Cofferdams and braced cuts

‫اُشؤف‬ ‫ػجذ‬ ‫اُغيذ‬ ٖٓ‫ٓإ‬ ‫د‬-‫األصٛش‬ ‫ٛ٘ذعخ‬
1
Cofferdams and Braced Cuts
1-Cofferdams
Cofferdams are temporary enclosures that keep away earth and water from the
construction area.
Figure (1) cofferdam
َٔ‫اُؼ‬ ‫ٓٞهغ‬ ٖ‫ػ‬ ‫اُزشثخ‬ ٝ‫أ‬ ٙ‫أُيب‬ ‫دجض‬ ‫ٜٓ٘ب‬ ‫اُـشع‬ ‫ٓإهزخ‬ ‫ٓ٘شئبد‬ ٠ٛ ‫أُذيطخ‬ ‫اُغذٝد‬,ٌَ‫ش‬(1)
1-2Classification of Cofferdams
٠‫ًبألر‬ ‫أُذيطخ‬ ‫اُغذٝد‬ ‫رظ٘يق‬ ٌٖٔ‫ي‬:
‫أوال‬:‫االوشاء‬ ً‫ف‬ ‫انمستخذمح‬ ‫انمادج‬ ‫حيج‬ ‫مه‬
٠‫األر‬ َٔ‫ٝرش‬:
‫أ‬-‫اُزشاثيخ‬ ‫اُغذٝد‬
‫ة‬-‫اُذجش‬ ‫ًغش‬ ‫عذٝد‬
‫ط‬-َٓ‫اُش‬ ‫أًيبط‬ ‫عذٝد‬
‫د‬-‫اُخشجيخ‬ ‫اُغذٝد‬
‫ٛـ‬-‫أُؼذٗيخ‬ ‫اُغذٝد‬
ٝ-‫اُخشعبٗيخ‬ ‫اُغذٝد‬

2
‫ًا‬‫ا‬‫حاوي‬:‫واالوشاء‬ ‫انتصميم‬ ‫طريقح‬ ‫حسة‬
٠‫األر‬ َٔ‫ٝرش‬:
‫أ‬-َٓ‫اُش‬ ‫أًيبط‬ ٝ‫أ‬ ‫ادجبس‬ ‫ًغش‬ ٖٓ ‫ٝأٌُٞٗخ‬ ‫اُزشاثيخ‬ َٔ‫ٝرش‬ ‫اُزضبهِيخ‬ ‫اُغذٝد‬
‫ة‬-‫ٓ٘لشدح‬ ‫ُٞديخ‬ ‫عزبئش‬ ٖٓ ‫أٌُٞٗخ‬ ‫اُغذٝد‬(‫خشجيخ‬-‫ٓؼذٗيخ‬-‫خشعبٗيخ‬)
‫ط‬-‫ٓضدٝجخ‬ ‫ُٞديخ‬ ‫عزبئش‬ ٖٓ ‫أٌُٞٗخ‬ ‫اُغذٝد‬
‫د‬-‫ٓؼذٗيخ‬ ‫خاليب‬ ٖٓ ‫أٌُٞٗخ‬ ‫اُغذٝد‬(‫اُخِٞيخ‬ ‫اُغذٝد‬)‫اُغبثوخ‬ ‫األٗٞاع‬ ٖٓ ‫ٗٞع‬ ًَ ‫ششح‬ ْ‫ٝعيز‬
َ‫ثبُزلظي‬.
‫ًا‬‫ا‬‫حانخ‬:‫انمىقع‬ ‫وىعيح‬ ‫حسة‬
‫أ‬-ٍٞ‫اُغي‬ ٖٓ ‫ُِذٔبيخ‬ ‫اٗشبؤٛب‬ ْ‫يز‬ ٠‫اُز‬ ‫اُغذٝد‬ َ‫ٓض‬ ‫رُي‬ ٝ‫اُجش‬ ٠ِ‫ػ‬ ‫أُوبٓخ‬ ‫اُغذٝد‬.
‫ة‬-ٝ‫أ‬ ‫اُو٘بؽش‬ ‫ث٘بء‬ ‫ػ٘ذ‬ ‫ٓإهزخ‬ ‫ٓ٘شئبد‬ ٌٕٞ‫ر‬ ً‫ب‬‫ؿبُج‬ ٠‫ٝاُز‬ ‫أُبئيخ‬ ٟ‫أُجبس‬ ٝ‫أ‬ ‫اُجذش‬ ٠‫ك‬ ‫أُوبٓخ‬ ‫اُغذٝد‬
ٟ‫اٌُجبس‬.
1-3Thecommon types of cofferdams
Following are some of the common types of cofferdams
(1) Earth fill cofferdam
(2) Rock fill cofferdam
(3) Single wall cofferdam
(4) Double wall cofferdam.
(5) Cellular cofferdam
1-3-1 The Earth cofferdams ‫اُزشاثيخ‬ ‫أُذيطخ‬ ‫اُغذٝد‬
‫ٝاُجذبسٝاُجذيشاد‬ ‫اُٜبدئخ‬ ‫أُبئيخ‬ ٟ‫أُجبس‬ ‫دبُخ‬ ٠‫ك‬ ّ‫ُالعزخذا‬ ‫ٓالئٔخ‬ ‫أًضش‬ ‫اُزشاثيخ‬ ‫اُغذٝد‬ ‫رؼزجش‬
‫ٓبئيخ‬ ‫ريبساد‬ ٝ‫أ‬ ‫آٞاط‬ ‫رٞجذ‬ ‫ٝال‬ ‫طـيش‬ ٙ‫أُيب‬ ‫ٝاسرلبع‬ ‫ػؼيلخ‬ ٙ‫أُيب‬ ‫عشػبد‬ ٌٕٞ‫ر‬ ‫ديش‬ ‫اُشاًذح‬
‫اُٞاهؼخ‬ ‫ٝاالعزبريٌيخ‬ ‫اُذي٘بٓيٌيخ‬ ‫اُؼـٞؽ‬ ‫صيبدح‬ ‫دبُخ‬ ٠‫ك‬ ‫ٝاالٜٗيبس‬ ‫ُِ٘ذش‬ ‫ػشػخ‬ ‫اُغذٝد‬ ٙ‫ٛز‬ ٌٕٞ‫ٝر‬
ٌَ‫ثبُش‬ ‫ٓٞػخ‬ ٞٛ ‫ًٔب‬ ‫ٝرُي‬ ‫ػِيٜب‬(2.)

3
Figure (2) Earth cofferdam
1-3-1-1 Materials used in Earth Cofferdams ‫االٗشبء‬ ٠‫ك‬ ‫أُغزخذٓخ‬ ‫أُٞاد‬
٠ُ‫ئ‬ ‫ٌٓٞٗبرٜب‬ ‫ٝكن‬ ‫اُزشاثيخ‬ ‫اُغذٝد‬ ْ‫ٝر٘وغ‬:
‫أ‬-‫ٓزجبٗغخ‬ ‫رشثخ‬ ٖٓ ‫أٌُٞٗخ‬ ‫اُغذٝد‬
‫ؽجوخ‬ ‫رؼبف‬ ‫ًٝزُي‬ َ‫أُي‬ ‫ُذٔبيخ‬ ‫ؽجوخ‬ ‫اُغطخ‬ ٠ِ‫ػ‬ ‫ٝيٞػغ‬ ‫ثبُٞهغ‬ ‫أُزٞاكشح‬ ‫اُزشثخ‬ ّ‫اعزخذا‬ ْ‫يز‬ ‫ديش‬
‫اُزغشة‬ ٖٓ ٚ‫ُذٔبيز‬ ‫اُغذ‬ ‫خِق‬ ‫طشف‬.
‫ة‬-٠‫دز‬ ‫اُوِت‬ ٖٓ ‫اُ٘لبريخ‬ ‫ٓزذسجخ‬ ‫ؽجوبد‬ ‫ػذح‬ ٖٓ ٌٕٞ‫ٝيز‬ ‫اُزشثخ‬ ٖٓ ‫ٗٞػيبد‬ ‫ػذح‬ ٖٓ ‫أٌُٞٗخ‬ ‫اُغذٝد‬
‫ٗلبريخ‬ َ‫أه‬ ‫اُوِت‬ ٌٕٞ‫ي‬ ‫ثذيش‬ ‫اُخبسط‬
‫ط‬-‫طٔبء‬ ‫هِٞة‬ ‫راد‬ ‫عذٝد‬
َ‫داخ‬ ٠ِ‫ػ‬ ‫ٝيضجذ‬ ‫اُخشت‬ ٝ‫أ‬ ٕ‫أُؼذ‬ ٝ‫أ‬ ‫اُخشعبٗخ‬ ٖٓ ٌٕٞ‫ي‬ ‫هذ‬ ‫اُوِت‬ ٠‫ك‬ ْ‫أط‬ ‫جضء‬ ‫ُِغذ‬ ‫يؼبف‬ ‫ديش‬
ٌَ‫ثبُش‬ ‫ٓٞػخ‬ ٞٛ ‫ًٔب‬ ‫اُغذ‬ ‫ػِيٜب‬ ّ‫أُوب‬ ‫اُظخشيخ‬ ‫اُطجوخ‬(3.)
Figure (3) Earth cofferdam with sheet pile core

