technical Sciences in Novi Sad.
Table 1: Average statistical quality indicators of geodetic network in both measurement epochs
Average statistical quality indicators Zero epoch Control epoch
Standard deviation of spatial positions [mm] 1.1 1.3 
Internal reliability coefficients for horizontal directions, slope distances and zenith 
angles, respectively
0.3; 0.8; 0.4 0.3; 0.7; 0.4
Elements of the error ellipsoid (A, B, C) for probability 1- α = 0.95 [mm] 2.8; 1.0; 1.2 3.3; 1.2; 1.4
Minimale detectable deformation in the direction of the semi-major axis for Y and 
X axis [mm]
2.6; 3.0 3.1; 3.6
Minimale detectable deformation in the direction of the semi-minor axis for Y and 
X axis [mm]
1.3; 1.1 1.5; 1.3
Minimale detectable deformation in the direction of vertical Z axis 1.7 2.1
The homogeneity of accuracy in both epochs was confirmed, which is a prerequisite for the application 
of deformation analysis methods. Two representative methods of deformation analysis, Pelzer's and 
IWST methods, were applied in the paper, after which the results of the two methods were compared.
3.1 Pelzer’s method (Hannover approach)
One of the pioneering CDA methods is the Pelzer’s method or the Hanover approach, which was pub-
lished by Pelzer in 1971. The first step in this method is to examine the homogeneity of accuracy in both 
epochs. After that, the unified variance is calculated based on the following expression:
 
12
22
10 20 2
0
ˆˆ
ˆ
,
ff
f
σσ
σ
+
= (1)
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 492 |
| 67/4 | GEODETSKI VESTNIK  
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES
SI | EN
where f
1
 and f
2
 are numbers of freedom degrees in zero and control measurement epoch, 
1
2
0
ˆ
σ and 
2
2
0
ˆ
σ are 
a posteriori variances at the zero and control epochs, respectively, with  f =  f
1
 +  f
2
 number of degrees of 
freedom.
In the next step, network congruence is tested using mathematical statistics testing methods. The test 
statistic of the global congruence point position test is formed:
 
2
1 ,, 2
0
,
ˆ
hf
TF
α
θ
σ
−
= 
 (2)
where is the probability 1 − α = 0.95, h is the rank of the coordinate difference cofactor matrix Q
d
 and  
θ 
2
 is average non-fitting, which contains information displacements of points, is calculated using the 
expression:
 
2
,
T
h
θ =
+
d
dQd
 (3)
where dx x
21
ˆˆ = − is vector of coordinate differences, x
1
ˆ and x
2
ˆ represent vectors of unknown parameters 
obtained from Least Squares estimates at individual epochs, 
+
d
Q is pseudo-inversion of coordinate differ-
ences cofactor matrix, and h is rank of the coordinate differences cofactor matrix 
+
d x xx x
Q Q QQ Q
1 21 2
ˆ ˆˆ ˆ
, and =+    
are cofactor matrices from both individual epochs. If it is valid T  ≤ F
1 − α,h,f 
, the hypothesis about the 
congruence of the positions of the points from the two epochs is not being rejected and the deformation 
analysis procedure ends there. If it is not valid, the null hypothesis is rejected, i.e. there is at least one 
unstable (displaced) point in the network.
In that case, the network is divided into two subvectors, one belonging to the points of the reference 
part of the network (S designates) and the other to the points on the object (O designates). Vector of 
the coordinate differences d and the pseudo-inversion of coordinate differences cofactor matrix 
+
d
Q are 
decomposed as follows (Pelzer, 1971; Ambrožič, 2001; Sušić et al., 2015):
 
+
dd
d PP
d QP
d PP
.
S SS SO
O OS OO
    
  
=          = =
  
    
  
 (4)                     
Then the quadratic form 
+
d
dQd
T
 can be decomposed into the first part related to the non-fitting of the 
reference part of the network, and the second to the non-fitting of points on the object, where average 
non-fitting is:
 
dPd
2
,
T
S SS S
S
S
h
θ =
 (5)
where P P PPP
1
SS SS SO OO OS
−
= − and h
S
 is a rank of P
SS
 (Pelzer, 1971; Ambrožič, 2001; Sušić et al., 2015).
If it is valid 
2
1 ,, 2
0
ˆ
S
S
hf
TF
α
θ
σ
−
= ≤ zero hypothesis is not being rejected, i.e. reference network points are 
congruent in two epochs or otherwise, at least one point is unstable. Now the approach is to find the 
unstable reference points. The procedure of localization of unstable (displaced) points of the reference 
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 493 |
GEODETSKI VESTNIK | 67/4 |
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES SI | EN
part of the network is approached in such a way that the coordinate difference evaluation vector is di-
vided into two subvectors: 
 
d PP
dP
d PP
,
F FF FB
S SS
B BF BB
    
  
=          =
  
    
  
 (6)
where the label F refers to conditionally stable points, and the label B refers to conditionally unstable 
(suspected) points. The decomposition of the quadratic form is carried out as in the previous expressions:
 
dPd dPd dPd,
TTT
S SS S F FF F B BB B
= +
 (7)
where
 d d PPd P P PPP
11
,.
B B BB BF F FF FF FB BB BF
−−
= +   = − (8)
Average non-fitting is calculated for all k points of the reference part of the network:
 
