Journal of Civil Engineering and Urbanism  
Volume 10, Issue 5: 42-52; September 25, 2020  
Identifying the Effective Parameters in Soil Arching for Retaining  
Structure; A case study of Line 2 of Mashhad Subway  
Mostafa Vahedian, Masoud cheraghi Seifabd and Alireza Baghbanan  
Department of Mining Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran  
Corresponding author’s Email:;  
The effective parameters on soil arching in retaining structures composed of the steel piles (2PIE300) and the steel  
anchors were considered using PLAXIS 3D TUNNEL for a three-dimensional numerical model. To better compare,  
it was assumed that external loading conditions and technical features of structural elements were the same. To  
determine the limits of effective parameters in fine (CL-ML) and coarse grains (SC-SM), according to the soil  
specifications of the stations A2 to L2 in in Mashhad urban railway line 2 (Iran), Hardening Soil Model (HS) was  
used. Modeling started with a horizontal and vertical distance of 2 meters and increased to a distance of 4 meters.  
The parameters of the soils including angles of internal friction, cohesion, density and elastic modulus and the  
distance between anchors have been selected to present the prediction model. All parameters of the soils have been  
used for multiple regression and artificial neural network modeling statistical analysis. To present a prediction  
model, 5 parameters including internal friction angles of soil, cohesion, soil density, distance between anchors and  
elastic modulus have been selected and all of them except final parameter have been used to analyze multiple  
regression and artificial neural network modeling. The results showed that the best regression model that could be  
presented is the correlation of 94% between measured and predicted values. The prediction effectiveness of the  
neural network model has been found to be acceptable as they produced higher correlation coefficient (99%)  
between the variables and for the prediction of the factor of safety.  
Keywords: Soil arching, Multiple regression, Artificial neural network, PLAXIS 3D TUNNEL, Line 2 of Mashhad  
urban railway, Excavation safety factor  
been used to describe the transfer stress phenomenon by  
mobilizing shear strength (Wang and Yen, 1974). In other  
words, aching is known as transferring stress from one  
failure mass to the next fix and stable masses (ASCE,  
example, applied a total of 131 2D trapdoor-like discrete  
element models to address the soil arching effect, stress  
state and deformational behaviours of the piled  
embankments. The importance of the stabilization of soil  
or rock wall at the time of excavation has been considered  
by engineers. Accordingly, different methods of retaining  
structures have been considered as tools for the  
stabilization; these include concrete or steel piles, truss  
methods, cable anchorage method, and nailing in the soil.  
Soil arching is one of the properties of in the soil  
One of the most widely applied cases in engineering is  
estimating and predicting one parameter according to  
available parameters effective on it. In the last years, there  
has been an attempt in different engineering branches, to  
find the methods which would not require complex  
calculations and not be time-consuming. For this reason,  
various methods have been used in Geotechnical  
Engineering, such as Multivariate Regression Analysis  
(MRA) and the recent years, Artificial Neural Network  
Arching is one of phenomena repeatedly occurring in  
the field and laboratory. It has been found in underground  
structures such as underground canals. In underground  
tunnels, arching can be used to decrease the overburden  
pressure on structures. Redistribution of stresses due to  
arching effects can lead to changing the loads acting on  
the structure. These loads may be from the overburden  
pressure, surface loads and the lateral pressure of ground.  
Arching effect can be found in the natural excavation; has  
To cite this paper: Vahedian M, Cheraghi Seifabd M and Baghbanan A (2020). Identifying the Effective Parameters in Soil Arching for Retaining Structure; A case study of Line 2  
J. Civil Eng. Urban., 10 (5): 42-52, 2020  
environments that can reduce the expenses of the project  
the excavation diameter of 9.43m and the completed  
diameter of 8.4m, has been extended along the north-east  
to south-west, with 13 stations, named A2 to L2 (Figure.  
1). This tunnel has been excavated by two TBM machines  
(EPB/Open) in two sides, one from the northern direction  
at the distance of 383m from the station A2 and the other  
from the southern direction (Station L2).  
without reducing safety. This study considered soil  
arching phenomenon and the influencing parameters  
including density and angle of internal friction angle to  
calculate the factor of safety for a 10 m long definite  
retaining structure. The factor of safety has been obtained  
using the finite element code of PLAXIS 3D TUNNEL  
(Plaxis, 2004). Finally, this paper presents an equation to  
calculate the factor of safety from the influencing  
parameters of soil arching for design of a safe retaining  
structure with a minimum displacement.  