4
1-3-1-2 Design of Earth cofferdams
٠ُ‫ًبُزب‬ ٠‫اُزشاث‬ ‫اُغذ‬ ْ‫رظٔي‬ ْ‫يز‬:
1-‫نهسذ‬ ‫األونيح‬ ‫األتعاد‬ ‫تحذيذ‬
‫ُِغذ‬ ٕ‫اُالصٓب‬ ٕ‫ٝاألٓب‬ ‫اُغالٓخ‬ ‫ُذسجخ‬ ‫األثؼبد‬ ٙ‫ٛز‬ ‫رذوين‬ ٖٓ ‫اُزأًذ‬ ْ‫يز‬ ْ‫ص‬ ‫ُِغذ‬ ‫األُٝيخ‬ ‫األثؼبد‬ ‫رذذد‬
ٌَ‫ثبُش‬ ‫ٓٞػخ‬ ٞٛ‫ًٝٔب‬(4)٠ُ‫ًبُزب‬:
1-‫ثبالسرلبع‬ ‫يؼشف‬ ٠‫ًبك‬ ‫ثبسرلبع‬ ٚٓ‫أٓب‬ ٙ‫أُيب‬ ‫ٓ٘غٞة‬ ٖٓ ٠ِ‫أػ‬ ٚ‫هٔز‬ ٌٕٞ‫ر‬ ‫ثذيش‬ ‫اُغذ‬ ‫اسرلبع‬ ‫يذذد‬
ٍٝ‫اُجذ‬ ٖٓ ٙ‫روذيش‬ ٌٖٔ‫ٝي‬ ‫ُِغذ‬ ‫اُذش‬(1. )
Figure (4) Dimensions of Earth Cofferdam
2-ْ‫سه‬ ٍٝ‫اُجذ‬ ٖٓ ‫اُغذ‬ ‫ُؼشع‬ ‫هئخ‬ َ‫أه‬ ‫رإخز‬(1)‫يإخز‬ ‫ُِٔشٝس‬ ‫ًطشين‬ ‫اُغذ‬ ‫هٔخ‬ ّ‫اعزخذا‬ ‫دبُخ‬ ٠‫ٝك‬
ٖ‫ػ‬ َ‫اليو‬ ‫ثٔب‬ ‫اُغذ‬ ‫ػشع‬6ْ‫سه‬ ٍٝ‫ثبُجذ‬ ‫ٝاسد‬ ٞٛ‫ُٔب‬ ‫ؽجوب‬ ‫ُِغذ‬ ‫اُجبٗجيخ‬ ٍٞ‫أُي‬ ‫رذذيذ‬ ْ‫يز‬ ‫ٓزشًٔب‬(2)
Table (1) Dimensions of Earth Cofferdam
The dam height H(m) Free height Hf (m) The top width A (m)
4.5> 1.2-1.5 1.85
4.5-7.5 1.5-1.8 1.85
7.5-15 1.85 2.5
15-22.5 2.1 3.0
22.5< 2.1 3.0

5
Table (2) Slopes of Earth Cofferdams
‫انمؤخرج‬ ‫ميم‬ ‫انمقذمح‬ ‫ميم‬ ‫انمىاد‬ ‫وىع‬
1:2 1:2.5 ‫اُزذسط‬ ‫جيذح‬ ‫ٓزجبٗغخ‬ ‫رشثخ‬
1:2.5 1:3 ‫ٓزجبٗظ‬ ٠ٔ‫ؽ‬
1:2 1:2.5 ٖٓ َ‫أه‬ ‫السرلبع‬ ‫ٓزجبٗغخ‬ ‫ؽي٘يخ‬ ‫ؽٔييخ‬15‫ٓزش‬
1:1.25 1:3 ٖٓ ‫أًضش‬ ‫السرلبع‬ ‫ٓزجبٗغخ‬ ‫ؽي٘يخ‬ ‫ؽٔييخ‬15‫ٓزش‬
1:2.5 1:3 ٖ‫ؽي‬ ‫هِت‬ ‫ٝجٞد‬ ‫ٓغ‬ ‫صُؾ‬ َٓ‫س‬ ٝ‫أ‬ َٓ‫س‬
1:2 1:2.5 ٠ٗ‫خشعب‬ ‫هِت‬ ‫ٝجٞد‬ ‫ٓغ‬ ‫صُؾ‬ َٓ‫س‬ ٝ‫أ‬ َٓ‫س‬
2-‫انهيذرونيكيح‬ ‫انسالمح‬ ‫اختثاراخ‬
‫ُِغذ‬ ٠‫اُخِل‬ ‫اُغطخ‬ ّ‫هذ‬ ‫ٝػ٘ذ‬ ٠‫ٝاُخِل‬ ٠ٓ‫األٓب‬ ‫اُغطخ‬ ٖٓ ٌَُ ‫ٝرُي‬ ‫ُِ٘ذش‬ ‫اُغذ‬ ‫ٓوبٝٓخ‬ ٖٓ ‫اُزأًذ‬ ‫يجت‬
‫اُغذ‬ ّ‫أٓب‬ ٖٓ ٙ‫أُيب‬ ‫ؽلخ‬ ‫ًٝزُي‬.
3-ً‫اسفه‬ ‫أو‬ ‫انسذ‬ ‫جسم‬ ‫خالل‬ ‫انتسرب‬ ً‫ف‬ ‫انتحكم‬
ّ‫ثبعزخذا‬ ‫اُزغشة‬ ‫اٗوبص‬ ٠ِ‫ػ‬ َٔ‫اُؼ‬ ْ‫يز‬ ْ‫ص‬ ‫اُزغشة‬ ‫ُذغبة‬ ‫أُؼشٝكخ‬ ‫ثبُطشم‬ ‫اُزغشة‬ ‫دغبة‬ ْ‫يز‬ ‫ديش‬
‫ُِغذ‬ ٠ٓ‫األٓب‬ ‫اُغطخ‬ ٠ِ‫ػ‬ ‫ؽٔييخ‬ ٝ‫أ‬ ‫اعلِزيخ‬ ٝ‫أ‬ ‫ثالعزيٌيخ‬ ‫ٓٞاد‬ ٖٓ ‫ؽجوخ‬ ‫ثٞػغ‬ ٝ‫أ‬ ‫ُِغذ‬ ْ‫اط‬ ‫جضء‬.
4-‫نهسذ‬ ً‫االوشائ‬ ‫انخثاخ‬
٠‫األر‬ ‫ُِغذ‬ ٠‫االٗشبئ‬ ‫اُضجبد‬ َٔ‫ٝيش‬:
‫أ‬-‫نهسذ‬ ً‫االجمان‬ ‫انخثاخ‬
ٚ‫رذز‬ ‫روغ‬ ٠‫اُز‬ ‫اُطجوخ‬ ‫ٜٗبيخ‬ ٟٞ‫ٓغز‬ ٖٓ ً‫ا‬‫اثزذاء‬ ٠‫اكو‬ ٟٞ‫ٓغز‬ ‫اػؼق‬ ٠ِ‫ػ‬ ِٚٓ‫ثٌب‬ ‫اُغذ‬ ‫دساعخ‬ ْ‫يز‬ ‫ديش‬
‫ادزٌبى‬ ٖ‫ػ‬ ‫اُ٘بشئخ‬ ‫أُوبٝٓخ‬ ٟٞ‫ٝه‬ ٙ‫ٝأُيب‬ ‫اُزشثخ‬ ٖٓ ‫اُ٘بشئخ‬ ‫اُذكغ‬ ٟٞ‫ه‬ ‫ٛٔب‬ ٕ‫هٞرب‬ ‫اُغذ‬ ٠ِ‫ػ‬ ‫يإصش‬ ‫ديش‬
‫االٗضالم‬ ‫عطخ‬ ‫ٓغ‬ ‫ُِغطخ‬ ‫أٌُٞٗخ‬ ‫أُٞاد‬ ‫ٝاُزظبم‬.
Fd=Pwl+Pel+Pw2-Pe2 ‫اُذكغ‬ ٟٞ‫ه‬
FR= S.C+W tan ϕ ‫أُوبٝٓخ‬ ٟٞ‫ه‬
Where:
Pwl,Pel, Pw2 and Pe2 ٠ُ‫اُزٞا‬ ٠ِ‫ػ‬ ‫اُغذ‬ ‫ٝخِق‬ ّ‫أٓب‬ ‫ٝأُبء‬ ‫اُزشثخ‬ ‫ػـؾ‬
S ‫ُِغذ‬ ٠ِ‫اُغل‬ ٠ٌُِ‫ا‬ ‫اُؼشع‬
C ‫االٗضالم‬ ٙ‫ػ٘ذ‬ ‫يذذس‬ ٟ‫اُز‬ ٟٞ‫أُغز‬ ‫ػ٘ذ‬ ‫اُزشثخ‬ ‫رٔبعي‬

