Interaction between Finite Stiffness Broadened ... - Science Direct

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ScienceDirect Procedia Engineering 111 (2015) 756 – 762

XXIV R-S-P seminar, Theoretical Foundation of Civil Engineering (24RSP) (TFoCE 2015)

Interaction between finite stiffness broadened heellong pile and the surrounding soil Armen Z. Ter-Martirosyana, Zaven G. Ter-Martirosyana * a

MSUCE, 26 Yaroslavckoye shosse, Moscow 129337, Russia

Abstract Given formulation and solution of the problem of the interaction of the long pile with finite stiffness broadened heel and the surrounding soil analytical and numerical methods and their comparative analysis. Stress distribution between the pile side surface and the heel essentially depends on the physico-mechanical properties of the surrounding soil, as well as stiffness, the length and diameter of the pile. At a certain ratio of the amount of force in the pile shaft is reduced with varying intensity and depth of only 10-15% of the total force on the pile. To increase the share of the load on the heel of the pile is proposed to find the optimal ratio of the parameters of the pile and broadened heel in the given geological conditions in order to increase the proportion of the stress efforts on the heel of the pile. As for the design of the surrounding soil is considered elastic-plastic model with a tensile strength on the Coulomb-Mohr, and the material of the pile - linear deformable model. © 2015 The Authors. Published by Elsevier B.V. © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of organizing committee of the XXIV R-S-P seminar, Theoretical Foundation of Civil (http://creativecommons.org/licenses/by-nc-nd/4.0/). under responsibility of organizing committee of the XXIV R-S-P seminar, Theoretical Foundation of Civil Engineering (24RSP) Peer-review Engineering (24RSP) Keywords: Pile; Broad heel; Pile foundation; Soil; Efforts in the barrel of the pile

1. Introduction Bored piles longer than 20 m used in the construction of heavy constructions increased responsibility (tall buildings, bridge supports, energy facilities etc.) in areas where weak saturated soils great capacity, underlain by a relatively dense (with deformation module E> 40 MPa), usually, coarse soils. These are regions of Southeast Asia, the coastal areas of seas and oceans, including the Russian Federation.

* Corresponding author. Tel.: +7-495-287-4914; fax: +7-495-287-4914. E-mail address: [email protected]

1877-7058 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of the XXIV R-S-P seminar, Theoretical Foundation of Civil Engineering (24RSP)

doi:10.1016/j.proeng.2015.07.142

Armen Z. Ter-Martirosyan and Zaven G. Ter-Martirosyan / Procedia Engineering 111 (2015) 756 – 762

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Experimental and theoretical studies of carrying capacity and long piles settlement show such that the load bearing capacity of piles provided mainly due to friction on the side surface of the pile, and that the share of the heel of the pile usually not more than 20-30% of the total load applied to the pile head, i.e. bearing capacity of the soil under the heel of the pile it is not fully implemented. Obviously, increasing the share of the load on the heel of the pile possible by reducing diameter of the pile as well as the broadening of the pile heel. The latest is not always possible to implement because of the complexity of the technology of the device of bored piles in deep water. Numerical simulation of stress-strain state (SSS) of soil interacting with long piles shows that, ceteris paribus (engineering geological structure, the length of the pile, and others.) it is possible to control the VAT of the pile and soil by reducing the diameter of the pile, the pile broadening heel, providing a predetermined safe load (pplc) enclosing a long pile (Fig. 1).

Fig. 1. Geomechanical PRGHORIORQJVLQJOHSLOHGLDJUDPLQGLFDWLQJVKHDUVWUHVVHVIJU DQGYHUWLFDOGLVSODFHPHQWV6U WKHVRLODURXQGLWDQG lc>>dc

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Armen Z. Ter-Martirosyan and Zaven G. Ter-Martirosyan / Procedia Engineering 111 (2015) 756 – 762

This design scheme was justified by the results of numerous experimental studies of long piles [1, 2, 4, 7, 11, 12], as well as numerical simulation SSS soil around long piles [9]. It is a model of a single cell in the pile field with a distance between piles at least 6dc. In this case, the mutual influence of long piles minimum. 3. Assumptions and equations According with the design scheme (Fig. 1) when moving relatively long pile and the surrounding ground assuming complete sticking the lateral surface of the pile with the soil, soils moving (S(r)) it is mainly due to shear VWUDLQȖU LHWHOHVFRSLFPHFKDQLVPKROGVWKHRIIVHWF\Oinders. Therefore, the interaction of long symmetrical pile with the surrounding soil on the contact surface of the shearing stresses occur IJc(z) and corresponding stresses in the pile shaft ız(z), which are determined from the equilibrium conditions of the unit length of the pile dz dV c ˜ Sa 2