Using Neural Networks  
High speed computers and algorithms have made it  
possible to use the neural networks to solve complex  
industrial problems previously requiring many calculations  
Figure 1. Mashhad Urban Railway line 2  
By using the trial and error method, different  
dimensions related to the geometry of models, such as  
width of excavation, could be simulated and the desirable  
distance would be obtained for the model borders.  
Regarding the dimensions of the district for excavation  
and the above-mentioned subjects, the geometry of model  
is illustrated in two dimensions, as can be seen in Figure.  
2. This geometry is the same for all models.  
Levenberg- Marquardt Algorithm  
In this research, the Levenberg-Marquardt algorithm  
was used to train the network. It is a kind of back  
propagation algorithm different from the Gaussian –  
Newton’s optimization algorithm. A new order of weights  
in the step of k+1 is calculated as follows (1):  
W (k+1)= w(k)- (JT J +λ. I)-1 JT .ε (k)  
J is the Jacobian Matrix written for a Neuron as follows  
J   
Where, λ is a non-negative damping factor, I is the  
identity matrix, w is the weight vector, and is the error  
vector. There is difference between the output of network  
and the real output. Parameter λ is corrected on the basis  
of the function of E. If E is deceased in any steps, it is  
accepted; otherwise, λ will change and w (k+1) will be  
calculated again.  
Figure 2. Dimensions of the model  
Soil material and proper behavioral model  
Soil of the station A2 is a fine grain one, while the soil  
of station L2 is a coarse one. According to this, the studied  
soil, from fine grain (CL-ML) to coarse grain (SC-SM), is  
in the same form without any lamination. The conformity  
with geotechnical conditions of the structures of the  
mentioned stations has been considered to simulate the  
soil behavior. Among the advanced models, those which  
have less parameters and involve simple relations, in spite  
of the important behavioral sides of materials, are more  
desirable for the geotechnical engineers.  
A case study: Line 2 project of Mashhad urban  
Mashhad, the second largest religious city in the  
world, is located in the north-east of Iran. Tunnel of  
Mashhad Urban Railway line 2, with the length of 14km,  
Vahedian et al., 2020  
According to the geotechnical reports of Mashhad  
failure strength of 18500 kg/cm2 are used. Each cable is  
made of seven twisted wires and cable diameter is 0.6  
inch. The excavation diameter is 116mm with the angle of  
10° in horizontal, to perform the anchors. The length of  
the injection masses is 8m for all anchors. The location of  
the anchor rods (including the distance of the first row  
anchor rod from surface and horizontal, and the vertical  
distances between the anchor rods from each other) and  
their lengths are according to the standard of FHWA. In  
this case, in all models, the distance of the first anchor rod  
from the surface is 1.2m, and the distance of the middle of  
the injected section of the end of the anchor rod in the first  
row is 4.5m from the surface. Then, the free length of the  
first anchor rod row is 15m for all models; the length of  
other anchor rods has been measured in terms of the first  
anchor rod row. There was no cover or retaining structure  
(Lagging or shotcrete) between spaces of the steel anchors.  
Tables 2 to 4 illustrate the physical specifications of the  
urban railway line 2, E50=10000 kPa is for the fine grain  
soils of the station A2 in the depth of 0-9m and m=0.85 is  
selected. Then, regarding the shear parameters of the fine  
grain soil in the mentioned stations and 3=100 MPa, the  
value of Eref50=10000 kPa is calculated.  
E50=80000 kPa is for the coarse grain soil and m=0.5  
is selected. Then, given the shear parameters of the coarse  
grain soil in the mentioned stations and 3=100 MPa, the  
value of Eref50=80000kPa is calculated.  
According to Erefur=3 Eref and Eref50=1.25 Eref for  
the fine grain soil and Erefur=3 Eref and Eref50= Eref for  
the coarse one, the limit of the input parameters of the  
Hardening Soil Model (HS) is as brought in Table 1.  
Table 1. Specifications of the Soil Materials  
The least  
The most  
Soil behavioral  
Table 2. Specifications of the steel anchors  
Soil behavior  
Symbol Value  
Unit of Measurement  
Density above water  
Axial stiffness  
x 10 6.  
