MASTER’S (MSc) GRADUATE THESIS

Title:

Study and project calculations of

a hybrid pile or other embedded

structure in soil

Thesis author :

HESAM RAHNAMA Thesis supervisor :

Prof. Włodzimierz BRZĄKAŁA Thesis reviewer :

Prof. Wojciech PULA

Academic year

2013/2014

Feb 2014

General Characteristics

• Categorized as DEEP foundation.

• Consisting of 2 different portions, one of D1 diameter and the other one of D2 diameter. (D1>D2)

• Intended to bear lateral load aiming specifically to minimize the Max lateral displacement on the top.

Analytical Scopes

• Solved based on Classical method of Winkler.

• Assumed as a finite beam leaned on an elastic support (referred to as subgrade/subsoil in Winkler definition).

• Analysis solved by means of Maple.17

Analytical Scopes

• 𝑬𝑰.𝒅𝟒𝒚

𝒅𝒙𝟒 + ₵. 𝑩. 𝒚 𝒙 = 𝒒𝟎(𝒙) ;

No uniform load → 𝑞0 𝑥 = 0 ; So, the general solution is :

• 𝒚 𝒙 = 𝒆𝒙

𝒍𝒘 𝑪𝟏. 𝑪𝒐𝒔 𝒙

𝒍𝒘+ 𝑪𝟐. 𝑺𝒊𝒏

𝒙

𝒍𝒘+ 𝒆

− 𝒙

𝒍𝒘 𝑪𝟑. 𝑪𝒐𝒔 𝒙

𝒍𝒘+ 𝑪𝟒. 𝑺𝒊𝒏

𝒙

𝒍𝒘

Where:

𝑙𝑤 ∶(Characteristic length of the pile) = 4𝐸𝐼

₵.𝐵

4 , [𝑚]

₵ : ( Coefficient of elastic subsoil) , [ 𝑀𝑁

𝑚3]

𝐶𝑖: (Integration coefficients)

Influential terms on the displacement function

1- ″EI ″ ( Stiffness)

Depending on geometry ( I )

Mechanical characteristics of construction material (E).

2- "₵“ - depending on soil characteristics. ₵ =𝑟

𝑦

Influential terms on the displacement function

Due to :

• Pretty complex mathematical calculations

• Trigonometric functions

𝑙𝑤 =4𝑬𝑰

₵ . 𝐵

4 ; 𝑦 𝑥 = 𝑒

𝑥

𝒍𝒘 𝐶1 𝐜𝐨𝐬𝒙

𝒍𝒘+ 𝐶2 𝐬𝐢𝐧

𝒙

𝒍𝒘+ 𝑒

− 𝑥

𝒍𝒘 𝐶3 𝐜𝐨𝐬𝒙

𝒍𝒘+ 𝐶4 𝐬𝐢𝐧

𝒙

𝒍𝒘

Precise calculation needed to determine the dominant term and influence

Analysis – Continuity conditions

• Analytical modeling leading to a system of 8 questions and 8 unknowns.

M= -EI . [𝐶1, 𝐶2, 𝐶3, 𝐶4].𝑑𝑦2

𝑑𝑥2 ;

θ=[𝐶1, 𝐶2, 𝐶3, 𝐶4].𝑑𝑦

𝑑𝑥

So,

Number of 𝑪𝒊 : 4 x 2 ( Left – Right) = 8

M=8 number of Unknowns

Q= -EI . [𝐶1, 𝐶2, 𝐶3, 𝐶4].𝑑𝑦3

𝑑𝑥3

Y =[𝐶1, 𝐶2, 𝐶3, 𝐶4]. 𝑦

N=8 number of Equations

Testing Analysis procedure

Test 1

Test 2

40 x 40 cm

40 x 40 cm 20 x 20 cm

Testing Analysis procedure

Test 3

Test 4

Determining “₵”

• Terzaghi’s Method;

¢ℎ = 𝑛ℎ .𝑧

𝐵

Where:

• ₵: 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑠𝑢𝑏𝑔𝑟𝑎𝑑𝑒 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑜𝑖𝑙

• 𝒏𝒉: 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡

• 𝑜𝑓 ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑠𝑢𝑏𝑔𝑟𝑎𝑑𝑒 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛

• 𝒁: 𝑑𝑒𝑝𝑡ℎ 𝑜𝑓 𝑎 𝑔𝑖𝑣𝑒𝑛 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝑓𝑖𝑛𝑖𝑠ℎ𝑒𝑑

𝑔𝑟𝑎𝑑𝑒 (Soil).

In this method, ¢ is highly

dependent on depth(z) .

• Polish code - PN-83/B-02482

for non-Cohesive soil (sand):

𝐾𝑥 = 𝑆𝑛 . 0,75. 𝐼𝐷2 + 0,225. 𝐼𝐷 + 0,150 .

𝛾

𝐷

(𝒌𝒙 ≣ ₵)

Where:

• 𝑰𝑫 : density index, 0.2 < ID < 1

• D : Diameter of the pile [m],D>0,2m;D=1,0m if

D>1,0m

• : Unit weight of the soil [kN/𝑚3],

• 𝑺𝒏: 1.101.20 if piling improves the soil (driven

piles in cohesion-less soil, especially loose ones)

𝑺𝒏: 0.800.90 if piling weakens the soil (bored-

piles, possibility of soil loosening not eliminated).

Generalization of the method

𝑁 = 2 + 𝑛 − 1 ∗ 4 + 2

N : Number of Unknowns

Can be applied in order to calculate multi-section hybrid foundation beams with different stiffness and different subsoil layers.

Application-Calculation part

1) Retaining walls’ support 2) Secant pile wall

Designing Approach

Reasonable 𝐿1

𝐿 regarding Maximum Displacement

Design Calculation

• ₵ : 20 MN

m3

• 𝑬𝑪𝒐𝒏𝒄. ∶ 30𝑀𝑃𝑎

• Soil : Dray Sand

• ɣ : 1,35 (Magnifications load factor)

• Standard:

EC 2 - CEN EN1992-1-1

Design Values

240

161

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 50 100 150 200 250

Pil

e d

ep

th-m

Moment-KN.m

74, 3

0

1

2

3

4

5

6

-100 -50 0 50 100

Pil

e l

en

gth

-m

Shearing force-KN

Drawing

• More details available on the

plotted drawing

Fin

H.Rahnama

Feb 2014-Wroclaw