2SaW c dz , ie we get

a dV c 2 dz

W ɫ z

(1)

)URPWKHHTXLOLEULXPFRQGLWLRQRIWKHVRLODORQJWKHF\OLQGHULWVKRZVWKDWWKHVKHDUVWUHVVIJU ZLWKGHFUHDVLQJ distance from the center, ie

W r W c

a r

(2)

ZKHUHIJU - piles pressure on contact with the ground. Under the influence of shear stresses IJU LQWKHVRLOWKHUH DUHDQJXODUGHIRUPDWLRQȖU DUHDVVRFLDWHG ZLWKWKH vertical Sv and horizontal Sr movement known dependence [7]. Given that the shear deformation mechanism of soil volumetric soil deformation can be neglected as well as the nature of the change Sv(r) with increase r and conditions dSr/dz=0.

J r 

dS v . dr

(3)

Below, on the basis set out in this section and the main provisions of the original equations are formulated and solved the problem in accordance with Section 2, taking into account non-linear model of soil around the pile. 4. Nonlinear shear deformable soil environment In this case, as the settlement is considered the most common non-linear model of soil shear [3], described by a power function of the form: 2

§ W r · ¸¸ , © W 0 z ¹

J r ¨¨

(4)

ZKHUHIJU DQGIJ] GHILQHGE\(2) and (3.5). Substituting formula (4) in (3) and, after integration with the boundary condition Sv(r=b)=0 we obtain S v r

W c2 a 2 W 02

§1 1· ¨  ¸. ©r b¹

(5)

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Armen Z. Ter-Martirosyan and Zaven G. Ter-Martirosyan / Procedia Engineering 111 (2015) 756 – 762

The maximum displacement of the pile or soil under r=a S v a

W a2 a 2 § b · ¸. ¨ W 02 © b  a ¹

(6)

It follows that

Wa

S v a

W0 a

b . ba

(7)

Substituting this expression into (1), we obtain

dV c dz

W 2 Sv 0 a a

b . ba

(8)

On the other hand the condition of linear deformability piles H c

dS v dz

1 dV c Ec dz

V c Ec obtain (9)

or

d 2 Sv dz 2

1 dV c . Ec dz

Fig.2. The distribution of the vertical displacements along the pile shaft with reference to various lengths of pile

(10)

Fig. 3. The distribution of the tangential movement along the barrel of the pile with reference to various lengths of the pile

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Armen Z. Ter-Martirosyan and Zaven G. Ter-Martirosyan / Procedia Engineering 111 (2015) 756 – 762

Substituting from this expression dV c dz in formula (8) obtain nonlinear differential equation of second order about Sv(z):

d 2 Sv dz 2

 O Sv

0

(11)

where

O

2W 0 aEc

b ab  a

(12)

The numerical solution of the nonlinear differential equation of the second degree obtained by using software package Mathcad v.15 with the boundary conditions

­ °z ° ® °z °¯

0 o S v 0 V 0 l o S vc l

Sa1  Q 2 2G2

;

p , Ec

(13)

showed that the diagrams Sv(z) (Fig. 2 IJc(z) (Fig. 3) and ıc(z) (Fig. 4) are nonlinear and satisfy the boundary conditions (13). With the growth of the load on the well head piles settlment develops linearly (Fig. 4.5). Accounting for the strength properties of soil around the pile situ reduces the amount of settlement of pile. With the growing length of the pile tension in the trunk of the pile at the pile heel decreases (Fig. 4).

