Flownets: Two-Dimensional Flow of Water Through Soils

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May 30, 2022

Table of Contents

Laplace’s equation is used to describe the movement of water through soils. By comparison, the flow of water through soils is analogous to the steady-state heat flow and steady-state current flow in homogeneous conductors. Flownets can be used to calculate the flow of water through soils based on the Laplace’s equation. The common form of Laplace’s equation for the flow of water through two-dimensional soils is:

k_x(∂²H/∂x²) + k_z(∂²H/∂z²) = 0 ——– (1)

where H is the total head and k_x and k_z are the hydraulic conductivities in the X and Z directions. The condition that the changes in hydraulic gradient in one direction are balanced by changes in the other directions is expressed by Laplace’s equation.

The assumptions in Laplace’s equation are:

• Darcy’s law is valid.
• Irrotational flow (vorticity) is negligible. This assumption leads to the following two-dimensional relationship in velocity gradients.

∂v_z / ∂Z = ∂v_x / ∂X

where v_z and v_x are the velocities in the Z and X directions, respectively. This relationship is satisfied for a uniform flow field and not a general flow field. Therefore, we will assume all flows in this chapter are uniform, i.e., v_z = v_x = constant.
• There is inviscid flow. This assumption means that the shear stresses are neglected.
• The soil is homogeneous and saturated.
• The soil and water are incompressible (no volume change occurs).

Laplace’s equation is also called the potential flow equation because the velocity head is neglected. If the soil is an isotropic material, then k_x = k_z and Laplace’s equation becomes;

(∂²H/∂x²) + (∂²H/∂z²) = 0 ——– (2)

Any differential equation requires knowledge of the boundary conditions in order to be solved. Since the boundary conditions of the majority of “real” structures are complex, an analytical or closed-form solution cannot be obtained for these structures. Using numerical techniques such as finite difference, finite element, and boundary element, it is possible to obtain approximate solutions.

We can also attempt to replicate the flow through the actual structure using physical models. There are two major techniques for solving Laplace’s equation. The first is an approximation known as flownet sketching, and the second is the finite difference method. In this article, we are going to focus on flownet sketching.

Flownet Sketching

The flownet sketching technique is straightforward and adaptable, and it represents the flow regime. It is the preferred method of analysing flow through soils for geotechnical engineers. Before delving into these solution techniques, however, we will establish a few key conditions necessary to comprehend two-dimensional flow.

The solution of Equation (1) is solely dependent on the total head values within the flow field in the XZ plane. Let us introduce a velocity potential (ξ) that describes the variation of total head in a soil mass as follows:

ξ = kH ——– (3)

where k is a generic hydraulic conductivity. The velocities of flow in the X and Z directions are;

v_x = k_x(∂H/∂x) = ∂ξ/∂x ——– (4a)
v_z = k_z(∂H/∂z) = ∂ξ/∂z ——– (4b)

illustration of flow terms — **Figure 1**: Illustration of flow terms.

The inference from Equations (4a) and (4b) is that the velocity of flow (v) is normal to lines of constant total head, as illustrated in Figure 1 The direction of v is in the direction of decreasing total head. The head difference between two equipotential lines is called a potential drop or head loss.

If we draw lines that are tangent to the flow velocity at each point in the flow field in the XZ plane, we will obtain a series of lines that are normal to the equipotential lines. These lines are known as streamlines or flow lines (Figure 1). A flow line represents the expected path of a particle of water in a steady-state flow. ψ_s is a stream function that represents a streamline family (x, z). According to the stream function, the components of velocity in the X and Z directions are as follows:

v_x = ∂ψ_s / ∂z ——– (5a)
v_z = ∂ψ_s / ∂x ——– (5b)

Since flow lines are normal to equipotential lines, there can be no flow across flow lines. The rate of flow between any two flow lines is constant. The area between two flow lines is called a flow channel (Figure 1). Therefore, the rate of flow is constant in a flow channel.

Criteria for Sketching Flownets

A flownet is a graphical representation of a flow field that satisfies Laplace’s equation and comprises a family of flow lines and equipotential lines. A flownet must meet the following criteria (Budhu, 2011):

The boundary conditions must be satisfied.
Flow lines must intersect equipotential lines at right angles.
The area between flow lines and equipotential lines must be curvilinear squares. A curvilinear square has the property that an inscribed circle can be drawn to touch each side of the square and continuous bisection results, in the limit, in a point.
The quantity of flow through each flow channel is constant.
The head loss between each consecutive equipotential line is constant.
A flow line cannot intersect another flow line.
An equipotential line cannot intersect another equipotential line.

An infinite number of flow lines and equipotential lines can be drawn to satisfy Laplace’s equation. However, only a few are required to obtain an accurate solution. The procedure for constructing a flownet is described next.

Flownet for Isotropic Soils

According to Budhu (2011), the procedure for constructing the flownet of isotropic soils are as follows;

Draw the structure and soil mass to a suitable scale.
Identify impermeable and permeable boundaries. The soil–impermeable boundary interfaces are flow lines because water can flow along these interfaces. The soil–permeable boundary interfaces are equipotential lines because the total head is constant along these interfaces.
Sketch a series of flow lines (four or five) and then sketch an appropriate number of equipotential lines such that the area between a pair of flow lines and a pair of equipotential lines (cell) is approximately a curvilinear square. You would have to adjust the flow lines and equipotential lines to make curvilinear squares. You should check that the average width and the average length of a cell are approximately equal by drawing an inscribed circle. You should also sketch the entire flownet before making adjustments.

Flownet of a sheet pile wall — **Figure 2:** Flownet for a sheet pile (Budhu, 2011)

The flownet in confined areas between parallel boundaries typically consists of elliptical and symmetrical flow lines and equipotential lines (Figure 2). Avoid abrupt changes between straight and curved flow and equipotential lines. Transitions should be smooth and gradual. For certain problems, portions of the flownet are enlarged, are not curvilinear squares, and do not satisfy Laplace’s equation.

For instance, the portion of the flownet beneath the base of the sheet pile in Figure 2 is not composed of curvilinear squares. Check these sections to ensure that repeated bisection results in a point for a precise flownet.

Another example of flownet are shown in Figures 3. Figure 2 shows a flownet for a sheet pile wall, and Figure 3 shows a flownet beneath a dam. In the case of the retaining wall, the vertical drainage blanket of coarse-grained soil is used to transport excess porewater pressure from the backfill to prevent the imposition of a hydrostatic force on the wall. The interface boundary, is neither an equipotential line or a flow line. The total head along the boundary is equal to the elevation head.

flownet for a dam — **Figure 3:** Flownet under a dam with a cutoff curtain (sheet pile) on the upstream end (Budhu, 2011)

Flow Rate

Let the total head loss across the flow domain be ΔH, that is, the difference between upstream and downstream water level elevation. Then the head loss (Δh) between each consecutive pair of equipotential lines is;

Δh = ΔH/N_d ——– (6)

where N_d is the number of equipotential drops, that is, the number of equipotential lines minus one. In Figure 1, ΔH = H = 8 m and N_d = 18. From Darcy’s law, the flow through each flow channel for an isotropic soil is;

q = Aki = (b × 1)k(Δh/L) = kΔh(b/L) = k(ΔH/N_d)(b/L) ——– (7a)

where b and L are defined as shown in Figure 14.3. By construction, b/L = 1, and therefore the total flow is;

q = kΔH(N_f/N_d) ——– (7b)

where N_f is the number of flow channels (number of flow lines minus one). In Figure 1, N_f= 9. The ratio N_f/N_d is called the shape factor. Finer discretization of the flownet by drawing more flow lines and equipotential lines does not significantly change the shape factor. Both N_fand N_d can be fractional. In the case of anisotropic soils, the quantity of flow is;

q = ΔH(N_f/N_d)√(k_xk_z) ——– (8)

Summarily, Flow nets are typically designed for homogeneous, isotropic porous media undergoing saturated flow to known boundaries. There are extensions to the basic method that make it possible to solve the following cases:

inhomogeneous aquifer: matching conditions at property boundaries
anisotropic aquifer: drawing the flownet in a transformed domain and scaling the results differently in the principal hydraulic conductivity directions before returning the solution
one boundary is a seepage face: iteratively solving for both the boundary condition and the solution throughout the domain

The method is typically applied to these types of groundwater flow problems, but it can be applied to any problem described by the Laplace equation, such as the flow of electric current through the earth.

References
Budhu M. (2011): Soil Mechanics and Foundations (3rd Edition). John Wiley & Sons, Inc.

Design of Buoyancy Raft Foundations | Compensated Foundation

By

Ubani Obinna

-

May 24, 2022

The purpose of a raft foundation is to spread the superstructure load across as much ground as possible and to provide the substructure some rigidity so that it can bridge over weaker or more compressible soil. The rigidity of a raft foundation also lowers differential settlement in soft clays. The principle of buoyancy is used in buoyancy rafts and basements (or box foundations) to lower the net weight on the soil. By so doing, the foundation’s total and differential settlements are therefore lowered. Bouyancy rafts are also called compensated foundations.

Buoyancy is produced by constructing a hollow substructure with a depth such that the weight of the soil excavated for it is equal to or slightly less than the combined weight of the superstructure and substructure.

Worked Example on Buoyancy Raft Foundation

A four storey building is to be founded on soft clay which extends up to a depth of about 8m. The ultimate load per floor on the building is 12.5 kN/m² while the proposed basement raft and the entire substructure is expected to weigh 25 kN/m². By what depth should the basement be excavated such that there is no net pressure on the foundation? Take unit weight of clay as 18 kN/m².