6
W ٕ‫ٝص‬‫االٗضالم‬ ٟٞ‫ٓغز‬ ٠ِ‫أػ‬ ‫اُزشثخ‬
ϕ ‫االٗضالم‬ ٟٞ‫ٓغز‬ ‫ػ٘ذ‬ ‫ُِزشثخ‬ ٠ِ‫اُذاخ‬ ‫االدزٌبى‬ ‫صاٝيخ‬
ٕ‫ُالرضا‬ ‫أُغججخ‬ ٟٞ‫اُو‬ ‫هغٔخ‬ َ‫ُذبط‬ ً‫ب‬‫ٓغبٝي‬ ٌٕٞ‫ي‬ ٕ‫األٓب‬ َٓ‫ٓؼب‬ ٕ‫كا‬ ‫رُي‬ ٠ِ‫ٝػ‬(‫أُوبٝٓخ‬ ٟٞ‫ه‬)٠ِ‫ػ‬
‫ُالٜٗيبس‬ ‫أُغججخ‬ ٟٞ‫اُو‬(‫اُذكغ‬ ٟٞ‫ه‬).
F.o.s= FR/ Fd
‫ب‬-‫انعازنح‬ ‫انطثقح‬ ‫اتسان‬
‫ًٔب‬ ‫اُطجوخ‬ ٙ‫ٛز‬ ‫اٗضالم‬ ٍ‫ادزٔب‬ ‫دساعخ‬ ‫كيجت‬ ‫ُِغذ‬ ٠ٓ‫االٓب‬ ٚ‫اُٞج‬ ٠ِ‫أػ‬ ‫عٔيٌخ‬ ‫ػبصُخ‬ ‫ؽجوخ‬ ‫ر٘ليز‬ ‫دبُخ‬ ٠‫ك‬
ٌَ‫ثبُش‬ ‫ٓٞػخ‬ ٞٛ(5)٠ُ‫ًبُزب‬ ‫ٝرُي‬:
Fd=(W1+W2+W3) sin α ‫اُذكغ‬ ٟٞ‫ه‬
FR= C. b+(W1+W2+W3) cos α . tan ϕ ‫أُوبٝٓخ‬ ٟٞ‫ه‬
Where:
W1 ‫اُغذ‬ ٠ِ‫أػ‬ ‫اُؼبصُخ‬ ‫اُطجوخ‬ ‫جضء‬ ٕ‫ٝص‬
W2 ‫اُغذ‬ َ‫أعل‬ ‫اُؼبصُخ‬ ‫اُطجوخ‬ ‫جضء‬ ٕ‫ٝص‬
W3 ‫اُغذ‬ ‫هذٓخ‬ َ‫أعل‬ ‫اُؼبصُخ‬ ‫اُطجوخ‬ ‫جضء‬ ٕ‫ٝص‬
C ‫اُغذ‬ ٚ‫ٝٝج‬ ‫اُؼبصُخ‬ ‫اُطجوخ‬ ٖ‫ثي‬ ‫االُزظبم‬ ‫اجٜبد‬
ϕ ‫اُغذ‬ ٚ‫ٝٝج‬ ‫اُؼبصُخ‬ ‫اُطجوخ‬ ٖ‫ثي‬ ‫االدزٌبى‬ ‫صاٝيخ‬
b ‫اُغذ‬ ٚ‫ٝج‬ ٍٞ‫ؽ‬
α ‫صاٝيخ‬‫ُِغذ‬ ٠ٓ‫األٓب‬ ٚ‫اُٞج‬ َ‫ٓي‬
Figure (5) Equilibrium of insulating layer
‫د‬-‫انسذ‬ ً‫نىج‬ ً‫انسطح‬ ‫االوسالق‬

7
ٍٞ‫أُي‬ ٕ‫ارضا‬ ‫ثذساعخ‬ ‫اُخبطخ‬ ‫ثبُطشم‬ ٚ‫دساعز‬ ٌٖٔ‫ي‬ ٟ‫ٝاُز‬
‫د‬–‫انماء‬ ‫سطح‬ ً‫ف‬ ‫مفاجئ‬ ‫اوخفاض‬ ‫حذوث‬ ‫عىذ‬ ‫نهسذ‬ ً‫االمام‬ ً‫انىج‬ ‫اتسان‬
‫ي‬-‫انسذ‬ ‫مه‬ ً‫انخهف‬ ‫انجسء‬ ‫اتسان‬
1-3-2 Rock fill cofferdams ‫اُذجبسح‬ ‫ًغش‬ ٖٓ ‫أُذيطخ‬ ‫اُغذٝد‬
‫جبٗجيخ‬ ٍٞ‫ثٔي‬ ٠٘‫رج‬ ٕ‫أ‬ ٌٖٔ‫ي‬ ‫اُذبُخ‬ ٙ‫ٛز‬ ٠‫ٝك‬ ‫أُذيطخ‬ ‫اُغذٝد‬ ‫ث٘بء‬ ٠‫ك‬ ‫االدجبس‬ ‫ًغش‬ ّ‫اعزخذا‬ ٌٖٔ‫ي‬
٠ُ‫ئ‬ َ‫ط‬ ‫دبدح‬1:1.25ٍ‫اُؼٞاص‬ ّ‫ثبعزخذا‬ ‫اُ٘لبريخ‬ َ‫روِي‬ ‫ٓشاػبح‬ ‫ٓغ‬ ‫أُغبدخ‬ ٖٓ ً‫ا‬‫ًضيش‬ ‫يٞكش‬ ‫ٓٔب‬
ٌَ‫ثبُش‬ ‫ٓٞػخ‬ ٞٛ ‫ًٔب‬ ‫ٝرُي‬ ‫أُ٘بعجخ‬(6.)
Figure (6) Rock fill cofferdam
1-3-3 Single sheet piles cofferdams ‫ٓلشدح‬ ‫ُٞديخ‬ ‫عزبئش‬ ٖٓ ‫أُذيطخ‬ ‫اُغذٝد‬
‫شبئؼخ‬ ٠ٛٝ ‫اُظِت‬ ٝ‫أ‬ ‫اُخشعبٗخ‬ ٝ‫أ‬ ‫اُخشت‬ ٖٓ ٌٕٞ‫ر‬ ‫ٓلشدح‬ ‫ُٞديخ‬ ‫عزبئش‬ ٖٓ ‫أُذيطخ‬ ‫اُغذٝد‬
ْ‫ص‬ ‫االٗشبء‬ ‫ٓ٘طوخ‬ ٍٞ‫د‬ ‫اُِٞديخ‬ ‫اُغزبئش‬ ‫دم‬ ْ‫يز‬ ‫ديش‬ ‫أُبئيخ‬ ٟ‫أُجبس‬ ٠ِ‫ػ‬ ٟ‫اٌُجبس‬ ‫اٗشبء‬ ٠‫ك‬ ّ‫االعزخذا‬
‫جبكخ‬ ‫ثيئخ‬ ٠‫ك‬ َٔ‫ُِؼ‬ ‫اُغذ‬ َ‫داخ‬ ٖٓ ٙ‫أُيب‬ ‫رلشيؾ‬,‫اُغزبئشيخ‬ ‫اُذٞائؾ‬ ٖٓ ٖ‫صٝجي‬ ٖٓ ‫اُغذ‬ ‫ي٘لز‬ ‫ديش‬
ٌَ‫ثبُش‬ ‫ٓٞػخ‬ ٞٛ ‫ًٔب‬ ‫أكويخ‬ ‫ٝدػبٓبد‬ ‫رضجيذ‬ ‫ثأُٞاح‬ ‫ثيٜ٘ٔب‬ ‫أُغبكبد‬ ‫ٝيذلظ‬(7).‫االعزـ٘بء‬ ٌٖٔ‫ي‬ ‫ًٔب‬
‫اُخِليخ‬ ‫اُزشثخ‬ ٠‫ك‬ ‫اُذبئؾ‬ ‫رضجيذ‬ ٝ ‫األكويخ‬ ‫اُذػبٓبد‬ ٖ‫ػ‬(ٌَ‫ش‬ ‫اٗظش‬8.)

