![NPTEL – ADVANCED FOUNDATION ENGINEERING-I
Figure 9.33 Calculation of the thickness of seal for an open caisson
𝑡𝑡 = 1.18𝑅𝑅𝑖𝑖�
𝑞𝑞
𝑓𝑓𝑐𝑐
(circular caisson) [9.48]
And
𝑡𝑡 = 0.866𝐵𝐵𝑖𝑖�
𝑞𝑞
𝑓𝑓𝑐𝑐�1+1.61�
𝐿𝐿 𝑖𝑖
𝐵𝐵 𝑖𝑖
��
(rectangular caisson) [9.49]
Where
𝑅𝑅𝑖𝑖 = inside radius of a circular caisson
𝑞𝑞 = unit bearing pressure at the base of the caisson
𝑓𝑓𝑐𝑐 = allowable concrete flexural stress (≈ 0.1 − 0.2 of 𝑓𝑓′
𝑐𝑐
where 𝑓𝑓′
𝑐𝑐
is than 28 −
day compressive strength of concrete)
𝐵𝐵𝑖𝑖, 𝐿𝐿𝑖𝑖 = inside with and length, respectively, of rectangular caisson
According to figure 9. 33, the value of q in equations (48 and 49) can be approximated as
𝑞𝑞 ≈ 𝐻𝐻𝛾𝛾𝑤𝑤 − 𝑡𝑡𝛾𝛾𝑐𝑐 [9.50]](https://image.slidesharecdn.com/caissontypes-150525091856-lva1-app6891/85/Caisson-types-5-320.jpg)
![NPTEL – ADVANCED FOUNDATION ENGINEERING-I
Where
𝛾𝛾𝑐𝑐 = unit weight of concrete
The thickness of the seal calculated by equations (48 and 49) will be sufficient to protect
it from cracking immediately after dewatering. However, two other conditions should
also be checked for safety.
1. Check for Perimeter Shear an Contact Face of Seal and Shaft
According to figure 9. 33, the net upward hydrostatic force from the bottom of the
seal is 𝐴𝐴𝑖𝑖 𝐻𝐻𝛾𝛾𝑤𝑤 − 𝐴𝐴𝑖𝑖 𝑡𝑡𝛾𝛾𝑐𝑐 (where 𝐴𝐴𝑖𝑖 = 𝜋𝜋𝑅𝑅𝑖𝑖
2
for circular caissons and 𝐴𝐴𝑖𝑖 = 𝐿𝐿𝑖𝑖 𝐵𝐵𝑖𝑖 for
rectangular caissons). So the perimeter shear developed is
𝑣𝑣 ≈
𝐴𝐴𝑖𝑖 𝐻𝐻𝛾𝛾𝑤𝑤 −𝐴𝐴𝑖𝑖 𝑡𝑡𝛾𝛾𝑐𝑐
𝑝𝑝𝑖𝑖 𝑡𝑡
[9.51]
Where
𝑝𝑝𝑖𝑖 = inside perimeter of the caisson
Note that
𝑝𝑝𝑖𝑖 = 2𝜋𝜋𝑅𝑅𝑖𝑖 (for circular caissons) [9.52]
And that
𝑝𝑝𝑖𝑖 = 2(𝐿𝐿𝑖𝑖 + 𝐵𝐵𝑖𝑖)(for circular caissons) [9.53]
The perimeter shear given by equation (51) should be less than the permissible
shear stress, 𝑣𝑣𝑢𝑢 , or
𝑣𝑣(MN/m2
) ≤ 𝑣𝑣𝑢𝑢 (MN/m2
) = 0.17𝜙𝜙�𝑓𝑓′𝑐𝑐
(MN/m2) [9.54]
Where
𝜙𝜙 = 0.85
In English units,
𝑣𝑣(lb/in2
) ≤ 𝑣𝑣𝑢𝑢 (lb/in2
) = 2𝜙𝜙�𝑓𝑓′𝑐𝑐
(lb/1n2
) [9.55]
Where](https://image.slidesharecdn.com/caissontypes-150525091856-lva1-app6891/85/Caisson-types-6-320.jpg)
![NPTEL – ADVANCED FOUNDATION ENGINEERING-I
𝜙𝜙 = 0.85
2. Check for Buoyancy
If the shaft is completely dewatered, the buoyant upward force, 𝐹𝐹𝑢𝑢 , is
𝐹𝐹𝑢𝑢 = �𝜋𝜋𝑅𝑅0
2
�𝐻𝐻𝛾𝛾𝑤𝑤 (for circular caissons) [9.56]
And
𝐹𝐹𝑢𝑢 = (𝐵𝐵0 𝐿𝐿0)𝐻𝐻𝛾𝛾𝑤𝑤 (for rectangular caissons) [9.57]
The downward force, 𝐹𝐹𝑑𝑑 , is caused by the weight of the caisson and the seal and
by the skin friction at the caisson-soil interface, or
𝐹𝐹𝑑𝑑 = 𝑊𝑊𝑐𝑐 + 𝑊𝑊𝑠𝑠 + 𝑄𝑄𝑠𝑠 [9.58]
Where
𝑊𝑊𝑐𝑐 = weight of caisson
𝑊𝑊𝑠𝑠 = weight of seal
𝑄𝑄𝑠𝑠 = skin friction
If 𝐹𝐹𝑑𝑑 > 𝐹𝐹𝑢𝑢 , the caisson is safe from buoyancy. However, if 𝐹𝐹𝑑𝑑 < 𝐹𝐹𝑢𝑢 , dewatering
the shaft completely will be unsafe. For that reason, the thickness of the seal
should be increased by Δ𝑡𝑡 [over the thickness calculated by using equation (48) or
(49)] or
Δ𝑡𝑡 =
