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THE COMPARATIVE ANALYSIS OF THE STRENGTH OF CONCRETE MADE FROM VARIOUS AGGREGATE
BAKGROUND OF THE STUDY
Retaining walls are structures used in providing stability for earth or materials where conditions do not give room for the material to assume its natural slope and are mostly used to hold back soil banks, coal or over, piles and water.
Retaining walls are distinguished from aone another based on the method of achieving stability.
There are six type of retaining walls and are:
i. The gravity wall
ii. The cantilever wall
iii. The counterfort retaining wall
iv. Buttressed retaining wall
v. The crib walls
vi. Semi-gravity wall
Bridge abutments are often retaining walls with using wall extension to retain the approach fill and provide protection against erosion. They differ in two major respect from the usual retaining walls.
i. They carry and reactions from the bridge span.
ii. They are restrained at the top so that on active earth pressure is unlikely to develop.
Foundation walls of building mduding residential construction and retaining walls, whose function is to contain the earth of the basement.
Retaining walls are required to be of adequate proportion to resist over turning and sliding as wall as being structurally a proportion to resist over turning and sliding as wall as being structurally adequate.
Terms used in retaining wall design are shown below (f.g 1-2).The toe is both the front base perfection and forward edge, similarly for the heel the backward perfection.
The different types representation diagrams of retaining walls are shown in fig (1-2) below.
a) Gravity walls of stone masony, brick, or plain concrete
The retaining wall as a whole must satisfy two basic conditions. They are
i. The base pressure as the toe of the wall must not exceed the allowable bearing capacity of the soil.
ii. The factor of safety against sliding between the are and the underlying soil must be adequate a value of at least usually being specified. (Rit Craig 2nd edition soil mechanical published by van nostrand rain hold co.ltd)
Retaining wall design goes on with the choosing of tentative dimensions, which are then analyzed for stability and structural requirements. Since this s a trail process overall solution to the problem may be obtained, all of which are satisfactory.
CANTILEVER RETAINING WALL
The cantilever wall is a reinforced concrete wall that utilizes cantilever action to retain step. The mass behind the wall from assuming natural slope. Stability of this wall mainly depends on the mass of the soil on the heel behind the wall.
Dimensions for a retaining wall should be adequate for structural stability and to satisfy local building code requirement.
The date shown below may be used where no other data is available but may result in a overly conservative design. The 200mm from a liberal interpretation. of act (1966) and preferably not less than 600mm so that the proper placement concrete off or is broke off a sufficient amount will remain to satisfy structural and aesthetic require (Bowles I . E)
The base slab dimension should be such that the resultant of the vertical loads fall within the middle one third otherwise. The toe pressure will be too much such that only a part (Bowles J-E and (Hansen and Peck) of the footing will be effective.
A better is increasing in order to save materials. A front better is more acceptable so that the forward wall movement to develop active pressure is not noticeable.
A slight increase in wall stability is usually obtain when the battler is on the Bach face (Ref Bowles J.E) see fig 1-3 below for illustration.
Ranking theory deals with pressure within a soil mass under the following condition (ie assumptions)
i. The wall is vertical
ii. The retaining wall face is smooth
iii. The wall yield above the base and satisfies the condition of plastic equilibrium
iv. It is isotropic
Ranking theory applies when the soil mass is in so called rankling sate.
When a soil mass is allowed to explain (active earth pressure) or contract (passive earth pressure rapture surface will form within the mass. if not interrupted by the back of the retaining wall or other strictures, the mature surface will be aeries of straight lines making an angle 1 with the horizontal.
Active earth pressure i = 45 + Ø/2
Passive earth pressure i = 45 – Ø /2
When the state above exists, the soil is said to be in the Rankin state and the Rankin theory is applicable.
Where pa and pp = unit active and passive earth pressure respectively, at a depth Z
q= vertical pressure or load due to the weight of the soil above Z
C = cohesion strength of the soil
Ka and kp – coefficient of active and passive earth pressure respectively
Ka = 1-sin Ø, kp =1+ sine Ø :.
1x sinØ 1 sinØ
According to ranking theory, earth pressure increase linearly with the depth of the same manner as the lateral pressure exerted by a fluid. For the reason engineers often refer earth pressure as equivalent fluid pressure.
For a cohesion less soil
Pa =1/2 ka rH2 and Pp = ½ rH2
When the back of the wall is inclined
Ka = cos B CosB-√CosB – Cos Ø2
CosB_√CosB - Cos Ø2
(Ref Civil Engineering and Engineering machines series by (ref Civil Engineering and Engineering machines series b Newmark & W.J. Hall)
FORCES ON A CANTILEVER RETAINING WALL
Due to the difficulty in getting or calculating the wall frication, Rankin active pressure is normally used (ie O=o) mainly for walls less than 6 to 7 matters in heights
It is more economical to use the coulombs equation for walls over 7m in height. It should also be clear that it is not the height it used for computation if max. Shear and bending moment that is used for sliding computation to get the driving force. It is left for the design to decide whether to use passive pressure from the soil in front of the toe and whether the soil covering the top portion will be available for existing over turning moment and sliding. Sometimes this is not considered. Just for conservative purpose
The triangular pressure diagram on the stem,wil yield a shear diagram that is a third degree curve.
The use of the different equations for shear and moment seems to be easier.
This enables the roped computation of the cut off points for there in forcing steel since it is uneconomical to use a constant amount of reinforcement for the entire wall height.
From the diagram shown below. The with of the base slab is deduced from the gross. Soil pressure diagram before computing the shear and moments diagrams. The eccentricity of computed by equation (iii) and (iv) shown below.
Differential equations can also be used to compute the shear and moments of the base slab if the safe of the cane is desired and even when numerical values are required.
Fig 1-4 shows these illustrations diagrammatically
Forces on cantilever wall (a) entire unit; free bodied for (ii) stem,(ii) toe, (iv) heel. Note that
M1+M2+M3 = Y0
Cantilever retaining wall (a) stem shear and moment (b) to and heel shear and moments.
CONTERFORT RETAINING WALL
Counterfort retaining wall, are similar to the cantilever retaining wall only that this type has counterforts built behind to hold the wall (stem) and base together and is used where the cantilever is long or for very high pressure behind the wall this counterforts behinds the wall are subjected to tensile forces.
The dimension indicated in the diagram below, only act as a guide, some walls which are about 100mm to 150mm thick have been built in area like united Kingdom. Any thickness which satisfies stability of the wall can be used.
Relative costs of forms, concrete, enforcement and labour will determine to use of counterfort but it is doubtful if a counterfor wall will provide any relative construction economy values it is over 7m is height.
The spacing in the counterforts is based on the trail and error in other to huiumise cost. The most economical method is placing them 1/3 to ½ H (height) apart. by conventional beam theory bending moments in the face slab cantilevered part of the wall as at the interior if the length of over hang is made 0.411 and a spacing between counterforts of L.
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