8
Figure (7) Single sheet piles cofferdams
Figure (8) Single sheet pile cofferdam
‫اُغذ‬ ‫ٝخبسط‬ َ‫داخ‬ ٙ‫أُيب‬ ‫ػـؾ‬ َٔ‫رش‬ ٠‫ٝاُز‬ ‫ػِيٜب‬ ‫أُإصشح‬ ٟٞ‫اُو‬ ّٝ‫ُزوب‬ ‫اُِٞديخ‬ ‫اُغزبئش‬ ْ‫رظٔي‬ ْ‫ٝيز‬
ٌَ‫ثبُش‬ ‫ٝساد‬ ٞٛ ‫ُٔب‬ ً‫ب‬‫ؽجو‬ ٚ‫دغبث‬ ٌٖٔ‫ي‬ ١‫ٝاُز‬ ‫اُغذ‬ ‫خبسط‬ ‫اُزشثخ‬ ‫ٝػـؾ‬(9)‫ٓشرٌضح‬ ‫اٜٗب‬ ‫ثبػزجبس‬ ‫ٝرُي‬
‫اُطشين‬ ّ‫ثبعزخذا‬ ‫االسرٌبص‬ ‫ٗوبؽ‬ ‫ػ٘ذ‬ َ‫اُلؼ‬ ‫سدٝد‬ ‫ٝرذغت‬ ‫األكويخ‬ ‫اُشثؾ‬ ‫اُٞاح‬ ٠ِ‫ػ‬ ً‫ب‬‫ثغيط‬ ‫اسرٌبصا‬
‫أُؼزبدح‬ ‫االٗشبئيخ‬.

9
Figure (7-9) Distribution of Earth pressure on Cofferdams
1-3-4 Double sheet piles cofferdams ‫ٓضدٝجخ‬ ‫ُٞديخ‬ ‫عزبئش‬ ٖٓ ‫أُذيطخ‬ ‫اُغذٝد‬
‫ال‬ ‫كوذ‬ ‫دجضٛب‬ ‫أُطِٞة‬ ‫أٝاُزشثخ‬ ٙ‫أُيب‬ ‫ٓ٘غٞة‬ ‫السرلبع‬ ‫ٗزيجخ‬ ‫ػبُيخ‬ ‫اُخبسجيخ‬ ‫اُؼـٞؽ‬ ٌٕٞ‫ر‬ ‫ػ٘ذٓب‬
‫اُغزبئش‬ ٖٓ ٖ‫ٓزٞاصيي‬ ٖ‫طلي‬ ‫ر٘ليز‬ ْ‫يز‬ ‫ػ٘ذٛب‬ ‫اُؼـٞؽ‬ ٙ‫ٛز‬ ‫ُٔوبٝٓخ‬ ‫اُِٞديخ‬ ‫اُغزبئش‬ ٖٓ ‫ٝادذ‬ ‫طق‬ ٠‫يٌل‬
‫اُخشعبٗخ‬ ٝ‫أ‬ ‫اُذجبسح‬ ‫ًغش‬ ٝ‫أ‬ ‫ثبألرشثخ‬ ‫ثيٜ٘ٔب‬ ‫اُلشاؽ‬ ‫َٓء‬ ْ‫يز‬ ْ‫ص‬ ‫ٓؼذٗيخ‬ ٕ‫ثوؼجب‬ ً‫ب‬‫ٓؼ‬ ْٜ‫رضجيز‬ ْ‫يز‬ ‫اُِٞديخ‬
ٍ‫ثبالشٌب‬ ‫ٓٞػخ‬ ٞٛ ‫ًٔب‬ ‫ٝرُي‬ ‫اُؼبديخ‬(10)ٝ(11.)

10
Figure (10) Double sheet pile cofferdam
Figure (11) Double sheet piles cofferdams
1-3-5 Cellular cofferdams ‫انمتالصقح‬ ‫انخهىيح‬ ‫انسذود‬
A cellular cofferdam is constructed by driving sheet piles of special shapes to
form a series of cells as shown in figure (12). The cells are interconnected to
form a watertight wall. These are filled with soils to provide stability against
the lateral forces.
‫اُغبثوخ‬ ‫اُغذٝد‬ ‫أٗٞاع‬ ٖٓ ‫ٝٗٞع‬ ٟ‫أ‬ ‫يظِخ‬ ُْٝ َ‫ا‬‫جذ‬ ‫ًجيش‬ ٌَ‫ثش‬ ‫عذ‬ ٠ِ‫ػ‬ ‫اُخبسجيخ‬ ‫اُؼـٞؽ‬ ‫صادد‬ ‫ئرا‬
ٌٕٞ‫يز‬ ٚٗ‫أ‬ ‫ديش‬ ‫االعزبريٌيخ‬ ‫اُ٘بديخ‬ ٖٓ ‫أُضدٝط‬ ٟ‫اُغزبئش‬ ‫اُغذ‬ ٚ‫يشج‬ ٞٛٝ ِٟٞ‫اُخ‬ ‫اُغذٝد‬ ّ‫اعزخذا‬ ْ‫كيز‬

11
‫اُِٞديخ‬ ‫اُغزبئش‬ ٖٓ ‫أُزالطوخ‬ ‫اُخاليب‬ ٖٓ ‫ٓجٔٞػخ‬ ٖٓ.‫أٝأُٞاح‬ ‫ُٞديخ‬ ‫عزبئش‬ ٖ‫ػ‬ ‫ػجبسح‬ ِٟٞ‫اُخ‬ ‫ٝاُغذ‬
‫ٓ٘بعت‬ ّ‫ثشد‬ ‫ِٓئٜب‬ ْ‫يز‬ ْ‫ص‬ ‫اُغذ‬ ‫ٌٓٞٗخ‬ ‫ثيٜ٘ب‬ ‫كئب‬ َ‫رزذاخ‬ ‫ٓزجبٝسح‬ ‫خاليب‬ ٌٕٞ‫ُز‬ ‫دهٜب‬ ْ‫يز‬ ‫خبطخ‬ ٍ‫أشٌب‬ ‫راد‬
‫أُطِٞة‬ ٕ‫االرضا‬ ‫ُزذوين‬.
Figure (7-12) Cellular cofferdams
1-3-1 -1Types of Cellular Cofferdams
There are two types of cellular cofferdams, namely diaphragm type cellular
cofferdam and circular type cellular cofferdam.
a)Diaphragm Type cellular cofferdam ‫اُـشبئيخ‬ ‫اُغذٝد‬
‫ٓؼب‬ ‫يشثطٜب‬ ‫ُِغذ‬ ‫ٝاُخبسجيخ‬ ‫اُذاخِيخ‬ ‫اُ٘بديخ‬ ٠‫ك‬ ‫دائشيخ‬ ‫ٓ٘ذ٘يبد‬ ٖ‫ػ‬ ‫ػجبسح‬ ‫اُـشبئيخ‬ ‫اُخِٞيخ‬ ‫اُغذٝد‬
‫خبطخ‬ ‫هطغ‬ ‫ثٞاعطخ‬ ‫اُذائشيخ‬ ‫ثبُٔ٘ذ٘يبد‬ ‫رشرجؾ‬ ‫ٓغزوئخ‬ ‫ؿشبئيخ‬ ‫دٞائؾ‬,‫ثذجيجبد‬ ‫اُخاليب‬ ‫ِٓئ‬ ْ‫يز‬ ْ‫ص‬
ٚ‫ػِي‬ ‫أُإصشح‬ ‫األكويخ‬ ٟٞ‫اُو‬ َٔ‫رذ‬ ٠ِ‫ػ‬ ٚ‫هذسر‬ ٠ُ‫ٝثبُزب‬ ‫اُغذ‬ ٕ‫ٝص‬ ‫ُضيبدح‬ ‫ٝرُي‬ ٖ‫خش‬ ّ‫سد‬.‫يجت‬ ‫ًٔب‬
‫اُزشثخ‬ ‫ػـؾ‬ َ‫ثلؼ‬ ‫اكويخ‬ ٟٞ‫ه‬ ‫ُزُٞذ‬ ‫رج٘جب‬ ٟ‫ٓزٞاص‬ ٌَ‫ثش‬ ّ‫ثبُشد‬ ‫أُزجبٝسح‬ ‫اُخاليب‬ ‫ِٓئ‬ ْ‫يز‬ ٕ‫أ‬ ‫ٓشاػبح‬
ٖٓ ‫اُ٘ٞع‬ ‫ٛزا‬ ‫ٝئزبص‬ ٠‫اُـشبئ‬ ‫اُذبئؾ‬ ٖٓ ‫ٝادذح‬ ‫ٗبديخ‬ ٖٓ ّ‫اُشد‬ ‫ُٞجٞد‬ ‫ٗزيجخ‬ ٠‫اُـشبئ‬ ‫اُجذاس‬ ٠ِ‫ػ‬
٠‫اُـشبئ‬ ‫اُذبئؾ‬ ٍٞ‫ؽ‬ ‫ثضيبدح‬ ٕ‫االرضا‬ ٠ِ‫ػ‬ ٚ‫هذسر‬ ‫صيبدح‬ ‫ثآٌبٗيخ‬ ‫اُغذٝد‬.
This type of cellular cofferdam consists of circular arcs at the inner and outer
sides, which are connected by straight diaphragm walls as shown in figure
(13). The connection between the curved parts and diaphragms are made by