Solution

Total load from the superstructure = 12.5 x 4 = 50 kN/m²
Weight of substructure = 25 kN/m²
Total load transmitted to the foundation = 75 kN/m²

Effective pressure at the required depth = (18 x D_f) = 18D_f
For zero net pressure on the foundation;
18D_f = 75
Depth of foundation D_f = 75/18 = 4.167 m (say 4.2 m)

In the example shown above, excavation to a depth of 4.2 m for the basement relieves the soil at foundation level of a pressure of about 75.6 kN/m². Since substructure itself weighs about 25 kN/m², a loading of 50 kN/m² can be placed on the basement before any additional loading causing settlement comes on to the soil at foundation level. A bearing pressure of 50 kN/m²is roughly equivalent to the overall loading of a four-storey block of flats or offices.

Note that a reinforced concrete framed structure with brick and concrete external walls, lightweight concrete partition walls, and plastered finishing weighs about 12.5 kN/m² each storey, which is a good rough estimate for calculating the weight of a multistory block of apartments. This figure includes a dead load of 100% and a maximum design live load of 60%.

As a result, a building of this height can theoretically be sustained on a basement founded in very soft and very compressible soil without settling.

If we assume that the building in the example studied above is placed on a mat foundation with dimensions of 20m x 15m, and the cohesion of the clay C_u is 30 kN/m². We can determine the depth of the foundation for a factor of safety of 3 against bearing capacity failure. This will now be a case of partially compensated foundation.

The net ultimate bearing capacity of a mat foundation founded on clay is given by;

q_net(u)= q_u – q = 5.14C_u[(1 + 0.195B/L)(1 + 0.4D_f/B) (Das, 2008)

For a partially compensated foundation, the factor of safety is given by;
FS = q_net(u) / q = q_net(u) / (Q/A – γD_f)

Hence, FS = 5.14C_u[(1 + 0.195B/L)(1 + 0.4D_f/B) / (Q/A – γD_f)

We can verify that Q/A = 75 kN/m²
B/L = 15/20 = 0.75

5.14C_u[(1 + 0.195B/L)(1 + 0.4D_f/B) = [5.14(30) × [1 + (0.195 × 0.75)] × (1 + 0.4(D_f/15)] = 176.751 + 4.719D_f
(Q/A – γD_f) = 75 – 18D_f

Therefore;
3 = (176.751 + 4.719D_f)/(75 – 18D_f)
225 – 54D_f = 176.751 + 4.719D_f
48.249 = 58.719D_f
On solving, D_f = 0.821 m

Challenges in the Construction of Buoyancy Rafts

In practice, however, balancing the loads so that no additional pressure is applied to the soil is not easily achievable. Fluctuations in the water table alter the foundation’s buoyancy, and the intensity and distribution of live loading cannot be accurately predicted in most circumstances. Another aspect that contributes to the settlement of a buoyant foundation is the reconsolidation of swollen soil caused by the elimination of overburden pressure during substructure excavation.

buoyancy raft foundation — Typical construction of a raft foundation

When the superstructure is built up, any swelling caused by elastic or long-term movements must be followed by reconsolidation when loading is replaced on the soil. For economy in the depth of foundation construction it is the usual practice to allow some net additional load to come on to the soil after the total of the dead load of the structure and its full live loading has been attained. The allowable intensity of pressure of this additional loading is determined by the maximum total and differential settlements which can be tolerated by the structure.

Both the ultimate and serviceability limit states must be considered in terms of limit states. Although a well designed buoyancy raft or basement should not experience bearing capacity failure, there is a danger of suffering an eventual limit condition owing to flotation of a fully or partially completed substructure.

An overestimation of soil density and ground-water table height could result in an underestimation of soil bearing pressure, resulting in excessive settling. Factors such as future groundwater table lowering or, conversely, future groundwater level rising due to site floods should be considered. In multi-cell buoyancy rafts, the weights of constructional materials and wall thicknesses (geometrical data) can be very critical.

Surcharges such as placing fill around a semi-buoyant substructure can be critical particularly if placed on one side only causing tilting. The latter can also be caused by variations in the position of imposed loading (spatial distribution), for example by stacked containers in a warehouse.

According to the EN 1997-1 (EC 7) regulation (Section 8, Retaining Structures), design values for the unit weight of water must take into account whether the water is fresh, saline, or chemically contaminated. Design parameters for water pressure and seepage forces are necessary to represent the limit state conditions with severe effects. The design values for limit states with less severe effects (often serviceability limit states) should represent the most unfavourable values that could occur in normal conditions.

Design of Buoyancy Rafts

It is very important to understand the differences between a basement and a buoyancy raft foundation. Although a basement functions as a type of buoyancy raft, it is not always constructed for that purpose. The main purpose of a basement is to provide the owner more room in the building, and the fact that it lowers the net bearing pressure due to the weight of the displaced soil may be purely coincidental. Basements are sometimes required for their function in decreasing net bearing stresses, and this is taken advantage of to create additional substructure floor area.

basement construction — Typical construction of a basement wall

The genuine buoyancy raft, on the other hand, is a foundation that is built only to sustain the structure using the buoyancy provided by the displaced earth, with no consideration for other uses of the space. The raft is designed to be as light and rigid as possible to achieve this goal. Cellular or ‘egg-box’ architecture is the best way to combine lightness with rigidity.

This structural form limits the usefulness of the space within the substructure to accommodate any pipework or service ducts passing through holes in the walls of the cells. Because of the many problems inherent in the design and construction of buoyancy rafts, they have, in most cases, been supplanted by other expedients, mainly by various types of piling.

Maintaining buoyancy under ground conditions that need the cells to be waterproof might cause issues. Where the rafts are built in the shape of caissons, asphalt tanking or other membrane protection is not possible, and any water that seeps through fractures in the exterior walls or base shall be pumped out. Interior cell walls should have openings to allow water to drain to a sump where an automated pump can be placed.

In structures supported by buoyancy rafts, when gas is used for household heating or industrial activities, the cells should be sealed to prevent dangerous gas accumulations within the substructure.

Buoyancy rafts can be constructed either as open well caissons or in-situ in an open excavation. The caisson method is appropriate for soft clays because the soil within the cells can be grabbed as the raft sinks under its own weight. This approach, however, is inadequate for ground conditions when rigidity and weight are required to facilitate sinking through obstructions. When the soil is disturbed by grabbing reconsolidates under the superstructure loading, some settling should be expected where the caissons are terminated within the soft clay.

Construction in open excavations is appropriate for sites where the ground-water level can be maintained by pumping without risk of ‘boiling,’ and where soil heave at the excavation’s base is not extreme.

Expansion Joints in Bridges

By

Ubani Obinna

-

May 23, 2022

Table of Contents

When two structural elements are designed to move relative to one another, an expansion joint is usually required to seal the gap between the two elements while also accommodating their relative movements. Expansion joints in bridges are usually provided to allow for thermal expansion and contraction of the bridge deck, and to also allow for movement due to traffic actions on the bridge. The gap between the deck end and the abutment wall is frequently the case for bridges. On long viaducts or continuous bridges, however, additional joints may be required between deck portions to limit the movement at any one place.

Expansion joints are a point of weakness within a bridge due to its function, and there have been several occurrences of joints leakage, which can cause problems to the bridge. For example, corrosion of the bridge reinforcement has commonly occurred when de-icing salt-laden water has seeped onto bearing shelves or pier supports.

The required repairs are substantially more expensive than the joint’s initial capital cost, especially when traffic delays are included. It is therefore important to pay careful attention to the design, detailing, and installation of bridge expansion joints in order to reduce the risk of future high repair costs for the bridge owner.

Expansion joint repair and maintenance works — **Figure 1:** On going bridge expansion joint maintenance and repair

One of the main reasons for the rising use of integral bridge design is the susceptibility of expansion joints. Integral bridge construction eliminates the requirement for expansion joints by attaching the deck directly to the abutments. The removal of expansion joints is often recommended where possible due to the problems they can cause.

An integral bridge, on the other hand, will have the same load effects and causes of movement as an expansion joint, however, the effects of the movement will need to be considered in its design. However, integral construction will not be a possibility for many bridges, especially those already built, and expansion joints will always be required.

Performance Criteria of Expansion Joints in Bridges

For an expansion joint to function well, it must possess a number of qualities. Some of them are listed below;

It must withstand loads and movements without causing failure to itself or other sections of the structure.
It should be watertight
It should provide a smooth ride, and pose no danger to road users such as cyclists, pedestrians, or equestrians.
The joint’s skid resistance should equal that of nearby surfacing
Noise emissions from the expansion joint should be kept to a minimum, especially if it’s going to be used in residential areas.
The joint should be easy to inspect and maintain.

Types of Expansion Joints in Bridges

Different types of expansion joint are presented below, together with an indication of typical movement ranges for each type of joint. Different types of expansion joints are listed in Reid et al (2008) and reproduced here.

Buried Expansion Joint

This expansion joint is essentially covered by the road surfacing. It permits movement up to 20 mm (±10 mm). For movements up to 10 mm the joint can be formed on top of the deck using a flashing and waterproofing layer to bridge the gap. For larger movements the flashing is dropped down into a recess below the top of the deck and an elastomeric pad used to fill the recess.

Buried joint — **Figure 3:** Buried expansion joint (Reid et al, 2008)

Asphaltic Plug Expansion Joint

This expansion joint consists of an in-situ joint of flexible bituminous material, which provides both an expansion medium and the running surface. The deck joint gap is covered by a thin plate. It permits a movement range of up to 40 mm (±20 mm).

Asphaltic plug joint — **Figure 4:** *Asphaltic plug expansion joint (Reid et al, 2008)*

Nosing Expansion Joint

This type of joint consists of a relatively stiff nosing material of cementitious polyurethane, polyuride or epoxy binders protects the adjacent edges of the surfacing and a compression seal (or poured sealant) protects against ingress of water. It permits a movement range of up to 12 mm with poured sealant and up to 40 mm with a preformed compression seal.

