an investigation into the mechanisms that generate …

AN INVESTIGATION INTO THE MECHANISMS THAT GENERATE PULLOUT RESISTANCE OF

STEEL CHAIN IN NON-COHESIVE SOILS

Kepha ABONGO1, Makoto KIMURA2, Tirawat BOONYATEE3, Akihiro KITAMURA4 and Kiyoshi KISHIDA5

1Post Graduate Student, Dept. of Urban and Environmental Eng., Kyoto University

(Nishikyo-Ku, Kyoto 615-8520, Japan) E-mail: [email protected]

2Member of JSCE, Professor, Innovative Collaboration Center, Kyoto University (Nishikyo-Ku, Kyoto 615-8520, Japan)

E-mail: [email protected] 3Associate Professor, Department of Civil Engineering, Chulalongkorn University

(Phyathai Road, Patumwan, Bangkok 10330, Thailand) E-mail: [email protected]

4Member of JSCE, Showa Kikai Shoji Co. Ltd, Osaka (Siminoue-Ku, Kitakagaya-1 Chome -3-23, Osaka 559-011, Japan)

E-mail: [email protected] 5Member of JSCE, Associate Professor, Dept. of Urban and Evironmental Eng., Kyoto University

(Nishikyo-Ku, Kyoto 615-8520, Japan) E-mail: [email protected]

Design method for reinforced chain wall has been developed even though the mechanisms that generate pullout force of chain are not clear. In order to evaluate the pullout mechanism, a series of pullout test were conducted on chains of varied configurations. Assuming that the total pullout resistance consists of three components which are bearing resistance, shearing resistance of the trapped soil inside each loop and the frictional resistance between the chain and soil, test results showed that the bearing resistance accounts for about 90 % of the total resistance. In addition it was found that the shearing resistance of the soil enclosed in the inside loop is too small and therefore can be neglected when computing the pullout force of steel chain. Key Words : pullout resistance, passive bearing resistance, frictional resistance

1. INTRODUCTION

The mechanism and construction technique of re-inforced soils have been investigated both in Labo-ratory and field research works. These activities have resulted in development of new reinforcement mate-rials and methods1), 2) with the most commonly used reinforcement inclusions being galvanized steel ei-ther in strip, bar or grid configurations connected to a concrete facing panel3).

The increase use of geogrids, steels and other re-inforcement have raised the need to evaluate the soil-reinforcement interaction parameters such as pullout resistance which is important in the design of reinforced walls. The behavior of soil and rein-

forcement inclusion is largely governed by the in-teraction mechanisms that develop between the in-clusion and the backfill soils. The main function of the inclusion is to redistribute the stresses within the soil mass in order to enhance the internal stability of the wall4). The evaluation of soil-reinforcement in-teraction parameters can be achieved through pullout test or shear box test5), 6). Dyer7) using photoelectric-ity clarified and identified different mechanisms of interaction between soil and reinforcement as either friction or bearing or a combination of both as shown in Table 1. Geotextile and plain strip generate bond with the soil by friction mechanism. In grid, de-pending on the geometry, the bearing mechanism may prevail due to the interaction between the grid

Journal of Japan Society of Civil Engineers, Ser.C (Geosphere Engineering), Vol. 67, No. 1, 1-15, 2011.

1

bearing members and the surrounding soil. Of im-portance then is the identification of the right mechanism and the choice of a convenient and right way of measuring the magnitude of bond stress be-tween the soil and the reinforcement. Reinforcement inclusions that rely on both mechanisms, the pullout resistance can be taken to be the sum of the two mechanisms8), 9) with the synergism between these two load transfer mechanisms being neglected4).

The most reliable method of checking the fric-tional resistance of an inclusion from pullout test is by evaluating the interface angle of friction (δ) de-veloped between the soil and the reinforcement in-clusion. Most interface friction angle values are smaller than the soil friction angle (φ) although val-ues of δ greater than φ may be expected due to boundary effect, scale problems or inaccurate meas-urement of soils friction angle10),11). The interface friction angle for geotextile are within the limits 0.75φ < δ < φ and that of plain grid are in the limit 0.3φ < δ < 0.7φ. Unlike the frictional resistance, bearing resistance of reinforcement is a complicated phenomenon to evaluate. Several failure mechanisms have been proposed to estimate the passive bearing resistance of the reinforcement that depends on pas-sive bearing as the main source that generates its pullout resistance12),13).

Besides the geogrids and strip reinforcements, steel chain has been used to reinforce fill slopes in Japan. This concept of earth reinforcement using chain emanated more than ten years ago2). Despite the fact that little is known about the mechanisms that generate pullout force of chain in reinforced fill, construction of walls using chain has been carried out specifically in Japan. Two factors have necessitated the use of chain as an inclusion in fill slope rein-forcement. One of the factors is its high frictional coefficient compared to other traditional reinforce-ment materials such as steel rods, ribbed flat plates and smooth flat bars. The other factor is its flexibility and hence the ability to be folded during transporta-tion. Fig. 1 shows results from omparative studies14) on chains of different shapes and sizes with other steel reinforcements. This chart shows that chain generate higher bond coefficient than these materials which are readily available in the market. The bond coefficient was calculated by dividing the peak pullout resistance for each reinforcement by the product of the effective area and the overburden pressure. Like any other reinforced methods, chain wall method involves compacting thin layers of soil and laying chain over these layers. The schematic repre-sentation of the components of reinforced chain wall is as shown in Fig. 2 where steel chains are integrated

with steel pipe frames which serve the purpose of the facing panel. During the construction of reinforced chain wall, bottom rails which hold the steel frames are first set. The hollow steel frames are held into position by the bottom rails and are joined to each other as the construction height progresses. The steel chains are attached to the steel frames using flexible joints which are capable of sliding over the frames hence can follow the movement of the chain incase of some eventualities such as consolidation of the ground. Pullout resistance of chain may be enhanced by attaching an L-shaped bearing plate anchor at the end of the chain as shown in Photo 1.

