STUDY OF STRESS PATHS IN ARCHING

EFFECT USING FRICTIONAL STRAIN

HARDENING AND SOFTENING IN FINE

SAND

Alireza Abbasnejad*

Assistant Professor, University of Tabriz, Tabriz, Iran

abbasnejad@tabrizu.ac.ir

Mahyar Soltani

MSc Student, University of Tabriz, Tabriz, Iran

maahyarsoltani@gmail.com

Reception: 18/02/2023 Acceptance: 15/04/2023 Publication: 02/05/2023

Suggested citation:

Abbasnejad, A. and Soltani, M. (2023). Study of Stress Paths in Arching

Effect Using Frictional Strain Hardening and Softening in Fine Sand. 3C

TIC. Cuadernos de desarrollo aplicados a las TIC, 12(2), 15-58. https://doi.org/

10.17993/3ctic.2023.122.15-58

https://doi.org/10.17993/3ctic.2023.122.15-58

3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529

Ed.43 | Iss.12 | N.2 April - June 2023

ABSTRACT

Arching is one of the most common phenomena that occur in most geotechnical

structures. To determine the properties and quality of this phenomenon, a physical

model has been designed and constructed. The apparatus comprises rectangular

trapdoors with different widths that can yield downward while stresses and

deformations are recorded simultaneously. As the trapdoor starts to fail, the whole soil

mass deforms elastically. However, after an immediately specified displacement,

depending on the width of the trapdoor, the soil mass behaves plastically. This

behavior of sand occurs due to the flow phenomenon and continues until the stress on

the trapdoor is minimized. Then the failure process develops in the sand, and the

measured stress on the trapdoor shows an ascending trend. This indicates a gradual

separation of the yielding mass from the whole soil body. Finally, the flow process

leads to the establishment of a stable vault of sand called the arching mechanism or

progressive collapse of the soil body. To simulate this phenomenon with continuum

mechanics, the experimental procedure is modeled in ABAQUS software using stress-

dependent hardening in an elastic state and plastic strain-dependent frictional

hardening-softening with Mohr Coulomb failure criterion applying user sub-routine.

The results show that the experimental data have an acceptable corresponding to the

numerical analysis data. So the selected soil behavior could indicate the main aspects

of the arching effect, such as the flow that occurs in specific periods of strains. In the

following, the stress path in p, q, and p, ν

space was extracted from numerical

analysis, and the results have been discussed.

KEYWORDS

ABAQUS, Arching Effect, Stress Path, PIV, Frictional Strain Hardening and Softening,

Fine Sand.

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Ed.43 | Iss.12 | N.2 April - June 2023

INDEX

ABSTRACT

KEYWORDS

1. INTRODUCTION

2. PHYSICAL MODEL

2.1. Soil under test

2.2. Specifications of the built physical model

3. NUMERICAL MODEL

3.1. Behavioral model governing the arcing phenomenon

3.2. Rupture cover

3.3. Friction hardening

3.4. Frictional softening

3.5. The dependence of the friction angle and expansion on the stress level

3.6. The parameters of the behavioral model obtained from the experiments

3.7. Calibration of the behavioral model

3.8. Numerical model of arc phenomenon and modeling assumptions

3.9. Eliminating the effect of the arc in the place of stress gauges

4. EXPERIMENTS CONDUCTED ON THE PHYSICAL MODEL

4.1. The results of the data of the stress gauge installed on the valve and in the

middle of it (S1).

4.2. Comparison of the laboratory results with the numerical model, taking into

account the data of the stress gauge installed on the valve and in the middle of

it.

4.3. The results obtained from the PIV method concerning the measurement of

strains during the occurrence of the arcing phenomenon

4.4. The results of strain analysis

5. THE NATURE OF THE FLOW PHENOMENON IN THE ARCING PHENOMENON

6. TENSION SPACE IN THE SELECTED BEHAVIORAL MODEL

6.1. The stress space of area 1 (elastic area)

6.2. The stress space of zone 2 (softening zone)

6.3. The stress space of the area near the valve (hardening and softening

expansion area)