Nosing joint — **Figure 5:** *Nosing expansion joint (Reid et al, 2008)*

Reinforced Elastomeric Expansion Joint

This joint consists of a prefabricated segmental joint of neoprene rubber with reinforcing angles and plates. It is bolted down to the concrete and epoxy resin mortar nosing transition strips protect the adjacent surfacing. There are various sizes giving movement range of up to ±165 mm.

Reinforced elastomeric joint — **Figure 6:** *Reinforced elastomeric expansion joint (Reid et al, 2008)*

Elastomeric in Metal Runners Expansion Joint

In this type of expansion joint, an elestomeric seal is fixed between two metal runners cast into recesses in the abutment and deck concrete. By introducing intermediate runners, multi-element joints can be provided (as illustrated) with greater capacity. As an alternative the rails can be embedded in a resin bonded to the concrete or a rubber element bolted to the concrete.

Movement range:
Single element up to 80 mm (±40 mm)
Multi-element up to 960 mm (±480 mm)
Embedded up to 150 mm (±75 mm)

Cantilever Comb or Tooth Expansion Joint

In this type of expansion joint, a prefabricated joint in which metal comb or tooth plates slide back and forth between each other across the gap. They are bolted down to the concrete and a drainage membrane is provided underneath to collect water. The movement range is typically up to 600 mm (±300 mm).

A variety of factors will influence the selection of the type of expansion joint for bridges. On an individual joint, different types of joints should not be mixed, and this will often define the type of maintenance work performed on an existing joint. For novel applications, the joint must clearly be able to accommodate the anticipated movements, but there are other factors to consider when evaluating the joint’s performance.

The treatment of the verges and footways, which may contain a variety of services, the road alignment (gradient, cross-fall, and curvature), the vicinity of junctions (where longitudinal loads will be more common), and how heavily trafficked the joint will be are all factors to consider. All of these factors can affect the performance and hence the life of an expansion joint, and they must be considered when calculating the total cost of the joint.

Design of Expansion Joints in Bridges

In the UK, BD 33 specifies the design loads and movements for expansion joints (Highways Agency, 1994a). Expansion joints in bridges should be designed for both serviceability and ultimate limit states to ensure that they function well without requiring unnecessary maintenance and that they can withstand ultimate design loads and movements.

For vertical loads, BD 33 specifies a 100kN single wheel load or a 200kN single axle load with a 1.8m track, as well as an 80 kN/m horizontal load. Vertical loads at the ultimate limit state (ULS) and serviceability limit state (SLS) have partial load factors of 1.50 and 1.20, respectively, whereas horizontal loads have partial load factors of 1.25 and 1.00. There are two key elements to remember.

In the Eurocodes, it is important to determine the traffic loads and combinations on expansion joints for (quasi-) static assessment at Ultimate Limit State and, where requested at Serviceability Limit State, and fatigue loads and relevant conditions for assessment of seismic behaviour. It shall be used in combination with pre-stressing, imposed deformations, dead loads and seismic loads.

Furthermore, it is important to verify and guarantee;

The movement capacity,
The water tightness,
The drainage capacity,
The content, emission and/or release of dangerous substances.

The vertical and horizontal loads for design of expansion joints are derived from EN 1991-2, 4.3, Load Model 1. Only tandem systems TS apply, not the uniformly distributed loads (UDL) as they are not relevant for the expansion joints. The selected position(s) of the axle loads shall be such that they produce the most adverse load effect on the underlying structure between the kerbs. This may result in several load cases with different positions.

First, the supporting structure should be designed to sustain the above loads. Second, to the above loads should be added those resulting from strains developed in the joint fillers over their design range of movement.

expansion joint maintenance — **Figure 9:** *Maintenance works on a bridge expansion joint*

At both ULS and SLS, calculation of movements are based on partial load factors of unity. Joint movements can come from a variety of sources, and they should all be added up to get a total movement range from which to choose a joint type. Because not all movements are reversible, it is desirable to analyse and establish limitations for both the closure and opening of the joint, rather than just the overall range of movement, because it is unclear if movements in either direction balance.

Temperature changes are determined by the effective bridge temperatures experienced by the deck and should be assessed in line with the applicable bridge design standard. Irreversible movements are caused by concrete creep and shrinkage, and they must be assessed using concrete or composite bridge design standards.

On curved or skew bridges, lateral movement of the joint should be considered because it can alter the joint design. Movements can be caused by settlement of supports, as well as sway of the bridge under longitudinal braking or traction stresses, depending on the articulation of the bridge. Rotation of the deck ends under live load on bridges with flexible or deep decks can produce significant displacement at the joint level. This explains why even a joint located above a fixed bearing will move. Installing the expansion joint as late as possible, after the majority of permanent movements have already occurred, avoids a comparable impact for permanent loads.

Drainage of Expansion Joints

Expansion joints rarely fail because their maximum movement capacity is surpassed. This is ensured by partial factors of safety embedded into their design. Because they are locally subjected to higher than expected stresses, parts of joints may deteriorate more quickly on occasion, maybe due to increased dynamic influences on wheel loads induced by uneven pavement.

Water leaks through the joints is usually the main cause of failure. This can be caused by inadequate joint details, poor installation technique, or just the inherent challenge of completely sealing any junction between two pieces moving relative to each other. Water management on the bridge deck is critical to an expansion joint’s success, and it should be addressed early in the design process rather than as an afterthought.

**Figure 10:** *Typical drainage for a bridge expansion joint*

While every effort should be made to make expansion joints waterproof, there is always the possibility of water from the surface leaking through the joint over time. It is usual practice to install a drainage system beneath the deck joint gap to collect water that leaks through the expansion joint. This system should allow for easy inspection and maintenance, as well as discharge into a proper road drainage system or soak away.

Before it reaches the expansion joint, water coming through the surfacing and running along the waterproofing should be collected and discharged through a subsurface drainage system.

Detailing of Expansion Joints

Good expansion joint details will go a long way toward making the joint low-maintenance and functional. A variety of regulations relating to bridge user safety are included in the Highways Agency document BD 33. Any open gap not bridged by a load-bearing part, for example, shall not be wider than 65 mm, and no gaps are allowed where pedestrians have access to the bridge.

A loadbearing seal or a cover plate can be used to solve this problem. Cover plates should be contoured and positioned in shallow recesses in the footway to prevent slipping. On one side of the joint, they are bolted, but on the other, they can slide. These plates are normally 12mm thick since they must withstand inadvertent wheel stresses. Over the parapet string course, thinner cover plates are frequently installed to hide what would otherwise be an open expansion junction.

At these potentially impact-prone locations, kerb cover plates should be provided to protect the expansion joint. To guarantee that cyclists may ride through tooth-and-comb joints where the gaps are oriented generally in the direction of traffic, extra care must be exercised during the installation.

expansion jont details — **Figure 11:** *Typical construction details of a bridge expansion joint*

It’s also vital to describe any services that pass through expansion joints, and the need to accommodate services may well decide which of the aforementioned alternatives for detailing joints in verges is used. Certain couplings require specific clearances to any service ducts, which should be examined. Service ducts should be sufficiently spaced to allow for the flow of joint material around them as well as the placement of fixings between ducts.

Installation and maintenance

Faulty installation and inferior materials are two of the most common causes of expansion joint failure. When installing expansion joints, take care and follow the manufacturer’s instructions. Trained workers should be used, with special attention paid to identified weak spots such the interaction with the bridge deck waterproofing.

Bridge expansion joints should be inserted as late as feasible in the construction process to allow for shrinkage, creep, and settlement movements to occur before the expansion joint gap is filled.

Expansion joints should be built such that all wearable pieces can be replaced or reset quickly, ideally during off-peak hours. Joints should be inspected regularly to ensure that they are still functioning correctly and have not blocked up or leaked. Because of the dangers of allowing water to spill onto other bridge parts, any blocked drainage should be cleaned as soon as possible. To avoid the transmission of excessive stresses across the joint, and silting up of joints must be cleaned.

Reference
Reid I. L. K., Thayre P. A., Jenkins D. E., Broom R. A. and Grout D. J. (2008): Bridge Accessories in ICE Manual of Bridge Engineering (Institution of Civil Engineers) doi: 10.1680/mobe.34525.0553.

Design of Stepped Foundation

By

Ubani Obinna

-

March 25, 2023

Strip foundations do not have to be at the same level throughout the building when it is built on sloping terrain. The foundation can be stepped as shown in Figure 1. For the strip foundation of duplexes and commercial buildings, it is also very common to step down the foundations, even though sometimes, it is not properly done. Therefore stepped foundation is fairly common in building construction.

**Figure 1:** Stepped foundation on a sloping ground

Strip foundations can also be stepped to follow any undulations in the bearing stratum if they are laid below a surface layer of infill or poor soil on to the underlying bearing stratum. Figure 2 shows the BS 8103 standards for a regular strip foundation. Unless extra precautions are taken, the step should not be higher than the thickness of the foundation. Foundation stepped on elevation should overlap by twice the height of the step, the thickness of the foundation, or 300 mm whichever is greater.

The heights of steps in deep trench fill foundations (Figure 3), require special consideration and it might be advisable to introduce reinforcing bars to prevent cracking at the steps. For a trench fill foundation, the overlap should be twice the height of the step or 1m, whichever is greater. Steps should not be thicker than the thickness of the foundation.

stepped foundation in narrow strip — **Figure 3:** Recommended construction practice for trench fill foundation

building on a stepped foundation — **Figure 4:** Building on a stepped foundation

stepped strip foundation — **Figure 5:** Masonry wall on a stepped foundation

Requirements for thickness

In a lightly loaded strip foundation, the thickness of concrete is typically equal to the projection from the face of the wall or footing, with a minimum thickness of 150 mm. This minimum is required to provide the rigidity that allows the foundations to bridge over loose spots in the soil and resist longitudinal stresses caused by thermal expansion and contraction as well as moisture movement in the footing walls. Swelling pressures on clay soils can be extremely high.