Since the steel frames are set 50 cm apart, large spaces are left between them. In order to minimize these spaces and to hold the soil firmly together, a woven wire net of aperture size 2 cm by 2 cm is laid around the facing panel. To the inside of the woven wire net, a vegetation mat is laid. This mat is laced with grass seeds that grow around the wall under suitable environmental conditions. Photo 2 shows-

Fig. 1 Comparative study between chain and other reinforcement materials14).

Table 1 Common types of reinforcement7).


2

such constructed wall in the mountainous region of Japan.

2. EXISTING DESIGN METHODS FOR

ESTIMATING PULLOUT RESIS-TANCE OF STEEL CHAIN

(1) Circle stripe model Little is known about the mechanisms that gen-

erate pullout force of steel chain in soil. Previous studies15) attempted to decompose the components that generate the pullout resistance into three parts namely (1) the frictional component generated along the perimeter of the shaft of the chain (2) the shear resistance of the soil enveloped in the inner space of the chain and (3) the passive bearing resistance acting at the front of the chain. Fig. 3 shows the circle stripe model used by Inoue et al.15) for evaluating the pullout capacity of the chain. In light of these three components, Equations (1) to (6) were proposed to evaluate the pullout resistance of chain in soil.

321 FFFFf μ++= (1)

NKAF v ×⎟⎠⎞

⎜⎝⎛××⎟

⎠⎞

⎜⎝⎛ +

×=2

tan2

1 001

φσ (2)

Inoue et al.15) assumed that due to the circular

shape of the bar, the distribution of the earth pressure acting at the shaft of the chain is non-uniform and expressed the earth pressure acting on the perimeter of the shaft as the average of the vertical and hori-zontal earth pressure. The quantity (1+K0)/2 in equation (2) denoted the evarage earth pressure act-ing on entire shaft of the chain. The angle of skin friction on the chain’s shaft was assumed to be half the angle of internal friction of the soil.

NAF vi ×××= φσ tan22 (3)

NDDBKF pv ××−××= )(3 σ (4)

φsin10 −=K (5)

φφ

sin1sin1

−+

=pK (6)

where Ff is pullout resistance of steel chain, F1 is the frictional force acting along the perimeter, F2 is the shear resistance of the soil enveloped in the inner space of the chain, F3 is the passive bearing acting in the front part of the chain, Ao is the surface area of bar portion in which the friction resistance occur, Ai is the area of the inner space of the loop, K0 and Kp are coefficient earth pressure at rest and coefficient of passive earth pressure respectively, φ is the angle of

internal friction of the soil, σv is the applied pressure, B is the outer with of the chain, D is the diameter of the wire from which the chain is made from, N is the number of links of the chain and μ is coefficient of bearing capacity acting in front of the chain. The value of μ was proposed to range from 1.0 to 2.5.

The pitfall of this model is the difficultly in choose the appropriate value μ for design.

Fig. 2 Components of a reinforced chain wall.

Photo 1 Laying of the chain and anchors in the field.

Photo 2 Fully constructed chain wall.


3

(2) Cylindrical model Fukuda et al.17) assumed that when chain is pulled

out, the shearing of the soil is expected to take an effect in the soil enveloped in the inner space of the chain and also in the outer surrounding soil. The filling of the inner space of the chain may be limited when the diameter of the soil grain becomes larger. By assuming that the inner space of the soil is entirely filled with soil, Fukuda et al.17) simplified the equa-tion of the circle strip model and proposed the cy-lindrical model shown in Fig. 4. In this model, a crossed shaped is assumed when the chain is viewed at the link. During pullout out, the shearing of the soil occurs and therefore the soil around the chain tends to dilate. The failure surface was taken to be circular and as dilatancy occurs the diameter of the slip sur-face was assumed to expand by an amount β times that of the outer width of the chain.

Equations (7) to (9) of the cylindrical model for calculating the pullout resistance of chain were proposed.

vfKLBF σφβπ ×⎟

⎠⎞

⎜⎝⎛ +

××××=2

1tan 0 (7)

⎟⎠⎞

⎜⎝⎛ +

=2

1 0Kβα (8)

vf LBF σφπα ××××= tan (9)

where L, is the apparent length of the chain embed-ded inside the soil, B is the diameter of the cylindrical model (which is equivalent to the outer width of the chain), β is the outer width correction coefficient that adjusts the outer diameter of the cylindrical model to the assumed slip surface, K0 is the coefficient of earth pressure, φ is the soil friction angle, α is the fric-tional correction coefficient and σv is the measured earth pressure. Through laboratory pullout tests, Fukuda et al.16) observed that the parameter α depends on the con-fining pressure. Due to dilatancy effect, α values are greater at low confining pressure than at high pres-sure. Fukuda et al.16) normalized each value of α with the ratio between testing pressure and a reference pressure of 100 kN/m2 using equation (10) to obtain normalized friction correction coefficient (α0) which is pressure independent. The value of n in equation (10) was proposed to be equal to 0.4.

n

v⎟⎟⎠

⎞⎜⎜⎝

⎛=

σαα 100

0 (10)

Two design equations (11) and (12) were proposed

for calculating the normalized frictional coefficient based on the angle of internal friction and the effect of dilatancy respectively.