dP d
2
,( 1,2, , ),
jj
j
T
B BB B
j
B
jk
h
θ= = 
 (9)
where h
B j
 is a rank of P
BB j
 and k is the number of reference points in the network.
The reference point, which has the maximum average non-fitting θ
j
2
, is declared unstable and further 
testing is conducted without it. 
dPd dPd
P
2
rank
TT
F FF F F FF F
REST
F FF
h
θ= = and test statistic 
2
2
0
ˆ
REST
T
θ
σ
= are also calcu-
lated. T esting on the remaining points continues until the hypothesis of the congruence of the reference 
points T ≤ F
1− α,h F ,f
 is not being rejected.
In the next step, unstable (displaced) points on the object are localized, which represents the last phase 
of the analysis. The decomposition of the displacement vector is performed in a similar way as in the 
previous expressions, where the first subvector contains stable reference points, while the second subvector 
contains points on the object and unstable reference points. The complete mathematical model of Pelzer's 
method is presented in a large number of papers (Pelzer, 1971; Ambrožić, 2001; Sušić et al., 2015).
3.2 IWST robust method 
The IWST method of deformation analysis is a well-established method that is often used in scientific 
research. This method has been implemented in several projects of observation of complex objects in 
practice, the most famous of which is the "Tevatron" accelerator within the Fermilab laboratory in the 
USA (not operational since 2011).
The IWST method consists of three steps. In the first step, the independent adjustment of measurements 
of the zero and control epoch is performed using the Least Squares method, where it is a free geodetic 
network. A detailed explanation of the free adjustment within the Least Squares method can be found 
in the literature (Tan, 2015). Also, in this step, the procedure of detecting outliers in observations using 
conventional tests (Data snooping test and τ test) or robust methods (L1 norm, Danish method, and 
others) is conducted.
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 494 |
| 67/4 | GEODETSKI VESTNIK  
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES
SI | EN
The second step involves a robust S transformation of the displacement vector of the network points. 
The vector x
2
ˆ is transformed into the datum of vector x
1
ˆ in order to define a single datum. This task 
consists of fitting the vector x
2
ˆ into the vector x
1
ˆ by reducing it to the center of gravity of the network. 
The transformed vector takes the following form:
 
x x Ht
'
22
ˆˆ , = −
 (10)
where t is a vector of parameters of the S transformation and H is a well-known design matrix of the S 
transformation in a common datum (Nowel and Kamiński, 2014; Batilović et al., 2021):
 S = I − H(H
T 
WH)
−1
H
T  
W, (11)
where I is the identity matrix, and W weight matrix, which in the first iteration is identical to the 
identity matrix.
The deformation model is as follows:
 
d xx xxH t
'
21 21
ˆˆ ˆˆ ( ). =−=−−
 (12)
Optimization problem IWST method is formed by the deformation model (12) and the objective function:
 
td
1
( ) min.
i
d ψ = = =
∑
 (13)
The optimization problem is solved numerically using the Iterative Reweighted Least Squares (IRLS) 
method:
 
( )( )
( )
xx
d
d Sxx
Q SQ Q S
W
12
() ()
21
() () ()
ˆ ˆˆ
( 1) ( 1)
,,
1,2,
ˆ
ˆˆ ()
,
, , ,,
kk
T
kk k
kk
PRP i O i
k
diag w w
++
=

               = −


       = +


=  



  
 (14)
where S
(k)
 is the S transformation matrix, W
(k +1)
 is the weight matrix and k is the iteration number.
In the first iteration of the transformation (k = 1) the weight matrix is the identity matrix (W = I). In the 
next iterations the weights of the reference network points are determined on the following expression:
 
( )
( 1)
' ,
()
1
1
ˆ
k
PRP i
k
w
dc
+
=
+
 (15)
where 
()
1
ˆ k
d is the corresponding component of the displacement vector, and c is a small constant value 
that prevents the occurrence of zero in the denominator. The weights of the object points w
O,i
 are equal 
to zero, because only reference points participate in the optimization process. In the third step, the 
stability of network points is tested, i.e. it is examined whether the estimated displacement vectors of 
individual points are the result of a real displacement or of random measurement errors. For this reason, 
the following hypotheses are posed:
 
dd
0
ˆˆ
:()0v e r s u s :()0
i ai
HE HE =      ≠
 (16)
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 495 |
GEODETSKI VESTNIK | 67/4 |
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES SI | EN
where d
ˆ
i
 is displacement vector of arbitrary points and E mathematical expectation operator. Stability 
testing of points is performed using a single-point test:
 