**Figure 6:** Typical stepping down of foundation on a construction site

The Cost of Laying Blocks in Nigeria

By

Ubani Obinna

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August 21, 2022

Sancrete blocks are popular precast masonry units that are used in the construction of residential, commercial, and industrial buildings in Nigeria. They are usually produced using sharp sand, limestone Portland cement, and water. In some cases quarry dust (stone dust) is added to the mix to increase the strength and density. This article discusses the cost of laying blocks in Nigeria.

Sandcrete blocks are usually produced as either hand-moulded or machine-vibrated. Commercially, these two types of blocks are priced differently, as the latter is deemed more quality and stronger. Furthermore, sandcrete blocks appear in a variety of sizes such as 225 mm (9 inches), 150 mm (6 inches), 125 mm (5 inches) and 100 mm (4 inches). They can be solid or hollow depending on the desired use.

Sandcrete blocks can be used as load bearing walls, or as partition elements in buildings. For the construction of bungalows and fences, smaller sizes of sandcrete blocks such as 6 inches (150 mm) and 5 inches (125 mm) are usually employed. They are also sometimes used for minor partitioning of toilets, stores, laundry rooms, etc in duplexes and commercial buildings. However, it is more common to see 9 inches hollow blocks used in the construction of duplexes in Nigeria.

4 inches hollow block — Laying of blocks using 4 inches block

The Standard Organisation of Nigeria (SON) has a document that provides the specification for both the manufacture and use of sandcrete blocks in Nigeria (NIS 87:2004). The standard requires that the mean compressive strength obtained from a set of five (5) blocks of 225mm (9 inches) and 150mm (6 inches) wide blocks must not be less than 3.45 N/mm² and 2.5 N/mm² respectively. The standards further state that the compressive strength of individual load bearing blocks shall not be less than 2.5 N/mm² for machine-compacted blocks (NIS 87:2004).

These values are higher than the minimum requirements of 1.75 N/mm²by the Nigerian National Building Code (2006) for individual block, and 2.0 N/mm²by the British Standard for non-load bearing walls.

The cost of laying blocks in Nigeria varies from location to location and the level of complexity involved. Blocks are laid by skilled masons or bricklayers who must be paid according to the agreement reached before the commencement of the work. Each mason/bricklayer usually has a minimum of one service labourer who provides him with mortar, blocks, and assists him throughout the duration of the work.

See also…
Cost of plastering a house in Nigeria

Typically, for an average daily job man who has no permanent employment contract with a construction company, the wages for laying blocks are usually determined by;

(a) Daily pay (minimum number of hours)
(b) Output (number of blocks laid)

Daily Pay

In a daily pay contract, the mason is entitled to a fixed amount of money at the of the day. The work hours are usually from 8:00 am to 5:00 pm (8 hours of work). Currently, the rate varies from ₦ 5000 to ₦ 8000 per day depending on the location and the complexity of the work. Currently, the wages of the service labourer will usually be between ₦ 2000 to ₦ 4000 per day. Under normal circumstances, it is expected that the mason will lay a minimum of 100 blocks per day.

Daily pay type of contract is suitable for small jobs or jobs where extreme carefulness is required such as block wall setting out and forming.

Pay based on output (counting)

In this type of contract, the mason is paid based on the number of blocks he lays per day. The cost per block can vary between ₦ 30 (thirty Naira) to ₦ 70 (seventy Naira) depending on the size of the block and the complexity of the work. Jobs that require scaffolding (work at height) is usually priced higher than jobs that do not require scaffolding. When block work contract is done based on counting, it is either the mason will pay his service labour (the price is negotiated) or the client pays the service labour.

Cost of Laying Blocks in Nigeria (For Bill of Quantity)

Let us evaluate the average cost of laying one square metre of sandcrete block wall in Nigeria. Currently, the cost of one unit of 9 inches block in Nigeria is ₦ 350.

Therefore, for one square metre of block wall, the cost of blocks is ₦ 3,500
Cost of sand for mortar required per square metre of wall = ₦ 255
Cost of cement for mortar required per square metre of wall = ₦855
Cost of labour per square metre of wall = ₦ 900
Total = ₦ 5510 per square metre of wall

Therefore currently, the cost of building one square metre of 9 inches hollow block wall in Nigeria is ₦ 5,510 (Five thousand, five hundred and ten Naira), ignoring the contractor’s profit and overhead.

Alkali-Silica Reaction in Concrete

By

Ubani Obinna

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May 20, 2022

Table of Contents

Some substances in aggregates can react with alkali hydroxides in concrete. It is only when this reactivity causes large expansion in the concrete it is deemed dangerous. There are two types of alkali-aggregate reactivity (AAR):

Alkali-silica reaction (ASR), and
Alkali-carbonate reaction (ACR).

Because aggregates containing reactive silica minerals are more common in concrete, alkali-silica reaction is of greater concern than alkali-carbonate reaction. Alkali-reactive carbonate aggregates have a unique composition that is not found in many other materials. Since the late 1930s, alkali-silica reactivity has been identified as a potential source of concrete distress. Alkali-silica distress in structural concrete is uncommon, despite the presence of potentially reactive aggregates across North America. This is due to a variety of factors:

Aggregates with good performance are plentiful in many places, and most aggregates are chemically stable in hydraulic cement concrete.
The majority of in-service concrete is dry enough to prevent ASR.
Certain pozzolans or slags can be used to control ASR.
The alkali concentration of certain concrete combinations is low enough to prevent damaging ASR
Some types of alkali-silica reaction do not cause considerable detrimental expansion.

Understanding the ASR mechanism, effectively performing tests to detect potentially reactive aggregates, and, if necessary, taking efforts to decrease the possibility for expansion and subsequent cracking are all required to reduce ASR potential.

Alkali-Silica Reaction (ASR)

A network of cracks, blocked or spalled joints, relative displacements of different components of a building, or pieces breaking out of the concrete surface (popouts) are all common symptoms of alkali-silica reaction in concrete. The risk of catastrophic failure is however low because ASR deterioration is slow. Alkali-silica reaction, on the other hand, might produce serviceability issues and increase other deterioration mechanisms, such as those caused by frost, deicer, or sulphate exposure.

dam affected by alkali silica reaction 1 — **Figure 1:** Dam affected by alkali-silica reaction in Norway

Mechanism of Alkali-Silica Reaction

The alkali-silica reaction produces a gel that expands as it absorbs water from the cement paste around it. ASR’s reaction products have a strong affinity for moisture. These gels can cause pressure, expansion, and breaking of the aggregate and surrounding paste by absorbing water. The reaction can be broken down into two steps:

Alkali hydroxide + reactive silica gel → reaction product (alkali-silica gel)
Gel reaction product + moisture → expansion

The amount of gel created in concrete is determined by the amount and kind of silica used, as well as the concentration of alkali hydroxide. The presence of gel does not always imply distress in concrete, and hence the presence of gel does not always imply damaging ASR.

Factors Affecting Alkali-Silica Reaction

The following three conditions must be present for the alkali-silica reaction to occur:

reactive forms of silica in the aggregate,
high-alkali (pH) pore solution, and
sufficient moisture.

ASR cannot occur if one of these conditions is not met.

Identification Test Methods for Distress due to ASR

It is important to distinguish between the damage caused by the reaction, and the reaction itself. A gel product will almost certainly be discovered in the diagnosis of concrete deterioration. However, considerable volumes of gel can accumulate without causing concrete damage in some circumstances. The existence of harmful ASR gel must be confirmed in order to designate ASR as the cause of damage.

An aggregate particle that is recognisably reactive or potentially reactive that is at least partially replaced by gel is described as a site of expansive reaction. Gel can be found in cracks and voids, as well as in a ring that surrounds an aggregate particle’s edges. Cracking caused by ASR is nearly often shown by a network of interior fissures linking reacted aggregate particles. The most reliable approach for detecting ASR gel in concrete is a petrographic study. Petrography can confirm the existence of reaction products and confirm ASR as the underlying cause of degradation when used to investigate a known reacted concrete.

Control of Alkali-Silica Reaction in New Concrete

The easiest approach to prevent ASR is to take proper precautions before pouring concrete. To address ASR, standard concrete specifications may need to be modified. To prevent limiting the concrete producer’s possibilities, these alterations should be carefully customised. This allows for a thorough examination of cementitious materials and aggregates, as well as the selection of a control plan that balances effectiveness and cost. There are no extra criteria if the aggregate is not reactive based on past identification or testing.

Identification of Potentially Reactive Aggregates

The easiest way to assess an aggregate’s susceptibility to alkali-silica reaction is to look at its field performance history. The concrete should have been in use for at least 15 years for the most accurate assessment. Comparisons should be performed between the mix proportions, constituents, and service settings of existing and projected concrete. This procedure should reveal whether unique requirements are required, whether they are not required, and whether aggregate or work concrete testing is required.

For preliminary screening, newer, faster test methods can be used. Longer testing can be performed to confirm results where there are uncertainties. Some of the different test procedures for evaluating possible alkali-silica reactivity are;

ASTM C 227: Potential alkali reactivity of cement-aggregate combinations (mortar-bar method)
ASTM C 289: Potential alkali-silica reactivity of aggregates (chemical method)
ASTM C 295: Petrographic examination of aggregates for concrete, etc

These tests should not be used to rule out the use of potentially reactive aggregates; reactive aggregates can be used safely with appropriate cementitious material selection, as explained below.

