The Study on the Influence of Pile Length-Diameter …...Revista de la Facultad de Ingeniería U.C.V., Vol. 32, N 6, 2017, 323-334 325 Considering the influence of the size of pile

Revista de la Facultad de Ingeniería U.C.V., Vol. 32, N°6, 2017, 323-334

323

The Study on the Influence of Pile Length-Diameter Ratio on the

Working Performance of the Rigid Pile Composite Foundation

Mingquan Liu1,2

, Chunyuan Liu1,Xiaozhi Li

2*

1School of civil engineering, University of Technology, Tianjin 300401, China

2School of civil engineering, Tangshan University, Tangshan 063000, China

Abstract

This paper studies the influence law of pile length-diameter ratio on pile top load distribution, load sharing and

composite foundation settlement with ABAQUS finite element models by combing coastal highway renovation

projects, so as to study the influence of pile length-diameter ratio on working performance of the rigid pile

composite foundation. The author puts forward a calculation method based on secondary composite modulus of

reinforcement zone according to the characteristics of composite foundation settlement. The research results

show that the pile length–diameter ratio has influence on both load distribution and settlement of composite

foundation. The load distribution is not uniform in the range of pile cap, but concentrated to the core area; the

load sharing ratio gradually decreases when the pile length-diameter ratio increases; the axial force of single pile

increases gradually when the pile length-diameter ratio increases; but when the pile length-diameter ratio K is

within the scope of 2-6, the change is minor. While, when the load is constant, the bigger the pile

length-diameter ratio is, the larger the settlement of the single pile is, but the smaller the differential settlement

between pile and soil is; and the settlement calculated through secondary composition modulus method fits in

well with the practice. Therefore, considering all of the factors above, it is recommended that the pile

length-diameter ratio K should be within the scope of2-4, and the secondary composition modulus method can

be used in project design.

Keywords: Highway Engineering, Working Performance, Finite Element, Pile Length-Diameter Ratio And

Secondary Composition.

1. INTRODUCTION

In recent years, the composite foundation method(Gong, 1992; JGJ79-2012)has been commonly used for soft

foundation reinforcement in the construction of new highways, as well as renovation and expansion of existing

highways in China. With regard to the composite foundation built with flexible piles, the continuity of pile

quality is hard to be ensured, and the construction raises high requirements on the operating level and

experience of technicians involved, but the construction cost is lower. While for the composite foundation built

with rigid piles, the strength and completeness of piles can be obtained easily due to the adoption of concrete

material; however, the cost is relatively higher. Moreover, great pile rigidity and obvious effect of load transfer

can easily result in concentration (Liu and Mu, 2013)of load on the top of piles.

With continuous development of engineering practices and theories, new technologies and methods for soft

foundation reinforcement have appeared, including multi-element composite foundation and pile-net composite

foundation (GB/T 50783-2012). As for the former, piles of different rigidities can be used for binary, ternary or

multi-element composite foundation; or different pile lengths can be combined to build long-short-pile

composite foundation in an alternative manner(Yin, 2011).Regarding pile-net composite foundation, there is soil

arching effect which can be solved by transferring partial load to piles so as to effectively control the settlement

(Li, 2016). Besides, the shape of pile section may change like tapered concrete screw piles and T-shaped

bidirectional dry jet mixing piles (Zhou, 2015; Xie et al., 2012).The placement of pile cap on top can effectively

reduce upward penetration of rigid piles, and ensure completeness of cushion, which has been successfully

applied in domestic highway projects with good results(Jiangsu, 2004; Tian et al., 2015; Liu et al., 2015).In

China, the following methods are mainly adopted to study the effect of pile cap: theoretical research, finite

element analysis (FEA) and field test (Guo, 2016; Lei, 2005; Zeng, 2012; Zhao et al., 2016);the study of

composite foundation characteristics mainly focus on the settlement and bearing capacity(Chen et al., 2016;


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Wang and Li, 2013; Wu, 2013), and most of the current findings are used for application or verification. This

paper is intended to study the influence of pile length-diameter ratio on the working performance of rigid pile

composite foundation, and provide a reference for the design of rigid composite foundation with pile caps.

