How to Achieve Grade 25 Concrete on-Site

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April 12, 2024

The characteristic compressive strength of concrete to be used in construction is usually specified in the working drawings, design calculation sheets, and contract documents. The grade of concrete specified is used by bidders/contractors in pricing the job. Therefore, it is expected that it must be achieved on site.

There are different ways of achieving grade 25 concrete on site, and it vary based on each contractor’s experience. This guide is from a personal site experience. If there is no special requirement from the consultants, contractors are usually free to use any acceptable way to achieve the specified grade of concrete.

Normally, trial mixes should be done before the commencement of any project, but experienced contractors are already familiar with the mixes that they have done over and over again unless there is a new consideration to be made. The aim of this article is to show you how you can achieve grade 25 concrete based on site experience only without any technical calculations.

The applicability of this procedure is for low scale – low budget construction where there is no batching plant and sophisticated machines/equipment. If you follow this simple procedure, your concrete cubes for grade 25 concrete will exceed 17 MPa and 25 MPa after 7 and 28 days crushing tests respectively.

To get started, you will need to have the following available:

(1) Trustworthy supervisors
(2) Functional concrete mixer
(3) Functional concrete vibrator/poker
(4) Headpans, 25 litre buckets, and shovels
(5) All materials needed for concrete production – gravel, sand, cement (grade 42.5R), and water
(6) Concrete cube moulds

Concrete mixer 1 — **Fig 1**: Concrete mixer

concrete vibrator — **Fig 2**: Concrete vibrator/poker

Steps for Achieving Grade 25 Concrete On-site

Having gotten all materials ready, you can follow the steps outlined below:

(1) Recommended mix ratio
To achieve grade 25 concrete in local construction, I recommend a mix ratio of 1:2½:3½. What this means is that for 1 bag of cement, you add 5 headpans of sand, and 7 headpans of granite. The coarse aggregate that has been verified for this mix proportion is 3/4″ granite (19 mm size aggregate). The sand should be properly graded, and the cement should be sound with a strength grade of 42.5N or 42.5R.

Note: The popular 1:2:4 mix ratio sums up to 7 (that is 1 + 2 + 4 = 7), and the recommended 1:2½:3½ mix ratio also sums up to 7. It has been discovered on site that for 3/4″ granite in a 1:2:4 mix ratio, the quantity of granite usually appears excessive at about 0.4 – 0.6 water/cement ratio, thereby giving workmen difficulty in mixing, placing, and consolidating the concrete.

This leads to the addition of excess water which compromises the strength of the concrete. While this can be taken care of by the use of superplasticizer admixture, low-budget constructions do not normally factor admixtures into the cost. Therefore, by slightly adjusting the sand and gravel content from 2:4 to 2½:3½ respectively, a better workable mix is achieved without any serious consequences.

(2) Water Content
For the mix ratio described above, the quantity of water to be added must not exceed 25 litres. If it exceeds 25 litres, you have deviated from the provisions of this guide for obtaining grade 25 concrete. On-site, you can achieve this by pouring one bucket of water only into the concrete mixer bunker.

There might be grumblings about the workability of the mix from the workmen, but stick to the plan as it will not affect your finished work. If you have a very tight reinforcement arrangement that you need very workable concrete, you might reconsider using this guide. The bucket size recommended for this is the 25 litres empty paint bucket shown in Figure 3. If you get the mix ratio right and add excess water, the test result will fail.

Empty paint bucket — **Fig 3**: 25 Litres empty paint bucket

(3) Do not heap the headpans
The granite and the sand must not be heaped if you are to achieve grade 25 concrete using this guide. The sand and granite must be made to flush with the top surface of the headpan as shown in Figure 4. If the sand and granite are heaped you have deviated from the provisions of this guide.

Headpans must not be heaped to achieve grade 25 concrete on site — **Fig 4**: Unheaped headpan of sharp sand

(4) Supervision
To achieve steps 1, 2, and 3 above, you need strict supervision and monitoring. First of all, you need a supervisor at the loading points, who must ensure that the granite and sand are not heaped. It is good to have different monitors for sand and granite.

