Visit Dr. Farouk’s Official Page 1

www.facebook.com/dr.farouk.elkadi

Prepared By:

Prof. Dr. Ing. Farouk El-Kadi

Professor of Geotechincal Engineering

Faculty of Engineering

Ain Shams University

2

Shorouk AcademyFaculty of EngineeringCivil Engineering DepartmentCourse : Foundation Engineering 2 – Fourth Year Civil

Year : 2013 - 2014

Version : 00

Design of classical

Retaining walls

Summery

1.0 Types of classical retaining

walls :

a- Gravity retaining wall.

b- Semigravity retaining wall.

c- Cantilever retaining wall.

d- Counter fort retaining wall.

e- Buttress retaining wall.

:حتى يمكن تصميم الحائط الساند يجب توافر البيانات اآلتية

.الالزمةالجساتالرفع المساحي للموقع قبل تنفيذ الحائط وعمل -أ

التصميم النهائي للموقع لتحديد االرتفاع الكلي للحائط .-ب

طبيعة التربة أسفل أساسات الحائط وخواصها الطبيعية والميكانيكية γØ,,C,Es)ج-

.ومنسوب المياه الجوفيةmv)أو

.المستخدممكالدخواص تربة الردم خلف الحائط أثناء التنفيذ وبعد التنفيذ وأسلوب -د

.ديدنوع الحائط المطلوب تصميمه وخواص الخامات المستخدمة مثل الخرسانة والح-ه

.األحمال المؤثرة على الحائط وعلى التربة خلف الحائط-و

a- Select type of wall.

b- Calculate the approximate dimensions for the wall.

c- Compute earth pressure and surcharge pressure.

d- Analyze the structural stability

d- Analyze the structural stability

i- Check overturning about toe.

ii- Check sliding along its base.

iii- Check bearing capacity.

IV- Check settlement and tilting.

V- Check deflection and movement of wall to satisfy the values needed For the Coef. Of earth pressure used in the calculation.

VI- Design structural elements.

VII- Check total stability of retaining wall.

إذا كانت الحوائط الساندة ذات ارتفاعات كبيرة نلجأ إلى بعض

الحلول التي تؤدي إلى تخفيض ضغط التراب على الحائط

باإلضافة إلى زيادة األوزان الرأسية على الحائط وذلك

للحائط وكذلك حديد التسليحالخرسانىلتخفيض القطاع

. المستخدم وفيما يلي بعض األمثلة

:يتضح من الرسم اآلتي

قيمة ضغط التراب الفع ال -أ

عن على الحائط يقل كثيرا

القيمة في حالة عدم وجود

.سمالكوابيل الموضحة بالر

األوزان اإلضافية علي -ب

ن وزن الحائط والتي تزيد م

( G1,G2)اتزانه هي

باإلضافة إلى وزن

. الكوابيل

عال ويتم رسم ضغط التراب الف

:على النحو التالي

φيتم رسم خط يميل بزاوية •

ىالكابولعلي األفقي من حرف

مع ليتقاطع( النقطة أ)السفلي

.(النقطة ب)سطح الحائط في

θيتم رسم خط يميل بزاوية •

(45+φ/2 )طع مع األفقي ليتقا

ي مع السطح الداخلي للحائط ف

(.جـالنقطة )

يتم تكرار ذلك مع حرف •

.الكابولي الثاني

:على النحو التالي( Active E.P)وبذلك يمكن حساب ضغط التراب الفعال

A=γh2Kaضغط التراب عند النقطة

B=γh3Kaضغط التراب عند النقطة

C=γh4Kaضغط التراب عند النقطة

D=γh5Kaضغط التراب عند النقطة

E=γh7Kaضغط التراب عند النقطة

F=γh8Kaضغط التراب عند النقطة

G=γHKaضغط التراب عند النقطة

ويمكن حساب وزن التراب أعال الكوابيل

:علي النحو التالي

G1 = γLh1 , G2 = γLh6

ويضاف إلي ذلك وزن الكابولي

بالطة في بعض الحاالت يتم ربط الحائط الساند ب

.احتكاك كما هو موضح بالرسم

و وتؤثر بالطة االحتكاك على الحائط علي النح

:التالي

ط التربة أعال البالطة ال تؤثر علي ضغ•

ة علي التراب أسفلها إال بقيمة رد فعل البالط

.L/2التربة في الطول

Hing)ترتبط البالطة بالحائط•

support )ربة وبالتالي فرد فعل أوزان الت

ة أعال البالطة ينتقل إلي الحائط عند نقط

ء ارتكازها علي الحائط باإلضافة إلي الجز

مباشرة التي ترتكز فيه البالطة علي التربة

وهذا الحمل المؤثر علي ( L/2)بطول

زان الحائط عند نقطة االرتكاز يساعد علي ات

.الحائط

لحائط التي تنتج ارتكاز البالطة علي التربة يولد احتكاك بين البالطة والتربة يساعد في منع حركة ا•

. مما يساعد في اتزان الحائط( Active E.P)عن ضغط التراب الفعال عليها

•Retaining wall must be safe against bearing capacity failure

•At the level of the base, the supporting soil is subjected to vertical

force (V) equal to the sum of the weight of wall, the weight of soil

above the base, plus the vertical component of the lateral pressure P

the resultant R of these forces acts at point b (see fig.).