Materials and Methods to Control Alkali-Silica Reaction

Designing combinations particularly to limit ASR, ideally utilising locally available materials, is the most effective approach of controlling expansion owing to ASR. The following options are not in any particular sequence of importance, and they can be used in conjunction with one another.

In North America, current procedures include controlling the alkali content of the concrete or using a supplemental cementitious ingredient or blended cement shown by testing to control ASR. Fly ash, powdered granulated blast-furnace slag, silica fume, and natural pozzolans are examples of supplementary cementitious materials. Slag, fly ash, silica fume, and natural pozzolans are used in blended cements to control ASR.

The use of low-alkali portland cement (ASTM C 150) with an alkali concentration of less than 0.60 percent (equivalent sodium oxide) has been successful in the control of ASR in aggregates that are marginally reactive to moderately reactive. Low-alkali cements, however, are not accessible everywhere. For controlling ASR, it is preferable to use locally accessible cements in combination with pozzolans, slags, or mixed cements. When pozzolans, slags, or mixed cements are used to control ASR, tests like ASTM C 1260 (modified) or C 1293 must be employed to determine their effectiveness.

Reduction of alkali-silica reaction using pozzolans — **Figure 2**: Influence of different amounts of fly ash, slag, and silica fume by mass of cementing material on mortar bar expansion (ASTM C 1260) after 14 days when using reactive aggregate

Different amounts of pozzolan or slag should be tested to establish the best dosage, if applicable. As the dosage of pozzolan or slag is increased, expansion normally decreases (see Figure 2). ASR can also be controlled with lithium-based admixtures. Limestone sweetening (changing around 30% of the reactive sand-gravel aggregate with crushed limestone) is useful in preventing concrete deterioration in various sand-gravel aggregate concretes.

Design of Industrial Ground Floor Slabs

By

Ubani Obinna

-

March 8, 2023

Table of Contents

The slab-on-grade, which includes industrial ground floors, can be defined as a slab continuously supported by ground with an area of more than twice the area required to support the imposed loads. The primary design objectives in industrial ground floor slabs are to carry the intended loads and to avoid surface cracking.

The slab may be plain or reinforced and may include stiffening elements such as ribs and hidden beams. The reinforcement may be provided for structural purposes or for the control of the effects of shrinkage and temperature changes.

Industrial ground floor slabs are essential components of industrial buildings and warehouses. In order for manufacturing equipment and forklifts to function properly, the slab must be uniformly flat and joints must be relatively level without excessive movements. The growth of the industry has necessitated the use of larger and heavier machinery and storage facilities.

In addition, the evolution of construction practices, such as the trend toward larger floor slabs with fewer joints, the use of high early-strength cement, and the increase in the use of admixtures, have all contributed to the rise in the cracking and curling of these slabs.

The typical layers in an industrial ground floor slab is shown in Figure 1;

Elements of concrete industrial floor and pavement — **Figure 1:** Typical layers in an industrial ground floor slab

The manner in which uniform loads are stacked in warehouses causes some cracking in the aisles between loaded areas. The predominant types of cracking in aisles fall into two categories. The first type is longitudinal, while the second is transverse. Transverse cracking is directly attributable to shrinkage, whereas longitudinal cracking is caused by the way external loads are stacked in warehouses.

In warehouses, heavy uniform loads are typically distributed over a portion of the slab, typically around the columns, leaving clear aisles in the middle of these columns.

The requirements for concrete industrial ground floors include the following:

The floor should remain serviceable, assuming planned maintenance and no gross misuse or overloading.
The floor must be able to carry the required static point loads, uniformly distributed loads and dynamic loads, without unacceptable deflection, cracking, settlement or damage to joints.
Joint layouts should take into account the location of racking uprights or mezzanine floor columns.
Joints should be robust in both design and construction.
Joints and reinforcement should be detailed to minimise the risk of cracking.
The floor surface should have suitable surface regularity.
The floor surface should have suitable abrasion, chemical and slip resistance.
The floor should have the required type of finish.

finishes on an indutrial ground floor — **Figure 2:** Surface finishing of industrial ground floor slab

Warehouse Equipment and Floor Loading

Point loads from pallet racking, accompanying materials handling equipment (MHE), and mezzanines are frequent loads on warehouse floors. Other loads come from uniformly distributed loads (UDL) like palletized products or bulk loose materials, as well as line loads like interior walls and floor railing systems.

Typical loading on industrial ground floors — **Figure 3:** Typical loads on the floor of a warehouse

In the design of industrial ground floors, point loads are usually the most critical for design, and reliance should not be placed solely on the commonly specified uniformly distributed loads (UDLs). In all cases, the design must be based on anticipated loads from all types of equipment and other loads, and the specifier must account for the floor’s potential future uses.

It is reasonable to anticipate that taller structures will be able to support greater loads, such as those imposed by pallet racking. Point loads from pallet racking and mezzanines are treated as static loads, whereas mobile heavy equipment (MHE) is treated as a dynamic load that requires greater design safety factors.

racking in a warehouse — **Figure 4:** Back to back arrangement of a storage rack in a warehouse

Design of Industrial Ground Floor Slab

For the commonly encountered point loads on industrial ground floor slabs from storage shelving, mezzanines, and materials handling equipment (MHE), there are two possible modes of ultimate strength failure:

flexure, and
punching

The design of slabs for flexure under point loads at the ultimate limit state (ULS) is based on yield line theory, which necessitates sufficient plasticity to assume plastic behaviour. Clearly, sufficient rotation capacity of the sagging yield lines is required in order to mobilise the hogging moment capacity.

At the ULS, it is assumed that the bending moment along the sagging (positive moment) yield lines is the full plastic (or residual post-cracking) value. As the avoidance of cracks on the upper surface is a primary requirement for serviceability, the bending moment of the slab along the hogging yield lines is limited to the design cracking moment of the concrete, albeit with the partial safety factor appropriate to the ULS.

According to TR34, this is not a true ULS because the floor will not have collapsed, and the design process is meeting a serviceability requirement instead. Therefore, there are no separate checks for design serviceability. The design of the slab against punching shear around concentrated loads is based on Eurocode 2 for suspended slabs. It is taken into account that a portion of the load will be transferred through the slab to the ground.

Line loads and uniformly distributed loads are evaluated using an elastic analysis based on Hetenyi’s Beams on Elastic Foundation. The minimum recommended slab thickness for a ground-supported slab is 150 millimetres.

The designer must account for the thickness reduction caused by mat wells, induction loops, guide wires, and other features. There are practical limitations on how much concrete can be poured in one day, so most floors have joints. In most instances, the critical loading condition is a point load close to a slab panel joint.

In all designs, the load-bearing capacity of the floor alongside joints must be evaluated. This capacity will depend heavily on the joint mechanism’s ability to transfer load to the opposite side of the joint. This is especially true for MHE, which cannot be positioned away from joints, unlike static loads.

Worked Examples

Quadruple Internal Point Loads

Verify the capacity of a 200mm thick concrete industrial ground floor slab subjected to a quadruple internal 300 x 300 point load in accordance with TR34, 4th Edition 2013;

Permanent load; G_k = 45.0 kN
Variable load; Q_k = 20.0 kN
Dynamic load; D_k = 30.0 kN

Slab details
Reinforcement type; Fabric
Concrete class; C25/30
Slab thickness; h = 200 mm
Fabric reinforcement type; A393
Characteristic strength of reinforcement; f_yk = 500 N/mm²
Area of top steel provided; A_s,prov = 393 mm²/m
Diameter of reinforcement; f_s = 10 mm
Nominal cover; c_{nom_b} = 50 mm
Effective depth of reinforcement; d = 0.75h = 150 mm

Partial safety factors
Concrete (with or without fibre); γ_c = 1.50
Reinforcement (bar or fabric); γ_s = 1.15
Permanent; γ_G = 1.20
Variable; γ_Q = 1.50
Dynamic loads; γ_D = 1.60

Subgrade reaction
Modulus of subgrade reaction; k = 0.030 N/mm³

Properties of Concrete
Characteristic compressive cylinder strength; f_ck = 25 N/mm²
Characteristic compressive cube strength; f_cu = 30 N/mm²
Mean value of compressive cylinder strength; f_cm = f_ck + 8 N/mm² = 33 N/mm²
Mean value of axial tensile strength; f_ctm = 0.3 N/mm² × (f_ck)^2/3 = 2.6 N/mm²
Flexural tensile strength; f_ctd,fl = f_ctm × (1.6 – h /1000) / γ_c = 2.4 N/mm²
Design concrete compressive strength (cylinder); f_cd = f_ck / γ_c = 16.7 N/mm²
Secant modulus of elasticity of concrete; E_cm = 22 kN/mm² × [f_cm/10 ]^0.3 = 31 kN/mm²
Poisons ratio; v = 0.2

Radius of relative stiffness (Eqn. 20); l = [E_cmh³ / (12(1 – v²) × k)]^0.25 = 924 mm
Characteristic of system (Eqn. 33); l = (3k / (E_cmh³))^0.25 = 0.773 m^-1

Moment capacity
Negative moment capacity (Eqn. 2); M_n = M_un = f_ctd,fl× (h²/6) = 16.0 kNm/m
Positive moment capacity (Eqn. 2); M_p = M_un = 16.0 kNm/m

Loading – Quadruple internal 300 x 300 point load
Loading length; l_l = 300mm
Loading width; l_w = 300mm
Distance x; x = 1000mm
Distance y; y = 1000mm
Permanent load; G_k = 45.0 kN
Variable load; Q_k = 20.0 kN
Dynamic load; D_k = 30.0 kN