𝐹𝐹𝑢𝑢 −𝐹𝐹𝑑𝑑
𝐴𝐴𝑖𝑖 𝛾𝛾𝑐𝑐
[9.59]
Example 10
An open caisson (circular) is shown in figure 9.34. Determine the thickness of the seal
that will enable complete dewatering.](https://image.slidesharecdn.com/caissontypes-150525091856-lva1-app6891/85/Caisson-types-7-320.jpg)
![NPTEL – ADVANCED FOUNDATION ENGINEERING-I
𝑡𝑡 = 2.2 ft
Use 𝑡𝑡 ≈ 2.5 ft
Check for Perimeter Shear
According to equation (51),
𝑣𝑣 =
𝜋𝜋𝑅𝑅𝑖𝑖
2
𝐻𝐻𝛾𝛾𝑤𝑤 −𝜋𝜋𝑅𝑅𝑖𝑖
2
𝑡𝑡𝛾𝛾𝑐𝑐
2𝜋𝜋𝑅𝑅𝑖𝑖 𝑡𝑡
=
(𝜋𝜋)(7.5)2[(45)(62.4)−(2.5)(150)]
(2)(𝜋𝜋)(7.5)(2.5)
≈ 3650 lb/ft2
= 25.35 lb/in2
The allowable shear stress is
𝑣𝑣𝑢𝑢 = 2𝜙𝜙�𝑓𝑓𝑐𝑐 = (2)(0.85)√300 = 29.4 lb/in2
𝑣𝑣 = 25.35 lb/in2
< 𝑣𝑣𝑢𝑢 = 29.4 lb/in2
− OK
Check Against Buoyancy
The buoyant upward force is
𝐹𝐹𝑢𝑢 = 𝜋𝜋𝑅𝑅0
2
𝐻𝐻𝛾𝛾𝑤𝑤
For 𝑅𝑅0 = 10 ft,
𝐹𝐹𝑢𝑢 =
(𝜋𝜋)(10)2(45)(62.4)
1000
= 882.2 kip
The downward fore, 𝐹𝐹𝑑𝑑 = 𝑊𝑊𝑐𝑐 + 𝑊𝑊𝑠𝑠 + 𝑄𝑄𝑠𝑠 and
𝑊𝑊𝑐𝑐 = 𝜋𝜋�𝑅𝑅0
2
− 𝑅𝑅𝑖𝑖
2
�(𝛾𝛾𝑐𝑐)(55) = 𝜋𝜋�102
− 7.52
�(150)(55) = 1,133,919 lb ≈ 1134 kip
𝑊𝑊𝑠𝑠 = �𝜋𝜋𝑅𝑅𝑖𝑖
2
�𝑡𝑡𝛾𝛾𝑐𝑐 = (𝜋𝜋)(7.5)2(1)(150) = 26,507 lb = 26.5 kip
Assume that 𝑄𝑄𝑠𝑠 ≈ 0. So
𝐹𝐹𝑑𝑑 = 1134 + 26.5 = 1160.5 kip
Because 𝐹𝐹𝑢𝑢 < 𝐹𝐹𝑑𝑑, it is safe. For design, assume that 𝑡𝑡 = 2.5 ft.](https://image.slidesharecdn.com/caissontypes-150525091856-lva1-app6891/85/Caisson-types-9-320.jpg)
Caisson types
- 1. NPTEL – ADVANCED FOUNDATION ENGINEERING-I Module 9 (Lecture 40) DRILLED-SHAFT AND CAISSON FOUNDATIONS Topics 1.1 CAISSONS 1.2 TYPES OF CAISSONS 1.3 THICKNESS OF CONCRETE SEAL IN OPEN CAISSONS 1.4 EXAMPLES & SOLUTIONS Check for Perimeter Shear Check Against Buoyancy
- 2. NPTEL – ADVANCED FOUNDATION ENGINEERING-I CAISSONS TYPES OF CAISSONS Caissons are divided into three major types: (1) open caissons, (2) box caissons (or closed caissons), and (3) pneumatic caissons. Open caissons (figure 9.30) are concrete shafts that remain open at the top and bottom during construction. The bottom of the caisson of the caisson has a cutting edge. The caisson is sunk into place, and soil from the inside of the shaft is removed by grab buckets until the bearing stratum is reached. The shafts may be circular, square, rectangular, or oval. Once the bearing stratum is reached, concrete is poured into the shaft (under water) to form a seal at its bottom. When the concrete seal hardens, the water inside the caisson shaft is pumped out. Concrete is then poured into the shaft to fill it. Open caissons can be extended to great depths, and the cost of construction is relatively low. However, one of their major of disadvantages is the lack of quality control over the concrete poured into the shaft for the seal. Also, the bottom of the caisson cannot be thoroughly cleaned out. An alternative method of open-caisson construction is to drive some sheet piles to form an enclosed area, which is filled with sand and is generally referred to as a sand island. The caisson is then sunk through the sand to the desired bearing stratum. This procedure is somewhat analogous to sinking a caisson when the ground surface is above the water table. Figure 9.30 Open caisson
