the study on the influence of pile length-diameter …...revista de la facultad de ingeniería...
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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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Revista de la Facultad de Ingeniería U.C.V., Vol. 32, N°6, 2017, 323-334
333
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
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