•The bearing capacity must be calculated for a footing subjected to

an eccentric and inclined loading.

(28ص(.د)3/5/3/3انظر الكود المصري بند )

* Contact stress under retaining wall normally is not uniform (see fig.A).

* Stress at point A = Ps1

* Stress at point B = Ps2

There are two methods to calculate settlement and differential settlement between the two points (A,B)

1st Method

Divide the contact stress in two ports, the first part is uniform stress and the second part is triangular stress.

The 1st part is uniform stress. To calculate settlement the charts from Kany or El-kadican be used (see fig I ,II)

For the triangular load calculate the values of бz on the vertical axis through point A and point B (see fig III) using Tsytovich tables.

Integrate the area of бz and divide the area by Es to get settlement.

12

13

1. Get z/b

2. Get a/b

3. Draw a

line from

z/b till it

intersect

with the

curve

which

represent

your a/b

4. Draw a

line from the

point of

intersection

to the upper

x-axis to get

f(s,0)

Settlement curves

for a rectangular

load acting on a

compressible

layer with

thikness z under

the characteristic

point c after Kany

Fig. I

14

1. Get ds/b’

2. Get l/b

3. Draw a

line from

ds/b’ till it

intersect

with the

curve

which

represent

your l/b

4. Draw a

line from the

point of

intersection

to the upper

x-axis to get

S*

Settlement

under rigid

foundation

after El-Kadi

1967

15

B

Fig. III

•In this case the eccentric load will be transfered to central load and

moment (fig IV).

•Due to the central load the contract stress will be uniform.

•Due to the moment the contact stress will be two triangles with

different signs (fig IV).

• Settlement due to P

(uniform contact stress)

can be calculated using

Kany or El-Kadi charts.

•The rotation of the

foundation due to moment

(M) can be calculated

from the 2nd chart from El-

Kadi (fig V).

•Adding the settlement

due to (P) and rotation due

to (M) (taken signs into

consideration) the final

settlement for point A&B

can be calculated.

17

1.Get ds/b’

2. Get l/b

3. Draw a

line from

ds/b’ till it

intersect

with the

curve

which

represent

your l/b

4. Get iα

Fig. V

El-Kadi

Curve for

tilting

ان العام اختيار االتزوبعد بعد اختيار أبعاد الحائط الساند طبقا للعالقات التقريبية السابق ذكرها للحائط يجب إجراء مراجعة التصميم اإلنشائي للحائط طبقا لألكواد المعمول بها سواء للخرسانةالعادية أو الخرسانة المسلحة أو مباني الطوب وفيما يلي موجز مختصر بالنسبة لألسس المراجعة

اإلنشائية مع ضرورة التأكد من اتفاقها مع األكواد المعمول بها

18

Gravity walls are made of plain masonry, rubble stone, orconcrete. In concrete walls a small amount of temperaturereinforcement is commonly provided. The wall should beproportioned such that there is no tensile stress at any point ofthe wall under any condition of loading. In favorable cases wherethe backfill consists of purely granular soil, a small amount oftension (not greater than 3 per cent concrete cylinder strength)may be permitted in the monolithic section of the wall.

19

A gravity wall may be analyzed by the principle of simplestatics. Any horizontal section of the wall is subjected to twoforces: a lateral force due to earth pressure and surcharge, anda vertical force equal to the weight of the wall above. Themagnitude, direction and point of application of the resultant Rof these two force can be readily determined, Let the resultantforce intercept the horizontal section at the point a, and let e bethe distance from point a to the middle of the horizontal section,then this section is subjected to a vertical pressure q and ahorizontal shear v

20

21

22

23

A cantilever wall consists of three structural elements: the stem,the toe, and the heel. Each of theses elements are designed as acantilever, In order to design the base slab (toe and heel), thesoil reaction (contact pressure) must be known. With themagnitude and the point of application of the verticalcomponent V already determined in the stability analysis, thesoil reaction is computed on the assumption of lineardistribution. The soil reaction is trapezoidal if the force V isLocated within the middle third of the base. If the force V isoutside the middle third (or e < B/6), the pressure distributionis triangular. (not recommended)

24

The toe is considered as a cantilever slab fixed at the front faceof the stem ce and is acted by a large upward pressure (due tothe trapezoidal soil pressure distribution) minus the weight ofthe toe and the weight of the overlying soil. The net pressuretends to bend the toe with tension on the bottom. Similarly theheel is a cantilever slab fixed at the back face of the stem dfand is subjected to a smaller upward pressure minus the weightof the heel and the large weight of the soil above it. The end ofthe heel slab is subjected to the lateral earth pressure belowpoint h . The net pressure tends to bent the heel with tension ontop.