2. WORKING MECHANISM

The rivet pile is rigid and in the shape of the rivet, which is comprised of the pile, cap and cushion. The rivet

pile, soil under pile cap and soil among piles together form the rivet-pile composite foundation as shown in

Figure1. The pile can be made of cast-in-place concrete, precast concrete, precast concrete pipes or thin-wall

stiffened piles; and the cap is made of concrete material, and requires reinforcement calculation and bearing

capacity inspection in general. When the pile suffers upper vertical load from the cushion, the cap can make the

pile and soil under pile cap be under uniform load; the total bearing capacity will be higher than that of a single

pile without cap, and the vertical load on top of pile cap will be much less than that of a single pile without cap

due to the increase in the size of pile cap; thereby reducing load concentrated on pile top and decreasing upper

penetration of the cushion.

Figure 1. Rivet-pile Composite Foundation

3. FINITE ELEMENT ANALYSIS (FEA)

3.1Load distribution in the range of pile cap

Table 1Modelparameters of materials

Material Thickness(

m)

Deformation

Modulus(MPa)

Cohesion Force

c(kPa)

Internal Friction

Angle φ(°)

Poisson's

Ratio u

Cushion 0.25 200 1 25 0.2

Fill 3 12 20 30 0.3

Muddy

clay 3 13.5 15.2 17 0.3

Muddy

clay 2 27.5 18.2 23 0.3

Silty clay 3 12.4 13.7 21 0.3

Silty clay 5 30.1 20.2 10 0.2

Silty clay 16 18.3 28.9 34 0.3

Concrete - 38000 - - 0.2

The author performs force analysis through conducting modeling of the single rivet-pile with ABAQUS finite

element; and conducts simulation of soil based on mohr-coulomb yielding criteria using CPE4P 4-node plane

strain quadrilateral element. The rivet pile and cap are made of concrete material which are considered as the

elastic material for simulation using CPS4R bilinear plane load quadrilateral element. The model parameters of

soil and pile material are as shown in Table 1, and data adopted for FEA in the table are used for comparison in

this paper, and will not be repeated in the following parts. The rivet pile has contact with soil in three parts,

namely, the base, side and cap below; while the regular pile has two contact surfaces of the base and side;

therefore, appropriate contact pairs are provided at these positions, which are of the same type and considered as

the elastic sliding face-to-face contact. The arranged contact pairs have a friction coefficient of 0.44, elastic

sliding deformation of 0.5% and rigidity scaling factor of 0.1.


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Considering the influence of the size of pile cap on pile top load, this research requires that the pile diameter of

500 mm should remain unchanged, and pile length-diameter ratio K is the ratio of the pile length to pile

diameter. The author conducts comparative analysis with K being0, 2, 4, 6, 8, and 10 respectively, and the

abstracts load values on top of pile cap from the calculation results. The curves of load distribution with the

change of distance to the center of pile are shown in Figures 2 and 3 respectively, from which load values at

each control point are obtained and listed in Table 2.

Figure 2. Load distribution curve of top of regular pile

Figure 3.Loaddistribution curves of top of rivet pile

Table 2.Value ofload at each control point(MPa)

Cap diameter ratio(K)

Distance to center of pile (m)

