foundation system of burj al arab

Loss of Workability of Concrete with Superplasticizers

The introduction of superplasticizers brings revolution in concrete construction making possible to place it where it was never possible before. With the use of superplasticizers, it is possible to render significantly higher strength with other properties known as high performance concrete. 

Initial dosage of superplasticizers should be applied just after water and cement become in contact with each other. It is considered logical as hydration associated initial reactions would produce difficulties to become superplasticizers effective; superplasticizers can’t produce sufficient deflocculation of cement particles. The preceding statement have been observed in concrete but yet not explained.



The optimum time for addition of superplasticizers in concrete is theoretically that period approximately the starting of inactive period without superplasticizers in concrete. Actually addition of them at this time was reported to produce maximum initial workability and result in lowest rate of decrease in workability. This special time depends on type of cement and has to be determined by experiment. The actual situation in concrete construction, this is the practicality of addition of superplasticizers that dominate. 



Effectiveness of them to available cement particles to get re agglomerate lasts till there have sufficient molecules of superplasticizers to encapsulate exposed periphery of cement particles. Some molecules of superplasticizers become entrapped within the hydration products of cement which results inadequate supply of superplasticizers and thus workability of concrete mix is lost drastically. 



It is found that prolonged agitation or mixing results some products produced during initial hydration of cement to be split from the surface of cement particles which enables again hydration of hitherto unexposed particles of cement to occur. The presence of dissociated products of hydration coupled with commencement of hydration has influence on the reduction of workability of concrete mix.
Loss of workability of concrete with time of concretes
Loss of workability of concrete with time of concretes: (A) water/cement ratio=0.58 without admixture; (B) water/cement ratio=0.47 with superplasticizer
A comparison of loss of workability of mix is described in above figure. Naphthalene based superplasticizer was used in this example; two concrete samples are compared here one without admixture and other with superplasticizers. It can be noticed that loss of workability occurs much quicker in concrete having superplasticizers; but obviously, concrete with superplasticizers has lower water/cement ratio which will yield higher strength. 


Because duration is a prime parameter for effectiveness of superplasticizers, it is advantageous to introduce superplasticizers into the concrete mix in two stage, or even more, operations. Such re-dosage or repeated addition is possible when concrete is delivered to construction site by agitator truck. If it is required to restore workability by re-dosage after some period of actual mixing, adequate amount of super plasticizers should be added to act on both hydration products of cement and cement particles that are not hydrated yet. Therefore a small re-dosage of superplasticizers will not work, higher re-dosage is necessary.

Though repeated addition of superplasticizers to concrete mix is found advantageous in respect of improvement of workability, they may increase segregation and bleeding. Other possibilities are to alter in amount of air entrainment and set retardation. Besides these side-effects, the second dosage applied to restore workability may reduce it at a faster rate than that of initial rate.

What is the Significance of Modulus of Subgrade Reaction of Soil?

Modulus of subgrade reaction is an important term that is frequently used in structural analysis of components of foundation. This is used to design continuous footings, rafts and different types of piles. Modulus of subgrade reaction is a relationship between pressure and associated deflection of soil. Plate load test can produce these data. A δ Vs σ plot is produced during testing; the plot is found non-linear in most cases. Whether tangent or secant lines are used to determine slope (i.e. Ks). The basic equation is
Modulus of subgrade reaction-1

Where 


Δσ=increment of soil pressure 
Δδ=respective change in deformation or settlement

Tangent line is shown as solid line and secant line is shown as dashed in the following figure. Generally, initial line passing through origin is used, but tangent at any point or average of two values taken at the points intersected by scant line drawn along the curve can be used.

Except significantly small plates, it is very difficult to conduct plate load test as reaction load is necessary to achieve uniform deflection of plate. Even in case of small plates like diameter of (450~750) mm, it is not possible to derive δ conforming definition of Ks as plates shown tendency to be too rigid to produce constant deflection along the plate dimension. The rigidity can be increased to some extent by staking smaller plates placed concentric with underneath larger one, whatever measures are taken, the plot is done with load applied on load block derived by contact area (i.e. nominal value q =P/A) and average value of measured deflection.