Density below  
water table  
x 10 4  
Flexural stiffness  
Secant stiffness in  
the standard triaxial  
1.8 x 104  
Poison’s ratio  
Material behavior  
Tangential stiffness  
for the initial  
1.44 x 104  
5.4 x 104  
Table 3. Specifications of the injected mass  
Stiffness of loading  
and unloading  
Unit of Measurement  
Potential of the  
stress level related  
to the stiffness  
5.28 x  
10 4  
Axial stiffness  
Effective cohesion  
C '  
Effective internal  
friction angle  
Table 4. Specifications of the steel anchors  
Unit of Measurement  
Dilation angle  
x 10 5  
Axial stiffness  
Material behavior  
Node to node anchor  
200 kN  
Method of pile and anchoring  
Pre-stress Force  
Along Y, the structural elements of the steel piles  
have been selected from the constructional profile  
(2IPE300). Specifications of the piles are schematically  
illustrated in Figure. 3. Four piles along the Z of models  
and at a distance of center to center is equal (s) to the  
distance between the anchor rods. Cable anchors in the  
Figure 4 illustrates the first phase of the construction  
stages. In this stage, the shafts are excavated for steel piles  
and these piles are interred in these shafts. In all models,  
the depth of the interred pile is 3m.  
J. Civil Eng. Urban., 10 (5): 42-52, 2020  
Figure 3. Schematic view of the profiles 2IPE300  
Figure 4. Perspective of the phase 1 of the model in stage  
Figure 6. Perspective of the phase 3 of the model –  
construction analysis  
activating the first row of anchors  
Figure 5. Perspective of the phase 2 of the model,  
Figure 7. Perspective of the phase 4 of the model the  
excavation in the depth of 1.7m  
second stage of excavation  
Vahedian et al., 2020  
Study of soil anchoring parameters  
Anchoring zone can be found with displacement  
counters in the soil movement direction, in addition to the  
rotation of the directions of the principal stress. The  
displacement contours in the direction x have been  
illustrated in Figures 10-15 to study, this case, the  
horizontal sections in x-z. At first, the relation between the  
safety factor and arching has been illustrated for  
quantification. After that, the parameters effective on the  
safety factor will be considered. As represented in figures  
10-15, the safety factors are 1.1, 1.7, 2.5, 3.0, 3.6 and 3.9,  
Figure 8. Perspective of the phase 5 of model activating  
the second row of anchors  
Figure 9. The final phase of excavation  
Figure 10. The circular pattern of the lateral displacement  
of soil (Ux) between piles with the safety factor of 1.1  
Figure 5 illustrates the second phase. At the beginning  
of this phase, the stress effect resulting from excavating  
piles has been omitted and the change of the first places  
as a result of stress will be zero. Then, the excavation will  
be performed to the level 0.5 m, which is lower than that  
of the first anchor rod row (in depth of 1.2). In this phase,  
the steel piles are active, while the steel anchors are not.  
Figure 6. illustrates the third phase that includes the pre-  
stress force on the steel anchors. The three first phases are  
the same for all models; however, after that (phase 4), the  
depth of excavation will be changed based on the change  
of the vertical distances between anchors in different  
models. In the phase 4, excavation is performed to the  
expected level. In this phase, the steel piles and the first  
row of anchors are used. For example, the vertical and  
horizontal distance is 2 m (Figure 7). In the phase 5, the  
pre-stress force of the second anchor rod row is used  
(Figure 8). All of the stages will be repeated to reach the  
final level of excavation, the depth of 10m, based on the  
distances of the anchors (Figure 9).  
Figure 11. The circular pattern of the lateral displacement  
of soil (Ux) between piles with the safety factor of 1.7  
J. Civil Eng. Urban., 10 (5): 42-52, 2020  
Figure 15. The circular pattern of the lateral displacement  
of soil (Ux) between piles with the safety factor of 3.9  
Figure. 12. The circular pattern of the  
displacement of soil (Ux) between piles with the safety  
factor of 2.5  
In Figures 9-18, the darker sections illustrate more  
displacement, while the lighter ones represent the less  
displacement. As shown, the deformation pattern of soil  
in the direction x is in the arch form between the piles.  
The height and width of these arches are different; the  
reason is that with a higher safety factor, the height and  
width of these arches will be decreased. The reason for  
this displacement between pile and block as a result of  
arching can be explained. This is because transferring the  
soil pressure to the piles and blocks supporting in the  
arching directions will occur. In other words, the transfer  
of stress to the piles and anchors will be increased, while  
the displacement will be decreased as a result of the  
arching phenomenon.  