0 0.25 0.5 0.75 1.0 1.25 1.5 1.75 2.0 2.25 2.5

2 5.21 2.83 0.18

4 4.98 2.70 0.17 0.12 0.21

6 4.45 2.57 0.14 0.08 0.11 0.14 0.26

8 5.98 3.23 0.17 0.05 0.09 0.10 0.11 0.15 0.20

10 6.45 3.49 0.18 0.06 0.08 0.09 0.09 0.09 0.10 0.16 0.18

3.2 Influence of the change of Kcon load sharing

As shown in Figures 2 and Figure 3, the load distribution non top of regular pile and rivet pile is in non-linear

form, there is no big load change for regular pile without cap and the load distribution is relatively even; while

the load of rivet pile is large in the middle but small at the boundary. As shown in Table 2, the ratio of maximum

load to minimum load varies greatly from28.9to119.6.With the same settlement developed, peak load of top and

average load of rivet pile are about 1/2 and 1/5 of that on top of regular pile, respectively; which indicates that

the installation of pile cap can reduce load of pile top. As shown in Fig. 3, the load curve peak of rivet piles


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appears at the center, and the curve becomes flat and stable starting from a point at a distance twice the pile

diameter to the pile center, with a little change in value which is about 1/30 of the peak; therefore, the load peak

interval is within the range of twice the pile diameter. When K is greater than 2, the pile cap does not play a

significant role in load sharing, so the range with K = 2 is defined as the core area, and remaining range as the

edge area, as shown in Fig. 4. The load curve for core area is nearly in the shape of a triangle, while the edge

area is a rectangle; which can help to calculate external load shared by the core area and edge area with Eq. (1)

respectively.

PTotal=PCore+PEdge= ACore×SCore+A Edge×SEdge(1)

P---Load, in kN;

A---Area, in m2;

S---Load, inMPa.

whereK=4,PCore=ACore×SCore=1×(4.98+0.17)/2×106=2575(kN),PEdge=AEdge×SEdge =

(2×2-1×1)×(0.17+0.12+0.21)/3×106=500(kN),the load sharing ratio in core area is 2575/(2575+500)=83.7%.

Likewise, the ratio for other K values can be calculated and curve plotted is shown in Fig. 5. It can be seen from

Fig. 5 that the load sharing ratio in core are a gradually decreases as K increases. Where K=10, this ratio is

about50%, and the soil under pile cap plays an increasingly important role; in other words, the function of rivet

pile gets weaker. From the perspective of rigid pile composite foundation, composite foundation should have

most of load supported by rigid reinforcement to make it play its load-bearing role. On the other hand, if K is

too small, soil among piles will bear most of the load, making the pile cap meaningless. However, as K

increases, the pile cap should provide sufficient rigidity in order to give a full play to the soil beneath it, which

means that there should be no excessive bending deformation or fracture. Therefore, a thick enough pile cap is

required. If the pile cap is relatively large and thick, large quantities of materials will be used, but the rivet pile

is actually a foundation for a single pile. Thus, it is recommended to control the value of K within the range

of2-4, and load sharing ratio in core area above 80%, then the pile cap thickness will be 300

mm–500mmaccording to experience.

Figure4. Core area and edge area

Figure 5.Curve of load sharing ratio in core area with the change ofK

3.3 Influence of pile cap on pile top load


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Pile cap doe not only affect the load transfer of soil below, but can also reduce load concentration on pile top.

Fig. 6 compares thepile top loadesof rivet-pile and common-pile composite foundationare comparedunder

different load levels when K=2 and pile spacing is 2 m,. As shown in Fig. 6, the rivet pile is underlowerload than

regular pile at the same positions, and ratio of rivet pile top load to regularpile top loadis not fixed and gradually

increases with the growing of the load level in a nonlinear manner. In this case, the ratio of rivet pile top load to

regular pile top load varies between 0.456 and 0.669. Besides, this study also findsthat the ratio isalso related to

the position of pile in composite foundation, which is slightly smaller in the middle than at the boundary, but the

impact is not significant. Moreover, this ratio also depends on the pile spacing which is not discussed herein.On

the whole, pile cap can reduce load concentration on pile top.

Figure 6.Top load comparison of rivet and regular pilesunder different load levels when K=2

3.4Influence of the change of K values on settlement

3.4.1 For single pile

In order to study the influence of different K values on settlement, this paper assumes that the pile top pressure

is 200 kPa, and only changes K values to obtain settlements of pile top as shown in Table 3.