To achieve this, after filling each head pan with sand/gravel, it must be levelled using a shovel or piece of wood before being carried to the bunker. Secondly, you need another supervisor at the bunker to ensure that the correct quantity of sand, granite, and water is being poured in for one bag of cement.

Concrete pouring supervision — **Fig 5**: Supervision of concreting during local construction

(5) Placement and consolidation
The concrete produced from the mixture should be transported without delay to the required point where it is poured and consolidated using a vibrator/poker. The curing process should also begin as soon as it sets.

Concrete placement — **Fig 6**: Placement and Consolidation of concrete for a floor slab

(6) Collection of samples for testing
The 150mm x 150mm steel moulds to be used for sample collection should be oiled, and the concrete poured in three layers. Each layer should be subjected to 25 tampings using at least 16 mm diameter reinforcement off-cut. You can do well by hitting the sides of the mould during compaction to ensure proper consolidation.

After filling the moulds and compacting the concrete properly, the surface is leveled and finished smoothly with a trowel. Remove the sample from under the sun (especially in tropics), and cover it with a polyethylene nylon sheet. You can label the sample after about one hour.

Demould the sample the following morning and cure in a clean water tank for the required number of days. 6 or 9 samples might be required for each batch of concreting. However, consultants usually require 7 days and 28 days test results, and an average of 3 cubes should be crushed for each test. In some cases, 14 days’ results might be required.

Consolidation of concrete cube — **Figure 7**: Preparation of concrete cube samples

If you have followed these procedures properly, you should get satisfactory results from the laboratory for grade 25 concrete. However, note that this does not substitute for proper concrete mix design where it is required. Find below some laboratory test results from the procedure described above. The target characteristic strength after 28 days was 25 MPa. In one of the cases (Figures 10 and 11), regulatory agencies came by themselves and collected samples from the point of casting, and the result was found satisfactory.

14 days test result — **Fig 8**: 14 days compressive test result of a floor slab (Average 14 days strength = 23.48 MPa)

28 days result — **Fig 9**: 28 days test result of the same floor slab (Average 28 days strength = 26.93 MPa)

**Fig 10**: 7 days test result of a floor beam (Average 7 days strength = 18.46 MPa)

**Fig 11**: 28 days test result of the same floor beam (Average 28 days strength = 27.14 MPa)

Structural Design of Ribbed Slabs

By

Ubani Obinna

-

April 22, 2022

A ribbed slab is a type of reinforced concrete slab in which some of the volume of concrete in the tension zone is removed and replaced with hollow blocks or left as voids. This reduction in the volume of concrete in the tension zone (below the neutral axis) is based on the assumption that the tensile strength of concrete is zero, hence all the tensile stress is borne by the reinforcements in the tension zone. The resulting construction is considerably lighter than a solid cross-section.

This design and construction concept is useful in long-span construction of floors (say spans greater than 5m), where the self-weight becomes excessive when compared to the applied dead and imposed loads, thereby resulting in an uneconomic method of construction. One method of overcoming this problem is to use ribbed slabs which are suitable for longer spans supporting light loading, as in residential or commercial buildings.

Design Example
The layout of a floor slab is shown in Figure 1 below. Design the floor to satisfy ultimate and serviceability limit state requirements. (Concrete grade = 30 MPa, Yield strength of reinforcement = 500 MPa, variable action on floor = 2.5 kPa, Fire rating = 1 hour 30 minutes).

Ribbed slab layout 1 — Fig 1: Ribbed slab layout

Load Analysis
For 550 mm c/c rib spacing;

Permanent Actions
Weight of topping: 0.050 × 25 × 0.55 = 0.6875 kN/m
Weight of ribs: 0.15 × 0.2 × 25 = 0.75 kN/m
Weight of finishes: 1.2 × 0.55 = 0.66 kN/m
Partition allowance: 1.5 × 0.55 = 0.825 kN/m
Self weight of clay hollow pot = 0.65 kN/m
Total dead load g_k = 3.572 kN/m

Variables Action(s)
Variable action q_k= 2.5 kN/m²
Variable action on rib beam = 2.5 × 0.55 = 1.375 kN/m

At ultimate limit state; 1.35g_k + 1.5q_k = 1.35(3.572) + 1.5(1.375) = 6.8847 kN/m

Structural Analysis
Maximum span moment = M_Ed = ql²/8 = (6.9 × 5²)/ 8 = 21.56 kNm
Shear force at the support, V_Ed = ql/2 = (6.9 x 5)/2 = 17.25 kN

The span should be designed as a T-beam. Follow this link to learn how calculate the effective flange width of beams according to Eurocode 2. In this case the flange width is taken as the centre to centre spacing of the ribs.