2.0tan8.10 −= φα (11)

6.05.30 +⎟⎠⎞

⎜⎝⎛−=

dvdεα (12)

The quantinty -dv/dε in equation (12) was defined

by Fukuda et al.16) as the absolute value of the dila-tancy coefficient of the soil.

Inspite of the fact that the cylindrical model gave a better way of evaluating the reinforcement effec-tiveness of chain by comparing the frictional coeffi-cient, α generated by chain and other commonly used steel reinforcement such as ribbed strips, it does not explain the mechanisms that generate the pullout resistance of steel chain. There is therefore need to evaluate the mechanisms that generate pullout resis-tance of chain and to develop equations that will

B

B

Assumed slip surface

Soil

Chain

Fig. 4 The cylindrical model of the chain.

Fig. 3 Chain circle stripe model.


4

estimate the pullout resistance of chain to some de-gree of accuracy. In order to achieve the above ob-jectives, parametric study was conducted by varying the configurations of the chain and the results from these study compared with circle strip model15). The cylindrical model17) even though mentioned in this paper was not used for comparision because the equation takes on a different form and does not ex-plain the actual mechanism of pullout resistance of chain.

3. PULLOUT TEST ARRANGEMENT (1) Test equipment

The experiment consisted of pullout tests on chains with arbitrary shapes. The soil was prepared in a cubic box with an inner volume of 0.125m3 (0.5m × 0.5 m ×0.5 m). The equipment shown in Fig. 5 was fitted with gauges to measure the pullout load and displacement of the chain. In the front and the back side of the chamber were two holes in which the chain passing the chain as it laid in chamber. To simulate the overburden pressure, the vertical load was applied through a rubber membrane over-lying the loading plate placed over the prepared ground. The pressure was applied using an electric pump. Pullout test was performed at a displacement controlled rate of 1 mm/min. corresponding to a value commonly adopted for most reinforcement18). The pullout data directly registered to the data ac-quisition system connected to the equipment. (2) Tested chains and soil properties

Pullout test was divided into two main patterns.

The first pattern was to find the mechanisms that generate pullout resistance of chain and the second pattern involved increasing the number of links of chain.

In the first pattern, pullout tests were performed on three special chains of varied configurations in order to evaluate the mechanisms that generate pullout force of steel chain. The first type of chain was 800 mm long loop (herein referred to as 2RB. The notation RB stands for round bar). This type of chain was fabricated with the aim of obtaining the contribution of the friction component of the chain. Additionally, pullout test was performed on a single 6 mm diameter round bar (1RB) for the purpose of comparing the resistance of round bar and two rounds bars in order to evaluate the contribution of the shear resistance from the soil between the two round bars. The second type of chain consisted of two loops with one link (N=1) fabricated in order to obtain the con-tribution of the passive bearing component in addi-tion to frictional and shear resistance that will be generated by the same chain (here in referred to as one link, N=1). The last type of chain consisted of three loops with two links (herein referred to as the two links, N=2) in which the pitch, P (distance be-tween the two links) was varied so as to obtain the effect of the soil enclosed inside the loop between the two links. Pitches of 2B, 5B, 10B 15B were selected for this study.

After the components that generate the pullout reistance of chain had been determine, the second set of pattern which involved pulling multi-link chains of pitches equal to 2B with number of links varied (2, 3, 4, 5, 7, 9, 11 and 13 links) was done in order to investigating the effect of link on pullout resistance

Fig. 5 Schematic diagram of the pullout device.


5

and for the purpose of estimating the pullout resis-tance of chain from know design concept.

The chain chosen for this study had a diameter, D of 6 mm and an outer width, B of 23 mm. Chain of these dimensions is currently being used in the con-struction of reinforcement of steel chain wall and therefore were chosen for experimental purpose.

The test patterns are as summarized in Tables 2. Fig. 6 shows the typical arrangement of the config-ured chains in pattern 1 inside the pullout chamber while Photo 3 and Photo 4 shows the shapes and configurations of the specimens and chains for used in pattern 1 and pattern 2 respectly.

Dry Toyoura sand whose properties are given in Table 3 was used as the testing ground. The testing ground was prepared at 85% of its relative density. This was achieved by raining the sand inside the test chamber into seven thin layers and slightly com-pacting with ply wood using an electric handheld vibrator in order to level the ground.

Direct shear test, performed at an initial weight of the soil equal to 85% of its maximum dry density yielded peak frictional angle φ of 39°. Pullout tests were performed under overburden pressures of 30, 90 and 150 kN/m2.

(3) Test procedure

Pullout test procedure was as follows; (1) Measuring the desired volume of the sand for

each layer then raining the sand inside the testing

chamber. (2) Slightly compacting each layer manuall with a

flat plywood using an electric vibrator in order to

Fig. 6 Shematic representation of test case in Pattern 1.