Table 3 Settlements of pile top with differentKvalues

K K=0 K =2 K =4 K =6 K =8 K =10

Settlement of pile top (mm) 0.167 0.796 3.745 13.411 23.593 40.816

As shown in Table 3, the settlement of rivet pile top gradually increases with growing of K values, indicating

that as the size of pile cap increases, the load is increasingly concentrated in the core area, which can be

reflected from the increase of centric and edge loads in the core area as shown in Fig. 3. The load transfersto pile

tip with the increase of load, resulting in greater settlement of pile tip, which is, in turn, caused by load transfer

of the rigid pile.

3.4.2 For multi-pile composite foundation

To study the influence of different K values on settlement in composite foundation, this paper builds 6-pile

composite foundation models for regular and rivet piles, respectively, with the pile diameter being 500 mm,

length being16 m and pile spacing being2 m. This paper also keeps the material parameters unchanged under

different load levels in analysis, and only changes K values so as to take settlement data of cushion surface from

analysis results and draw a comparison curve as shown in Figure 7.


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Figure 7.Settlement curve of composite foundation with different K values

As shown in Figure 7,with the increase of K values, the settlement of rivet pile top increases gradually at a very

low speed; but the settlement of soil among piles increases at a greater rate than that on pile top, resulting in a

gradual increase in differential settlement between pile top and soil among piles. Regular pile (K=0)has the least

top settlement, but the biggestpile-soil differential settlement, that is because for the rivet-pile composite

foundation, when load is concentrated to the core area through pile cap, load that is distributed to soil among

piles decreases gradually, causing a gradual decrease both in pile top–soil differential settlement and in total

settlement in composite foundation as K increases, which is consistent with the research results of other scholars.

Therefore, the increase of Kvalues makes settlement of the rivet pile increase, but reduces the pile–soil

differential settlement and total settlement in composite foundation.

It can be seen from both cases that with the increase of K values, the settlement of rivet pile top tends to increase

at a very low speed in composite foundation, while pile-soil differential settlement increases rapidly. Therefore,

the increase of K values can effectively reduce pile-soil differential settlement in design. However, the oversized

pile cap does not only increase pile settlement but also makes pile cap under excessive bending moment, which

substantially increases the thickness of pile cap, adds cost and creates inconvenience to construction; thus, the

values of K should not be too large, and recommended to be less than 6.

4. CALCULATION BASED ON THE COMPOSITE MODULUS IN THE REINFORCEMENT AREA

With regard to the composite modulus method, the reinforcement area is regarded as a whole, which is a

complex composed of reinforcement and foundation soil, where the deformation occurs under the action of load.

The composite compressive modulus of each layer which is related to the replacement rate, the modulus of pile

and soil is used to conduct calculation. This method is derived from the equivalent deformation of the pile and

soil. Regarding the regular rigid pile composite foundation, since the pile top may pose a large upward piercing,

and the pile end may pose a downward piercing, the condition of equal strain cannot be strictly met; thus this

method has certain applicability. As for the composite foundation of the rivet pile, the pile cap which has a

larger area than the cross section of the regular pile makes the upward piercing force be smaller than that of the

pile without a cap. Field test data reveals that under the design load, the regular pile without a cap has a piercing

of almost 23.3cm long in the gravel cushion which is reinforced by the geo grid with a thickness of 40cm; while

for the rivet pile, the length of piercing is less than 1cm, showing that the pile cap can greatly reduce the

piercing of the pile[19]

. It can be seen from Fig. 7 that under constant load, with the increase of the pile

length-diameter ratio K, the differential settlement of the pile and soil gradually decreases, and the settlement of

the reinforcement area is gradually reduced. Therefore, the coordination deformation ability of the rivet pile

composite foundation in the reinforcement area is better than that of the regular composite foundation; and the

deformation between pile and soil tends to be unified; therefore, the composite modulus method can be used to

calculate the deformation. The rivet pile and the soil under the cap form the first composite pile due to combined

deformation; then the secondary composition of the first composite pile and the soil between piles creates the

rivet pile composite foundation. The formation process is shown in Figure8.