25

The stem is a vertical cantilever fixed at the base and isassumed to be subjected to a lateral pressure acting on thevertical section gh , where the line dh is drawn parallel to theground surface. The stem is keyed to the base slab by means ofa raised key, a depressed key, or a roughened surface. TheCode permits a shear stress of 0.25 f`cat the root of a key.

26

27

. The forces acting on the various elements of a counterfortwall are similar to that on a cantilever wall, the toe slab is acantilever in both the cantilever wall and the counterfort wall.The difference lies on the method of structural function of theface slab and the heel slab.

The face slab spans horizontally between the counter forts.It is subjected to a negative bending moment with tension onthe inside face and a positive moment with tension on theoutside face. The horizontal reaction of the face slab istransmitted to the counterforts by reinforcing bars tying thesetwo elements together. In the simplest form, each horizontalstrip of the face slab is designed as a continuous slabsubjected to a uniform horizontal pressure.

28

The counterfort may be designed as a wedge-shapedcantilever fixed at the subjected to the horizontal reaction fromthe face slab, when it is made an integral part with the face slabit is a T-beam with the face of wall as the compression flanges ofthe beam. The common arrangement of reinforcement andother construction details in a counterfort wall is shown in (Fig17)

29

30

The heel slab is subjected to net downward pressure due to the large weight of soil above it. This pressure causes a negative bending moment at the counterfort with tension on the top of slab and a positive bending moment at mid-span between counterforts. The base slab must be tied to the counterfort to transmit the vertical reaction. In addition to this bending parallel to the length of the wall, the heel slab is also subjected to a bending moment from the cantilevered toe slab.

This procedure of design of counterfort walls gives rather conservative design of the face slab because it ignores the benefit of the slab rigidity and the fixity, or partial fixity, of the lower edge of the face of wall. Furthermore, no established rule of design takes into account the stresses in the heel slab as a result of bending moment of the toe slab.

31

ل لذلك يجب ضرورة التنويه بأن الحائط الساند يعم. كافة ما ذكر يركز علي تصميم قطاع الحائط في االتجاه الطولي ككمره محمله بأحمال رأسية وترتكز علي التربة مما يستلزم ضرورة إضافة

(.17شكل )حديد طولي في الحائط كما هو موضح في

32

33

Reinforcement in long

direction

Main Reinforcement in

toe slab

For the given retaining wall

calculate the following:

a- Reaction of friction slab soil

for the length between A,B

(Computer program can be

used).

b- Earth pressure on wall.

c- design of friction slab.

d- contact stress at plane C-D

(Foundation).

e- Check sliding and

overturning for the retaining

wall taken passive earth

pressure into consideration

and the friction slab and soil.

f- Calculate settlement and

tilting of the wall.

Sand

γ =1.8t/m3

φ=30°

γ conc.=2.2t/m3

Es=50kg/cm2

N.B: neglect

Earth Pressure

acting on left

hand side of

wall.

σall.=2.5kg/cm2

Proplem 2

For the given Retaining wall,

calculate the following:

a- The value of horizontal force H to

assure no lateral movement for the

wall.

b- The value of force H to activate full

active earth pressure.

c- The value of force H to activate full

passive earth pressure.

h=7.2m

N=10.0 t/m'

H= t/m'

h0= 7.0 m

b' = 1.4mh' = 0.4

0.2m

0.4m

a

1.4 m

b=1.0m'

2.5

36

The two retaining walls shown in the above figure are the sent-up of a

bridge, the filling between the walls is highly compacted siliceous

sand with a of 350 , the walls are resting on a layer of Sandy Silty

Clay. Taking the properties of this layer as the following = 1.9 t/m3

and =250 and c = 0.5 kg/cm2 the following is required.

• Design the retaining wall.

• Check the stability of the retaining wall against sliding, over-

turning, stresses , settlement and tilting

• Design all the structural elements of the wall and find the

reinforcement needed

• Draw the concrete dimensions and reinforcement arrangement

71

50

-7

75

0

71

50

-7

75

0

22000 mm

N.G.LN.G.L