Following figure describes the situation, figure 1 shows two region of q Vs δ plot where Ks is considered constant up to average deflection value Xmax. When deflection exceeds Xmax, the soil pressure is taken as constant as defined by

qcon = Ks (Xmax)

one can split q- δ plot into several potions so that modulus of subgrade reaction (Ks) attains it actual values on the slope of respective regions; but these approach will produce difficulty in analysis as it require too much adjustment into these problems. So, most analyses are based on estimated values or approximate load test.



Some engineers don’t believe on this conceptual term, modulus of subgrade reaction, rather they prefer stress-strain modulus Es (and poisson’s ratio, µ) to apply in some types of finite-element analysis. But until precision in determining Es has been developed, application of modulus of subgrade reaction in finite element analysis is preferable  as  it offer greater ease in solving and significant saving in consumption of time in calculating with computer. Though there have direct relationship between Ks and Es

The main problem in this regard is to determine Ks value. Terzaghi proposed some equations to determine Ks based on plate-load test for full-sized foundations considering size effects and soil type; but not recommended for general use. Bowels recommended following approximation to determine Ks based on allowable bearing capacity as suggested by geotechnical engineer.


Ks =40 (SF) qin KN/m3

Ks = 12 (SF) qa in K/ft3

Where SF = safety factor and qis in Ksf or Kpa

Modulus of subgrade reaction-2
When ultimate soil pressure is considered at settlement of 0.0254 m (i.e. ΔH= 0.0254 m)
When ΔH is considered 6, 12, 20 mm and so on, the factor 40 or 12 should be changed to 160, 83, and 50 (48. 24, 16 for FPS). 40 is considered sufficiently conservative, but one can choose smaller displacement.

A general form may be introduced as below for either horizontal/ lateral modulus of subgrade reaction

Ks =  As + BZn …. ….. ….  (1)

Where

As = constant for members may be either horizontal or vertical Bs=coefficient for variation of depth

Z= depth at which investigation conducted below ground

n= exponent to provide Ks best fit [when load test or other source of data is available]

Either As or Bs may be zero in this equation; at ground surface As=0 for lateral Ks but As>0 for any small depth. In case of footings & mats As>0 but Bs≈0.

Several hundred words have been included, but what about significance of modulus of subgrade reaction? Significance of this term will be discussed in two categories; for footings and raft foundation and for deep foundations like piles and sheet piles. The previous discussion is essential to explain these.

Shallow foundations:


When mats or combined footings are considered rigid, we can solve this without modulus of subgrade reaction. But when flexibility is considered, the inclusion of modulus of subgrade reaction is required whether it may approximate flexible method or discrete element methods.
In flexible methods for mat foundation, the approximate method was recommended by ACI committee 336. Plate rigidity is measured depending on geometric property, poisson’s ratio and modulus of elasticity of concrete. Effective stiffness radius is determined and then tangential and radial moments, shear and deflection are determined. The radial moments (Mr) and tangential moments (Mt) at load point are found in polar co-ordinates are then converted into rectangular co-ordinates Mx and My referred to origin. This conversion and shear deflection depends on influence radius as discussed above.
zone of a column influence
[Where D=plate stiffness]

It is assumed that approximate zone of a column influence ≈4L

In the discrete element methods, mat is divided into some elements arranged by gridding, the methods included:

1. Finite-difference method (FDM)
2. Finite-element method (FEM)
3. Finite-grid method (FGM)


Above three discrete element methods use modulus of subgrade reaction Ks to support plate. These methods are required to calculate node springs depending on contributing element area in the plan of footing to a node is shown in following Fig.
Application of modulus of subgrade reaction to form node springs

Node springs and spring coupling:


As shown in figure the contributory areas are:
contributory areas for node springs
In case of triangular area, we can distribute arbitrary 1/3 of triangle area to a corner node. Thus considering these area contributions, a fraction Ks resistance for any element will be


Ki = Ks (KN/m3) X Area (m2)


As above computation yields units of a spring, it is generally called effect of node spring. Unit will be KN/m, for FPS unit system it will be Kips/ft. In such form, springs are not dependent on each other and these springs are not coupled. Thus plate is supported by this system of springs and as recommended by Winkler (1987) to consider foundation as bed of springs (classical Winkler solution), this system termed as Winkler foundation.