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Figure 8. Formation of the rivet pile composite foundation

More attention should be paid to two key points when using this method. First of all, the compressive modulus

of the rivet pile shaft should be determined, followed by the compressive modulus of the pile after first

composition which can be determined by the pile material. The compressive modulus of the ―first composite

pile‖ can be calculated based on the composite modulus of the soil and the pile. It can also be determined using

the results of the field load test. However, the calculation results may be different from the test results, which

should be adjusted by multiplying the adjustment factor ω.

The calculation of compressive modulus of the composite pile after the first composition should be conducted as

follows:

fpi 1 pi 1 si(1 )E m E m E (2)

fpiE The compression modulus of composite pile (MPa);

1 :m The replacement rate of the pile shaft area of the composite pile, when the pile cap is square

1 24m

K

, and the pile cap is around 1 2

1m

K .

The calculation of compressive modulus of the composite soil of the rivet pile after the second composition

should be conducted calculated as follows:

spi fpi si. . (1 )E m E m E (3)

m —:The area replacement rate of the composite pile with rivet pile composite foundation;

—:The adjustment factor of the compressive modulus of the composite pile.

According to previous studies, the deformation modulus obtained from the field load test is used as the

compressive modulus of the pile to calculate the settlement which is close to the experimental results [20]

. For the

deformation modulus of concrete material, it should be 0.5-1 time of the elastic modulus [21]

; and the

compressive modulus of the soil and the deformation modulus of the composite pile are obtained respectively

based on the test results of the soil samples and the results of the single rivet pile load test. The finite element

simulation is adopted to obtain the compressive modulus of the first composite pile with different pile

length-diameter ratios. The data collected is shown in Table 4.

It can be seen from Table 4 that the area replacement rate of the composite pile decreases gradually with the

increase of the cap-diameter ratio K, and the composite modulus also decreases gradually. The composite

modulus calculated is strikingly different from the moduli obtained from the test and simulation. The smaller the

K is, the bigger the gap will be; thus, the effect of pile cap size still exists. The cap- diameter ratio K, which is

related to adjustment coefficient ω, can be used to adjust the compressive modulus of the composite pile as well


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as the overall area replacement rate of rivet pile composite foundation. The influence of the first two effects can

be calculated based on the actual design and the pile arrangement; while, the relationship between K and the

ratio of the modulus can be reflected by the mathematical fitting method according to the calculation results

there from. The fitting curve is shown in Fig.9, and the expression of the curve is depicted in formula (4).

Table 4 The compressive modulus of first composite pile with different K values

Cap

diameter

ratio

K

Area

replacement

rate

m(%)

Soil

compressive

modulus

Es(MPa)

Compressive

modulus of

concrete pile

Ep(MPa)

Calculated

value of

Efp(MPa)

Tested

value

Efp(MPa)

Ratio of the

calculated and

the tested

value of Efp

2 19.6 5.83 19000 3728.7 188.5 19.78

4 4.9 5.83 19000 931 98.9 9.41

6 2.18 5.83 19000 419.9 60.4 6.95

8 1.23 5.83 19000 238.5 38.9 6.13

10 0.78 5.83 19000 154.7 29 5.34

3 21 1 1 1

1445.56 64.75 8.16 5.45K K K (4)

Figure 9. Fitting curve of the cap-diameter ratio

Figure 10. The load settlement curves under different K values

The settlement calculation procedures of the reinforcement area with the composite modulus are as follows: first,

calculate the compression modulus Efp of the composite pile with formula (1) based on the cap-diameter K, the

pile deformation modulus Ep and the soil compression modulus Es; then calculate the adjustment coefficient ω

based on K with formula (3) as well as the compression modulus Esp of the composite foundation with formula

(2). Finally, calculate the settlement s1 of the reinforcement area using the stratification method.


