BASES AND FOUNDATIONS, UNDERGROUND STRUCTURES

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1 Scientific Herald of the Voroneh State University of Architecture and Civil Engineering. Construction and Architecture BASES AND FOUNDATIONS, UNDERGROUND STRUCTURES UDC Tambov State Technical University D. Sc. in Engineering, Prof., Head of Dept. of Structures of Building and Facilities V. V. Ledenyov Student Chu Thi Hoang Anh Russia, Tambov, tel.: (475) ; V. V. Ledenyov, Chu Thi Hoang Anh LOAD BEARING CAPACITY OF DRILLED PIER FOUNDATIONS UNDER ARBITRARY APPLICATION OF INCLINED FORCE Problem statement. The aim of the paper is to describe a method for calculation of cylindrical drilled pier foundation under the action of spatial force system. Results and conclusions. Contact stress contours are taken from results of the experiments. The relations between foundation load bearing capacity and different forms of shearing stress distribution diagrams are obtained. It is established that calculation of load bearing capacity of drilled pier foundations under arbitrary action of inclined force can be reduced to the solution of simpler twodimensional problems. It is concluded that the force acting on the foundation can be resolved into components located in the plane which goes through the foundation axis. Keywords: foundation, base, load, normal contact stress, tangential contact stress, load bearing capacity. Introduction In civil, industrial, hydrotechnical engineering and road engineering, concrete and reinforced concrete drilled pier foundations or short piles of diameter d from 0.5 to m and of length L 34

2 Issue 1 (9), 011 ISSN from to 10 m are used successfully in erecting landslide protection facilities. Such structures (L/d 5) are considered as rigid. Unlike shallow foundations, such foundations require to take into consideration resistance along the lateral surface of the pile. In the general case, the structures under consideration experience the action of the system of forces which is related to eccentric inclined axis with eccentricity e (e 0 = e/r is the relative value, R is the radius of foundation) and inclination angle to the vertical δ. These parameters can vary in a wide range. Often, e 0 = 1 1; δ = The nature of contact foundation-base interaction, dimensions of separation one and values of displacements depend on relation e/δ. Available methods of design, for example [1] are based on rigorous assumptions (of unchanged coordinate of Instantaneous center of rotation, etc.) and rather conventional soil models (Fuss-Winkler hypothesis). Combined experimental studies conducted on large-scale strain model [, 3] cause us to develop validate methods of design. In [, 3] experimental findings on contact stress distribution are given. Equations for normal and shear stresses under the action of force F located in the plane which goes through the axis of foundation are presented in [4, 5]: x [. a.. a. ]; (1) x 0 F f cos sin x 1 4e f 1 R R ; () y f a 0.6a a 0.43, (3) where F f cos sin a 0.49hh 0.88 / 0.33h h 0.94h.97 ; f 1 B f is the internal friction coefficient; h is the depth of foundation. 35

3 Scientific Herald of the Voroneh State University of Architecture and Civil Engineering. Construction and Architecture These equations are set up for cylindrical system of coordinates О (r, α, ). Point with coordinates (x, y, ) is denoted by (R, α, ), where x = Rcosα, y = Rsinα. Tangential contact stresses are determined by the formula x k cos xmac cos cos 3 a ( ) cos ; (4) x sin 0.6a a 0.43 sin cos ; (5) Stresses on subgrade f a 0.6a a 0.43 cos. (6) F f cos sin x F f cos sin 1 4e0 1 4e0 cos ; f 1 R R f 1 R (7) F f cos sin x F f cos sin 1 4e0 f 1 4e0 cos ; f 1 R R f 1 R (8) where F a 0.49hh 0.88 / 0.33h h 0.94h.97. f 1 1. General case Forces F 1 and F are in a plane which goes through the axis of foundation (Fig. 1, ). The angle between plane of action of forces γ. Points of force application О 1 (e 1. 0,0) and О (е,γ,0). Following assumptions are introduced: normal stresses on the foundation underside are taken as distributed by the linear law; lateral surface friction is constant in depth; normal stress distribution in a horiontal plane is a function of cosα: σ х (α) = σ х () cos k α; к = 1,, 3..., n. 36

4 Issue 1 (9), 011 ISSN a) b) rupture rupture Fig. 1. Stress distribution diagram: а) general view of foundation; b) longitudinal section a) b) rupture Fig.. Stress distribution diagram: a) diagram of stress distribution over the outlines of cross-section plane for force F 1 ; b) planes of force action 37

5 Scientific Herald of the Voroneh State University of Architecture and Civil Engineering. Construction and Architecture Stresses in each point are equal to the sum of stresses caused by each force, i. e., 3 a a1 0.6a a1 0.43cos 3 a a a cos ; a a1 0.6a a1 0.43sin cos a a a sin cos ; f a1 0.6a a cos f a 0.6a a 0.43 cos ; F f cos sin 1 4 cos e 1 F f 1 R f cos sin 1 4 cos ; e f F 1 R f cos sin n f 1 4e 1 cos F f 1 R f cos sin f e f 1 R 1 4 cos. (9) (10) (11) (1) (13) where F i ai 0.49hh 0.88 / 0.33h h 0.94h.97. f 1 f A f A f R B cos sin ; cos sin ; 1 ; Let e1 cos c1; 1 4e cos c, F Ac / D F A c / B ; then / / ; n f. n f F1 Ac 1 1 B f F Ac B. The special case Force F is not located in any plane which goes through the axis of foundation (Fig. 3). 38

Issue 1 (9), 011 ISSN 075-0811 а) b) Fig. 3.