- 3. NPTEL – ADVANCED FOUNDATION ENGINEERING-I Box caissons (figure 9. 31) are caissons with closed bottoms. They are constructed on land and then transported to the construction site. They are gradually sunk at the site by filling the inside with sand, ballast, water, or concrete. The cost for this type of construction is low. The bearing surface must be level, and if it is not, it must be leveled by excavation. Figure 9.31 Box caisson Pneumatic caissons (figure 9. 32) are generally used for depths of about 50-130 ft (15-40 m). This type of caisson is required when an excavation cannot be kept open because the soil flows into the excavated area faster than it can be removed. A pneumatic caisson has a work chamber at the bottom that is at least 10 ft (≈ 3 m) high. In this chamber, the workers excavate the soil and place the concrete. The air pressure in the chamber is kept high enough to prevent water and soil from entering. Workers usually do not counter severe discomfort when the chamber pressure is raised to about 15 lb/in2 (≈ 100 kN/m2 ) above atmospheric pressure. Beyond this pressure, decompression periods are required when the workers leave the chamber. When chamber pressures of about 44 lb/in2 (≈ 300 kN/m2 ) above atmospheric pressure are required, workers should not be kept inside the chamber for more than 11 2 2 hours at a time. Workers enter and leave the chamber through a steel shaft by means of a ladder. This shaft is also used for the removal of excavated soil and the placement of concrete. For large caisson construction, more than one shaft may be necessary, an airlock is provided for each one. Pneumatic caissons gradually sink as excavation proceeds. When the bearing stratum is reached, the work
- 4. NPTEL – ADVANCED FOUNDATION ENGINEERING-I chamber is filled with concrete. Calculation of the load-bearing capacity of caissons is similar to that for drilled shafts. Therefore, it will not be further discussed in this section. Figure 9.32 Pneumatic caisson THICKNESS OF CONCRETE SEAL IN OPEN CAISSONS In section 3, we mentioned that, before dewatering the caisson, a concrete seal is placed at the bottom of the shaft (figure 9.33) and allowed to cure for some time. The concrete seal should be thick enough to withstand an upward hydrostatic force from it bottom after dewatering is complete and before concrete fills the shaft. Based on the theory of elasticity the thickness, t, according to Teng (1962) is