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This research also finds that the modulus variation of the two types of piles is not significant under the same

load level on pile top when the K changes in the range of 8-10. The load settlement curves are also very close as

shown in Fig.10. This indicates that with the increase of the cap-diameter ratio, the influence of the size of the

pile cap on the bearing capacity and deformation is gradually weakened; therefore, the value of K should not

exceed 6.

In order to calculate the lower layer s2, the pressure diffusion method should be adopted for the composite

foundation of the bulk material pile, and the equivalent entity method should be adopted for the rigid pile

composite foundation. While for the flexible pile composite foundation, the above two methods maybe used

alternately according to the pile-to-soil modulus ratio.

5. ENGINEERING APPLICATION

In a highway renovation project, a flyover will be built with the abutment backfill height being 6 meters, and the

new road under construction having a width of 8 meters according to the design. The flyover is located in the

sea-land intersecting sedimentary plain, which is of flat and open terrain. The strata are mainly composed of the

sea-land intersecting sedimentary earth of the Quaternary Holocene series (Q4mc). According to the

investigation report, the groundwater level is 1.30m-2.80m, and the distribution of soil layers from the top to the

bottom is as follows:

(1) miscellaneous fill (① 1, Q4me): grayish brown; loose - slightly dense, damp; mainly gravel-based, with a

small amount of clay, a thickness of 1.60-3.40m exposed, and poor engineering geological properties.

(2) mucky silty clay (②93, Q4mc): light gray - dark gray; soft plastic; high dry strength, medium toughness,

smooth surface, with a small amount of shell fragments and humus, a thickness of 6.10-10.50m exposed, and

poor geological properties. Its negative friction on the pile should be considered. [fa0] = 80 kPa, qik = 20 kPa.

(3) silty clay (②22, Q4mc): light gray-grayish brown; soft plastic; high dry strength, medium toughness, smooth

and shiny section mixed with some silt layer, a thickness of 3.30-11.40m exposed, and poor geological

properties. It can only be used as the holding layer near the pile. [fa0] = 120-140 kPa, qik = 30-40 kPa.

(4) silty clay (②23, Q4mc): brown-grayish brown; plastic; high dry strength, medium toughness, smooth

section with rust. This layer is widely distributed in the bridge site, witha thickness of 7.30-9.60m exposed and

poor engineering geological properties. It can only be used as the holding layer near the pile. [fa0] = 180 kPa, qik

= 40-50 kPa.

(5) silty clay (②24, Q4mc): light gray-brown; hard plastic; high dry strength, high toughness, smooth section

mixed with some clay and silt layer. This layer is widely distributed in the bridge site, with athickness of

10.30-13.60m exposed and poor engineering geological properties. It can only be used as the holding layer near

the pile. [fa0] = 200 kPa, qik = 60 kPa. Soil parameters are shown in Table 5.

Table 5 Parameters of materials

Numbe

ring Material

Thickn

ess

(m)

Weig

ht

(kN/

m3)

Deformation

modulus(MPa)

Cohesion

(kPa)

Internal friction

angle(°)

Poisson’s

ratio

1 Miscellaneo

us fill 2

18.1 2.84 20.0 30 0.30

2 Mucky silty

clay 6

18.3 5.20 15.2 17 0.30

3 Silty clay 8 19.6 9.15 13.7 21 0.30

4 Silty clay 4 19.7 4.95 20.2 10 0.25

5 Silty clay 12 20.3 4.63 28.9 34 0.30


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Figure 11.Site view of composite foundation of rivet pile

The composite foundation of rivet pile is employed for the reinforcement of the new roadbed at the back of the

abutment so as to improve the bearing capacity of foundation and reduce the settlement. The rivet pile shaft

adopts C80 preloaded concrete pipes, with an outer diameter of 500mm, a wall thickness of 60mm, and a pile

length of 16m; and the pile cap adopts square concrete prefabricated caps, with the pile length-diameter ratio K

being 2, and pile spacing being 2.2m. Piles are distributed in the shape of an equilateral triangular, on top of

which the gravel cushion of300mm thick with a layer of geo grid is laid, which is shown in Figure 11.