dQ d
ˆ
1 ,,
ˆˆ
ˆ
ii
ii
i hf
TF
 (17)
where d
ˆ
i
 is the displacement vector, 
d
Q
ˆ
i
 is cofactor matrix of the displacement vector, h
i
 is a rank of 
d
Q
ˆ
i
 , 
f  is the unified number of degrees of freedom, 
2
0
ˆ
σ is the unified a posteriori dispersion factor, α
i 
represents 
the local level of significance, which is determined depending on the global level of significance α by 
the well-known expression (Caspary, 1987):
 α
i
 = 1 − (1 − α)
1/m
, (18)
where m is number of geodetic network points.
If it is valid T  ≤ F
1 − α i ,h i ,f 
, the null hypothesis is not rejected, and the point can be regarded as stable. 
When  T  > F
1 − α i ,h i ,f  
, the null hypothesis is rejected, and it can conclude that the point is significantly 
displaced. A complete mathematical model of the IWST method with applications in geodetic de-
formation analysis can be found in numerous literature (Chen, 1983; Nowel, 2014, 2015, 2016; 
Batilović et. al., 2021).
4 ANALYSIS OF RESULTS AND DISCUSSION
Analysis of the congruence of the reference network using the Pelzer method showed that 4 points are 
stable and 5 are unstable. Statistical stability was confirmed at the following reference points: R4, V3, 
V4 and V5, where is the value of the test statistic and the average non-fitting:
 T = 1.792 ≤ F
0.99,12,955
 = 2.209,   θ 
2
REST
 = 2.442.
Analysis of the congruence of the reference network using the IWST method showed that 7 points are 
stable and 2 are unstable. Statistical stability was confirmed at the following reference points: R1, R4, 
V2, V3, V4, V5 and V6. Localization of points on the bridge using the Pelzer method showed that 26 
points on the bridge were identified as statistically stable, while the remaining 111 points were signifi-
cantly unstable. 
Localization of points on the bridge using the IWST robust method showed that 65 points on the 
bridge were identified as statistically stable, while the remaining 72 points were significantly displaced 
(Appendix 1). The average intensity of the displacement vector in the horizontal plane for all points on 
the bridge is 6.7 mm using the Pelzer method, while it is 6.6 mm using the IWST method. The displa-
cement intensities for characteristic points with higher displacement intensities along all three axes (Y, 
X and H) are shown for both methods (Pelzer and IWST) in Table 2. Also, the table 2 shows the values 
of the average non-fitting θ 
2
  (eq. 9) for the Pelzer’s method, as well as the value of the test statistic T 
(eq. 17) and the value of Fisher's distribution F for each point in the IWST method. The complete 
displacement results at all points on the bridge are shown in Appendix 1.
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 496 |
| 67/4 | GEODETSKI VESTNIK  
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES
SI | EN
Table 2: Results of deformation analysis using the Pelzer method (CDA) and the IWST (robust) method for reference points 
of the geodetic network and characteristic points on the bridge  
Points
Pelzer - Intensity of displacements [mm] IWST- Intensity of displacements [mm]
Status θ
2
dY dX dH T F Status dY dX dH
Reference points of the geodetic network
R1 Unstable 3586.3 7.5 7.9 0.8 3.3 6.2 Stable 0.4 0.9 -1.3
R3 Unstable 3518.3 -6.6 -6.8 -1.0 19.2 6.2 Unstable 0.7 0.2 2.4
R4 Stable 1.9 0.3 0.4 -0.3 0.2 6.2 Stable -0.1 -0.5 -0.1
V1 Unstable 553.7 -0.6 3.1 -1.1 7.3 6.2 Unstable 0.0 2.4 -0.4
V2 Unstable 39.1 0.5 0.5 -1.6 4.2 6.2 Stable 0.2 0.0 1.3
V3 Stable 2.7 -0.9 -0.2 -0.1 1.8 6.2 Stable -1.0 -0.1 0.4
V4 Stable 3.3 -0.4 -0.8 -0.1 1.3 6.2 Stable -0.6 -1.2 0.0
V5 Stable 2.5 -0.2 -0.6 0.4 1.7 6.2 Stable 0.1 -1.0 0.6
V6 Unstable 165.8 -0.7 2.7 2.0 1.2 6.2 Stable -0.5 0.5 -0.2
Points on bridge spans
LL1 Unstable 3768.2 -11.0 -21.7 3.2 312.5 6.2 Unstable -10.2 -19.4 2.4
LL2 Unstable 216.2 -8.4 -13.9 0.5 123.3 6.2 Unstable -9.1 -13.2 0
LL3 Unstable 1432.8 -6.8 -11.5 2.1 654.1 6.2 Unstable -8.1 -11.3 1.6
LL4 Unstable 135.8 -5.9 -9.2 2.1 86 6.2 Unstable -7.0 -9.5 2
LL12 Unstable 85.6 9.4 10.1 -0.9 53.4 6.2 Unstable 9.5 9.5 -0.4
LL13 Unstable 404.5 9.8 10.3 0.1 120.9 6.2 Unstable 9.7 9.6 0.6
LR1 Unstable 2211.4 -4.8 -17.6 3.1 185.8 6.2 Unstable -6.4 -16.3 1.7
LR2 Unstable 335.8 -6.8 -14.5 -0.1 168.2 6.2 Unstable -7.8 -14.5 0.2
LR3 Unstable 1029.7 -7.1 -11.5 2.2 508.3 6.2 Unstable -8.3 -11.3 1.8
LR12 Unstable 543.2 9.2 6.4 -1.9 111.6 6.2 Unstable 9.1 5.6 -1.5
LR13 Unstable 80.2 8.1 6.6 0.2 34.7 6.2 Unstable 8.0 5.9 0.6
RL1 Unstable 163 -8.9 -16.5 1.3 77.2 6.2 Unstable -9.2 -15.9 0.2
RL2 Unstable 77.7 -7.2 -13.2 1.6 40.9 6.2 Unstable -8.3 -13.5 1.5
RL3 Unstable 143.8 -5.0 -9.1 1.7 100.4 6.2 Unstable -5.8 -9.3 2.0
RL4 Unstable 36 -5.5 -7.0 2.1 25.7 6.2 Unstable -6.3 -7.1 2.4
RL10 Unstable 151.3 6.1 8.1 0.7 23.8 6.2 Unstable 6.1 7.4 0.8
RL11 Unstable 1527.8 7.6 8.8 -1.5 91.1 6.2 Unstable 7.4 8.0 -1.0
RL12 Unstable 248.9 9.5 10.5 -0.2 90.2 6.2 Unstable 9.5 9.7 0.2
RR1 Unstable 204.9 -6.4 -16.2 1.9 114.7 6.2 Unstable -7.3 -15.6 1.3
RR2 Unstable 78.3 -5.0 -11.9 1.7 36 6.2 Unstable -5.9 -12.1 1.6
RR3 Unstable 15.8 -4.4 -9.0 1.3 11 6.2 Unstable -5.3 -9.2 1.6
RR4 Unstable 38.4 -2.7 -7.3 1.8 25.8 6.2 Unstable -3.5 -7.5 2.1
RR10 Unstable 157.9 7.2 8.2 1.1 39.3 6.2 Unstable 7.1 7.4 1.3
Points on the tops of the pillars
LS21 Unstable 383.4 -7.1 -13.2 1.7 179.5 6.2 Unstable -7.8 -14 2.5