Figure. 13. The circular pattern of the  
Box-Cox method  
When the relation between error and average is not  
displacement of soil (Ux) between piles with the safety  
factor of 3.0  
clear as that  
in the logarithmic and square  
transformations, then a potential transformation can be  
used. Box-Cox transformation function is a nonlinear  
monotonic transformation including log-linear and some  
special linear functions (Fitzenberger et al., 2005). It is an  
important transformation covering many distribution  
functions. Hence, this linear transformation can transform  
to normal distribution. The general form of this  
transformation is as follows (3):  
Where, x is the data that should be normalized, λ is a  
real value and Z is a transformed value. If this  
transformation does not give the data to the normal  
distribution, the minimum data will be ordered. Also, the  
reverse transformation of this function is simple, and this  
Figure. 14. The circular pattern of the  
displacement of soil (Ux) between piles with the safety  
factor of 3.6  
Vahedian et al., 2020  
is one of the advantages of this method. In this case, the  
distribution function of data is as follows (4):  
ꢀ ꢂ  
− [ −훼]  
ꢁ ꢃ  
( )  
푓 푥 = 훽  
and refer to the average and standard deviation  
of the transformed data, respectively. Definitions of  
( )  
average and skewness (s) should be used to calculate  
the real average and variance (5, 6).  
( )  
= 퐸 푋 =  
( )  
푋푓 푋 푑푥  
( )  
푥 ꢇ 푥̅  
( )  
푓 푥 푑푥  
푠 = 퐸 푥 ꢇ 푥  
Method of estimating λ  
Using standard curves to calculate λ  
As shown in Figures 16 and 17, the data related to the  
normal distribution have not been covered completely; so,  
the distribution of the safety factor is normal if λ= 0.06.  
This method has also been used for four independent input  
variables. λ values of the variables are illustrated in Table  
Figure 17. (A) Cumulative distribution of the safety factor  
with the raw data; (B) Cumulative distribution of the  
safety factor after using the Box- Cox transformation  
Table 5. λ Values for the dependent and independent  
The distance between anchor rods  
The internal friction angle  
Soil density  
Safety factor  
Selecting the best regression model  
As there are few input variables, using all possible  
regression methods is preferred over other strategies for  
selecting the variable. Using this method seems to be  
logical. Then, in the first step, all possible regression  
methods (25-1) are processed by the mentioned method;  
after that, the processed patterns are divided to a set  
Figure 16. (A) Histogram of the safety factor distribution  
with raw data; (B) Histogram of the safety factor  
distribution after using the Box- Cox transformation  
J. Civil Eng. Urban., 10 (5): 42-52, 2020  
composed of 1-5 variables. Then, the patterns will be  
As shown, cohesion and internal friction angle have  
the most positive effect on the safety factor; , while soil  
density and the distance between anchor rods have a  
negative effect . These cases were expected.  
selected according to some criteria such as the coefficient  
of determination, the coefficient of determination adjusted,  
Mean Square Error (MSE), Mallow’s Cp and the best  
model used by the five mean variables. (Table. 6)  
As represented in Table 6, the processed models  
includes cohesion; the second model includes cohesion  
and the internal friction angle. The three-variable model  
includes cohesion, internal friction angle and soil density;  
the fourth model consists of cohesion, internal friction  
angle, soil density and the distance between anchor rods.  
Finally, the fifth model covers cohesion, internal friction  
angle, soil density, the distance between anchor rods and  
the elastic modulus of soil.  
The results obtained from neural networks  
The neural network has been considered to expect the  
safety factor. It is supposed that there is a nonlinear and  
complex relation between the safety factor and the  
specifications of soil. Consequently, the neural network  
has been considered to study the correlation between the  
safety factor and the model parameters and to compare  
the results obtained from multiple regression analysis.  
Preprocessing the data  
Table 6. Summary of the results obtained from all  
possible regression models  
Training of the neural network can be more effective  
if some targets and inputs are preprocessed. Error  
estimation method is used to scale the inputs whose value  
of error is equal to zero. Then, the inputs and target will be  
Number of  
Adjusted R2  
Mallow ‘sCp  
Making model by back propagation networks to  
estimate the safety factor  
In this research, to estimate the safety factor, a leading  
network with a back propagation algorithm and error was  
used. To train the network, the data were divided  
randomly in three classes including training, validation  
and test. Then, 70%, 15% and 15% of the data were  
divided for training, validation and test, respectively.  