(b) 2RB

Chain

(c) N=1

Chain

(d) N=2 P

Chain

(a) 1RB

Pullout direction

Round bar Pullout equipment

Photo 3 Test specimens used in pattern 1. Photo 4 Multi-link chains used in pattern 2.

Table 2 Summary of the test cases.

B=23 mm

Table 3 Physical properties of the soil.

Property Value

d (kN/m3)

Gs

(°)

emax

emin

2.68

39

0.982

0.600


6

achieve the desired relative density and to level the testing ground.

(3) After the third layer had been prepared, chain was set into position. A soft sponge was then inserted in the hole on both sides of the chamber walls in order to avoid the soil coming out of the chamber during pullout.

(4) After all layers have been compacted, the loading plate was placed the machine was covered and the pressure duct attached on the cover plate.

(5) The vertical confining pressure was applied to the loading plate through the cover and pullout test commenced.

(6) The pullout data was recorded on the automatic data acquisition system attached to the pullout device.

4. RESULTS AND DISCUSSION

(1) Result from single and two round bars

Pullout force-displacement curves obtained from 2RB and 1RB are as shown Fig. 7. The graphs shown here are for a confining pressure of 30 kN/m2. Comparing the pullout resistance graphs from the two cases, it can be seen that the frictional resistance generated by 2RB was found to be about twice the resistance generated by 1RB. This shows that slip occurred between the steel and surrounding soil and therefore, the shear resistance (similar to F2 in Fig. 2) of the soil contained in the space between the 2RB was not mobilized in this case.

(2) Effect of the link on pullout resistance

Fig. 8 shows the relationships between pullout resistance and displacement for 2RB and N=1 under confining pressure of 30 kPa (test cases for 90 and 150 kPa also showed similar trends). The graphs obtained from the two cases showed completely different patterns. In the case of 2RB, where two round bars were pulled out, the resistance increased with displacement until a displacement of 5 mm (about 22% of B) then remained constant with dis-placement as the test progressed. This case showed the typical characteristics of force displacement curves obtained from piles that entirely rely on fric-tion. In the case of N=1 (one link) the pullout dis-placement graph increased rapidly until a displace-ment of 8 mm where the curves changes slope (slopes become less steeper). After 8 mm, the pullout force continues to increase with displacement until 30 mm where no change in pullout force with dis-placement was observed. It can be noted that the pullout force generated by N=1 was 70 % higher than that generated by 2RB. The additional pullout resis-

tance in the case of N=1 arose from the passive bearing developed at the link. This passive bearing resistance was deduced from the difference between the graphs of N=1 and 2RB.

Fig. 7 Pullout force displacement graphs for 1RB and 2RB (30 kPa pressure).

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50

Pullo

ut fo

rce

[kN

]

Pullout displacement [mm]

Fig. 9 Variation of passive bearing and frictional resistance with σv.

0

0.5

1

1.5

2

2.5

0 50 100 150 200

Pullo

ut fo

rce

[kN

]

Applied pressure , σv [kPa]

Fig. 8 Pullout force displacement graphs for N=1 and 2RB (30 kPa pressure).

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60

Pullo

ut fo

rce

[kN

]



7

Fig. 9 shows the variation of the measured maximum friction resistance from 2RB and the gen-erate maximum passive bearing with confining pressure. The maximum passive bearing was taken at a displacement of 10 mm. Results from Fig. 9 indi-cated that much of the pullout resistance generated by chain in fill slope comes from the passive bearing resistance developed at the link as a result of the chain thrushing the soil during pullout.

(3) Effect of the enclosed soil

Chain with two links forms a loop in which some soil is trapped. The loop can be entirely filled if the particle sizes of soil are small. The enclosed soil in the loop produces some shear resistance which also contributes to the total pullout resistance of chain.

Since the two link chain is different from the one link chain by an introduction of a closed loop in the middle of the two links, the contribution of one loop link of a standard chain can be evaluated from the difference between the resistances of the two link chain and theone link chain.

Fig. 10 shows the pullout force displacement graphs obtained from pulling out two links of chain (N=2) of various pitches (2B, 5B, 10B and 15 B). The curves in the figure show a linear increase until the yielding value (about 5 mm displacement for all the curves) then continues to increase until the peak value (occurred at different displacement for each the curves). Up to the yielding points, the frictional re-sistance of the chain is fully mobilized however the passive bearing component and shear resistance of the soil in the inner space continues to be mobilized until the peak pullout values are reached. After the peak value has been reached, the graphs show sof-tening behavior which occurs suddenly until the re-sidual value is reached in which the pullout force remains constant with displacement. As the pitch increased, the peak pullout force in-creased and so was the displacement value at which the maximum pullout force occurred. The reduction from peak to the residual resistance was higher for chain of longer pitches. This softening phenomena was not observed in the case of N=1 (pullout resis-tance of one link). The sudden drop of pullout force from peak to residual value can be attributed to the fact that during pullout the chain loop is displaced at a faster rate than the soil entrapped inside it thereby leaving a gap behind the passive bearing member. When this gap become sufficiently large and the soil resistance cannot accommodate the force transferred through the bearing mechanism, it suddenly burst thereby resulting in the reduction of the pullout re-sistance.