The total settlement calculated through composite modulus method is already specified in section3. When the

thickness of stratum is 2m, the point where σz= 0.2σcz is located at 18m underground, and σz= 0.1σcz is located at

26m underground. The calculated results are shown in Table 6.

Table 6 Calculation results by the stratification method.

Layer

Depth

(m)

First-composite

modulus (MPa)

Secondary composite

foundation modulus

(MPa)

Adjustment

factor

Calculation of

modulus (MPa)

Settlement

(mm)

1 2 3726.28 891.25 0.05 44.56 5.28

2 4 3728.18 893.50 0.05 44.68 4.78

3 6 3728.18 893.50 0.05 44.68 4.00

4 8 3728.18 893.50 0.05 44.68 3.28

5 10 3731.36 897.27 0.05 44.86 2.74

6 12 3731.36 897.27 0.05 44.86 2.33

7 14 3731.36 897.27 0.05 44.86 2.00

8 16 3731.36 897.27 0.05 44.86 1.76

9 18 —— —— —— 4.95 14.10

10 20 —— —— —— 4.95 12.62

11 22 —— —— —— 4.63 12.22

12 24 —— —— —— 4.63 11.26

13 26 —— —— —— 4.63 10.16

Total 86.53

Table 6 shows that the total settlement of the composite compression modulus corrected usingthe adjustment

coefficient ω is 86.5mm with the corner-point method, where the settlement of the reinforcement area is

26.1mm, accounting for 30.2% of the total settlement; and the settlement of the substratum is 60.4mm,

accounting for 69.8% of the total settlement. It also shows that the setting of the rivet pile greatly reduces the

deformation of the reinforcement area and the amount of deformation a well; the total settlement of the

substratum accounts for a majority of the total settlement; the most effective way to reduce the total settlement

is to increase the pile length; and if the pile length is fixed, it is recommended to appropriately increasethepile

length-diameter ratio K.


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Figure 12. Overall settlement curve of composite foundation of rivet pile

Figure 13. Settlement curve of roadbed section settlement curve of composite foundation of rivet pile

Under embankment load, the settlement of the composite foundation is not uniform but concave. Therefore, it

can be concluded that the total settlement is composed of the overall settlement and the section settlement. The

overall settlement curve of the composite foundation of the rivet pile can be obtained through field monitoring

as shown in Figure 12, and the section settlement curve is shown in Figure 13.

In Figure 12 above, the maximum settlement value is52.2mm; while in Figure 13, the settlement peak appears

below the center line of the new road, with the maximum value being 30.7mm; therefore, the total settlement

observed is 82.9mm. The comparison between the calculated results and the measured results shows that the

calculated results are slightly larger than the measured results, but they are very close tothe error of 4.3%, which

meets the engineering requirements. Thus, the results obtained through theoretical calculations are consistent

with the actual results, no matter for both the calculation results and the position where the maximum point

appears.

6. CONCLUSIONS

(1) This paper proposes a calculation method of the secondary composite modulus using the modulus

adjustment factor ω of pile shaft.

(2) The mathematical relationship between the cap-diameter ratio K and the modulus adjustment factor ω of the

pile shaft is obtained.

(3) The settlement of the composite foundation of the rivet pile can be adjusted through changing the

cap-diameter ratio if the pile length is fixed.

(4) The secondary composition modulus method generates better accuracy in calculating the settlement of the

reinforcement zone of the rivet pile.

(5) The value of cap-diameter ratio K should not be too large, with the recommended value being from2-4.

-60

-40

-20

0

0 100 200 300

Set

tlem

en0

t (m

m

Period (d)Overall settlement

-40

-30

-20

-10

0

10

0 5 10 15 20

Set

mtl

emen

t (m

m)

distance (m)Settlement curve of roadbed section

30d

60d

90d

150d

270d


334

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