Levenberg-Marquardt algorithm was used to train the  
network and the root-mean-squared error was also applied  
as a cost function. The network was composed of two  
hidden layers and one output layer with arrangement (1,  
50, and 20); the tangent sigmoid function was in the  
hidden layers and linear function was in the output layer  
(Figure.19). The number of the optimized layers and  
neurons was obtained based on the trial and error; then the  
desirable network was not unique. The results obtained  
from three subsets of training, validation and test have  
been illustrated in Figure 20. The correlation coefficient  
between the measured and expected values was 0.998,  
0.993 and 0.994 for training (Figure 20 A), validation  
(Figure 20 B) and test (Figure 20 C), respectively.  
Standardized regression coefficients  
It is difficult to compare the regression coefficients,  
because j (dependent variables coefficients) is a reflex of  
the measurement units of the independent variable Xj . It  
will be useful to use the scaled dependent and independent  
variables that can lead to the regression coefficients  
without unit. There are currently two scaling methods. The  
first one is unit normal scaling. The second one is unit  
length scaling. Then, the effect of each independent  
variables can be addressed by the standardized regression  
coefficients (Figure 18).  
Figure 19. Schematic network including two hidden  
layers and one output layer  
Figure 18. The standardized regression coefficients for  
the regression model with 4 variables  
Vahedian et al., 2020  
Analyzing post-training  
Training network efficiency is measured by using the  
errors of training, test and validation sets; however, it is  
better to study the details of the net reaction carefully.  
Postreg method has been designed to implement the  
analyses. So, the following instructions can illustrate how  
regression analyses can be done in the training network.  
[m, b, r] = postreg (a, t)  
where m and b refer to the slope and linear fit and y  
is the best regression linear related to the outputs. If there  
is a perfect fit (that is the outputs are equal to the target  
completely), the slope will be equal to 1. As found in this  
research, the result was very close to the desirable values.  
The correlation coefficient was 0.9770, which was  
increased in comparison with the regression results. The  
graphic output has been illustrated in Figure 22.  
Figure 20. Correlation coefficients for training, validation  
and test  
Square error curve based on the training cycles has  
been illustrated in Figure 21. The error values of  
validation and test were very close to each other; so, the  
result was good, and preprocessing would not occur.  
Figure 22. The linear correlation between the measured  
and expected values after post training  
In this research, we tried to provide a useful relation by  
using multiple regression and neural network so that it  
would the ordinary methods; it could serve as a fast and  
simple solution for the engineers and employers to solve  
problems. By conducting the initial studies and finding  
the geotechnical parameters of soil, different models with  
effective parameters were made by PLAXIS 3D  
Figure 21. Square error curve based on the training cycles  
for training, validation and test  
J. Civil Eng. Urban., 10 (5): 42-52, 2020  
As the time of response was very long, the safety  
Competing interests  
factor curve opposite of this parameter was drawn  
coincidently with making these models to omit the  
ineffective parameters and save the time. Totally, 212  
models were made on the basis of the available  
possibilities. 5 parameters were measured on 212 models  
and they were made by the data. Then, various models  
with various variables were processed by using multiple  
linear regression. The best model was obtained by using  
all regression models method. In this study, although data  
was not normal, since the result of parametric regression  
was desirable, nonparametric methods such as  
nonparametric regression could not be used.  
It should be , however, noted that multiple regression  
analysis and artificial neural network training are used to  
expect the parameter which is the safety factor; so, they  
cannot be useful tools to analyze the effect of each  
independent variable on the dependent parameter. To  
The authors declare that they has no competing  
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1. There is a direct relation between safety factor  
and arching; as arching is increased by enhancing the  
safety factor (displacement will be decreased), then the  
safety factor can considered to reach a quantity concept  
and a relation.  
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stability of the excavation.  
4. Soil density (γ) is the first effective parameter on  
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if soil density is increased, the safety factor will be  
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5. The distance between anchor rods (sh) is the next  
parameter. Although it has less effect in comparison to the  
mentioned parameters, it is an important parameter as  
there is a reverse relation between it and the safety factor;  
so, when this parameter is increased, the safety factor  
will be decreased.  
6. The correlation coefficient as a result of the  
neural network was 0.994 for the subset of test. This was  
more than that of multiple regression, thus indicating that  
the neural network can be very strong in determining the  
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All authors contributed equally to this work.  
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