(4) Explanation of the softening behaviour Fig. 11 shows the typical representation of a two

link chain. The forces generated by this type of chain during pullout are as shown in Fig. 11(b). The fric-tion acting on the outer perimeter of the chain des-ignated by Fr, the passive bearing generated in frontof the chain acting on the outer soil designated by B1, the shear resistance produced between the enclosed soil in loop 2 and the soil on both sides of loop 2 by S and finally the bearing resistance of the enclosed soil which presses itself against the portion in which the two links close designated by B2 are assumed to be generated by the two link chain as shown in Fig. 11(b). Cross section X-X of two crossing unit intersect where B1 and B2 act is as shown in Fig.11(c).

Fig.12 shows a typical pullout resistance –displacement curve for a two link chain (N=2). Three distinct features can be noted from the curve that is section OQ where the pullout force rises rap-idly at very low displacement (about 5 mm), section

0123456

0 10 20 30 40 50 60

Pullo

ut fo

rce

[kN

]


Fig. 10 Pullout-displacement graphs for N=2 (90 kPa testing pressure).

Fig. 11 Forces generated by two links chain during pullout.


8

QR where the slope of the curve changes but continue to rise until the peak is reached at R and lastly section RT where pullout resistance suddenly drop till it reaches the residual value at T where no change in pullout force is observed. These three phenomenons can be explained with aid of Fig. 11. From the start of the test O to Q in the curve, forces Fr, B1 , and B2 are generated by the chain, however Fr become fully mobilized at Q be-cause results from two round bars shows that the friction component is fully mobilized at displacement of about 5 mm. The components B1 and B2 continue to be mobilized until the peak value at R. The shear resistance S of the enclosed soil is in equilibrium with B2 because it is generated as a result of the soil in the inner loop pressing itself against the crossing unit of the chain where B2 acts. The total pullout resistance from O to R is the sum of three components generated by the chain and is given by;

21 BBFF r ++= (13a) SB =2 (13b)

In the portion QR of Fig. 12, a gap was developed in loop 2 as shown in Fig. 11(d). When the pullout resistance reached the peak the enclosed soil in loop 2 busted and as a result, the shearing resistance S of the soil diminished and so is the bearing resistance B2. This sudden busting of the soil inside the inner loop caused a reduction of the pullout resistance from peak to residual value. After peak pullout force has been reached the total pullout force is given by;

1BFF r += (14a) 02 == SB (14b)

The reduction of the pullout force from peak to residual value increased as the pitch of the inner loop increased (Fig. 10). For pitch equal to 2B, the area of the inner loop is small and therefore the enclosed soil cannot develop enough shear resistance, S to be overcome by the bearing resistance B2 hence its burst at low displacement and the reduction from peak to residual is also low. However as the pitch becomes larger, the displacement at which the peak pullout force occur increases and also the reduction from peak to residual pullout resistance also increased. This is because as the pitch increases, the area of the loop increases and so is the amount of soil in the loop which could develop enough shear resistance, S to be overcome by the bearing resistance B2. Fig. 13 shows the plots of the peak and residual resistance for the different pitches. The peak resis-

tance increases as the pitch increases while the re-sidual resistance decreases as the pitch increases for pitches greater than 5B.

The difference between the peak and residual re-sistance δF are plotted in Fig. 14 for different

Fig.12 Typical pullout force-displacement curve for N=2 with pitch.

O

Pullo

ut F

orce

Displacement

Q

R

T

Fig.13 Variation of peak and residual pullout force with pitch (150 kPa pressure).

4

5

6

7

2B 5B 10B 15B

Pullo

ut fo

rce

[kN

]

Chain Pitch, P [mm]

Fig.14 Variation of δF with chain pitch, P of a two link chain (N=2).

0

0.5

1

1.5

2

2B 5B 10B 15B

δF [k

N]

Chain Pitch, P [mm]

v =150 kPa

v =30 kPa

v =90 kPa


9

pitches. From Fig. 14, it can be seen that δF is a function ofpitch and the testing pressure. For all the testing pressures, δF increases as the pitch increases. For the case in which the pitch is equivalent to 2B, δF was small and therefore the effect of the inner space can be concluded to be negligible.

In the In-situ construction of chain reinforced wall, chain of pitch equal to 2B is employed and therefore it is prudent if the shearing resistance of the enclosed soil is neglected when considering the pullout resistance of chain. If however chains of pitch greater than 2B are to be used in construction, the effect of the enclosed soil should be taken into ac-count. (5) Effect of blocking the inner space of chain

An attempt was made to visualize the effect of enclosed soil by pulling out the 2B pitch chain with the inner space filled with a soft sponge as shown in Photo 4. In Photo 5 only the inner loop of the chain

was bloched. The contribution of the sponge to the total pullout resistance was assumed to be negligible.

Fig. 15 shows the force-displacement graphs for the case where the inner space is blocked and not blocked. It is evident that when the inner space of the chain is blocked, the softening behaviour does not occur implying that the sudden fall in pullout force

Photo 5 Two link chain with the inner loop blocked by a soft sponge. Fig. 15 Graphs for blocked and unblocked inner

space for P=2B (30 kPa pressure).

0

1

2

3

4

0 10 20 30 40 50

Pullo

ut fo

rce

[kN

]


Fig. 16 Isolated effect of the inner space for various testing pressure (for P=2 B).