LS23 Unstable 141 -7.5 -13.5 1.8 83.7 6.2 Unstable -8.6 -14.1 1.6
LS31 Unstable 49.8 -6.2 -11.1 1.4 25.3 6.2 Unstable -7.1 -11.1 1.7
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 497 |
GEODETSKI VESTNIK | 67/4 |
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES SI | EN
Points
Pelzer - Intensity of displacements [mm] IWST- Intensity of displacements [mm]
Status θ
2
dY dX dH T F Status dY dX dH
LS33 Unstable 30.5 -6.8 -12.3 1.5 22.4 6.2 Unstable -7.7 -12.4 1.8
LS41 Unstable 305.1 -3.9 -7.2 -0.2 56.2 6.2 Unstable -5.9 -7.4 1.6
LS43 Unstable 52.7 -7.1 -7.9 2.4 37.1 6.2 Unstable -7.9 -8.1 2.7
LS93 Unstable 62.6 9.5 12.4 2.8 31.7 6.2 Unstable 9.3 11.9 2.7
RS21 Unstable 202.7 -4.6 -9.8 2.0 138.5 6.2 Unstable -5.8 -9.8 1.9
RS23 Unstable 18.1 -3.7 -9.0 0.1 10.9 6.2 Unstable -4.7 -9.1 0.5
RS31 Unstable 54.9 -2.9 -6.8 2.6 38.3 6.2 Unstable -3.7 -7.0 2.9
Figure 3: Sketch of the geodetic network of the Ratkov Laz bridge with Pelzer and IWST displacement vectors 
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 498 |
| 67/4 | GEODETSKI VESTNIK  
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES
SI | EN
As can be seen from Figure 3, the interpretation of the displacement vector for points on the bridge is 
similar in both deformation analysis methods. The points located at the top of the pillars (from pillar 
S1 to pillar S4), as well as the points on the spans between these pillars show significant movements 
with the azimuth of the displacement in the southwestern direction of the road towards Podgorica. 
Displacements range is from 10 to over 15 mm. It is important to point out the different influence of 
temperature on measurements in zero and control epochs. Most of the points on the pillars in the mid-
dle of the bridge (from pillar S4 to pillar S9) are generally statistically evaluated as stable by applying 
the IWST robust method. The points located at the top of the pillars on the north side of the bridge 
(from pillar S10 to pillar S12), as well as the points on the spans between these pillars show significant 
movements with the azimuth of the displacement in the northeastern direction of the road towards 
Mateševo. The displacement intensities are similar to those on the southern side of the bridge (from 
10 to over 15 mm), while the displacement azimuths are oriented in the opposite direction compared 
to the southern side of the bridge.
5 CONCLUSION
Monitoring during the construction and exploitation of traffic infrastructure facilities, especially bridges, 
includes the traditional and modern approach of geodetic observation. If the engineering facilities during 
construction are affected by factors such as wind, sun radiation, the influence of cranes, etc., it is impor-
tant to consider the use of continuous GNSS measurements in combination with special geotechnical 
sensors (inclinometers, extensometers, etc). However, in a large number of cases in engineering practice, 
an important segment is traditional geodetic monitoring approach using total stations (conventional or 
robotized) in the process of periodic geodetic monitoring. 
The paper presents an example from the practice of geodetic monitoring of the Ratkov Laz bridge 
on the highway in Montenegro, whose stability is assessed by models of the congruence of the 
geodetic network in individual measurement epochs. For the purpose of applying the deformation 
analysis of two epochs of measurement, representative methods from the group of CDA (Pelzer’s) 
and robust methods (IWST) were used. The intensities and azimuths of the displacement vectors 
showed similar results for both methods. However, the conclusions about the statistical stability/
instability of certain points on the bridge, showed significant differences. A significantly smaller 
number of points on the bridge were evaluated as statistically stable with the Pelzer’s method com-
pared to the IWST method. By applying the IWST method, more objective results were obtained, 
considering the practical significance of moving points on the bridge. The results of displacements 
of the points on the top of the pillars on the south and north sides of the bridge showed the op-
posite direction of displacements and similar intensities of displacements, while the points on the 
central part of the bridge were generally assessed as stable by applying the IWST method. It is 
known that numerous modifications of the IWST method are available in the scientific literature, 
which differ from each other in the use of the optimization condition of robust estimation, i.e. 
objective functions (Huber’s, Danish, etc). Testing the efficacy of different weight functions can 
be examined using the MSR factor (Hekimoglu et al., 2010; Sušić et al., 2017), which was not 
the subject of research in this paper.
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 499 |
GEODETSKI VESTNIK | 67/4 |
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES SI | EN
Although the interpretation of the displacement vector is interesting both from a geodetic and con-
struction point of view, the main focus of the paper is on the comparative research of conventional and 
robust methods of deformation analysis, which have their role in geodetic observation of all kinds of 