Uncoupled springs means, any deflection of a spring is not a influence of adjacent springs. According to Boussinesq’s analysis it can be said that contact pressure at base has contribution to settle other points. This means a flexible base, loaded uniformly, subjected to more settlement at center than that at edges. Application of constant Ks over a uniformly loaded rectangular base will result also a constant settlement (ΔH) when we calculate node springs considering contributing area under nodes. This approach is discrete elements methods is off course incorrect; for this reasons many engineers do not agree to use Ks. In simple words, settlement under a base is coupled but these soil springs computed from Ks are not coupled.

Some designers, instead of Ks prefer elastic parameters µ and Es to use in FEM of elastic continuum. The uncoupling problem is solved to some extent, but computation effort is increased extensively and refinement is function of accurate estimation of µ and Es. Again only terms associated with diagonal translation are effected with the Ks in spring concept. Ks has widespread use in analyzing mat foundation because it offers greater convenience.

Moreover, there have few computational evidence about superiority of application of elastic continuum concept over solutions offered by applying Winkler foundation. Bowels suggested to couple spring approximately as follows:

1. Simply use double value of end springs of mat; provided that following conditions must be fulfilled to apply this




a. The mat or plate is loaded uniformly except tank where base is subjected to edge moments
b. Not applicable to sides of very narrow long members
c. The mat or plate has one or at best two column loads
d. The estimated node soil pressure, q should be within range of load on mat


Where Am= Area of mat


2. The higher value of Ks can be provided at ends by zoning; and transitioning to minimum value at central zone. This can be expressed as to provide softer springs in central or the inner most zone which transition to outer zone.

Generally, weight of mat should be considered in analysis. Self-weight of mat doesn’t result internal bending as mat is poured with concrete directly on subgrade, moreover in plastic condition, concrete takes the shape of irregularity remain on surface before hardening. The deflection measure in analysis will be more when self-weight included in calculation as soil springs subjected to reaction of all vertical loads.


Laterally loaded piles:


Early designers of pile used to design pile assuming loaded only axially. To carry lateral loads better piles was introduced. Power poles, sign posts and marine piling are represented as piles embedded partially which are subjected to lateral loads and need to be designed as laterally loaded piles.

Current design principle considers laterally loaded piles as full slender batter or vertical structural members loaded laterally, partially or fully embedded into ground. Early developed analysis method for this type of pile is finite-difference method (FDM). Now finite element method (FEM) offers us significant improvement; FEM offers to analyze complete piles and moment of inertia can vary with length. The lateral program developed for lateral pile can be used to analyze lateral piers. Piers are nothing but pile with large cross section.


Application of modulus of subgrade reaction of soil to FEM modeling:

Pile is divided into number of segments convenient to analysis. Nodes are placed at the point on the pile of

• Cross-sectional changes

• Changes in soil strata

• Where boundary conditions or forces are applied.

It can be concluded from previous experiences that top third of embedded depth is generally critical for displacements and moments; thus segment length should be shorted in this zone. Usually 10~15 number of elements are sufficient having 4~8 element in upper third of pile embedment. Don’t place too short elements immediate below/above a too long element.

A suitable method is used to calculate modulus of subgrade reaction establish a Ks profile as shown in following figure. Node springs are estimated based on Ks;value and are contributing to particular node (Ac).
Calculation of modulus of subgrade reaction

Equation (1) can be used to calculate Ks. The Ks value can be changed for particular node as stratified soil profile is very common and Ks can only be determined from CPT or SPT data.

It is usually accepted that lateral subgrade modulus (Ks) is reduced if piles are spaced closely. According to Boussinesq’s pressure bulb under rectangular footing, we can conclude that when D/B > 6, a negligible pressure increase is observed. Thus treating a clear spacing of pile S’ as depth D and projected width of pile as B, we can establish that when S’/B >6, no modification of Ks is required.

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