-1

-0.5

0

0.5

1

0 10 20 30 40 50

Pullo

ut fo

rce

[kN

]


Fig. 17 Isolated components that generate pullout force of P =2B chain (30 kPa pressure).

-0.50

0.51

1.52

2.53

0 10 20 30 40 50

Pullo

ut fo

rce

[kN

]


Table 4 Contribution of the componets that generate pullout force of steel chain (P=2B).


10

from peak to residual value is attributed to the shearing effect of the soil in the inner space of the chain loop. When the inner space is filled with sponged, the bearing resistance B2 produced by the cross part of the chain Fig. 11(b) is lost to the soft sponge and therefore cannot fully develop like in the case where the inner loop is not blocked.

Fig. 16 shows the difference between the data from blocked and unblocked test. The effect of the inner space increased as the testing pressure in-creased. Fig. 17 shows the variation of the three re-sisting components with displacement. The frictional component was taken from the test result obtained from two round bars (2RB). The lost shearing resis-tance of the entrapped soil as explained earlier was gotten from subtracting the graphs of blocked and unblocked pullout test on 2B pitch while the passive bearing (B1) generated by the two links was obtained by subtracting the test result of two round bars from that of pitch 2B with inner space blocked. Percentage contributions of each of the three components that generate pullout resistance of steel chain are as shown given Table 4. From Table 4 it can be seen that passive bearing resistance is the predominant mechanism that generate pullout force of steel chain, accounting for over 50% of the total pullout force. The shear resistance of the enclosed soil is the least contributor account for between 8-10% of the total pullout resistance of steel chain.

Table 5 shows the comparison of the maximum pullout force obtained from experiment and the cal-culated value using equation (1) of the circle stripe model. The calculated values are given in italics. μ of 2.5 was assumed in the calculation. The calculate passive bearing from equation (4) are much less than that measured from the pullout test. It is therefore necessary that the equation (4) of the circle stripe model be improved to estimate the pullout resistance of steel chain with some degree some degree of ac-curacy. (6) Increasing number of links

Fig. 18 shows the comparison of the pullout

curves obtained from increasing the number of links N of the chain from two to full length thirteen links. The pitch of each loop was kept constant at 2B. In-cluded also in this plot is the result from one link chain (N=1). As the number of links increased, the total pullout resistance increased. Neglecting the shear resistance of the soil enclosed inside the loop, the pullout resistance can be taken as the sum of the passive bearing (B1) and the frictional resistance (Fr). Assuming the loss in frictional area as a result of increase in number of links to be negligible, the passive bearing resistance for each pattern was ob-tained by subtracting the frictional resistance of two round bars (2RB).

Fig. 19 shows pullout force-displacement graphs showing the passive bearing isolated from the result of pullout test on thirteen links of chain and two round bars. Comparing the friction resistance and the passive bearing values at same displacement level, the variation of the percentage contribution of each of the two components to the total pullout force is as shown in Fig. 20. From the start of pullout test, the percentage of frictional resistance decreases while that of the bearing resistance increases. At low dis-placements of less than 0.38 mm the frictional re-sistance is predominant accounting for about 60% of the total pullout force while the remaining 40% comes from the passive bearing. At a displacement of 0.38 mm both of the resistances are the equal at 50%. Beyond a displacement of 0.38 mm the percentage contribution of the passive bearing continue to in-creases until it reaches maximum value of 90% at a displacement of 7 mm while the percentage of fric-tional resistance decreases and reached 10% at the same displacement of 7 mm. From this result it can be concluded that the passive bearing resistance de-veloped in the front part of the chain account for 90% of the total pullout resistance of steel chain.

Fig. 21 shows the variation of the maximum pas-sive bearing resistance with the number of links of chain, N. Even though the passive bearing increases with number of links, the increase is not linear due to the interference among bearing members and proba-

Table 5 Comparion of the experimental result and the calculated from Inoue’s equation for N=2 (P=2B).


11

bly due to the boundary effect.

5. IMPROVEMENT OF THE CIRCLE STRIPE MODEL

The equations of the circle stipe model although

explains the mechanisms that generate pullout resis-tance of steel chain, it falls short of accurately esti-mating the pullout resistance of chain. An attempt is herein made to estimate the pullout force of steel chain by considering the skin friction and the passive bearing resistance. These two components are as-sumed to be independent but additive. In light of these, a modified version of the circle stripe model that ignore the shear effect of the encloded soil in the inner space of the chain shown in Fig. 22 (a) is con-sidered and an assumed equivalent geometry of the same model without the curved edges of the front bearing part is shown in Fig. 22 (b).

(1) Skin friction angle

The estimation of the skin friction angle was done by modifying equation (2) of the circle stripe model. The soil-chain interaction coefficient δ was calcu-lated by rearranging equation (2). Equation (2b) be-low is obtained that expresses the skin friction oc-curring at the outer perimeter of the chain. Test re-sults obtained from pulling out 2RB was used for the calculation of the skin friction angle δ mobilized between the surface of the two round bars and the soil. Due to the circular nature of the bar, the earth pressure acting on the surface of the bar is therefore taken to be the average of the vertical and horizontal earth pressure calculated from equation13). The skinn friction acting acting on the perimeter of the chain can be expressed as;

δσ tan××= aveor AF (2b)

2/)1( 0Kvave +×= σσ (15)

Fig.18 Pullout curves for various number of links for P=2B chain (150 kPa pressure).