6.4. The stress space of zone 3 (hardening zone) - farther from the valve

7. CONCLUSION

REFERENCES

https://doi.org/10.17993/3ctic.2023.122.15-58

3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529

Ed.43 | Iss.12 | N.2 April - June 2023

1. INTRODUCTION

The arch phenomenon is one of the most important phenomena that we deal with

in geotechnical engineering. The impact of this phenomenon can be clearly seen in

underground and buried structures, so that the amount of force applied to the

structure depends on the redistribution of the stress caused by overburden or

overburden. Many scientists and researchers have worked in this field in a laboratory

and theoretical manner and have written numerous articles. This phenomenon was

first observed in the gunpowder storage silos belonging to the French army, and in

1895 John Sen presented the theory of silos. This phenomenon was shown for the

first time in a scientific way by an experiment on sand with an open valve conducted

by Terzaghi. It was proposed by him in geotechnical engineering. Usually, this

phenomenon occurs in places where there are sudden differences in the type of

materials in the soil mass. In other words, in the mass, two types of materials with a

different modulus of elasticity come into contact and exchange stress with each other.

In general, it can be said that arching occurs wherever there is a change of location in

the soil mass enclosed between stable supports, whether horizontal or vertical. Also,

this phenomenon can exist in all extents of deformation in the soil, so it starts with the

occurrence of elastic shear deformations and continues until the irreversible (plastic)

deformations and the breaking of parts of the soil mass.

To investigate the arching phenomenon in underground structures, Terzaghi

conducted an experiment in which a horizontal valve was lowered. When it was

moved, the amount of stress applied to the center of the valve was simultaneously

read. Using the results of these experiments and assuming plastic behavior for soil,

Terzaghi presented the theory of shear plates. In fact, by considering the balance of

forces in the plastic state of the soil, Tarzaghi was able to make the arch phenomenon

mathematically legal. After V. Finn, he modified the hypothesis related to Terzaghi's

theory and considered the elastic state of the soil. In the following years, many

experimental and numerical studies have been conducted to investigate the failure

mechanisms of the soil mass above the tunnel (Atkinson and Potts, 1977; Jiang and

Yin, 2012; Guo and Zhou, 2013; Han et al., 2017; Franza et al., 2018; Chen et al.,

2018; Jin et al., 2021; Zheng et al., 2021). These studies play an important role in

improving the understanding of the interaction between tunnels and soil and create a

solid foundation for developing theoretical models. After that, the parameters of silo

width and lateral stress ratio in Terzaghi theory were modified by many researchers

based on model tests and numerical analyzes (Stein et al., 1989; Hendi, 1985; Chen

et al., 2015; Zhang et al., 2016). Although many significant modifications have been

made based on Terzaghi's loose earth pressure theory, most of the research has

focused on shallow tunnels where the failure zone at the top of the tunnel extends to

the ground surface when the soil mass is in a limited state. However, for deep tunnels,

local failure occurs at the top of the tunnel according to many laboratory tests (Jacobs,

2016; Song et al., 2018) to evaluate the earth pressure on deep tunnels. Based on the

existing theoretical models for the shallow tunnel, a limited height of the silo was

further considered. Chen and Peng (2018) assumed that the height is 1.5 times the

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radius of the tunnel based on the numerical results in the soft ground of Shanghai.

The local failure height for the deep tunnel is related to the ground subsidence, the

phenomenon of soil expansion (change), and the depth of the tunnel cover in the light

of the previous study. Zhang et al. (2016) obtained a formula for calculating the local

failure height caused by the construction of the deep jacked pipe, in which the

relationship between the local failure height, the volume of loosened soils, and soil

bulking factors are simultaneously considered, was taken. Zhang's method assumed

that the shear bands start from the spring lines of the tunnel section. However,

according to the numerical results of Lin et al. (2019), the shear bands developed

diagonally from the bottom of the tunnel in the sandy ground. Therefore, the formula

presented by Zhang et al. (2016), used to calculate the local failure height, is limited to

sand.

However, the previous models for calculating the earth pressure in deep tunnels

assumed that the soil mass above the failure zone was not disturbed by the

construction of the tunnel and that the earth pressure applied above the failure zone is

the stress caused by the weight of the soil above, in fact, soil arching in occurs above

the failure zone, which leads to the transfer of earth pressure to both sides of the

failure zone. When the arch-bearing capacity of the soil is greater than or equal to the

weight of the soil above the failure zone, a cavity can be created above the failure

zone. The failure zone is zero. Such an arching effect of the soil above the failure

zone has been neglected by previous analytical approaches, which may consequently

overestimate the earth pressure exerted on the silo. A new 3D model considering the

arch effect above the fracture zone was developed by Chen et al. in 2019. To predict

the confining pressure exerted on the surface of the deep shield tunnel. The

calculated results by obtaining the new model agree with the experimental results.

