AbstractThis paper deduced the cavity geometry of the plate under the action of one-way and two-way squeeze equipment which is hyperbolic for two-way squeezed, hyperbolic and arc for one-way squeezed. This paper points out the different stress characteristics and applicable conditions of bearing plate for the two kinds of squeezed branch pile, and provides references for the development of the squeezed branch pile

Baolin, Liu

Chun, Yang

Dequan, Shi

Jian, Xiao

Elsevier - Publisher Connector 

Research on the Plate Cavity Geometry of the Squeezed Branch Pile 

 Procedia Engineering  73 ( 2014 )  29 – 34 
Available online at www.sciencedirect.com
1877-7058 © 2014 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. 
Selection and peer-review under responsibility of Geological Engineering Drilling Technology
doi: 10.1016/j.proeng.2014.06.166 
ScienceDirect
Geological Engineering Drilling Technology Conference (IGEDTC), New International 
Convention Exposition Center Chengdu Century City on 23rd-25th May 2014 
Research on the Plate Cavity Geometry of the Squeezed Branch Pile 
Shi Dequana  Xiao Jianb*  Yang Chuna,c  Liu Baolina 
aKey Laboratory on Deep Geological Drilling Technology, Ministry of Land and Resources, Beijing, 100083,China 
bMCC Communication Engineering Technology Co., Ltd., Beijing 100028, China 
cSino-mine Resource Exploration Co. Ltd., Beijing 100089, China 
Abstract 
This paper deduced the cavity geometry of the plate under the action of one-way and two-way squeeze equipment which is 
hyperbolic for two-way squeezed, hyperbolic and arc for one-way squeezed. This paper points out the different stress 
characteristics and applicable conditions of bearing plate for the two kinds of squeezed branch pile, and provides references for 
the development of the squeezed branch pile. 
© 2014 The Authors. Published by Elsevier Ltd. 
Selection and peer-review under responsibility of Geological Engineering Drilling Technology. 
Keywords: Squeezed Branch Pile; Plate Cavity Curve; Hyperbolic Curve 
1. Introduction 
Since 1992, the squeezed branch pile has been applied in the domestic civil engineering, municipal, shipping, 
aviation and highway, which bring the enormous social benefit and economic benefit. The invention of this pile is a 
great improvement and innovation for the traditional uniform section, renovates the pile structure, and makes 
fundamental changes on stress behavior and load transfer mechanism[1]. 
The squeezed branch pile is composed of the main pile, bearing plate, several numbers of branches and is 
surrounded by dense extrusion soil. The squeezed branch pile transfer the only one end bearing point of the end 
bearing friction pile into the pile body provided with a plurality of end bearing point of friction and end bearing piles, 
so that the ultimate bearing capacity of single pile is greatly increased. The geometry of the bearing disk is formed 
* Corresponding author. Tel.: +8613691254211. 
E-mail address: xj49752@163.com 
  Published by Elsevier Ltd. Open access under CC BY-NC-ND license. 
electi  a  eer-re ie  nder responsibility of Geological Engineering Drilling Techn logy
30   Shi Dequan et al. /  Procedia Engineering  73 ( 2014 )  29 – 34 
by the squeezed machine for multiple extrusions. The physical and mechanical properties of the undisturbed soil 
under the extrusion force is changed[2]. 
2. Analysis on Disc Cavity Curve 
For forming a bearing disk, variety of squeezed branch disk machine, which it’s working principle are basically 
the same, can be used. The squeezed form is divided into two kinds, one kind is unidirectionally squeezed, another 
is bidirectionally squeezed. 
 
a) unidirectionally squeezed       b) bidirectionally squeezed 
     Fig.1 The schematic diagram of the squeezed machine 
When using bidirectional squeezed machine, hydraulic equipment push the bow pressing arm from two directions. 
The force of the upper arm and the lower arm is symmetric, which are symmetrically outward expansion, and to 
move equipment center. In this process, the soil is squeezed by the bow pressing arm. The soil produces a certain 
plastic deformation. 
   When using the one-way squeezed machine, lower fulcrum remained stable under bow pressing arm, hydraulic 
cylinder applied thrust from the upper bow pressing arm, push and squeezed the soil. At this time, compared with 
the upper soil, the soils under the bow arm deserve the bigger pressure and the better compacting effect. 
   The length of bow pressing arm is unchanged in the squeezing process, while only the angle of the arm is changed. 
Two kinds of outline of disc cavity after squeezed can be showed by drawing, as shown in Fig.2. 
\
[
\
[
 
a) bidirectional squeezed        b) unidirectionally squeezed 
Fig. 2 disc cavity outline 
 