engineering facilities. When considering the conclusions from the analysis of the stability of points, and 
bearing in mind the practical importance of the displacement of points on the bridge, it is concluded 
that the IWST method gives more objective results that correspond more closely to the real situation 
compared to the Pelzer’s method.
Acknowledgement
The research has been conducted within the project "Scientific theoretical and experimental research and 
improvement of educational process in the field of civil engineering", developed at the Department of 
Civil Engineering and Geodesy, Faculty of Technical Sciences, University of  Novi Sad, Serbia.
Literature and references: 
Ambrožič, T . (2004). Deformacijska analiza po postopku Karlsruhe. Geodetski vestnik, 
48 (3), 315–331
Ambrožič, T . (2001). Deformacijska analiza po postopku Hannover . Geodetski vestnik, 
45 (1&2), 38–53
Batilović, M., Đurović, R., Sušić, Z., Kanović, Ž., Cekić, Z. (2022a). Robust estimation of 
deformation from observation differences using some evolutionary optimisation 
algorithms. Sensors, 22 (1), 159, 1–26. DOI: https://doi.org/10.3390/s22010159
Batilović, M., Kanović, Ž., Sušić, Z., Bulatović, V. (2022b). Deformacijska analiza po 
modificirani metodi GREDOD. | Deformation analysis: the modified GREDOD 
method. Geodetski vestnik, 66 (1), 60–75. DOI: 10.15292/geodetski-
vestnik.2022.01.60-75
Batilović, M., Sušić, Z., Kanović, Ž., Marković, M.Z., Vasić, D., Bulatović, V. (2021). 
Increasing efficiency of the robust deformation analysis methods using genetic 
algorithm and generalised particle swarm optimisation. Survey Review, 53, 378, 
193–205. DOI: 10.1080/00396265.2019.1706294
Caspary, W .F . (1987). Concepts of Network and Deformation Analysis. Kensington: The 
University of New South Wales, School of Surveying, Australia.
Chen, Y .Q. (1983).  Analysis of deformation surveys – a generalized method. T echnical 
Report. Fredericton: UNB Geodesy and Geomatics Engineering. University of 
New Brunswick.
Chrzanowski, A., Chen, Y.Q., Secord, J.M. (1982). A Generalized Approach to the 
Geometrical Analysis of Deformation Surveys. In 3rd International Symposium 
on Deformation Measurements by Geodetic Methods. 25-27 August 1982, 
Budapest, Hungary.
Duchnowski, R. (2013). Hodges–Lehmann estimates in deformation analyses. Journal 
of Geodesy 87:873–884. DOI 10.1007/s00190-013-0651-2
Duchnowski, R., Wyszkowska, P . (2022). Msplit Estimation Approach to Modeling 
Vertical Terrain Displacement from TLS Data Disturbed by Outliers. Remote 
Sensing 14(21):5620. DOI:10.3390/rs14215620
Heck, B. (1983). Das Analyseverfahren Des Geodätischen Instituts Der Universität 
Karlsruhe Stand 1983, In Deformationsanalysen ’83-Geometrische Analyse 
und Interpretation von Deformationen Geodätischer Netze. 22 April 1983, 
München, Germany.
Heck, B., Kok, J.J., Welsch, W., Baumer, R., Chrzanowski, A., Chen, Y .Q., Secord, J.M. 
(1982). Report of the FIG Working Group on the Analysis of Deformation 
Measurements. In 3rd International Symposium on Deformation Measurements 
by Geodetic Methods. 25-27 August 1982, Budapest, Hungary.
Hekimoglu, S., Erdogan, B., Butterworth, S. (2010). Increasing the Efficacy of the 
Conventional Deformation Analysis Methods: Alternative Strategy. Journal of 
Surveying Engineering 136(2). DOI:10.1061/(ASCE)SU.1943-5428.0000018
Marković, Z.M., Bajić, S.J., Batilović, M., Sušić, Z., Joža, A., Stojanović, M.G. (2019). 
Comparative Analysis of Deformation Determination by Applying Fiber-optic 2D 
Deflection Sensors and Geodetic Measurements. Sensors,  19 (4), 844, 1–14. 
DOI: https://doi.org/10.3390/s19040844
Nowel, K. (2015). Robust M-Estimation in Analysis of Control Network Deformations: 
Classical and New Method. Journal of Surveying Engineering, 141 (4), 1–10. 
DOI: https://doi.org/10.1061/(ASCE)SU.1943-5428.0000144
Nowel, K. (2016). Investigating efficacy of robust M estimation of deformation from 
observation differences. Survey Review, 48, 346, 21–30, DOI: http://dx.doi.or
g/10.1080/00396265.2015.1097585
Nowel, K., Kamiński, W . (2014). Robust estimation of deformation from observation 
differences for free control networks. Journal of Geodesy, 88 (8), 749–764. DOI: 
https://doi.org/10.1007/s00190-014-0719-7
Olaszek, P ., Wyczałek, I., Sala, D., Kokot, M., Świercz, A. (2020). Monitoring of the 
Static and Dynamic Displacements of Railway Bridges with the Use of Inertial 
Sensors. Sensors, 20 (10), 2767, 1–24. DOI: https://doi.org/10.3390/s20102767
Pelzer, H. (1971). Zur Analyse geodätischer Deformationsmessungen. München: 
Deutsche Geodätische Kommission. Reihe C. No. 164
Savšek, S., Ambrožič, T. (2023). Modificirana metoda deformacijske analize po 
postopku München. Modified method of deformation analysis according to 
the Munich approach. Geodetski vestnik, 67 (2), 131-b164. DOI: 10.15292/
geodetski-vestnik.2023.02.131-164
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 500 |
| 67/4 | GEODETSKI VESTNIK  
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES
SI | EN
Sušić, Z., Batilović, M., Ninkov, T., Aleksić, I., Bulatović, V. (2015). Identification of 
movements using different methods of deformation analysis. Geodetski vestnik,  
59 (3), 537–553. DOI: 10.15292/geodetski-vestnik.2015.03.537-553
Sušić, Z., Batilović, M., Ninkov, T ., Bulatović, V ., Aleksić, I., Nikolić, G. (2017). Geometric 