However, it is assumed that the earth pressure distribution in the loosened zone is

uniform. The distribution of earth pressure on the tunnel can be different due to the

difference in the distribution of earth losses caused by the construction of the tunnel.

For the circular tunnel, Chen and Teng in 2018 pointed out that the vertical earth

pressure distribution shows a concave curve; that is, it is smaller in the center line and

increases with the increase of the horizontal distance from the center of the tunnel.

However, the current tunnel design for tunnels generally assumes vertical earth

pressure of uniform width. To reflect the uneven distribution of the vertical earth

pressure in the tunnel, Chen and Teng in 2018 assumed that the vertical earth

pressure on the tunnel conforms to the distribution of the Gaussian function, and then

presented a formula for calculating the earth pressure. However, there is a relatively

large error between the model results and the numerical analysis. Based on particle

flow theory, Wu et al. in 2019 obtained a modified formula by assuming that the

vertical earth pressure on the tunnel corresponds to a trapezoidal distribution. But, in

fact, the vertical pressure distribution of the earth is a smooth concave curve.

In this article, in order to determine the characteristics and how this phenomenon

occurs, a physical model has been designed and built that can model the arcing

phenomenon in a laboratory. In this physical model, valves with different widths have

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3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529

Ed.43 | Iss.12 | N.2 April - June 2023

been installed to investigate the effect of valve width on the occurrence of this

phenomenon. To determine the pattern of stress changes during the event of the

arcing phenomenon, miniature stress gauges with a diameter of 14 mm have been

used, and to determine the pattern of strain changes, the PIV method has been used.

Also, numerical modeling of this phenomenon has been done in Abaqus software and

the finite element method. To model the arch phenomenon, the hardening behavior

dependent on the stress level in the elastic range and the hardening and softening

depending on the plastic strain in the plastic range were used; for this purpose, a

program was written in the form of a subroutine in the Fortran environment and then

with the help of a compiler Visual Studio has been introduced to Abaqus software.

2. PHYSICAL MODEL

In this research, to model the arcing phenomenon, a physical model was designed

and built to provide the ability to model the arcing phenomenon on a laboratory scale.

2.1. SOIL UNDER TEST

A type of non-sticky silty sand passed through a grade 10 sieve, with a constant

humidity of 2% and a specific gravity of 2.62, was used for the experiments. The

granulation diagram and characteristics of the soil used are presented in Fig. 1 and

Table 1, respectively.

Figure 1. Sand grading curve

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3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529

Ed.43 | Iss.12 | N.2 April - June 2023

Table 1. Characteristics of the soil used in the research

2.2. SPECIFICATIONS OF THE BUILT PHYSICAL MODEL

To physically model the arcing phenomenon, a device was designed and built. Fig.

2 shows the fabricated device and test details. The physical model consists of a

metal skeleton, in the upper part of which is a rectangular cube tank with a steel frame

with internal dimensions of 400 x 1830 and a height of 1250 mm. Its main skeleton is

made of steel plates with a thickness of 10 mm and a stud profile. 200 were made. In

the outer part of the side plates, five rows of 80-grade corner type hardeners have

been used. To increase the strength, the two parts of the skeleton are welded

together using 100-grade stud material to eliminate lateral deformation in the skeleton

due to the lateral pressure of the soil and the overhead pressure caused by the

loading jack. The lower part of the structure consists of three rows of grade 200 stud

profiles, along with a 100 mm thick plate welded, and the upper skeleton is made of

100- grade studs with the help of four legs to this 3000 x 600 mm plate is connected.

In total, the height of the device is 2200 mm. Two 10 mm thick steel plates are

installed on the bottom of the machine's tank, which can be moved to the sides in a

sliding manner, and as a result, the distance between the two plates, which is equal to

the width of the valve, can be adjusted. Four separate rectangular pieces with widths

of 10, 20, 30, and 35 cm were used for movable valves. When using each valve, the

two side plates are opened to the sides as wide as the valve, and the desired valve is

placed between the two jaws embedded in the side plates, which serve both as a

stiffener and as a guide for the valve movement would take. The valve is secured in

place using eight provided screws. These valves are made of a 10 mm thick sheet

and could move down up to 40 mm. On both sides of the tank, two transparent

Plexiglas plates with a thickness of 30 mm were installed to observe the changes in

soil locations. To increase the rigidity, a steel grid with stiffeners of 50 mm height and

20 mm thickness was installed, which could be opened, and each of them was

connected to the skeleton by 20 screws.