Designing the span as a T-beam;
M_Ed = 21.56 kN.m

Effective depth (d) = h – C_nom – ϕ/2 – ϕ_links
Assuming ϕ12 mm bars will be employed for the main bars, and ϕ8 mm bars for the stirrups (links)
d = 250 – 25 – (12/2) -8 = 211 mm

k = M_Ed/(f_ckbd²) = (21.56 × 10⁶)/(30 × 550 × 211²) = 0.0293
Since k < 0.167, no compression reinforcement required

z = d[0.5+ √(0.25 – 0.882k)]
k = 0.0709
z = d{0.5+ √[0.25 – (0.882 × 0.0293)]} = 0.95d = 200.45 mm

Depth to neutral axis x = 2.5(d – z) = 2.5(211 – 200.45) = 26.375 mm < 1.25h_f (62.5 mm)

Therefore, we can design the rib as a rectangular section;

Area of tension reinforcement A_s1 = M_Ed/(0.87f_yk z)
A_s1 = M_Ed / (0.87f_yk z) = (21.56 × 10⁶) / (0.87 × 500 × 0.95 × 211) = 247.26 mm²

Provide 3H12 Bot (A_Sprov = 339 mm²)

Check for deflection
ρ = A_s,req/bd = 247.25 / (550 × 211) = 0.00213
ρ₀ = reference reinforcement ratio = 10^-3√(f_ck) = 10^-3√(30) = 0.00547
Since ρ ≤ ρ₀;
L/d = k [11 + 1.5√(f_ck) ρ₀/ρ + 3.2√(f_ck) (ρ₀ / ρ – 1)^(3⁄2)]
k = 1.0
L/d = 1.0 [11 + 1.5√(30) × (0.00547/0.00213) + 3.2√(30) × [(0.00547/0.00213 – 1)^(3⁄2)]
L/d = 1.0[11 + 21.098 + 34.416] = 66.514

β_s = (500 As_prov)/(f_yk As_req) = (500 × 339) / (500 × 247.26) = 1.371

b_eff/b_w = 550/150 = 3.66 > 3

Therefore multiply basic length/effective depth ratio by 0.8

Therefore limiting L/d = 1.37 × 0.8 × 66.514 = 72.899
Actual L/d = 5000/211 = 23.696

Since Actual L/d (23.696) < Limiting L/d (72.899), deflection is satisfactory.

Shear Design
Maximum shear force in the rib V_Ed = 17.25 kN

V_Rd,c = [C_Rd,c.k.(100ρ₁ f_ck)^(1/3) + k₁.σ_cp]b_w.d ≥ (V_min + k₁.σ_cp) b_w.d

C_Rd,c = 0.18/γ_c = 0.18/1.5 = 0.12
k = 1 + √(200/d) = 1 + √(200/211) = 1.973 < 2.0, therefore, k = 1.973
V_min = 0.035k^(3/2) f_ck^0.5
V_min = 0.035 × (1.973)^1.5 × 30^0.5 = 0.53 N/mm²
ρ₁ = As/bd = 339/(150 × 211) = 0.0107 < 0.02; Therefore take 0.0107

V_Rd,c = [0.12 × 1.973 (100 × 0.0107 × 30 )^(1/3)] × 150 × 211 = 23814.989 N = 23.815 kN

Since V_Rd,c (23.815 kN) > V_Ed (17.25 kN), no shear reinforcement is required.

According to clause 6.2.1(4), minimum shear reinforcements may be omitted in ribbed slabs where transverse distribution of loads is possible. But for this design, we will therefore provide minimum shear reinforcement.