Contact radius ratio
Equivalent contact radius ratio; a = [(l_l × l_w) / π]^0.5 = 169.3 mm
Radius ratio; a/l = 0.183

Ultimate capacity under single internal concentrated loads
For a/l equal to 0 (Eqn. 21); P_{u_0} = 2π(M_p + M_n) = 200.6 kN
For a/l equal to 0.2 (Eqn. 22); P_{u_0.2} = 4π(M_p + M_n) / [1 – (a / (3 × l))] = 427.2 kN
Thus for a / l equal to 0.183; P_u = min(P_{u_0.2}, P_{u_0} + (P_{u_0.2} – P_{u_0}) × (a / (l × 0.2))) = 408.2 kN
4 No. individual; P_{u_4x1} = 4P_u = 1632.6 kN

Ultimate capacity under dual internal concentrated loads
For a/l equal to 0 (Eqn. 27); P_{u_0} = [2π + (1.8 × min(x, y) / l)] × [M_p + M_n] = 262.7 kN
For a/l equal to 0.2 (Eqn. 28);P_{u_0.2} = [4π / (1 – (a / (3 × l))) + 1.8 × min(x, y) / (l – (a/2))] × [M_p + M_n] = 495.7 kN
Thus for a / l equal to 0.183; P_u = min(P_{u_0.2}, P_{u_0} + (P_{u_0.2} – P_{u_0}) × (a / (l × 0.2))) = 476.1 kN
2 No. dual; P_{u_2x2} = 2 × P_u = 952.2 kN

Ultimate capacity under quadruple internal concentrated loads
For a/l equal to 0 (Eqn. 29); P_{u_0} = [2π + 1.8 × (x + y) / l] × [M_p + M_n] = 324.9 kN
For a/l equal to 0.2 (Eqn. 30); P_{u_0.2} = [4π / (1 – (a / (3 × l))) + 1.8(x + y) / (l – (a / 2))] × [M_p + M_n] = 564.1 kN
Thus for a / l equal to 0.183; P_u = min(P_{u_0.2}, P_{u_0} + (P_{u_0.2} – P_{u_0}) × (a / (l × 0.2))) = 544.0 kN
quadruple;P_{u_1x4} = P_u = 544.0 kN
Ultimate load capacity for 4 No. loads; P_u = min(P_{u_4x1}, P_{u_2x2}, P_{u_1x4}) = 544.0 kN

Check ultimate load capacity of slab
Number of loads; N = 4
Loading applied to slab; F_uls = N × [(G_kγ_G) + (Q_kγ_Q) + (D_kγ_D)] = 528.0 kN
Utilisation; F_uls / P_u = 0.971
PASS – Total slab capacity exceeds applied load

Punching shear at the face of the loaded area
Shear factor; k₂ = 0.6(1 – f_ck / 250 N/mm²) = 0.54
Length of perimeter at face of loaded area; u₀ = 8 (l_l + l_w) = 4800 mm
Shear stress at face of contact area; v_max = 0.5k₂f_cd = 4.500 N/mm²
Maximum load capacity in punching; P_p,max = v_max × u₀ × d = 3240.0 kN
Utilisation; F_uls / P_p,max = 0.163
PASS – Total slab capacity in punching at face of loaded area exceeds applied load

Punching shear at the critical perimeter
Shear factor; k_s = min(1 + (200mm / d)^0.5, 2) = 2.00
Minimum shear stress at 2d from face of load; v_Rd,c,min = 0.035k_s^3/2 × (f_ck)^0.5 = 0.495 N/mm²
Ratio of reinforcement by area in x-direction; r_x = A_s,prov / d = 0.00262
Ratio of reinforcement by area in y-direction; r_y = A_s,prov / d = 0.00262
Reinforcement ratio; r₁ = (r_x × r_y)^0.5 = 0.00262

Maximum shear stress at 2d from face of load; v_Rd,c = max(0.18 × k_s / γ_c × (100 × r₁ × f_ck )^1/3, v_Rd,c,min) = 0.495 N/mm²
Length of perimeter at 2d from face of load; u₁ = 2 × (l_w + y + l_l + x + 2π × d) = 7085 mm
Max. load capacity in punching at 2d from face; P_p = v_Rd,c × u₁ × d = 526.0 kN
Ground reaction (cl.7.10.2); R_p = 1.4 × (d / l)² × F_uls + 0.47 × (l_l + x + l_w + y) × d × F_uls / l² = 132.9 kN
Total imposed shear load; F_{uls_total} = F_uls – R_p = 395.1 kN
Utilisation; F_{uls_total} / P_p = 0.751
PASS – Total slab capacity in punching at 2d from face of loaded area exceeds applied load

Design Summary

Description	Unit	Provided	Required	Utilisation	Result
Slab capacity in flexure	kN	544.0	528.0	0.971	PASS
Shear at face	kN	3240.0	528.0	0.163	PASS
Shear at 2d	kN	526.0	395.1	0.751	PASS

Uniformly Distributed Load

Verify the capacity of a 150mm thick concrete industrial ground floor slab to support a uniformly distributed load of 45 kN/m² in accordance with TR34, 4th Edition 2013;

Slab details
Reinforcement type; Fabric
Concrete class; C25/30
Slab thickness; h = 150 mm
Fabric reinforcement type; A252
Characteristic strength of reinforcement; f_yk = 500 N/mm²
Area of top steel provided; A_s,prov = 252 mm²/m
Diameter of reinforcement; f_s = 8 mm
Nominal cover; c_{nom_b} = 50 mm
Effective depth of reinforcement; d = 0.75 × h = 112 mm

Partial safety factors
Concrete (with or without fibre); γ_c = 1.50
Reinforcement (bar or fabric); γ_s = 1.15
Permanent; γ_G = 1.20
Variable; γ_Q = 1.50
Dynamic loads; γ_D = 1.60

Subgrade reaction
Modulus of subgrade reaction; k = 0.030 N/mm³

Strength properties for concrete
Characteristic compressive cylinder strength; f_ck = 25 N/mm²
Characteristic compressive cube strength; f_cu = 30 N/mm²
Mean value of compressive cylinder strength; f_cm = f_ck + 8 N/mm² = 33 N/mm²
Mean value of axial tensile strength; f_ctm = 0.3 N/mm² × (f_ck)^2/3 = 2.6 N/mm²
Flexural tensile strength; f_ctd,fl = f_ctm × (1.6 – h / 1000) / γ_c = 2.5 N/mm²
Design concrete compressive strength (cylinder); f_cd = f_ck / γ_c = 16.7 N/mm²
Secant modulus of elasticity of concrete; E_cm = 22 kN/mm² × [f_cm/ 10 ]^0.3 = 31 kN/mm²
Poisons ratio; v = 0.2
Radius of relative stiffness (Eqn. 20); l = [E_cm × h³ / (12 × (1 – n²) × k)]^0.25 = 745 mm
Characteristic of system (Eqn. 33); l = (3 × k / (E_cm × h³))^0.25 = 0.959 m^-1

Moment capacity
Negative moment capacity (Eqn. 2); M_n = M_un = f_ctd,fl × (h² / 6) = 9.3 kNm/m
Positive moment capacity (Eqn. 2); M_p = M_un = 9.3 kNm/m

Load 1 – UDL 45 kN/m²

Working load capacity of UDL
UDL; U_k = 45.0 kN/m²
Critical aisle width; l_crit = π / (2 × l) = 1637 mm
Loaded width of single UDL (max positive moment); l_{load_p} = π / (2 × l) = 1637 mm
Loaded width of dual UDL (max nagative moment); l_{load_n} = π / l = 3275 mm
Working load capacity of slab; q = 5.95 × l² × M_n = 50.9 kN/m²
Utilisation; U_k / q = 0.884
PASS – Total slab capacity exceeds applied load

Design Summary

Description	Unit	Provided	Required	Utilisation	Result
Slab capacity in flexure	kN/m²	50.9	45.0	0.884	PASS

Joints in Concrete Pavements and Industrial Floors

By

Ubani Obinna

-

May 15, 2022

Table of Contents

Except where they join other structures, concrete pavements and industrial floors should ideally be free of joints. However, joints in concrete pavements are usually provided for a variety of reasons, including construction considerations, reducing the possibility of unanticipated shrinkage cracking, and avoiding conflict with adjacent structures and/or penetrations. The number of joints in concrete pavements should be kept to a minimum because they not only affect the evenness of the pavement in most cases, but they are also the most prone to wear and require repairs.

The type of joint, joint configuration, sealant required, and quantity of reinforcement employed in the pavement panels are all interconnected. For example, increasing the amount of reinforcement allows for wider joint spacing, but it also means that the joints will move more, increasing the possibility of random cracking inside the pavement panels.

Load Transfer Across Joints in Concrete Pavements

Load transfer mechanisms like dowels can be utilized to transfer loads across a joint to adjacent pavement panels, resulting in lower flexural stresses in the panel than at free edges with no effective load transfer. They also prevent stepping by preventing differential vertical movements of adjacent concrete floor panels.

Aggregate interlock over the rough crack faces, keyed joints, dowels, or a combination of these can enable load transfer in contraction joints. If the opening is greater than 0.9 mm, as is common when panel lengths exceed 3 m, load transfer by aggregate interlock or keyways may become ineffective, and either an effective load-transfer device for these situations should be installed, or the base thickness for a free-edge condition should be determined.

According to ACI 302.1, the base thickness of dowels should be at least 125 mm to be fully functional. It also suggests using dowels for load transfer across joints, because regulating the differential vertical movement across joints can help prevent slab edge damage from vehicles with harsh wheels, such as forklifts.