12
means of specially fabricated Y- elements. The cofferdam is made from
interconnected steel sheet piles. The cells are filled with coarse-grained soils,
which increase the weight of the cofferdam and its stability. The leakage of
the cofferdam is also reduced. To avoid rupture of the diaphragm due to
unequal pressures on the two sides, it is essential to fill all the cells at
approximately the same rate. The advantage of the diaphragm type is that the
effective width of the cofferdam may be increased easily by lengthening the
diaphragm.
Figure (13) Diaphragm cellular cofferdams
b) Circular Type cellular cofferdam ‫اُذائشيخ‬ ‫اُغذٝد‬
‫ثخاليب‬ ‫ٓؼب‬ ‫ٓشرجطخ‬ ْ‫اُذج‬ ‫ًجيشح‬ ‫اُذائشيخ‬ ‫اُخاليب‬ ٖٓ ‫ٓجٔٞػخ‬ ٖ‫ػ‬ ‫ػجبسح‬ ‫اُـشبئيخ‬ ‫اُذائشيخ‬ ‫اُغذٝد‬
‫اطـش‬ ‫دائشيخ‬.ٍ‫األدٔب‬ ‫يٞصع‬ ٟ‫اُز‬ ٟ‫اُذائش‬ ‫ُشٌِٜب‬ ‫ٗزيجخ‬ ‫ثزارٜب‬ ‫ٓغزوِخ‬ ‫اُخاليب‬ ٖٓ ‫خِيخ‬ ًَ ‫ٝرؼزجش‬
‫ثزارٜب‬ ‫ٓغزوِخ‬ ‫ػِٔيخ‬ ‫خِيخ‬ ًَ ّ‫سد‬ ‫ػِٔيخ‬ َ‫يجؼ‬ ‫ٓٔب‬ ‫اُوششيخ‬ ‫أُ٘شئبد‬ ٠ِ‫ػ‬ ٍ‫األدٔب‬ ‫رٞصيغ‬ ٚ‫يشبث‬ ٌَ‫ثش‬
ٟ‫األخش‬ ِٞ‫ر‬ ‫ٝادذح‬ ‫اُخاليب‬ ّ‫سد‬ ٌٖٔ‫ي‬ ‫ثذيش‬.ٍ‫األدٔب‬ َٔ‫رذ‬ ٠ِ‫ػ‬ ‫اُؼبُيخ‬ ‫ثوذسرٜب‬ ‫رٔزبص‬ ‫اُذائشيخ‬ ‫ٝاُخاليب‬

13
‫أًجش‬ ‫ُؼذد‬ ‫الدزيبجٜب‬ً‫ا‬‫ٗظش‬ ‫رٌِلخ‬ ‫ٜٓ٘ب‬ ‫أًضش‬ ‫ٌُٜٝ٘ب‬ ‫اُـشبئيخ‬ ‫اُخاليب‬ ٖٓ ‫أًجش‬ ٌَ‫ثش‬ ‫ػِيٜب‬ ‫اُٞاهؼخ‬ ‫األكويخ‬
‫أُؼذاد‬ ‫ديش‬ ٖٓ ‫ٝاُزشًيت‬ ‫اُذم‬ ٠‫ك‬ ‫ػبُيخ‬ ‫آٌبٗيبد‬ ٠ُ‫ئ‬ ‫ادزيبجٜب‬ ٠ُ‫ئ‬ ‫ثبإلػبكخ‬ ‫اُذائشيخ‬ ‫اُوطغ‬ ٖٓ
‫أُذسثخ‬ ‫أُبٛشح‬ ‫ٝاُؼٔبُخ‬.
It consists of a set of large diameter circular cells interconnected by arcs of
smaller diameter. This is shown in Figure (14). The walls of the connecting
cells are perpendicular to main circular cell of large diameter. The segmental
arcs are joined by special T-pile to the main cell. The circular type of cellular
cofferdam is self sustaining, independent of the adjacent circular cells. Each
cell can be filled independently. The stability of such cells is much larger as
compared with the diaphragm type. The circular type is more expensive as
compared to the diaphragm type, because these require more sheet piles and
skilled technology for setting and driving the pile. As the diameter of the
circular cell is limited by interlock tension, their ability to resist large lateral
pressures due to high head is restricted.
Figure (14) Circular cellular cofferdams

14
Problem (1)
State the types of cofferdams, indicating the circumstances under which each
is most suitable.
Solution
a)Following are some of the common types of cofferdams
(1) Earth fill cofferdam
(2) Rock fill cofferdam
(3) Single wall cofferdam
(4) Double wall cofferdam.
(5) Cellular cofferdam.
b) Circumstances:
(1) Earth fill cofferdam:- The use of this variety is limited in the vicinity
where the impervious earth is available and the water depth is shallow with
low velocity of flow. This type is not used where there is danger of
overtopping of water.
(2)Rock fill cofferdam:- These are constructed by placing rock along stream.
They can be used for depths of water up to about 3 m and are suitable even in
swift waters. These are economical in places where rock is available in plenty.
(3)Single wall cofferdam:- This type of cofferdam is suitable when available
working space is limited and area enclosed is small. It can be used up to a
depth of water equal to 25 m.
(4) Double wall cofferdam:- Double wall cofferdams are provided to enclose a
larger area. This type is useful where scour problems and space limitations are
prevalent.
(5) Cellular cofferdam:- These are suitable for dewatering large areas. These
can withstand overtopping of water. These types of cofferdams are used in
case of bridges with long spans.

15
1-3-1 -2Design of cellular cofferdams
‫ًا‬‫ال‬‫أو‬-‫االتتذائيح‬ ‫االتعاد‬
٠ُ‫ًبُزب‬ ٚ‫اسرلبػ‬ ٖٓ ‫ٗغجخ‬ ‫اُغذ‬ ‫ػشع‬ ٕ‫أ‬ ‫ٗلزشع‬ ‫أُضدٝجخ‬ ‫اُِٞديخ‬ ‫اُغزبئش‬ ٖٓ ‫ُِغذ‬ ‫ثبُ٘غجخ‬:
B=0.85H
‫اُزبُيخ‬ ‫اُؼالهخ‬ ‫أُزٞعؾ‬ ٚ‫ػشػ‬ ‫يذون‬ ‫ٝثذيش‬ ٌِٚ‫ُش‬ َ‫ب‬‫ٝكو‬ ٚ‫هطبػ‬ ‫اثؼبد‬ ‫رذذد‬ ‫اُخاليب‬ ٝ‫ر‬ ‫ُِغذ‬ ‫ثبُ٘غجخ‬:
B=A/2L
Where:
A ‫اُخاليب‬ ٖٓ ‫أُزٌشس‬ ‫اُجضء‬ ‫ٓغبدخ‬
2L ‫أُزٌشس‬ ‫اُجضء‬ ‫ٛزا‬ ٍٞ‫ؽ‬
‫األريخ‬ ‫اُؼالهخ‬ ٖٓ ِٟٞ‫اُخ‬ ‫اُغذ‬ ‫اثؼبد‬ ٠ِ‫ػ‬ ٍٞ‫اُذظ‬ ٌٖٔ‫ي‬ ‫ًٔب‬:
B= 0.78 D to 0.875 D
Where:
D=1.2H ‫اُخِيخ‬ ‫هطش‬
H ِٟٞ‫اُخ‬ ‫اُغذ‬ ‫اسرلبع‬
L ‫أُذٞس‬ ٠ُ‫ئ‬ ‫أُذٞس‬ ٖٓ ‫اُخاليب‬ ٖ‫ثي‬ ‫أُغبكخ‬
‫َا‬‫ا‬‫حاوي‬:‫انمؤحرج‬ ‫انقىي‬
ٌَ‫ثبُش‬ ‫ٓٞػخ‬ ٞٛ ‫ًٔب‬ ‫ٝرُي‬ ‫أُإصشح‬ ٟٞ‫اُو‬ ٖٓ ٕ‫ٗٞػب‬ ‫ٛ٘بى‬(15)‫ٛٔب‬:
‫أ‬-‫اُخبسجيخ‬ ٟٞ‫اُو‬:‫األٓٞاط‬ ‫ٝػـؾ‬ ٙ‫ٝأُيب‬ ‫ُِزشثخ‬ ٠‫اُجبٗج‬ ‫ٝاُؼـؾ‬ ‫اُغذ‬ ٕ‫ٝص‬ َٔ‫ٝرش‬.
‫ة‬-‫داخِيخ‬ ٟٞ‫ه‬:‫اُغذ‬ َ‫داخ‬ ‫اُزغشة‬ ٟٞ‫ه‬ َٔ‫ٝرش‬
٠ُ‫ًبُزب‬ ‫اُخِيخ‬ َ‫داخ‬ ٙ‫ُِٔيب‬ ‫اُذش‬ ‫اُغطخ‬ َ‫ٓي‬ ٌٕٞ‫ي‬ ‫ديش‬:
‫اُزظشف‬ ‫دش‬ ٖ‫خش‬ ّ‫سد‬(1٠‫اكو‬:1٠‫سأع‬)
٠‫ؽٔي‬ ٖ‫خش‬ ّ‫سد‬(2٠‫أكو‬:1٠‫سأع‬)
‫اُذيجبد‬ ْ‫ٗبػ‬ ّ‫سد‬(3٠‫اكو‬:1٠‫سأع‬).
‫َا‬‫ا‬‫حانخ‬:‫نهسذ‬ ‫انسالمح‬ ‫اختثاراخ‬
٠‫األر‬ َٔ‫رش‬ ٠‫ٝاُز‬ ُٚ ‫اُغالٓخ‬ ‫اخزجبساد‬ ٠‫ك‬ ‫ًبكيخ‬ ٕ‫أٓب‬ ‫ٓؼبٓالد‬ ‫اُغذ‬ ‫يذون‬ ٕ‫أ‬ ‫يجت‬:
‫أ‬-‫االوسالق‬ ‫ضذ‬ ‫انسالمح‬ ‫اختثار‬
Check against sliding can be calculated as follow:

16
Where:
W=B {(H-H1) γT+H1 γsub} ٕ‫ٝص‬‫اُخِيخ‬ َ‫داخ‬ ‫اُزشثخ‬
Pw= 0.5γw H2
‫أُبئيخ‬ ‫أُغذخ‬ ‫ٗبديخ‬ ٖٓ ٙ‫أُيب‬ ‫ػـؾ‬ ‫ٓذظِخ‬
PA=0.5γsub Ka H2² ٍ‫اُلؼب‬ ‫اُزشثخ‬ ‫ػـؾ‬ ‫ٓذظِخ‬
Pp= Ppˋ+Pw1 ّٝ‫أُوب‬ ‫اُزشثخ‬ ‫ػـؾ‬ ‫ٓذظِخ‬+‫ُِغذ‬ ٠ِ‫اُذاخ‬ ٚ‫اُٞج‬ ‫ٗبديخ‬ ٖٓ ٙ‫أُيب‬
Ppˋ=0.5γsub Kp H4² ‫اُغذ‬ ٚ‫ُٞج‬ ‫اُذاخِيخ‬ ‫اُ٘بديخ‬ ٖٓ ّٝ‫أُوب‬ ‫اُزشثخ‬ ‫ػـؾ‬ ‫ٓذظِخ‬
Pw1= 0.5γw H3
2
‫ُِغذ‬ ‫اُذاخِيخ‬ ‫اُ٘بديخ‬ ٖٓ ٙ‫أُيب‬ ‫ػـؾ‬ ‫ٓذظِخ‬
λ =0.5 for smooth rock, ‫اُغذ‬ ‫ػِيٜب‬ ‫أُشرٌض‬ ‫اُزشثخ‬ ٝ ‫اُغذ‬ َ‫داخ‬ ‫اُزشثخ‬ ٖ‫ثي‬ ‫االدزٌبى‬ َٓ‫ٓؼب‬
λ = tan ϕ for other soil
Figure (15) Forces affected on cellular cofferdams
‫ب‬-‫االوقالب‬ ‫ضذ‬ ‫انسالمح‬ ‫اختثار‬
Check against overturning can be calculated by taking a moment about point
A, as follow:
Where:
MR =Resistance moment
50.125.1
W.
=.S. 
 pAW pPP
F

50.33=.S. 
O
R
M
M
F

17
MO= Overturning Moment
‫د‬-‫األساش‬ ‫ترتح‬ ً‫ف‬ ‫االوهيار‬ ‫ضذ‬ ‫انسالمح‬ ‫اختثار‬
Factor of safety can be calculated as follow:
Where:
qult ٠‫ششيط‬ ‫ألعبط‬ ٠‫االهظ‬ َ‫اُزذٔي‬ ‫جٜذ‬
٠ٛٝ ٟ‫األخش‬ ‫االخزجبساد‬ ٖٓ ‫ٓجٔٞػخ‬ ‫رٞجذ‬ ‫ًٔب‬:
‫د‬-‫اُغذ‬ ‫ٓذٞس‬ ‫ػ٘ذ‬ ٠‫اُشأع‬ ‫ثبُوض‬ ‫االٜٗيبس‬ ‫ػذ‬ ‫اُغذ‬ ‫عالٓخ‬ ‫اخزجبس‬
ٙ-‫االعبط‬ ‫ٝرشثخ‬ ّ‫اُشد‬ ٖ‫ثي‬ ٠‫دجيج‬ ٍ‫اٗلظب‬ ‫دذٝس‬ ‫ػذ‬ ‫اُغذ‬ ‫عالٓخ‬ ‫اخزجبس‬
ٝ-٠ِ‫اُذاخ‬ ّ‫اُشد‬ ٠ِ‫ػ‬ ‫اُخبسجيخ‬ ‫ُِغزبئش‬ ‫اٗضالم‬ ‫دذٝس‬ ‫ػذ‬ ‫اُغذ‬ ‫عالٓخ‬ ‫اخزجبس‬
‫ص‬-٠ِ‫اُذاخ‬ ‫اُ٘ذش‬ ‫ػذ‬ ‫اُغذ‬ ‫عالٓخ‬ ‫اخزجبس‬
Problem (2)
Design the cofferdam shown in the figure below:
332
.
= 3
1
4
1R
HP
H
P
BW
M wp 
33
P=
2
wo
H
P
H
M a
50.20.2
/6/
=.
2
b.c 
 BMBW
q
F
O
ult

18
Solution
B=0.85 H = 0.85x20=17m
Where the fill is fine particles, so the inclination of saturation line =3:1
H3=20-17/3=14.34 m
H1=20-8.5/3=17.16m
ka=(1-sin35°)/(1+sin35°) = 0.27
kp=3.69
PA=0.5γsub Ka H2² = 0.5x10x0.27x8²= 86.4kN, ya=8/3=2.67m
Pw= 0.5γw H2
= 0.5x10x20²=2000 kN, y1= 20/3=6.67m
Ppˋ=0.5γsub Kp H4² = 0.5x10x3.69x5²=461.25kN, yp=5/3=1. 67m
Pw1= 0.5γw H3
2
=0.5 x10 x 14.34²= 1028.178kN, y2=4.78m
Pp= Ppˋ+Pw1 = 461.25+1028.178=1489.428kN
W=B {(H-H1) γT+H1 γsub}=17{ (20-17.16)x18+17.16x 8}=3202.8kN
Check against sliding
W=3202.8kN
λ = tan ϕ=tan35°=0.7
50.125.1
W.
=.S. 
 pAW pPP
F

safe
x
F 50.125.175.3
42.14894.862000
7.08.3202
=.S. 


19
Check against overturning:
Check against overturning can be calculated by taking a moment about point
A.
=3202.8x8.5+461.25x1.67+1028.178x4.78 =32908.77 kN.m
= 2000x6.67+86.4x2.67=13570.68kN.m
F.S.=32908.77/13570.68=2.42<3 unsafe
Take B=20m, B/2 =10 m
W=B {(H-H1) γT+H1 γsub}=20{ (20-17.16)x18+17.16x 8}=3768kN
MR=3768x10+461.25x1.67+1028.178x4.78 =43364.97 kN.m
F.S.=43364.97/13570.68=3.2 safe
ٖٓ ٕ‫األٓب‬ َٓ‫ٓؼب‬ ‫هئخ‬ ٖ‫ػ‬ ‫ثبُزؼٞيغ‬ ‫ػٌغيخ‬ ‫ثطشيوخ‬ َ‫اُذ‬ ٌُٖٔٔ‫ا‬ ٖٓ3:3.5‫أُؼبدُخ‬ ٠‫ك‬ ‫اُزؼٞيغ‬ ْ‫ص‬
‫اُغذ‬ ‫ػشع‬ ‫هئخ‬ ٠ِ‫ػ‬ ٍٞ‫ُِذظ‬.
W=B {(H-H1) γT+H1 γsub}=B{ (20-17.16)x18+17.16x 8}=188.4B
W.B/2= (188.4B).B/2=94.2B²
MR= 94.2B²+5684.97
3.25= 94.2B²+5684.97/13570.68
B=20.34 m ≈20.5m
50.33=.S. 
O
R
M
M
F
332
.
= 3
1
4
1R
HP
H
P
BW
M wp 
33
P=
2
wo
H
P
H
M a
25.3=.S. 
O
R
M
M
F
78.4178.102867.125.461
2
.
=R xx
BW
M 