According to Fig. 2, in order to measure the displacements applied to the valves, a

strain gauge was installed under the valves. Also, to measure the stresses involved

on the valves by the sand, a stress gauge was also established under the device, so

that the applied stress from the valves is directly transferred to the stress gauge.

γ max 17.35 (kN/m3) Fc9.5%

γd max 17.01(kN/m3) Gs2.62

γmin 12.88 (kN/m3) M(moisture) 2 %

γd min 12.63 (kN/m3) Classification SP-SM

Dmax 2 mm

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Ed.43 | Iss.12 | N.2 April - June 2023

To apply displacement to the valve, a 10-ton hydraulic jack with a stroke of 70 mm

with the ability to adjust the speed was installed under the stress gauge, which

enables displacement be applied to the valves. Also, a 20-ton hydraulic jack with a 50

mm stroke with a rigid pressure plate was designed and built to spread the overhead

pressure. This overhead pressure system was able to be installed on the device

using a roof crane made for this purpose. This capability provided the possibility of

filling the tank by installing the sand precipitation system and then re-installing the

loading system.

The dimensions of the tank have been chosen according to the maximum width of

the valve and the type of soil used, and other physical models have been designed in

such a way that while removing the effect of the side borders (walls of the tank) on the

results, it is not too large as required so that It is possible to fill and empty the tank.

Researchers have chosen physical models with different dimensions to study the

arcing phenomenon. In this research, the criteria considered for the study of

underground tunnels have been used to select the size of the tank size. In the model

made by Branko and his colleagues, the distance from the center of the tunnel with a

diameter of 55 cm to the lateral borders of the model is 1.2 times the diameter of the

tunnel. in the model made by Kim and his colleagues, for a tunnel with a diameter of 7

cm, this distance is 7 times The diameter of the tunnel selected. On average, in most

of the designed modes, the distance from the side walls to the center of the tunnel is

in the range of 4 to 6 times the diameter of the tunnel. In this research, taking into

account the recommendations of previous researchers and the difficulties caused by

building a physical model with large dimensions as well as filling and emptying the

tank for multiple tests, the distance from the side walls to the center of the valve with a

maximum width (35 cm) is more than 5 times the width of the valve (exactly 5.22

times) was chosen. The width of the built model is equal to 183 cm and equal to the

length of the full Plexiglas sheet.

After designing the initial dimensions of the model, the effect of the distance of the

side walls selected for the tank was investigated using a numerical model. In this

way, in the built numerical model corresponding to the dimensions of the physical

model, the distance of the lateral borders of the model was increased to 1.5 and 2

times the initial value, and the results were compared with the values obtained from

the selected state. Based on the results obtained from the numerical model, the

stresses and strains created as a result of the occurrence of the arch phenomenon did

not change with the increase in the distance of the lateral borders. Therefore the

distance of 5 times the width of the valve is acceptable for the lateral boundaries of

the model.

In the construction of the physical model, the issue of model rigidity and removal of

model deformations should be considered. The physical model should have been

designed and built so that it would not show any deformation due to the overhead jack

force. This issue is significant, especially in the strain measurement results using the

image speed measurement method. For this purpose, the box’s design was done

with great care, and steel sheets with the required hardeners were used to make the

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3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529

Ed.43 | Iss.12 | N.2 April - June 2023

box. To check the rigidity, the designed physical model was also modeled in the

Abaqus software environment. The displacements caused by the lateral pressure

caused by the soil and the force applied by the overhead jack were calculated. It was

found that the amount of horizontal displacement caused by using a uniform pressure

of 2 kg/cm2 on the vertical sides of the steel tank and the Plexiglas plate, which is

more than the maximum pressure applied to the walls during the tests, is at most 1

mm. In general, the amount of deformations is minimal and can be ignored, and

therefore the built physical model has sufficient rigidity against the applied loads.

Modeling of the machine body in Abaqus software is shown in Fig. 3.

https://doi.org/10.17993/3ctic.2023.122.15-58

3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529

Ed.43 | Iss.12 | N.2 April - June 2023