Types of Joints in Concrete Pavements

Pavement construction uses four different types of joints:

Isolation Joints
Expansion joints
Contraction Joints
Construction joints

Isolation Joints

These joints allow for horizontal and vertical movement as well as rotation between abutting pieces, allowing them to function independently. They should be installed between a pavement panel and the building’s fixed components (such as columns, walls, machinery bases, pits, etc).

To avoid the buildup of stresses due to differential movements, isolation joints should be provided at the junction when an existing pavement is being extended, as well as at connections between internal and external pavements. Typically, load transmission between the existing pavement and the pavement extension will be required in the design.

Typical joints in concrete pavements — **Figure 1:** Typical isolation joints (CCAA, 2009)

To ensure a complete separation, isolation joints in concrete pavements are often formed by casting against a compressible, prepared filler material (e.g., self-expanding cork) over the full depth of the joint. If loads are predicted to occur close to an isolation joint, the base edges adjacent to these joints may need to be thickened due to the edge loading condition. Figure 1 shows the typical characteristics of this type of joint. Note that the sealant should be applied to both the top and free edges of the joint to keep dirt and other incompressible materials out of the joint, preventing or restricting movement.

Expansion Joints

Pavements feature expansion joints to allow for temperature and moisture-induced movement of the base. These joints may, however, be required in places with significant temperature changes. Figure 2 shows the typical details of this type of joint. Note that the sealant should be applied to both the top and free edges of the joint to keep dirt and other incompressible materials out of the joint, preventing or restricting movement.

**Figure 2:** Typical expansion joint (CCAA, 2009)

Internal floors do not require expansion joints because they do not experience severe temperature variations. Internally, the expansion due to heat movement is usually less than the concrete’s initial shrinkage. Even the thermal movement of a cold-store floor will not be greater than the floor’s original shrinkage. In interior applications, AS 3600 recommends design shrinkage values of 670 x 10^–6 for 200-mm-thick slabs and 450 x 10^–6 for 400-mm-thick slabs.

According to TR 35, the overall shrinkage coefficient for pavements is around 300 x 10^–6. With a coefficient of thermal expansion of 10 x 10^–6/°C, an expansion equal to the drying shrinkage would require a temperature of around 30°C above the putting temperature. As a result of the lack of thermal ranges in industrial floors, expansion joints are not necessary.

Furthermore, if drying shrinkage is ignored and the restraint to slab lengthening due to temperature rise and/or moisture increase is ignored, the maximum compressive strain in the concrete will be 300 x 10^–6 for a temperature rise of 30°C above the placing temperature (and the slab moisture content returns to saturation), assuming no expansion joints are provided. Assuming f’_c = 40 MPa, E_c is 31975 MPa, while the compressive stress is 9.6 MPa. The absence of expansion joints in industrial floors is supported by this minimal compressive stress development.

Designers should determine whether expansion joints are necessary inside before specifying their use, as the required joint width will necessitate additional considerations.

To reduce forklift vehicle wear and accompanying high maintenance costs, treatment (armouring of joint edges) is used. Expansion joints in concrete pavements also necessitate the use of load transfer devices, such as dowels, bars, or plates, due to the separation of adjacent panels. Whenever expansion joints are not provided, alternative joints within the pavement should be sealed to avoid the intrusion of incompressible material, which could limit subsequent floor expansion.

Contraction Joints

The random drying shrinkage cracking of concrete is controlled by contraction or control joints, which cause the base to crack exclusively at the joint positions. They allow the base to move horizontally at right angles to the joint, relieving pressures that could otherwise induce random cracking. A plane of weakness is generated by shaping (with crack-inducing tapes or formers) or cutting a groove to a depth of one-quarter to one-third of the base thickness to ensure that shrinkage cracking develops at a contraction joint. Figure 3 shows the typical details.

key joint pressesed metal — **Figure 3:** Typical contraction joints – with or without reinforcement (CCAA, 2009)

However, if the groove is created early enough using an appropriate grooving tool or early-age saw cutting, the groove depth can be reduced in concrete slabs that are either plain or reinforced (mesh).

The spacing of contraction joints in jointed unreinforced pavements should be chosen to suit the shape of the pavement while ensuring that load transfer by aggregate interlock is not compromised. If this is the case, load transfer must be accomplished through other means, or the base thickness should be built as a free edge.

Contraction joints are commonly made by cutting a groove in the top of freshly laid concrete (Formed Joint) or by sawing the concrete after it has set but before it cracks uncontrollably (Sawn Joint).

Formed Joints

Forming a groove with a T-section and edge tools or inserting a prepared crack inducer into the surface while the concrete is still plastic can be used to produce formed joints. After the pavement has been completed, a sealer can be put in the contraction joints by applying an appropriate sealant reservoir and bond-breaking backing tape. The reinforcement in reinforced pavements must not obstruct the created joint. Figure 4 shows how the reinforcement could be terminated short of the joint.

joints okay — **Figure 4:** Typical transverse construction joints (CCAA, 2009)

Sawn Joints

Sawn joints are constructed just after the concrete has hardened enough that the sawing will not damage it but before shrinkage cracking develops (see Figure 5). The best time to saw depends on a variety of factors that influence concrete hardening, such as concrete strength and ambient temperature. The depth of the initial saw cut should be 3 to 5 mm. The joint can be enlarged later if necessary for the installation of a joint sealer.

Saw cut in construction joint — **Figure 5**: Sawn joint in contraction joint

When using dowels, it is important to ensure that they don’t get in the way of the joint’s opening or closing; otherwise, an uncontrolled crack could form in the joint’s surroundings. Round or square dowels cut on both ends, for example, should not be utilized because the end deformation may interfere with the joint opening or closing. Dowels should be coated with a suitable bond breaker on one side of the joint and aligned to within close tolerances parallel to the longitudinal direction of the panel and the surface of the base.

Diamond-shaped load plates can be used to replace dowels and allow the slab to travel horizontally without restraint; they also allow some differential movement in the joint’s direction, especially when shrinkage opens the joint. They can be placed within 150 mm spacings, whereas dowels should be kept at a distance of 300 mm. It is worth noting that dowels near crossings need to have expansion material on the vertical sides to allow the slab to move both parallel and perpendicular to the connection. Square dowels will almost always be required for this.

Individual panels in jointed reinforced pavements are usually joined by construction, expansion, or isolation joints, rather than contraction joints. Joint spacing should be limited to roughly 15 m for these pavements so that joint movement does not become excessive and joint sealing remains effective.

Construction Joints

Longitudinal construction joints separate portions of concrete poured at different times and form the borders of each pour. Transverse construction joints are necessary at predetermined points, such as the end of each day’s work, and at unanticipated pauses, such as those induced by bad weather or equipment breakdowns.

Simple keyed joints will frequently suffice for longitudinal construction joints if the pavement is lightly loaded, not more than 150 mm thick, and built over a strong, unyielding subgrade that is not subject to volume variations, or over a bound subbase or stabilised subgrade. Longitudinal construction joints should be provided with some type of load-transfer mechanism, such as dowels or diamond load plates, if the pavement is thicker or more heavily loaded. Figure 6 shows typical details of this sort of joint.

A keyed joint will not perform well as a load transfer device if it opens up more than 1 mm. When employing this type of joint for load transfer, it’s important to keep the joint opening to a minimum. Deformed tie bars can be used to hold keyed longitudinal joints together.

However, unless dowelled longitudinal contraction joints are additionally provided at a spacing not exceeding 15 m, such tie bars should not be utilized in panels having a total width of more than 15 m. Tie bars should be 800-mm length N12 bars with a spacing of 800 mm or 650000/DS_jmm, whichever is lesser. Where D is the base thickness in millimeters and S_j is the joint spacing in millimeters (mm).

In reinforced pavement construction, using split or slotted formwork to ensure continuity of reinforcement across the junction can provide positive control against vertical movement at the joints. However, creating and removing the formwork presents construction challenges. The reinforcement must be planned for the entire length of the pavement, not just the panel length. In jointed unreinforced pavements, transverse construction joints should be placed where a planned contraction joint would be. Unplanned construction joints should be placed in the panel’s middle third. Figure 6 shows some typical details.

A dowelled butt joint, which allows horizontal movement and performs all of the duties of a contraction joint, is recommended when a transverse construction junction is intended to coincide with the place where a contraction joint would ordinarily occur Figure 1.5. Planned construction joints are often built at regular contraction joint sites in jointed reinforced pavements. Because there is no aggregate interlock to enable weight transfer, butt joints with dowels (perhaps also with expansion material) are recommended. The dimensions, spacing, and debonding of the dowels are the same as for a transverse contraction joint.

A transverse construction joint is made in continuously reinforced pavements by putting a special header board that allows reinforcing steel to pass through. Prior to resuming concrete placement, the header is removed. Both slotted and split header boards are utilized, but the slotted form is preferred since it can be removed with the least amount of disruption to the already cast concrete.

References
Cement Concrete & Aggregates Australia (2009): Guide to Industrial Floors and Pavements – design, construction and specification CCAA T48

Some Harmful Materials in Aggregates for Concrete

By

Ubani Obinna

-

May 15, 2022

Table of Contents

Potentially harmful materials in aggregates for concrete are substances that react chemically with Portland cement concrete to produce one or more of the following:

(1) Significant volume change in the cement paste, aggregate, or both;
(2) interfering with cement’s regular hydration; and
(3) producing additional potentially hazardous byproducts

Organic impurities, silt, clay, shale, iron oxide, coal, lignite, and some lightweight and soft particles are all harmful materials in aggregates, that can affect the performance of the concrete in the fresh and/or hardened state (see Table 1). Alkali-reactive rocks and minerals include certain cherts, strained quartz, and some dolomitic limestones. Furthermore, sulfate attacks on concrete can be caused by gypsum and anhydrite. Popouts can be caused by swelling (absorption of water) or freezing of absorbed water in some aggregates, such as certain shales.