0

5

10

15

0 10 20 30 40 50 60

Pullo

ut fo

rce

[kN

]


Fig.20 Percentage contribution of bearing and friction with displacement, P = 2B (30 kPa pressure).

0

20

40

60

80

100

0 10 20 30 40 50

Perc

enta

ge p

ullo

ut fo

rce

(%)


Fig.19 Bearing resistance of thirteen link chain of P=2B (30 kPa pressure).

01234567

0 10 20 30 40 50 60

Pullo

ut fo

rce

[kN

]


Fig.21 Variation of maximum pullout force with number of links (P =2B).

02468

101214

0 2 4 6 8 10 12 14Max

imum

pul

lout

forc

e [k

N]

Number of links, N

v=150 kPa

v= 90 kPa

v= 30 kPa


12

DLAo π2= (16)

where Ao is the frictional area calculated from equa-tion (16) and L is the length of the chain embedded inside the soil. The chain-soil interaction coefficient tan δ was calculated by rearranging equation (2b). The K0 used for calculation was computed from equation (5).

Table 6 shows the calculated δ/φ at various test-ing pressures. The value δ/φ were found to be close to 1.0. The value of the soil chain interaction frictional angle δ was found to be greater than the angle of internal friction of the soil at low pressure. However at a testing pressure of 150 kPa, the value of δ was close to that of the soil friction angle φ.

The higher values of skin friction angle, δ greater than the friction angle of the soil φ obtained from these test could be attributed to the over compaction of the testing soil in pullout condition. (2) The bearing component

Test results from multi link chain revealed that the pullout resistance is a function number of the links and the normal stress level. The area of the front part of the chain available for generating the passive (B1) was calculated from equation (17). It therefore fol-lows that follows that the general expression for computing the passive bearing resistance of chain in soil is of the form;

NAqNNBcNB bqc ×++= )(1 γγ (17)

DDBAb ×−= )( (18)

)tanexp(24

tan 2 φπφπ⎟⎠⎞

⎜⎝⎛ +=qN (19)

φγ tan)1(2 += qNN (20)

where c is the cohesion of the soil, γ is the dry unit weight of the soil, Ab is the area of the front part of the chain in which passive bearing acts, q is the applied load, N is the number of links, φ is the friction angle of the soil while Nq, Nγ and Nc are bearing capacity factors. Since c for sand is zero and the chains outer diameter, B is small, the first and the second terms of the bracket in equation (16) can be neglected. Comparison of the passive bearing resistance mo-bilised in the front part of the chain during pullout (obtained from the difference of multi link graphs and 2RB) and the calculated passive bearing resis-tance from equation (16) are as show in Fig. 23 (testing pressure of 150 kPa). The calculated passive bearing resistance are slightly lower than the meas-ured passive bearing resistance. As the number of links increases the measured and calculated values

tends to converge and the discrepancy between the measured and calculated value becomes low. In order to evaluate the reason for the occurance of such dis-crepancy between the measured and calculate passive bearing resistance, the mobilised frictional angle between the soil and the front bearing part of the chain (φm) was back calculated using the equations

Fig. 22 The modified circle stripe model.

Table 6 Soil chain interaction of the frictional component.

Fig.23 Measured and calculated passive bearing resistance of P=2B (150 kPa).

02468

101214

0 2 4 6 8 10 12 14

Pass

ive

bear

ing

[kN

]

Number of links, N


13

(17) and (19b) with the assumption that the mobilized friction angle (φm) was higher than the soil friction angle(φ) obtained from direct shear test.

)tanexp(24

tan 2m

mqN φπ

φπ⎟⎠

⎞⎜⎝

⎛ += (19b)

Fig. 24 shows the variation of φm with the number of links at various testing pressures also showed in the same graph is a straight line representing the friction angle of the soil. From Fig. 24 the it can be seen that the mobilsed friction angle (φm) calculated were found to be higher than the soil frictional angle (φ) with somes the values being as high as 49° and some being as low as 40° depending on the testing pressure. For low testing pressure the value of φm were higher than those calculated at higher testing pressure. However, these values of φm were relatively close to the value of δ calculated for 2RB.

The mobiled friction angle φm decreased with increase in testing pressure and the number of links. This due to the fact that as the testing pressure in-creases the dilatancy effect decreases and therefore at low confining pressure the value of mobilized φm were higher than at high testing pressure pressure. As the number of links increases, the bearing members acts as a group and with regard to this, the efficiency of the group decreases as the number of links in the group increases.

The value of calculated mobilised friction angle φm was found to be higher than the soil friction angle φ. This could be attributed to the fact that the test ground could have been over compacted and hence the soil in pullout testing condition was denser than that in shear box testing condition.

6. CONCLUSIONS

The following conclusions can be drawn from

the study. (1) Pullout test results from two round bars, one link

of chain and two links of chain showed that the mechanisms that generate pullout resistance of chain is a combination of friction resistance that develop on shaft of the chain, the passive bearing resistance developed on the front part of chain and the shear resistance of the soil enclosed in the inner loop of chain. Results from one link and two links chain of pitch equal to 2B showed that the passive bearing is the highest contributor of the three mechanisms.