31 Shi Dequan et al. /  Procedia Engineering  73 ( 2014 )  29 – 34 
3. Disc Cavity Curve Derivation 
˄1˅When bidirectional expanded, upper and lower arm are symmetric. Because of the movement of the 
upper arm, the profile of disc cavity can be drawn. 
\
[/ / /
[\
[\
θ 
θ 
θ 

7DQJHQW l ,( )24
l 2
4
y=-x+l      /2  2
\
[
y=x
 
Fig.3 general gesture of bow pressing arm         Fig.4 especial gesture of bow pressing arm 
As shown in figure 3, the length of the bow pressing arm is l . At the moment 321 ,, ttt , the gesture line of the arm 
are 321 LLL ǃǃ . The intersection of  L1 and L2 are ),( 1212 yx . The intersection of L2 and L3 are ),( 2323 yx . The 
angle between arms and the vertical axis are 321 TTT ǃǃ . The slope of the three line 321 ,, kkk  are 1cotT ,
2cotT , 3cotT . 
   When 
^ TTT TTT ' ' 21 23 ,and o' 0T , then o ),(),( 12122323 yxyx . The line between ),( 1212 yx  and 
),( 2323 yx  is the tangent of the outer contour line. 
 Let 
1223
1223
1223
lim
xx
yyk
xx 
 o  , which is the tangent slope of outer contour line at point ),( 1212 yx . As shown in 
figure 3, 2kk  , and x
yk   2cotT , then : 
x
y
dx
dy                                                                                                                                                       (1) 
Solute the differential equation above, the general solution of contour equation: 
        
x
cy                                                                                                                                                           (2) 
As shown in figure 4, because of the symmetry, contour and the line 2/2lxy   tangent to the point 
32   Shi Dequan et al. /  Procedia Engineering  73 ( 2014 )  29 – 34 
)
4
2,
4
2( ll , tangent slope 1 k , then: 
        1' 4/22     lxx
cyk                                                                                                                         (3) 
8
2lc                                                                                                                                                           (4) 
Therefore, expanded by the two-way squeezed machine, the disc cavity contour curve is hyperbola, curve equation 
as follows: 
8
2lxy                                                                                                                                                         (5) 
˄2˅When unidirectional squeezed, the lower arm under constraint of the lower fulcrum . The lower arm is in 
circular motion when the lower fulcrum is fixed as center of the circle. This trajectory is relatively simple. The two 
endpoint of the upper arm are in the changing, the trajectory of the contour curve needs to be calculated. 
\
[
[\
/
/
/
\
[
+\SHUEROLF
$UF
θ

[\
&ULWLFDO
l 12 + l 22
l 1 l 2
,
l 12 + l 22
l 2 l 2( )
θ 
θ 
θ 
SRLQW
 
A)                             B) 
Fig. 5 bow pressing arm gesture of one-way squeezed machine   Fig. 6 one-way squeezed machine disc cavity contour 
As shown in figure 5, the length of the upper arm is 1l , the length of the lower arm is 2l .At the moment 321 ,, ttt , 
the gesture line of the arm are 321 LLL ǃǃ . The intersection of L1 and L2 are ),( 1212 yx . The intersection of L2 and 
L3 are ),( 2323 yx . The angle between arms and the vertical axis are 321 TTT ǃǃ . So the slope of the three line 
321 ,, kkk  are 1cotT , 2cotT , 3cotT . 
When ^ TTT TTT ' ' 21 23 , and o' 0T , then o ),(),( 12122323 yxyx . So the line between ),( 1212 yx  and 
33 Shi Dequan et al. /  Procedia Engineering  73 ( 2014 )  29 – 34 
),( 2323 yx  is the tangent of the outer contour line. 
 Let 
1223
1223
1223
lim
xx
yyk
xx 
 o  , which is the tangent slope of outer contour line at point ),( 1212 yx . As shown in 
figure 3, 2kk  , and x
yk   2cotT , then : 
     