6 Issue 1 (9), 011 ISSN а) b) Fig. 3. Location of the force with varying inclination angle to the vertical: а) general view; b) top view Force F can be located on F 1, F' and М: Force F1 F, e ; (14) F ' F sin sin / ; (15) M F ' ecos / F sin sin / e cos /. (16) F ' goes through 0 and is located in plane ХОУ, δ = 90 0, е = 0. In equation for τ α, values of lateral shear stresses from moment М: M / xrh R F sin sin / ecos / / hnr. (17) Normal and shear stresses are obtained with consideration for (14), (15), (16), (17): 3 a a1 0.6a a1 0.43cos 3 a a a cos 1.5 ; (18) 39

7 Scientific Herald of the Voroneh State University of Architecture and Civil Engineering. Construction and Architecture a a1 0.6a a1 0.43sin cos a 0.6a a 0.43sin 1.5 cos 1.5 e F sin sin / cos / ; h R f a1 0.6a a cos f a 0.6a a 0.43 cos 1.5 ; (19) (0) F f cos sin F sin sin / 1 4e0 cos f 1 R f 1 R ; (1) n F f cos sin F sin sin / f 1 4e0 cos f 1 R f 1 R, () where F a1 i 0.49h h 0.88 / 0.33h h 0.94h.97 ; f 1 4F sin sin / a 0.49h h 0.88 / 0.33h h 0.94h.97. f 1 Load bearing capacity of drilled pier foundations is determined from condition (3) max R u ; (4) max Rh, where R u is the design horiontal soil strength; R u = ξ R h, ξ < 1; R h is the design vertical strength of soil under foundation bed according to Building standards and rules (SNiP) *. Since R h lost its initial sense, it is expedient to use up-to-date approach to its determination, for example, with the help of techniques described in [6]. Conclusions 1. Force acting on a foundation can be resolved into components located in the plane which goes through the axis of foundation. 40

8 Issue 1 (9), 011 ISSN The calculation of load bearing capacity of drilled pier foundations under arbitrary application of inclined force can be reduced to the solution of simpler two-dimensional problems. References 1. Завриев, К. С. Расчеты фундаментов глубокого заложения / К. С. Завриев, Г. С. Шпиро. М.: Стройиздат, с. = Zavraev, K. S., Shpiro, G. S. Calculations of deep foundations. Moscow, 1970, 1 pp.. Леденев, В. В. Прочность и деформативность оснований заглубленных фундаментов / В. В. Леденев. Воронеж: изд-во Воронеж. гос. ун-та, с. = Ledenyov, V. V. Strength and deformation of deep foundation bases. Voroneh, 1990, 4 pp. 3. Леденев, В. В. Экспериментальное исследование оснований заглубленных фундаментов / В. В. Леденев. Воронеж: изд-во Воронеж. гос. ун-та, с.= Ledenyov, V. V. Experimental study of deep foundation bases. Voroneh, 1985, 156 pp. 4. Леденев, В. В. Расчет несущей способности буронабивных фундаментов / В. В. Леденев, Тью Тхи Хоанг Ань // Вестник Тамбов. гос. техн. ун-та Т. 13, 3. С = Ledenyov, V. V., Chu Thi Hoang Anh. Calculation of load bearing capacity of drilled pier foundations. Herald of Tambov State Technical University, 007, Vol. 13, N 3, pp. 5. Леденев, В. В. Расчет несущей способности буронабивных фундаментов (с учетом касательных напряжений) / В. В. Леденев, Тью Тхи Хоанг Ань // Вестник центрального регионального отделения РААСН Вып. 8. С = Ledenyov, V. V., Chu Thi Hoang Anh. Calculation of bearing capacity of drilled pier foundations (with consideration for shear stresses). Herald of the Central Regional Department of RAABS, 008, Iss. 8, 4 3 pp. 6. Шапиро, Д. М. Расчетное моделирование нагружения буронабивных свай осевой силой / Д. М. Шапиро, Н. Н. Мельничук // Проблемы механики грунтов и фундаментов строения в сложных условиях: тр. междунар. науч.-практ. конф. Уфа, 006. Т. 1. С = Shapiro, D. M., Melnichuk, N. N. The design modeling of drilled pile load by axial force. Problems of Soil Mechanics and Foundation Arrangement in Difficult Conditions. Materials of International Scientific and Practical Conference. Ufa, 006, Vol. 1, pp. 41

D DAVID PUBLISHING. Port and Marine Structures Made of Sheet Piling with Staggered Toe. 1. Introduction. 2. Design Approach and Main Dependencies

D DAVID PUBLISHING. Port and Marine Structures Made of Sheet Piling with Staggered Toe. 1. Introduction. 2. Design Approach and Main Dependencies Journal of Shipping and Ocean Engineering 4 (2017) 168-173 doi 10.17265/2159-5879/2017.04.004 D DAVID PUBLISHING Port and Marine Structures Made of Sheet Piling with Staggered Toe Doubrovsky Michael 1,