deformation analysis in free geodetic networks: case study for Fruška Gora 
in Serbia. Acta Geodynamica et Gromaterialia, 14 (3), 187, 341–355. DOI: 
10.13168/AGG.2017.0017
Tan, W . (2015). Inner constraints for 3-D survey networks. Journal of Spatial Science. 
Taylor & Francis
Vrečko, A., Ambrožič, T. (2013). Deformacijska analiza po postopku Fredericton. 
Geodetski vestnik, 57 (3), 479–497. DOI: https://doi.org/10.15292/
geodetskivestnik.2013.03.479-497
Xingmin, H., Xueshan, Y., Qiao, H. (2005). Using Inclinometers to Measure Bridge 
Deflection. Journal of Bridge Engineering, 10 (5), 1–6. DOI: 10.1061/
(ASCE)1084-0702(2005)10:5(564)
Appendix 1: Results of deformation analysis using the Pelzer method (CDA) and the IWST (robust) method
Points
Pelzer - Intensity of displacements [mm] IWST- Intensity of displacements [mm]
Status θ
2
dY dX dH T F Status dY dX dH
R1 Unstable 3586.3 7.5 7.9 0.8 3.3 6.2 Stable 0.4 0.9 -1.3
R3 Unstable 3518.3 -6.6 -6.8 -1.0 19.2 6.2 Unstable 0.7 0.2 2.4
R4 Stable 1.9 0.3 0.4 -0.3 0.2 6.2 Stable -0.1 -0.5 -0.1
V1 Unstable 553.7 -0.6 3.1 -1.1 7.3 6.2 Unstable 0.0 2.4 -0.4
V2 Unstable 39.1 0.5 0.5 -1.6 4.2 6.2 Stable 0.2 0.0 1.3
V3 Stable 2.7 -0.9 -0.2 -0.1 1.8 6.2 Stable -1.0 -0.1 0.4
V4 Stable 3.3 -0.4 -0.8 -0.1 1.3 6.2 Stable -0.6 -1.2 0.0
V5 Stable 2.5 -0.2 -0.6 0.4 1.7 6.2 Stable 0.1 -1.0 0.6
V6 Unstable 165.8 -0.7 2.7 2.0 1.2 6.2 Stable -0.5 0.5 -0.2
LL1 Unstable 3768.2 -11.0 -21.7 3.2 312.5 6.2 Unstable -10.2 -19.4 2.4
LL10 Unstable 66.0 5.9 6.4 0.4 20.3 6.2 Unstable 6.1 6.0 0.5
LL11 Unstable 17.5 6.8 8.6 1.2 11.3 6.2 Unstable 7.0 8.2 1.4
LL12 Unstable 85.6 9.4 10.1 -0.9 53.4 6.2 Unstable 9.5 9.5 -0.4
LL13 Unstable 404.5 9.8 10.3 0.1 120.9 6.2 Unstable 9.7 9.6 0.6
LL2 Unstable 216.2 -8.4 -13.9 0.5 123.3 6.2 Unstable -9.1 -13.2 0.0
LL3 Unstable 1432.8 -6.8 -11.5 2.1 654.1 6.2 Unstable -8.1 -11.3 1.6
LL4 Unstable 135.8 -5.9 -9.2 2.1 86.0 6.2 Unstable -7.0 -9.5 2.0
LL5 Unstable 34.3 -4.5 -7.4 2.7 23.9 6.2 Unstable -5.3 -7.6 3.0
LL6 Unstable 37.8 -1.7 -4.8 1.5 22.2 6.2 Unstable -2.6 -5.0 1.8
LL7 Unstable 5.0 -0.6 -0.5 1.9 4.6 6.2 Stable -1.4 -0.6 2.3
LL8 Unstable 5.2 1.3 1.5 0.8 1.3 6.2 Stable 1.0 0.5 0.8
LL9 Unstable 4.6 5.1 3.8 0.6 2.6 6.2 Stable 4.6 3.2 1.1
LLA1 Unstable 132.8 -12.4 -4.8 -3.2 64.7 6.2 Unstable -13.6 -6.5 -2.3
LLAO Unstable 15.4 2.6 1.3 -0.8 1.9 6.2 Stable 1.6 1.2 -0.4
LR1 Unstable 2211.4 -4.8 -17.6 3.1 185.8 6.2 Unstable -6.4 -16.3 1.7
LR10 Unstable 56.9 5.2 6.3 0.3 14.6 6.2 Unstable 5.5 5.9 0.4
LR11 Unstable 29.9 8.9 7.7 1.5 17.6 6.2 Unstable 8.6 6.9 1.4
LR12 Unstable 543.2 9.2 6.4 -1.9 111.6 6.2 Unstable 9.1 5.6 -1.5
LR13 Unstable 80.2 8.1 6.6 0.2 34.7 6.2 Unstable 8.0 5.9 0.6
LR2 Unstable 335.8 -6.8 -14.5 -0.1 168.2 6.2 Unstable -7.8 -14.5 0.2
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 501 |
GEODETSKI VESTNIK | 67/4 |
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES SI | EN
Points
Pelzer - Intensity of displacements [mm] IWST- Intensity of displacements [mm]
Status θ
2
dY dX dH T F Status dY dX dH
LR3 Unstable 1029.7 -7.1 -11.5 2.2 508.3 6.2 Unstable -8.3 -11.3 1.8
LR4 Unstable 145.0 -2.6 -7.9 4.1 95.2 6.2 Unstable -3.4 -8.0 4.4
LR5 Unstable 36.5 -4.3 -8.0 2.0 24.6 6.2 Unstable -5.1 -8.2 2.3
LR6 Unstable 22.6 -3.2 -4.5 1.7 13.9 6.2 Unstable -3.9 -4.8 2.0
LR7 Unstable 11.2 1.4 -2.5 1.8 6.6 6.2 Unstable 0.3 -3.6 1.9
LR8 Unstable 6.2 2.4 -0.5 0.5 1.8 6.2 Stable 1.8 -0.6 0.9
LR9 Unstable 5.6 3.3 5.4 0.7 2.8 6.2 Stable 2.7 4.7 1.0
LRA1 Stable 2.3 0.1 0.0 -1.0 0.5 6.2 Stable 0.1 -1.0 -0.5
LS101 Unstable 16.8 6.3 7.5 0.5 9.5 6.2 Unstable 6.5 7.1 0.7
LS102 Stable 1.6 -0.5 1.0 -0.4 0.3 6.2 Stable -0.6 0.3 -0.3
LS103 Unstable 49.1 7.8 8.4 1.4 23.6 6.2 Unstable 7.4 7.6 1.4
LS104 Stable 0.6 1.5 0.5 0.0 0.7 6.2 Stable 1.3 -0.2 0.1
LS11 Unstable 5.4 -2.2 -2.3 0.6 4.7 6.2 Stable -3.1 -2.3 0.9
LS111 Unstable 17.0 5.9 6.5 0.3 11.9 6.2 Unstable 6.0 5.9 0.7
LS112 Stable 3.2 -0.4 2.6 -0.3 0.8 6.2 Stable -0.4 1.7 0.1
LS113 Unstable 707.1 9.7 7.9 -0.2 76.8 6.2 Unstable 9.4 7.2 0.2
LS114 Unstable 122.0 1.9 4.8 -0.4 8.5 6.2 Unstable 1.9 3.8 -0.1
LS12 Stable 0.4 0.2 -0.4 0.0 0.2 6.2 Stable -0.7 -0.5 0.3
LS121 Unstable 10.6 1.6 2.6 -1.0 3.4 6.2 Stable 1.6 1.8 -0.4
LS122 Unstable 3.7 -6.4 -11.1 -0.7 3.0 6.2 Stable -6.6 -12.1 -0.7
LS21 Unstable 383.4 -7.1 -13.2 1.7 179.5 6.2 Unstable -7.8 -14.0 2.5
LS22 Unstable 16.8 -1.7 -3.5 0.0 13.6 6.2 Unstable -2.5 -3.6 0.3
LS23 Unstable 141.0 -7.5 -13.5 1.8 83.7 6.2 Unstable -8.6 -14.1 1.6
LS24 Stable 2.4 -0.6 -2.3 -0.2 1.7 6.2 Stable -1.5 -2.4 0.1
LS31 Unstable 49.8 -6.2 -11.1 1.4 25.3 6.2 Unstable -7.1 -11.1 1.7
LS32 Unstable 4.3 -1.4 -1.0 -0.1 2.8 6.2 Stable -2.5 -1.2 0.2
LS33 Unstable 30.5 -6.8 -12.3 1.5 22.4 6.2 Unstable -7.7 -12.4 1.8
LS34 Unstable 4.9 -2.8 0.2 0.2 5.1 6.2 Stable -3.7 0.1 0.5
LS41 Unstable 305.1 -3.9 -7.2 -0.2 56.2 6.2 Unstable -5.9 -7.4 1.6
LS42 Stable 2.3 -1.0 -1.7 1.1 1.8 6.2 Stable -1.6 -1.7 1.4
LS43 Unstable 52.7 -7.1 -7.9 2.4 37.1 6.2 Unstable -7.9 -8.1 2.7
LS44 Unstable 15.5 0.0 -1.4 0.3 1.8 6.2 Stable -0.8 -1.3 0.7
LS51 Stable 2.4 -3.0 -4.4 -0.1 2.0 6.2 Stable -3.3 -5.0 -0.1
LS52 Stable 1.7 -0.8 0.7 -1.4 1.1 6.2 Stable -1.2 0.6 -1.2
LS53 Unstable 9.9 -2.8 -4.2 2.9 8.0 6.2 Unstable -3.6 -4.4 3.3
LS54 Unstable 8.1 0.7 -1.0 -0.7 0.7 6.2 Stable -0.3 -1.3 -0.3
LS61 Unstable 7.7 -0.6 -3.0 3.0 5.6 6.2 Stable -1.1 -3.8 3.0