Table 1: Some harmful materials in aggregates for concrete

Substances	Effect on Concrete
Organic impurities	Affects setting and hardening, may cause deterioration
Materials finer than the 75-μm (No. 200) sieve	Affects bond, ASTM C 117 (AASHTO T 11) increases water requirement
Coal, lignite, or other lightweight materials	Affects durability, and may cause stains and popouts
Soft particles	Affects durability
Clay lumps and friable particles	Affects workability and durability, and may cause popouts
Cherts of less than 2.40 relative density	Affects durability, and may cause popouts
Alkali-reactive aggregates	Causes abnormal expansion, map cracking, and popouts

Most standards usually provide the maximum allowed levels of these harmful materials in aggregates. When defining limitations for dangerous compounds, the performance history of an aggregate should be a deciding factor.

coarse aggregates — Coarse aggregates in concrete

Organic Impurities

Organic impurities can cause concrete to take longer to set and harden, diminish strength increase, and, in rare situations, cause degradation. Organic impurities like peat, humus, and organic loam are less harmful, but they should still be avoided.

Fine Materials (Clay and Silt)

Very fine materials, such as silt and clay, may be present as loose dust and form a coating on aggregate particles finer than the 75μm (No. 200) sieve. Even tiny silt or clay coatings on gravel particles might be hazardous because they can damage the cement paste-aggregate bond. Water requirements may be greatly increased if certain types of silt or clay are present in excessive levels.

The grinding motion in a concrete mixer causes some fine aggregates to degrade; this effect, which is assessed using ASTM C 1137, can affect mixing water, entrained air, and slump requirements.

Low-density Materials (coal, lignite, wood, or fibrous materials)

Excessive volumes of coal or lignite, as well as other low-density components like wood or fibrous materials in concrete, will compromise the durability of concrete. These contaminants may dissolve, pop out, or generate stains if they exist near the surface. The ASTM C 123 standard can be used to identify potentially dangerous chert in coarse aggregate (AASHTO T 113).

Popout is an effect of harmful materials in aggregates — Popout in concrete

Soft, friable particles

Soft particles in coarse aggregates are particularly problematic because they produce popouts and can compromise concrete’s durability and wear resistance. If they are friable, they may break up when mixing, increasing the amount of water requirement. Testing may show that more inquiry or a different aggregate source is required where abrasion resistance is crucial, such as in heavy-duty industrial floors.

Clay Lumps

Clay lumps in concrete can absorb some of the mixing water, causing popouts in hardened concrete and reducing the durability and wear resistance of the concrete. They can also break up while mixing, increasing the amount of mixing water required.

Iron oxide and iron sulfide particles

Iron oxide and iron sulfide particles can occasionally be found in aggregates, causing unattractive stains on exposed concrete surfaces (see image below). When tested according to ASTM C 641, the aggregate should meet the staining standards of ASTM C 330 (AASHTO M 195); the quarry face and aggregate stockpiles should not exhibit evidence of staining.

iron stains on concrete — Iron stains on concrete

The aggregate can also be submerged in a lime slurry to help detect stained particles. If staining particles are present, a blue-green gelatinous precipitate will form within 5 to 10 minutes; when exposed to air and light, it will quickly turn brown. Within 30 minutes, the reaction should be completed. When a suspicious aggregate is placed in lime slurry and no brown gelatinous precipitate forms, there is little chance of a reaction occurring in concrete. When aggregates with no prior successful use in architectural concrete are utilized, certain tests should be required.

Buckling of Thin Plates

By

Ubani Obinna

-

November 27, 2022

Buckling of thin plates occurs when a plate moves out of plane under compressive load, causing it to bend in two directions. The buckling behaviour of thin plates is significantly different from the buckling behaviour of columns. Buckling in a column terminates the member’s ability to resist axial force, and as a result, the critical load is the member’s failure load. The same cannot be said for the buckling of thin plates due to the membrane action of the plate.

Plates under compression will continue to resist increasing axial force after achieving the critical load, and will not fail until a load far greater than the critical load is attained. As a result, a plate’s elastic critical load is not the same as its failure load. Instead, the load-carrying capability of a plate must be determined by examining its post-buckling behaviour.

A governing equation in terms of biaxial compressive forces N_x and N_y and constant shear force N_xy, as shown in Figure 1, can be developed to estimate the critical in-plane loading of a plate using the idea of neutral equilibrium.

D[δ⁴w/δx⁴ + 2(δ⁴w)/(δx²δy²) + δ⁴w)/δy⁴] + N_x(δ²w/δx²) + N_y(δ²w/δy²) + 2N_xy(δ⁴w/δxδy) = 0 ——— (1)

All the stress components are expressed in terms of the deflection w of the plate (where w is a function of the two coordinates (x, y) in the plane of the plate). D = Eh³/12(1 – v²) is the flexural rigidity of the plate per unit length; E is the modulus of elasticity; h is the thickness of the plate, and v is Poisson’s ratio.

The critical load for uniaxial compression can be determined from the differential equation:

D[δ⁴w/δx⁴ + 2(δ⁴w)/(δx²δy²) + δ⁴w)/δy⁴] + N_x(δ²w/δx²) = 0 ——— (2)

which is obtained by setting N_y = N_xy = 0 in equation (1). For example, in the case of a simply supported plate, equation (1) can be solved to give:

N_x = π²a²D/m² (m²/a² + n²/b²)² ——— (3)

Taking n equal to 1 yields the critical value of N_x (i.e. the smallest value). This means that a plate buckles in such a way that there are several half-waves in the compression direction but only one half-wave in the perpendicular direction. As a result, the formula for the compressive force’s critical value becomes:

N_x(crit) = π²D/a² [m + 1/m(a²/b²)]² ——— (4)

The Euler load for a strip of unit width and length a is represented by the first factor in this expression. The second factor denotes the proportion of greater stability gained by the continuous plate compared with that of an isolated strip. The amount of this factor is determined by the magnitude of the a/b ratio as well as the number m, which indicates how many half-waves the plate buckles into. If a is less than b, the second term in the parenthesis of equation (4) is always less than the first, and the expression’s minimum value is reached by assuming m = 1, i.e. that the plate buckles in one half-wave. N_x critical value can be written as follows:

N_cr = kπ²D/b² ——— (5)

The factor k depends on the aspect ratio a/b of the plate and m, the number of half-waves into which the plate buckles in the x-direction. The variation of k with a/b for different values of m can be plotted as shown in Figure 2. The critical value of N_x is the smallest value that is obtained for m = 1 and the corresponding value of k is equal to 4.0. This formula is analogous to Euler’s formula for buckling of a column.

plot — **Figure 2**: Buckling stress coefficients for uniaxially compressed plate (Shanmugam and Narayanan, 2008)

In the more general case in which normal forces N_x and N_y and the shearing forces N_xy are acting on the boundary of the plate, the same general method can be used. The critical stress for the case of a uniaxially compressed simply supported plate can be written as:

σ = 4π²E/[12(1 – v²)] × (h/b)² ——— (6)

The critical stress values for different loading and support conditions can be expressed in the form:

f_cr = kπ²E/[12(1 – v²)] × (h/b)² ——— (8)

in which f_cris the critical value of different loading cases. Values of k for plates with different boundary and loading conditions are given in Figure 3.

Table — **Figure 3:** Values of k for plates with different boundary and loading conditions (Shanmugam and Narayanan, 2008)

Buckling of Thin Plates in Staad Pro

plate buckling — **Figure 4:** Model example of buckling analysis of thin plate

plate model — **Figure 5:** Buckling analysis of thin plate on Staad Pro

           CALCULATED BUCKLING FACTORS FOR LOAD CASE       1

   MODE               BUCKLING FACTOR

     1                   2957.15142
     2                   3056.42462
     3                  -3102.59328
     4                  -3107.05926

References
Shanmugam N. E. and Narayanan R. (2008): Structural Analysis. In ICE Manual of Bridge Engineering. doi: 10.1680/mobe.34525.0049

Flownet Sketching

Criteria for Sketching Flownets

Flownet for Isotropic Soils

Flow Rate

Worked Example on Buoyancy Raft Foundation

Challenges in the Construction of Buoyancy Rafts

Design of Buoyancy Rafts

Performance Criteria of Expansion Joints in Bridges

Types of Expansion Joints in Bridges

Buried Expansion Joint

Asphaltic Plug Expansion Joint

Nosing Expansion Joint

Reinforced Elastomeric Expansion Joint

Elastomeric in Metal Runners Expansion Joint

Cantilever Comb or Tooth Expansion Joint

Design of Expansion Joints in Bridges

Drainage of Expansion Joints

Detailing of Expansion Joints

Installation and maintenance

Requirements for thickness

Cost of Laying Blocks in Nigeria (For Bill of Quantity)

Alkali-Silica Reaction (ASR)

Mechanism of Alkali-Silica Reaction

Factors Affecting Alkali-Silica Reaction

Identification Test Methods for Distress due to ASR

Control of Alkali-Silica Reaction in New Concrete

Identification of Potentially Reactive Aggregates

Materials and Methods to Control Alkali-Silica Reaction

Warehouse Equipment and Floor Loading

Design of Industrial Ground Floor Slab

Worked Examples

Quadruple Internal Point Loads

Uniformly Distributed Load

Load Transfer Across Joints in Concrete Pavements

Types of Joints in Concrete Pavements

Isolation Joints

Expansion Joints

Contraction Joints

Formed Joints

Sawn Joints

Construction Joints

Organic Impurities

Fine Materials (Clay and Silt)

Low-density Materials (coal, lignite, wood, or fibrous materials)

Soft, friable particles

Clay Lumps

Iron oxide and iron sulfide particles

Buckling of Thin Plates in Staad Pro

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