20
Check on soil stresses under the cofferdam
MT=MR-Mo=94.2x20.5²+5684.97-13570.68=31701.84 kN.m
W=188.4B=188.4x20.5=3862.2kN
xˋ=MT/W =31701.84/3862.2=8.2 m
xˋ: ‫اُغذ‬ ٠ِ‫ػ‬ ‫أُإصشح‬ ٟٞ‫ُِو‬ ‫أُذظِخ‬ ‫رأصيش‬ ‫ٗوطخ‬
e=B/2- xˋ=20.5/2-8.2=1.75m
e : ‫اُغذ‬ ٠ِ‫ػ‬ ‫أُإصشح‬ ٟٞ‫ُِو‬ ‫أُذظِخ‬ ‫رأصيش‬ ‫ٝٗوطخ‬ ‫اُغذ‬ ‫ٓشًض‬ ٖ‫ثي‬ ‫أُغبكخ‬ ٠ٛ
F1,2 : ‫اُغذ‬ َ‫أعل‬ ‫االجٜبداد‬
F1=3862.2/20.5 (1+ (6x1.75)/20.5)=284.9 kN/m²
F2=3862.2/20.5(1-(6x1.75)/20.5)=91.9 kN/m²>0.0 ok
)
6
1(=1,2
B
e
B
W
F 

21
2-Braced Cuts
َ‫ٓض‬ ‫اُزذزيخ‬ ‫اُج٘يخ‬ ‫ٝخطٞؽ‬ ‫اُجذسٝٓبد‬ ‫اٗشبء‬ ٍ‫اػٔب‬ ّٝ‫ُض‬ ‫اُذلش‬ ٍ‫ثأػٔب‬ ّ‫اُويب‬ ٠‫اُٜ٘ذع‬ َٔ‫اُؼ‬ ٠‫يغزذػ‬
‫ُِٔٞاطلبد‬ ً‫ب‬‫ٝكو‬ ٍ‫األػٔب‬ ّ‫الرٔب‬ ‫اُذلش‬ ‫ٛزا‬ ‫جٞاٗت‬ ‫ع٘ذ‬ ّ‫يغزِض‬ ‫ٓٔب‬ ٠‫ٝاُظذ‬ ‫ٝاُظشف‬ ‫ٝاٌُٜشثبء‬ ٙ‫أُيب‬
‫اُخشجيخ‬ ‫األُٞاح‬ ّ‫ثبعزخذا‬ ‫اُذلش‬ ‫جٞاٗت‬ ْ‫رذػي‬ ْ‫يز‬ ‫ديش‬ ْ‫أُذػ‬ ٝ‫أ‬ ‫أُغ٘ٞد‬ ‫ثبُذلش‬ ‫يؼشف‬ ‫ثٔب‬ ‫أُطِٞثخ‬
‫ٓخزِلخ‬ ‫ألعبُيت‬ ً‫ب‬‫ٝكو‬ ‫أُؼذٗيخ‬ ‫اُغزبئش‬ ٝ‫أ‬.
2-1Using of Braced Cuts
Braced cut is used for different purposes.
1-It is used to resist the lateral pressure. ‫اُجبٗجيخ‬ ‫اُؼـٞؽ‬ ‫ٓوبٝٓخ‬
2-It provides safety to the construction work ‫اإلٗشبء‬ ‫أص٘بء‬ ٍ‫األػٔب‬ ٖ‫رأٓي‬.
3-It enables deep excavation. ‫اُؼٔين‬ ‫اُذلش‬ ٍ‫ثأػٔب‬ ّ‫اُويب‬ ٖٓ ٖ‫اُزٌٔي‬
2-3 Types of Braced Cuts
1-Vertical Timber sheeting ‫سأعيخ‬ ‫خشجيخ‬ ‫عزبئش‬
2- Steel Sheet Piles ‫ٓؼذٗيخ‬ ‫ُٞديخ‬ ‫عزبئش‬
3-Soldier Beams ْ‫اُزذدػي‬ ‫ًٔشاد‬
4- Tie Backs ‫اُخِليخ‬ ‫األسثطخ‬
2-3-1 Vertical Timber Sheeting
ٖٓ ‫ثغٔي‬ ‫اُخشجيخ‬ ‫األُٞاح‬ ٖٓ ‫عزبسح‬ ‫رشًيت‬ ْ‫يز‬ ‫اُطشيوخ‬ ٙ‫ٛز‬ ٠‫ك‬8٠ُ‫ئ‬10ٍٞ‫د‬ ‫ر٘ليزٛب‬ ْ‫يز‬ ٠‫ٝاُز‬ ْ‫ع‬
٠‫اُظذ‬ ‫اُظشف‬ ‫خ٘بدم‬ ‫ع٘ذ‬ ٍ‫ًأػٔب‬ ‫اُظـيشح‬ ‫أُششٝػبد‬ ٠‫ك‬ ّ‫االعزخذا‬ ‫شبئؼخ‬ ٠ٛٝ َٔ‫اُؼ‬ ‫ٓٞهغ‬
٠ُ‫ئ‬ َ‫رظ‬ ‫ألػٔبم‬ ‫ٝاُـبص‬ ٙ‫ٝأُيب‬2.5‫ٓزش‬.ٍٞ‫د‬ ‫رِزق‬ ‫خشجيخ‬ ْ‫ثوٞائ‬ ‫اُخشجيخ‬ ‫األُٞاح‬ ْ‫رذػي‬ ْ‫يز‬ ‫ًٔب‬
‫ٝرُي‬ ‫ٓبئِخ‬ ٝ‫أ‬ ً‫ب‬ٓ‫رٔب‬ ‫أكويخ‬ ٌٕٞ‫ر‬ ٠‫ٝاُز‬ ‫ػٞاسع‬ ٝ‫أ‬ ‫دػبٓبد‬ ٠ُ‫ئ‬ َٔ‫اُذ‬ َ‫ر٘و‬ ٠‫ٝاُز‬ ‫اُخشجيخ‬ ‫األُٞاح‬
ٌَ‫ثبُش‬ ‫ٓٞػخ‬ ٞٛ ‫ًٔب‬(16.)

22
Figure (16) Vertical Timber sheeting
2-3-2 Steel Sheet Piles
ٍٞ‫اُٞط‬ ‫ٝثؼذ‬ ‫اُز٘ليز‬ ‫ٓٞهغ‬ ٍٞ‫د‬ ‫اُزشثخ‬ ٠‫ك‬ ً‫ب‬‫ٓؼ‬ ‫ٓؼشوخ‬ ‫ٓؼذٗيخ‬ ‫ُٞديخ‬ ‫عزبئش‬ ‫دم‬ ْ‫يز‬ ‫اُطشيوخ‬ ٙ‫ٛز‬ ٠‫ك‬
ٖٓ ٌٕٞ‫ر‬ ٠‫ٝاُز‬ ‫اُذػبٓبد‬ ٝ ‫اُظِت‬ ٖٓ ‫أُظ٘ٞػخ‬ ‫األكويخ‬ ‫اُؼٞاسع‬ ‫رضجيذ‬ ْ‫يز‬ ‫اُذلش‬ ٠‫ك‬ ٖ‫ٓؼي‬ ‫ُؼٔن‬
ٍ‫ثبألشٌب‬ ‫ٓٞػخ‬ ٞٛ‫ًٔب‬ ‫ٝرُي‬ ‫أُطِٞة‬ ‫ُِؼٔن‬ ٍٞ‫اُٞط‬ ٠‫دز‬ ‫ٝرُي‬ ْ‫ُِزذػي‬ ‫اُخشت‬ ٝ‫أ‬ ‫اُظِت‬(17)
ٝ(18. )
Figure (17) Steel sheet piles