- 5. NPTEL – ADVANCED FOUNDATION ENGINEERING-I Figure 9.33 Calculation of the thickness of seal for an open caisson 𝑡𝑡 = 1.18𝑅𝑅𝑖𝑖� 𝑞𝑞 𝑓𝑓𝑐𝑐 (circular caisson) [9.48] And 𝑡𝑡 = 0.866𝐵𝐵𝑖𝑖� 𝑞𝑞 𝑓𝑓𝑐𝑐�1+1.61� 𝐿𝐿 𝑖𝑖 𝐵𝐵 𝑖𝑖 �� (rectangular caisson) [9.49] Where 𝑅𝑅𝑖𝑖 = inside radius of a circular caisson 𝑞𝑞 = unit bearing pressure at the base of the caisson 𝑓𝑓𝑐𝑐 = allowable concrete flexural stress (≈ 0.1 − 0.2 of 𝑓𝑓′ 𝑐𝑐 where 𝑓𝑓′ 𝑐𝑐 is than 28 − day compressive strength of concrete) 𝐵𝐵𝑖𝑖, 𝐿𝐿𝑖𝑖 = inside with and length, respectively, of rectangular caisson According to figure 9. 33, the value of q in equations (48 and 49) can be approximated as 𝑞𝑞 ≈ 𝐻𝐻𝛾𝛾𝑤𝑤 − 𝑡𝑡𝛾𝛾𝑐𝑐 [9.50]
- 6. NPTEL – ADVANCED FOUNDATION ENGINEERING-I Where 𝛾𝛾𝑐𝑐 = unit weight of concrete The thickness of the seal calculated by equations (48 and 49) will be sufficient to protect it from cracking immediately after dewatering. However, two other conditions should also be checked for safety. 1. Check for Perimeter Shear an Contact Face of Seal and Shaft According to figure 9. 33, the net upward hydrostatic force from the bottom of the seal is 𝐴𝐴𝑖𝑖 𝐻𝐻𝛾𝛾𝑤𝑤 − 𝐴𝐴𝑖𝑖 𝑡𝑡𝛾𝛾𝑐𝑐 (where 𝐴𝐴𝑖𝑖 = 𝜋𝜋𝑅𝑅𝑖𝑖 2 for circular caissons and 𝐴𝐴𝑖𝑖 = 𝐿𝐿𝑖𝑖 𝐵𝐵𝑖𝑖 for rectangular caissons). So the perimeter shear developed is 𝑣𝑣 ≈ 𝐴𝐴𝑖𝑖 𝐻𝐻𝛾𝛾𝑤𝑤 −𝐴𝐴𝑖𝑖 𝑡𝑡𝛾𝛾𝑐𝑐 𝑝𝑝𝑖𝑖 𝑡𝑡 [9.51] Where 𝑝𝑝𝑖𝑖 = inside perimeter of the caisson Note that 𝑝𝑝𝑖𝑖 = 2𝜋𝜋𝑅𝑅𝑖𝑖 (for circular caissons) [9.52] And that 𝑝𝑝𝑖𝑖 = 2(𝐿𝐿𝑖𝑖 + 𝐵𝐵𝑖𝑖)(for circular caissons) [9.53] The perimeter shear given by equation (51) should be less than the permissible shear stress, 𝑣𝑣𝑢𝑢 , or 𝑣𝑣(MN/m2 ) ≤ 𝑣𝑣𝑢𝑢 (MN/m2 ) = 0.17𝜙𝜙�𝑓𝑓′𝑐𝑐 (MN/m2) [9.54] Where 𝜙𝜙 = 0.85 In English units, 𝑣𝑣(lb/in2 ) ≤ 𝑣𝑣𝑢𝑢 (lb/in2 ) = 2𝜙𝜙�𝑓𝑓′𝑐𝑐 (lb/1n2 ) [9.55] Where
- 7. NPTEL – ADVANCED FOUNDATION ENGINEERING-I 𝜙𝜙 = 0.85 2. Check for Buoyancy If the shaft is completely dewatered, the buoyant upward force, 𝐹𝐹𝑢𝑢 , is 𝐹𝐹𝑢𝑢 = �𝜋𝜋𝑅𝑅0 2 �𝐻𝐻𝛾𝛾𝑤𝑤 (for circular caissons) [9.56] And 𝐹𝐹𝑢𝑢 = (𝐵𝐵0 𝐿𝐿0)𝐻𝐻𝛾𝛾𝑤𝑤 (for rectangular caissons) [9.57] The downward force, 𝐹𝐹𝑑𝑑 , is caused by the weight of the caisson and the seal and by the skin friction at the caisson-soil interface, or 𝐹𝐹𝑑𝑑 = 𝑊𝑊𝑐𝑐 + 𝑊𝑊𝑠𝑠 + 𝑄𝑄𝑠𝑠 [9.58] Where 𝑊𝑊𝑐𝑐 = weight of caisson 𝑊𝑊𝑠𝑠 = weight of seal 𝑄𝑄𝑠𝑠 = skin friction If 𝐹𝐹𝑑𝑑 > 𝐹𝐹𝑢𝑢 , the caisson is safe from buoyancy. However, if 𝐹𝐹𝑑𝑑 < 𝐹𝐹𝑢𝑢 , dewatering the shaft completely will be unsafe. For that reason, the thickness of the seal should be increased by Δ𝑡𝑡 [over the thickness calculated by using equation (48) or (49)] or Δ𝑡𝑡 = 𝐹𝐹𝑢𝑢 −𝐹𝐹𝑑𝑑 𝐴𝐴𝑖𝑖 𝛾𝛾𝑐𝑐 [9.59] Example 10 An open caisson (circular) is shown in figure 9.34. Determine the thickness of the seal that will enable complete dewatering.