(2) For two link chain, the effect of the inner space was found to be small when the pitch was 2B and

therefore it can be neglected in the computation of pullout force of chain. However the effect became evident for pitches greater than 2B, and therefore there is need for elaborate research to evaluate the contribution of the soil enclosed in the chain loop.

(3) Neglecting the contribution of shear resistance of the soil in the inner space of chain for chain of pitch equal to 2B, and considering only the pas-sive bearing and the frictional resistance, for a standard chain with 13 links embedded inside the pullout device, the passive bearing resistance was found to be the predominant mechanism that generate the pullout resistance of the chain ac-counting for about 90% of the total pullout re-sistance.

(4) When the equations of the circle stripe model proposed by Inoue was used to back calculate the pullout resistance of chain, the calculated value and the measured value were found to be not in a good agreement especially the passive bearing was under estimated from the Inoue’s equation. In the formulation of the passive bearing resis-tance developed infront of the chain the product of the coefficient of bearing resistance μ and Kp as suggested by Inoue can be replaced with the bearing capacity factor Nq given by equation (18) and the value of φ can be taken to be the equal to that of the soil.

ACKNOWLEDGEMENT: The Authors would like to acknowledge the contributions and support of Showa Kikai Shoji Co. Ltd., Osaka, in denotating the pullout test equipment to our laboaratory, helping fabricate the special type of chains used in this study and their continual support in all the researches that

Fig.24 Variation of φm with the number of links for

various testing pressure.

35

40

45

50

0 2 4 6 8 10 12 14Mob

lised

fric

tion

angl

e φ m

(o )

Number of links, N


14

apartains to chain reinforced walls.

REFERENCES 1) Matsui, T., San, K. C., Nabeshima, Y. and Amin, U. N.:

Bearing mechanism of steel grid reinforcement in pullout test, IS-Kyushu, pp.101-105, 1996.

2) Tanaka, K., Fukuda, M., Kitamura, A. and Hayakawa, K.: Construction of steep and high fill reinforced by steel made chain and steel made frames, 57th Civil Engineering Society Annual Conference, pp.843-844, 2002 (In Japanese).

3) Alfaro, M. C. and Pathak, Y. P.: Dilatant stresses at the interface of granular fill and geogrid strip reinforcement, Geosynthetics International, Vol.12, No.5, pp.239-252, 2006.

4) Sidnei, H., Teixeira, C., Benedito, S. and Jorge, G. Z.: Pullout resistance of individual longitudinal and transverse geogrid ribs, Journal of Geotech. and Goenvi. Engineering, Vol.133, No.1, pp.37-49, 2007.

5) Jewell, R. A., Milligan, G. W. E., Sarsby, R. W. and Dubois, D.: Interaction between soil and geogrid, Proc. of Sympo. on Polymer Grig Reinforced Slope, ICE, London, pp.18-30, 1984.

6) Pameira, E. M. and Milligan, G. W. E.: Scale and other factors affecting the results of pullout tests on grid buried in sand, Geotechnique, Vol.39, No.3, pp.511-524, 1989.

7) Dyer, M. R.: Observation of the stress distribution in crashed glass with application to soil reinforcement, PhD Dissertation, Univ. of Oxford, Oxford, UK, 1985.

8) Elias, V. and Christopher, B. R.: Mechanically stabilized earth walls and reinforced soil slopes design and construc-tion guidelines: FHWA-SA-96-071, FHWA, Washington, D.C., 1996.

9) Jewell, R. A.: Reinforcement bond capacity, Geotechnique, Vol.40, No.3, pp.513-518, 1990.

10) Scholosser, F. and Elias, V.: Friction in earth reinforcement, Symp. on Earth Reinforcement, ASCE, Pittsburgh, USA, pp.735-763, 1979.

11) Ingold, T. S.: Laboratory pullout testing of geogrid rein-forcement in sand, Geotechnical Testing Journal, Vol.6, No.3, pp.101-111, 1983.

12) Peterson, L. M. and Anderson, L. R.: Pullout resistance of welded wire mesh mats embedded in soil, Research report submitted to Hilfiker Co., 1980.

13) Jewell, R. A.: Soil Reinforcement with Geotextiles, CIRIA special publication, No.123, Thomas Telford Ltd., London, 1996.

14) Kitamura, A., Shigeyoshi, M., Fukuda, M., Hongo, T., Inoue, S. and Fujimura, E.: Frictional pullout characteristcs of chain as a reinforcing material, 41st Geotechnical Engi-neering Society Annual Conference, pp.1843-1844, 2006 (In Japanese).

15) Inoue, O. and Konami, K.: Pullout force of steel made chain reinforcement applied to fill slope, 51st Japan Civil Engi-neering Society Annual Conference (III), pp.626-627, 1996 (In Japanese).

16) Fukuda, M., Kitamura, A., Mochizuki, Y., Hongo, T., Inoue, S., Fujimura, E. and Kimura, M.: Resistance of steel chain in pullout test with and without sliding box, IS-Kyushu, pp.299-305, 2007.

17) Fukuda, M., Hongo, T. and Konishi, K.: Frictional force of steel made chain reinforcement applied to fill slope, IW-Shiga, pp.158-166, 2003.

18) Alfaro, M. C., Miura, N. and Bergado, D. T.: Soil geogrid reinforcement interaction by pullout and direct shear test, Geotechnical Testing Journal, Vol.18, No.2, pp.157-167, 1995.

(Received March 4, 2010)


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