Fig. 4. Vertical distribution of stresses along the pile shaft with reference to various lengths of the pile

Fig. 5. The distribution of the vertical displacements along the pile shaft with the rigidity of the material taking into account the different piles

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Armen Z. Ter-Martirosyan and Zaven G. Ter-Martirosyan / Procedia Engineering 111 (2015) 756 – 762

Other things being equal, there is a critical value of rainfall at the level of the heel of the pile, which is more than the solution (11) does not seem possible. If the predetermined voltage in the trunk of the pile at the pile heel ıc S”S  ZKHUHp* - under the base pressure calculated round shaped punch [6], it is possible to determine the corresponding rainfall pile at the pile heel. ie we have:

Sp

p*

Sa1 Q 2 2G2

, p* S p

2G2 . Sa1 Q 2

(14)

The initial critical load under the heel of the pile can be determined by the formula [8]

p* J 2 d 

2J 2 d sin M 2  2c cos M 2 , 1  2Q 2

(15)

where Ȟ2 - Poisson's ratio underlayment; Ȗ2 - unit weight of soil below the pile heel; d - the depth of the heel of the pile from the surface. Note that p* to point r=a+0 and z=0, because at this point p* minimal compared to point r=a-0, z=0 and at point r=0 z=zma under the center of the loaded area [8]. 5. Main findings 1. The total force on drilled piles of great length (l>20 ɦ) used in construction in regions where the power of weak saturated soils up to 100 meters distributed between the side surface T (friction force) and fifth pile (R) ie N=T+R. However, generally, the proportion R is not higher than 30%, and therefore the bearing capacity of soils, fifth pile is not fully realized. 2. To reduce the share of the load on the heel of the pile should find the optimal ratio of the length, the diameter of the pile, as well as broadening the heel to provide the pile when it is necessary to satisfy the condition S”S ZKHUHS - initial critical load. 3. Using nonlinear models allows you to build diagrams of soils Sv] IJc(z) and ıc(z), that it is necessary to clarify the nature interaction of pile with the surrounding soil. This work was financially supported by Ministry of Education and Science of the Russian Federation (RFMEFI59314X0002). All tests were carried out using research equipment of Head Regional Collective Research Centre of Moscow State University of Civil Engineering. :LWKWKHVXSSRUWRIWKH0LQLVWU\RI(GXFDWLRQDQG6FLHQFHRIWKH5XVVLDQ)HGHUDWLRQ7DVNʋ. 7DVNʋ  6. References [1] [2] [3] [4] [5]

A. A. Bartolomej, Basis of calculation of pile foundations for the maximum permissible draft. Moscow: Strojizdat. 1982. 221 p. (in Russian). A. A. Bartolomej, I. M. Omel'chak, B. S. Jushkov, Forecast sediment pile foundation. Moscow: Strojizdat. 1994. 384 p. (in Russian). S. S. Vjalov, Rheological basics of soil mechanics. Moscow: Vysshaja shkola. 1978. 447 p. (in Russian). B. I. Dalmatov, F. K. Lapshin, Ju. V. Rossihin, Design of pile foundations in soft soils. Leningrad:Strojizdat. 1975. 240 p. (in Russian). R. Katcenbah, Recent advances in the field of foundation of high-rise buildings on the basis of compressible // Vestnik MGSU. 2006. No 1. pp. 105-118. (in Russian). [6] Z. N. Nguen, Determination of rainfall round stamp in recognition of his burial. Proceedings of the 4th International scientific conference of young scientists, post-graduate and doctoral students «Building-forming living environment». Moscow: MGSU, 2006. pp. 40-43. (in Russian). [7] Z. G. Ter-Martirosjan Z.G. Stress-strain state in a ground massif and its interaction with the pile and deep foundations // Vestnik MGSU. 2006. No 1. pp. 38-49. (in Russian). [8] Z. G. Ter-Martirosjan, A. Z. Ter-Martirosjan, V. V. Sidorov, Initial critical pressure under the heel of the round foundation and bored piles under the heel of round section // Estestvennye i tehnicheskie nauki.. 2014. No 11-12 (78). pp. 372-376. (in Russian). [9] Z. G. Ter-Martirosjan, Z. N. Nguen, Interaction long piles with a two-layer elastic-creeping ground // Vestnik grazhdanskih inzhenerov SPbGASU. 2007. No 1(10). pp. 52-55. (in Russian). [10] N. A. Cytovich, Soil mechanics. Moscow: Gosstrojizdat. 1963. 636 p. (in Russian).

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Armen Z. Ter-Martirosyan and Zaven G. Ter-Martirosyan / Procedia Engineering 111 (2015) 756 – 762

[11] 11.Booker J., Poulos H. Analysis of creep settlement of Pile foundation . Journal of the Geotechnical Engineering division. Proc. of the ASCE.1976. Vol. 1.102 No GT. pp. 1-14. (In English). [12] 12.Seed H.G., and Reese, L.C. The action of soft clay along friction piles. Transactions, ASCE. 1957. Vol. 122. pp. 731-754. (In English).