23
Figure (18) Steel sheet piles
Design of Steel sheet pile
• The sheet pile can be calculated as continuous beam resting on the wales, so
the sheet pile can be designed/m
• The Wales must be designed as continues beam resting on the struts, so the
reaction on the Wales can be calculated
• With the reaction in the struts, the struts can be designed as compression
member. The moment in the strut due to its own weight and buckling must be
taken into consideration.
2-3-3 Soldier Beam
٠ِ‫ػ‬ ‫االٗشبء‬ ‫ٓٞهغ‬ ٍٞ‫د‬ ‫دهٜب‬ ْ‫يز‬ ‫ارش‬ ‫دشف‬ ٌَ‫ش‬ ٠ِ‫ػ‬ ‫دذيذيخ‬ ‫خٞاصين‬ ٖ‫ػ‬ ‫ػجبسح‬ ْ‫اُزذػي‬ ‫ًٔشاد‬
ٖٓ ‫ٓغبكبد‬1.5:2.5ٖ‫ثي‬ ‫اُزجٜيض‬ ‫عبثوخ‬ ‫ثالؽبد‬ ٝ‫أ‬ ‫خشجيخ‬ ‫اُٞاح‬ ‫ٝػغ‬ ْ‫يز‬ ‫اُذلش‬ ّ‫روذ‬ ‫ٝٓغ‬ ‫ٓزش‬
ٌَ‫ثبُش‬ ‫ًٔب‬ ‫أكويخ‬ ‫ٝدػبٓبد‬ ‫ػٞاسع‬ ‫رشًيت‬ ْ‫يز‬ ْ‫ص‬ ‫اُذذيذيخ‬ ‫اُخٞاصين‬(19).ٌٕٞ‫ي‬ ‫اُذبُخ‬ ٙ‫ٛز‬ ٠‫ٝك‬
َ‫ب‬‫ثغيط‬ ‫رشرٌضاسرٌبصا‬ ٠‫ٝاُز‬ ‫اُزجٜيض‬ ‫عبثوخ‬ ‫اُجالؽبد‬ ٝ‫أ‬ ‫اُخشجيخ‬ ‫األُٞاح‬ ٠ِ‫ػ‬ ‫ٓجبششح‬ ‫ٓإصش‬ ‫اُزشثخ‬ ‫ػـؾ‬
‫ثغيطخ‬ ‫ًٔشاد‬ ‫أٜٗب‬ ٠ِ‫ػ‬ ٠‫األكو‬ ٙ‫االرجب‬ ٠‫ك‬ ‫رظٔئٜب‬ ْ‫يز‬ ٠ُ‫ٝثبُزب‬ ‫اُذذيذيخ‬ ْ‫اُزذػي‬ ‫ًٔشاد‬ ٠ِ‫ػ‬
‫االسرٌبص‬.‫عبثوخ‬ ‫اُجالؽبد‬ َ‫كؼ‬ ‫سد‬ َٔ‫رذ‬ ‫سأعيخ‬ ‫ًٔشاد‬ ‫أٜٗب‬ ٠ِ‫ػ‬ ‫رظٔئٜب‬ ْ‫يز‬ ْ‫اُزذػي‬ ‫ًٔشاد‬ ‫ثي٘ٔب‬
‫أٜٗب‬ ٠ِ‫ػ‬ ‫رظٔئٜب‬ ْ‫يز‬ ٠‫اُز‬ ‫اُذػبٓبد‬ ٠ُ‫ئ‬ َٔ‫اُذ‬ َ‫ر٘و‬ ٠‫ٝاُز‬ ‫األكويخ‬ ‫اُؼٞاسع‬ ٠ِ‫ػ‬ ‫ٝرشرٌض‬ ‫اُزجٜيض‬
٠‫اُزار‬ ‫ٝصٜٗب‬ ٖ‫ػ‬ ‫اُ٘بشئ‬ ‫االٗذ٘بء‬ ّ‫ػض‬ ٠ُ‫ئ‬ ‫ثبالػبكخ‬ ‫األكويخ‬ ‫اُؼٞاسع‬ َ‫كؼ‬ ‫سد‬ ‫رأخز‬ ‫ػـؾ‬ ‫ػ٘بطش‬
‫االٗجؼبط‬ ‫ٝهئخ‬.

24
Figure (19) Soldier Beam
2-3-4 Tie Backs
‫األكويخ‬ ‫اُؼٞاسع‬ ّ‫اعزخذا‬ ‫يظجخ‬ ‫ثذيش‬ ‫ًجيش‬ ٌَ‫اُذلشثش‬ ‫ػشع‬ ‫يضيذ‬ ‫ػ٘ذٓب‬ ‫اُطشيوخ‬ ٙ‫ٛز‬ ّ‫رغزخذ‬
‫دلش‬ ْ‫يز‬ ‫ديش‬ ‫اُغبٗذ‬ ‫اُذبئؾ‬ ْ‫ُزذػي‬ ٠‫خِل‬ ‫ثشثبؽ‬ ‫اعزجذاُٜب‬ ْ‫يز‬ ‫ديش‬ ً‫ب‬‫اهزظبدي‬ ‫ٌِٝٓق‬ ‫طؼت‬ ‫ٝاُذػبٓبد‬
ٞٛ‫ًٔب‬ ‫ٝرُي‬ ‫اُذلشح‬ َ‫داخ‬ ‫خشعبٗخ‬ ‫ٝطت‬ ‫رغِيخ‬ ‫دذيذ‬ ٍ‫ادخب‬ ْ‫يز‬ ْ‫ص‬ ‫اُغبٗذ‬ ‫اُذبئؾ‬ ‫خِق‬ ‫ٓبئِخ‬ ‫دلشح‬
ٌَ‫ثبُش‬ ‫ٓٞػخ‬(20.)
Figure (20) Tie Back

25
2-4 Lateral Earth Pressure Distribution on Braced Cuts
‫اُزوِيذيخ‬ ‫اُطشم‬ ٍ‫خال‬ ٖٓ ٚ٘‫رؼيي‬ ٌٖٔ‫ي‬ ٟ‫ٝاُز‬ ‫اُزشثخ‬ ‫ػـؾ‬ ٞٛ ‫اُغ٘ذ‬ ‫دبئؾ‬ ٠ِ‫ػ‬ ‫أُإصشح‬ ٍ‫األدٔب‬
ٌَ‫ثبُش‬ ‫أُٞػذخ‬ ‫اُزوشيجيخ‬ ْ‫اُوي‬ ٍ‫خال‬ ٖٓ ٝ‫أ‬ ‫أُؼشٝكخ‬(21)ٍ‫خال‬ ٖٓ ‫ػِيٜب‬ ٍٞ‫اُذظ‬ ْ‫ر‬ ٠‫ٝاُز‬
‫ٝدوِيخ‬ ‫ٓؼِٔيخ‬ ‫رجبسة‬.
Figure (21) Lateral Earth Pressure on Braced Cuts
Problem (3)
A long trench is excavated in medium dense sand for the foundation of a
multistory building. The sides of the trench are supported with sheet pile walls
fixed in place by struts and Wales as shown in the Figure below. The soil
properties are: γ= 18.5 kN/m3
, c = 0 and ϕ = 38°
Determine:
(a) The pressure distribution on the walls with respect to depth.
(b) Strut loads. The struts are placed horizontally at distances L = 4 m center
to center.
(c) The maximum bending moment for determining the pile wall section.
(d) The maximum bending moments for determining the section of the wales.

26
Solution
(a) The pressure distribution on the walls
Ka = tan2
(45 - ϕ/2)
Pa = 0.65 γ H Ka = 0.65 x 18.5 x 8 tan2
(45 - 38/2) = 23 kN/m2

27
(b) Strut loads
The reactions at the ends of struts A, B and C are represented by RA, RB and Rc
respectively.
For reaction RA , take moments about B.
RA x3 - 4x23x (4/2) = 0
RA = 61.33 kN
RB1 = 23 x 4-61.33 = 30.67 kN
Due to the symmetry of the load distribution,
RB1 = RB2 = 30.67 kN, and RA = Rc = 61.33 kN.
Now the strut loads are (for L - 4 m)
Strut A, PA = 61.33 x 4 - 245 kN
Strut B, PB = (RBl + RB2 ) x 4 = 61.34 x 4 ≈ 245 kN
Strut C, Pc = 245 kN.
(c) Moment of the pile wall section
To determine moments at different points it is necessary to draw a diagram
showing the shear force distribution as shown in the figure below
MA = 0.5 x 1 x 23 = 1 1.5 kN. m
Mc = 0.5 x 1 x 23 = 1 1.5 kN. m
Mm =1.33x30.67-(23x1.33²/2)= 20.4 kN. m

28
Mn = 1.33x30.67-(23x1.33²/2)= 20.4 kN. m
The maximum moment = 20.4 kN.m
A suitable section of sheet pile can be determined
(d) Maximum moment for Wales
The bending moment equation for Wales is
Mmax=RL2
/8
Where:
R = maximum strut load = 245 kN
L = spacing of struts = 4 m
Mmax= 245x42
/8=490 kN.m
A suitable section for the Wales can be determined
2-4Check to avoid heave
Braced cuts in clay become unstable as a result of heaving of the bottom of the
excavation. The bottom of a cut in sand is generally stable. When the water
table is encountered, the bottom of the cut is stable as long as the water level
inside the cut (excavation) is higher than the ground water table. In case
dewatering is needed the factor of safety, against up lift should be checked.
‫اُذلش‬ ‫هبع‬ ٠‫ك‬ ‫اٗزلبر‬ ‫ُذذٝس‬ ‫ٗزيجخ‬ ‫ٓغزوش‬ ‫ؿيش‬ ‫يظجخ‬ ٕ‫أ‬ ٌُٖٔٔ‫ا‬ ٖٓ ‫اُطي٘يخ‬ ‫اُزشثخ‬ ٠‫ك‬ ‫أُغ٘ٞد‬ ‫اُذلش‬
‫أُطِٞة‬ ٕ‫األٓب‬ ‫ُزذوين‬ ‫رأًيذيخ‬ ‫دغبثبد‬ َٔ‫ثؼ‬ ّ‫اُويب‬ ٠‫يغزذػ‬ ‫ٓٔب‬ ‫جٞكيخ‬ ٙ‫ٓيب‬ ‫ٝجٞد‬ ‫دبُخ‬ ٠‫ك‬ ‫ٝرُي‬(‫ًٔب‬
‫اُجٞكيخ‬ ٙ‫أُيب‬ ‫رخليغ‬ ‫ٓذبػشح‬ ٠‫ك‬ ٚ‫ششد‬ ‫عجن‬).

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