- 8. NPTEL – ADVANCED FOUNDATION ENGINEERING-I Figure 9.34 Solution From equation (48), 𝑡𝑡 = 1.18𝑅𝑅𝑖𝑖� 𝑞𝑞 𝑓𝑓𝑐𝑐 For 𝑅𝑅𝑖𝑖 = 7.5 ft, 𝑞𝑞 ≈ (45)(62.4) − 𝑡𝑡𝛾𝛾𝑐𝑐 With 𝛾𝛾𝑐𝑐 = 150 lb/ft3 , 𝑞𝑞 = 2808 − 150𝑡𝑡 and 𝑓𝑓𝑐𝑐 = 0.1𝑓𝑓′𝑐𝑐 = 0.1 × 3 × 103 lb/in2 = 0.3 × 103 lb/in2 So 𝑡𝑡 = (1.18)(7.5)� (2808−150 ft 300×144 Or 𝑡𝑡2 + 0.07𝑡𝑡 − 5.09 = 0
- 9. NPTEL – ADVANCED FOUNDATION ENGINEERING-I 𝑡𝑡 = 2.2 ft Use 𝑡𝑡 ≈ 2.5 ft Check for Perimeter Shear According to equation (51), 𝑣𝑣 = 𝜋𝜋𝑅𝑅𝑖𝑖 2 𝐻𝐻𝛾𝛾𝑤𝑤 −𝜋𝜋𝑅𝑅𝑖𝑖 2 𝑡𝑡𝛾𝛾𝑐𝑐 2𝜋𝜋𝑅𝑅𝑖𝑖 𝑡𝑡 = (𝜋𝜋)(7.5)2[(45)(62.4)−(2.5)(150)] (2)(𝜋𝜋)(7.5)(2.5) ≈ 3650 lb/ft2 = 25.35 lb/in2 The allowable shear stress is 𝑣𝑣𝑢𝑢 = 2𝜙𝜙�𝑓𝑓𝑐𝑐 = (2)(0.85)√300 = 29.4 lb/in2 𝑣𝑣 = 25.35 lb/in2 < 𝑣𝑣𝑢𝑢 = 29.4 lb/in2 − OK Check Against Buoyancy The buoyant upward force is 𝐹𝐹𝑢𝑢 = 𝜋𝜋𝑅𝑅0 2 𝐻𝐻𝛾𝛾𝑤𝑤 For 𝑅𝑅0 = 10 ft, 𝐹𝐹𝑢𝑢 = (𝜋𝜋)(10)2(45)(62.4) 1000 = 882.2 kip The downward fore, 𝐹𝐹𝑑𝑑 = 𝑊𝑊𝑐𝑐 + 𝑊𝑊𝑠𝑠 + 𝑄𝑄𝑠𝑠 and 𝑊𝑊𝑐𝑐 = 𝜋𝜋�𝑅𝑅0 2 − 𝑅𝑅𝑖𝑖 2 �(𝛾𝛾𝑐𝑐)(55) = 𝜋𝜋�102 − 7.52 �(150)(55) = 1,133,919 lb ≈ 1134 kip 𝑊𝑊𝑠𝑠 = �𝜋𝜋𝑅𝑅𝑖𝑖 2 �𝑡𝑡𝛾𝛾𝑐𝑐 = (𝜋𝜋)(7.5)2(1)(150) = 26,507 lb = 26.5 kip Assume that 𝑄𝑄𝑠𝑠 ≈ 0. So 𝐹𝐹𝑑𝑑 = 1134 + 26.5 = 1160.5 kip Because 𝐹𝐹𝑢𝑢 < 𝐹𝐹𝑑𝑑, it is safe. For design, assume that 𝑡𝑡 = 2.5 ft.
- 10. NPTEL – ADVANCED FOUNDATION ENGINEERING-I