LS62 Stable 2.2 -2.9 -1.4 0.1 1.6 6.2 Stable -3.1 -1.6 0.2
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 502 |
| 67/4 | GEODETSKI VESTNIK  
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES
SI | EN
Points
Pelzer - Intensity of displacements [mm] IWST- Intensity of displacements [mm]
Status θ
2
dY dX dH T F Status dY dX dH
LS63 Unstable 24.4 -2.9 -1.8 2.8 17.0 6.2 Unstable -3.8 -2.0 3.2
LS64 Stable 1.4 0.7 2.9 -0.1 1.0 6.2 Stable -0.3 2.4 0.2
LS71 Stable 3.4 -1.4 -1.0 1.5 2.6 6.2 Stable -1.8 -1.9 1.5
LS72 Stable 0.5 -0.6 -0.2 0.5 0.3 6.2 Stable -0.7 -0.5 0.5
LS73 Unstable 6.6 -3.0 0.0 2.1 5.8 6.2 Stable -3.7 -0.2 2.5
LS74 Unstable 7.6 0.7 3.1 0.4 2.7 6.2 Stable 0.0 3.0 0.7
LS81 Unstable 134.3 4.1 2.7 -0.3 26.3 6.2 Unstable 4.0 1.6 -0.1
LS82 Stable 2.1 0.5 1.3 -0.4 1.0 6.2 Stable 0.4 0.5 -0.5
LS91 Unstable 94.7 4.4 4.8 0.6 16.4 6.2 Unstable 4.7 4.4 0.8
LS92 Stable 2.2 0.6 0.3 0.6 0.9 6.2 Stable 0.5 -0.2 0.5
LS93 Unstable 62.6 9.5 12.4 2.8 31.7 6.2 Unstable 9.3 11.9 2.7
LS94 Unstable 5.0 3.5 3.3 -0.5 1.9 6.2 Stable 3.0 2.4 -0.3
RL1 Unstable 163.0 -8.9 -16.5 1.3 77.2 6.2 Unstable -9.2 -15.9 0.2
RL10 Unstable 151.3 6.1 8.1 0.7 23.8 6.2 Unstable 6.1 7.4 0.8
RL11 Unstable 1527.8 7.6 8.8 -1.5 91.1 6.2 Unstable 7.4 8.0 -1.0
RL12 Unstable 248.9 9.5 10.5 -0.2 90.2 6.2 Unstable 9.5 9.7 0.2
RL2 Unstable 77.7 -7.2 -13.2 1.6 40.9 6.2 Unstable -8.3 -13.5 1.5
RL3 Unstable 143.8 -5.0 -9.1 1.7 100.4 6.2 Unstable -5.8 -9.3 2.0
RL4 Unstable 36.0 -5.5 -7.0 2.1 25.7 6.2 Unstable -6.3 -7.1 2.4
RL5 Unstable 7.2 -2.0 -4.0 2.1 5.5 6.2 Stable -2.7 -4.2 2.4
RL6 Unstable 4.6 -0.8 -0.2 2.1 4.1 6.2 Stable -1.4 -0.5 2.3
RL7 Stable 2.4 2.1 0.6 0.7 1.5 6.2 Stable 1.5 -0.4 0.7
RL8 Unstable 84.3 3.3 2.7 -0.1 13.7 6.2 Unstable 3.1 2.4 -0.3
RL9 Unstable 119.2 5.6 7.0 -0.6 33.1 6.2 Unstable 5.1 6.1 -0.4
RLA1 Unstable 16.5 -4.4 2.5 1.0 11.1 6.2 Unstable -3.1 -0.2 2.2
RLAO Unstable 657.7 1.5 0.4 -0.4 6.6 6.2 Unstable 0.6 0.3 0.0
RR1 Unstable 204.9 -6.4 -16.2 1.9 114.7 6.2 Unstable -7.3 -15.6 1.3
RR10 Unstable 157.9 7.2 8.2 1.1 39.3 6.2 Unstable 7.1 7.4 1.3
RR11 Unstable 53.5 8.1 10.8 -0.4 30.0 6.2 Unstable 8.0 9.8 0.0
RR12 Unstable 183.9 8.5 10.3 -0.8 67.3 6.2 Unstable 8.4 9.5 -0.4
RR2 Unstable 78.3 -5.0 -11.9 1.7 36.0 6.2 Unstable -5.9 -12.1 1.6
RR3 Unstable 15.8 -4.4 -9.0 1.3 11.0 6.2 Unstable -5.3 -9.2 1.6
RR4 Unstable 38.4 -2.7 -7.3 1.8 25.8 6.2 Unstable -3.5 -7.5 2.1
RR5 Unstable 17.4 0.3 -3.9 0.2 7.9 6.2 Unstable -0.2 -4.1 0.4
RR6 Unstable 4.9 1.3 -0.9 1.6 3.1 6.2 Stable 0.3 -1.7 1.7
RR7 Stable 3.3 0.2 1.3 1.1 1.7 6.2 Stable -0.2 0.5 1.1
RR8 Unstable 4.3 2.7 3.0 -0.1 1.4 6.2 Stable 2.2 2.3 0.1
RR9 Unstable 74.7 6.0 6.5 0.2 24.6 6.2 Unstable 5.7 5.6 0.5
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 503 |
GEODETSKI VESTNIK | 67/4 |
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES SI | EN
Points
Pelzer - Intensity of displacements [mm] IWST- Intensity of displacements [mm]
Status θ
2
dY dX dH T F Status dY dX dH
RRA1 Unstable 17.1 -5.3 1.0 1.0 8.9 6.2 Unstable -5.5 0.0 1.5
RRAO Unstable 28.2 4.0 -2.7 0.5 2.6 6.2 Stable 3.0 -2.8 0.8
RS101 Unstable 13.9 6.5 7.3 0.7 7.0 6.2 Unstable 6.3 6.5 0.7
RS102 Stable 2.5 3.1 3.1 0.2 1.2 6.2 Stable 2.9 2.3 0.1
RS103 Unstable 1257.3 5.2 9.1 1.1 51.1 6.2 Unstable 5.0 8.2 1.4
RS104 Unstable 7.4 -0.7 0.5 -1.1 1.1 6.2 Stable -1.1 -0.3 -0.9
RS11 Unstable 28.0 -0.3 -3.0 1.0 7.4 6.2 Unstable -1.2 -3.1 1.3
RS111 Stable 3.2 0.2 1.6 1.1 1.8 6.2 Stable -0.1 0.4 1.2
RS112 Stable 1.8 1.0 0.8 -0.3 0.5 6.2 Stable 0.6 -0.4 -0.1
RS12 Unstable 6.6 0.7 -1.0 0.3 1.1 6.2 Stable -0.2 -1.1 0.6
RS21 Unstable 202.7 -4.6 -9.8 2.0 138.5 6.2 Unstable -5.8 -9.8 1.9
RS22 Unstable 4.6 1.6 -1.6 -0.6 0.9 6.2 Stable 0.6 -1.8 -0.2
RS23 Unstable 18.1 -3.7 -9.0 0.1 10.9 6.2 Unstable -4.7 -9.1 0.5
RS24 Stable 1.3 -0.7 -2.2 -0.4 0.6 6.2 Stable -1.7 -2.3 0.0
RS31 Unstable 54.9 -2.9 -6.8 2.6 38.3 6.2 Unstable -3.7 -7.0 2.9
RS32 Unstable 7.9 1.4 0.1 -0.5 0.1 6.2 Stable 0.3 -0.1 -0.1
RS33 Unstable 48.4 -3.4 -6.6 1.4 18.7 6.2 Unstable -4.5 -6.6 1.8
RS34 Stable 3.1 -0.4 -1.6 -0.5 0.7 6.2 Stable -1.4 -1.7 -0.1
RS41 Unstable 5.2 -5.9 -1.0 0.8 4.7 6.2 Stable -6.7 -1.2 1.1
RS42 Stable 1.1 0.9 1.4 -0.3 0.5 6.2 Stable 0.2 1.2 0.0
RS43 Unstable 5.6 -4.7 -4.1 1.2 4.1 6.2 Stable -5.1 -4.2 1.4
RS44 Unstable 18.5 1.6 -0.6 -0.7 0.7 6.2 Stable 0.8 -0.8 -0.3
RS51 Unstable 12.5 -3.0 0.2 1.3 9.3 6.2 Unstable -3.9 0.0 1.6
RS52 Unstable 8.1 -1.0 1.3 -1.5 3.9 6.2 Stable -1.9 1.1 -1.1
RS53 Unstable 7.3 0.5 -1.7 1.0 3.9 6.2 Stable 0.3 -2.0 1.1
RS54 Unstable 14.1 -1.0 3.6 -0.7 7.3 6.2 Unstable -2.0 3.1 -0.3
RS61 Unstable 9.8 -3.1 1.6 1.2 6.6 6.2 Unstable -4.0 1.4 1.6
RS62 Stable 0.7 -0.7 0.0 0.6 1.0 6.2 Stable -1.2 -0.8 0.8
RS63 Unstable 5.5 3.1 2.6 2.0 3.3 6.2 Stable 2.9 2.0 2.0
RS64 Stable 0.8 -0.8 -1.9 0.3 0.8 6.2 Stable -1.0 -2.1 0.5
RS71 Unstable 15.7 3.5 -2.0 -0.2 4.5 6.2 Stable 2.9 -2.3 0.1
RS72 Unstable 19.0 3.3 2.0 -0.2 4.9 6.2 Stable 2.8 0.9 -0.1
RS73 Unstable 9.2 0.2 0.6 1.3 3.7 6.2 Stable 0.1 -0.2 1.2
RS74 Unstable 7.8 2.6 1.2 -0.9 2.0 6.2 Stable 2.1 0.9 -0.6
RS81 Unstable 19.7 4.1 0.9 1.0 4.8 6.2 Stable 3.8 0.5 0.9
RS82 Unstable 138.1 2.0 2.8 0.1 2.9 6.2 Stable 1.4 1.7 0.2
RS91 Unstable 21.1 3.9 4.6 -0.3 7.9 6.2 Unstable 3.7 3.9 -0.2
RS92 Unstable 9.6 4.3 2.8 -0.2 5.0 6.2 Stable 3.8 1.5 -0.1
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |

| 504 |
| 67/4 | GEODETSKI VESTNIK  
RECENZIRANI ČLANKI | PEER-REVIEWED ARTICLES
SI | EN
Points
Pelzer - Intensity of displacements [mm] IWST- Intensity of displacements [mm]
Status θ
2
dY dX dH T F Status dY dX dH
RS93 Unstable 40.3 5.4 7.4 0.5 15.4 6.2 Unstable 5.1 6.6 0.7
RS94 Stable 1.9 1.3 1.2 -0.4 0.7 6.2 Stable 0.8 0.0 -0.3
Assoc. Prof. Zoran Sušić, Ph.D. 
Faculty of Technical Sciences, University of Novi Sad
Trg Dositeja Obradovića 6, 21101 Novi Sad, Serbia
e-mail: zsusic@uns.ac.rs
Assist. Prof. Mehmed Batilović, Ph.D. 
Faculty of Technical Sciences, University of Novi Sad
Trg Dositeja Obradovića 6, 21101 Novi Sad, Serbia
e-mail: mehmed@uns.ac.rs
Assoc. Prof.  Radovan Đurović, Ph.D.
Faculty of Civil Engineering, University of Montenegro
Bulevar Džordža Vašingtona bb, 81000 Podgorica, Montenegro
e-mail: zlatko1979@yahoo.com
Assoc. Prof. Marko Marković, Ph.D.
Faculty of Technical Sciences, University of Novi Sad
Trg Dositeja Obradovića 6, 21101 Novi Sad, Serbia 
e-mail: marko_m@uns.ac.rs
Assist. Marijana Vujinović, M.Sc.
Faculty of Technical Sciences, University of Novi Sad
Trg Dositeja Obradovića 6, 21101 Novi Sad, Serbia
e-mail: marijana.petkovic@uns.ac.rs
Sušić Z., Batilović M., Đurović R., Marković M., Vujinović M. (2023). Deformation analysis of Ratkov Laz bridge using Pelzer and IWST method. 
Geodestski vestnik, 67 (4), 487-504. 
DOI: https://doi.org/ 10.15292/geodetski-vestnik.2023.04.487-504
Zoran Sušić, Mehmed Batilović, Radovan Đurović, Marko Marković, Marijana Vujinović | DEFORMACIJSKA ANALIZA MOSTU RATKOV LAZ PO PELZERJEVI METODI IN METODI IWST | DEFORMATION ANALYSIS OF 
RATKOV LAZ BRIDGE USING PELZER AND IWST METHOD  | 487-504 |