x
y
dx
dy                                                                                                                                                        (6) 
   Solute the differential equation above, the general solution of contour equation: 
      
x
cy                                                                                                                                                             (7) 
   As shown in figure 6, with the angle between the upper arm and the vertical axis becomes larger and larger, the 
angle between lower arm and the vertical axis becomes larger, until the upper and lower  arms is orthogonal when 
they are in the critical state. At the moment, upT  is the critical angle 
2
1arctan'
l
l T .  With upT  becomes larger, the 
upper arm and the soil out of contact, only the lower arm squeeze soil. The lower arm continues to squeeze the soil 
to be a sector whose side profile is arc. 
   When in a critical state, activities endpoint of the lower arm 2l  is the critical point whose coordinate is: 
  ¸¸¹
·
¨¨©
§
 2221
22
2
2
2
1
21 ,,
ll
ll
ll
llyx                                                                                                                    (8) 
   This point is the intersection of side profile which squeezed by line 1l  and 2l . Because x
cy  , then: 
          2
2
2
1
3
21
2
2
2
1
22
2
2
2
1
21
ll
ll
ll
ll
ll
llxyc                                                                                                       (9) 
   When the upper and the lower arm lengths are equal, that is lll   21 , then : 
           
2
2lxy                                                                                                                                                    (10) 
   Therefore, expanded by the one-way squeezed machine, the disc cavity contour curve is combination of 
hyperbolic line and arc: 
    2
2
2
1
3
21
ll
llxy   when 2
1arctan'
l
l dTT                                                                                                 (11) 
34   Shi Dequan et al. /  Procedia Engineering  73 ( 2014 )  29 – 34 
    22
22 lyx     when
2
1arctan'
l
l !TT                                                                                               (12) 
4.  Analysis on Applicability 
Squeezed by two-way squeeze machine, the side profile of soil under the plate and soil above plate is hyperbola. 
The soil far which is away from the hole wall soil is under the higher level of compression which can obtain better 
bearing capacity. But the soil which is close to borehole wall is under the lower level of compression.  By Contrast, 
its force performance is not good. 
   Squeezed by one-way squeeze machine, the situation of the soil is: the disc cavity contour curve is combination 
of hyperbolic line and arc. The length of the arc is relative of the critical angle and finally squeezed angle . Disc 
bottom is straight. The level of compression of disc bottom is higher than disc upper. It meets the requirement of 
that disc bottom soil bearing most of the force. So when they are same of arm length, soil can be more close-grained 
which is squeezed by one-way squeeze machine. So the bearing capacity of soil under the plate increase more than 
two-way squeeze machine. 
   Overall, the pile which its plate is squeezed by one-way machine is more suitable for compressive pile because 
of higher level of the compressive degree of soil under the plate. When squeezed by the two-way squeeze machine, 
the level of compression of the soil under the plate and above the plate is equal. Compare with squeezed by one-way 
squeeze machine, the compressive degree of soil above the plate squeezed by two-way squeezed machine obtain 
higher bearing capacity, so it is more suitable for uplift pile. 
5. Conclusion 
(1) The disc cavity curve is hyperbola when squeezed by two-way squeeze machine, which is different from the 
combination of hyperbolic line and arc when squeezed by one-way squeeze machine. 
(2) The pile which its plate is squeezed by one-way machine is more suitable for compressive pile, while pile 
which its plate is squeezed by two-way machine is more suitable for uplift pile. 
(3) Through the analysis of different squeeze ways of squeezed branch pile and their disc cavity curve, enhance 
mutual understanding to the structure of this pile and its bearing feature, which provide a reference for development 
of the squeeze branch pile technology. 
References 
[1] Wang Mengshu, He Dexin, Tang Songtao. the New Pile Technology of 21 Century-DX Rotary Drilling Squeezed Branch Pile[J]. Engineering 
Science.2012,14(1):5-11. 
[2] Zhang Yanqing, Zhou Mingfang. Study on the Molding Process of the Hydraulic Pressure Squeezed Branch Pile[J]. Journal of Beijing 
University of Technology.2001,27(1):54-56. 
 
  


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Research on the Plate Cavity Geometry of the Squeezed Branch Pile

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