Minimum shear reinforcement;
A_sw / S = ρ_w,min × b_w × sinα (α = 90° for vertical links)
ρ_w,min = (0.08 × √(f_ck)) / f_yk = (0.08 × √30)/500 = 0.000876
A_sw/S_min = 0.000876 × 150 × 1 = 0.131
Maximum spacing of shear links = 0.75d = 0.75 × 211 = 158.75 mm
Provide H8mm @ 150 mm c/c as shear links.

Slab Topping
A142 BRC Mesh can be provided or H8 @ 250mm c/c

For more information on design and consultancy to accomplish the most challenging design brief, contact the author on info@structville.com. Thank you, and God bless you.

Construction of Underground Water/Septic Tanks by Sinking

By

Ubani Obinna

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October 5, 2020

Underground water retaining structures have wide applications in residential, commercial, and industrial buildings. According to Lagos State Development Laws (2005), a building with more than 5 floors must have an underground water tank with a minimum capacity of 20,000 litres.

Sometimes, the conventional method of constructing an underground water tank which involves excavating the area, preparing the bottom and slope of excavation, blinding, placing of reinforcements/formwork, bracing, etc before concreting and backfilling may not always be feasible or easy for the contractors. This may be a result of high water table, soft/unstable soils, lack of space, etc. In this case, a top-down construction approach is usually adopted, where the shell of the tank is cast on the ground surface and then sunk to the desired depth in a process similar to the construction of caissons or well foundations.

The advantages of this procedure are;
(1) Improved quality assurance of the tank shells due to easy inspection.
(2) The quality of concreting is assured since it is done on the surface.
(3) The problem of dealing with groundwater is minimised.
(4) The challenge of bracing and supporting the sides of excavation is completely obliterated.
(5) There will be no need for backfilling the sides of the tank

The disadvantages of this procedure are;
(1) The perfect verticality of the tank after sinking may not be guaranteed
(2) The shell will need to cure and achieve enough strength before the sinking will begin, otherwise the sinking stresses might damage the shell
(3) Adequate care will need to be taken during concreting of the base, since it may not be done in a perfectly dry condition.
(4) Extra care is needed to guarantee the water tightness of the base.
(5) Sinking gets difficult when an obstruction is encountered.

Let us now explain the process of constructing and sinking underground water tanks and septic tanks in high water table areas in full.

Step 1: Geometric design
The sizing of the tank should be based on occupancy usage and projected water demand of the building. This can be carried out according to the process described in Ubani (2018). A typical tank dimension (plan and section) is shown in Figure 1.

Geometric design of underground water tanks — Fig 1: Typical sizing of an underground tank (Ubani, 2018)

Step 2: Structural design
The structural design of the tank should take into account the earth pressure, water pressure, imposed load on top of the tank (since the compound will serve as useful space), etc. The sizing of the tank members and the reinforcements provided should satisfy ultimate limit state requirements (for example bending, shear, etc) and serviceability limit state requirements (for example, cracking). The tank should also be able to resist uplift due to groundwater, and the structural engineer should detail the processes required for the water tightness of the structure. These processes are well described in Ubani (2018).

To purchase the full textbook and have it delivered in your mailbox within minutes, click HERE

Step 3: Setting out
After the design has been properly done and approved, the contractor will need to set out the tank shell so that it will be cast at the exact intended position which is usually specified in the site layout drawing. The tank should be positioned in such a way that the supply and discharge pipes will have minimum obstruction. The contractor can set out the tank using the popular 3-4-5 method and ensure that the edges are square depending on the orientation of the tank. For cylindrical tanks, the appropriate setting out method should be used. Just like in a building, the four edges of the tank (centre to centre) should be established, and a little setback (say 600 mm) established to give the iron benders a good space to position their rebars (see Figure 2). A profile board should be established around the setback, and the exact width of the tank walls established on the profile board.

Step 4: Leveling and blinding
The ground surface (perimeter of the tank walls) should be levelled and made firm so that the base of the walls will be horizontal and level. After that, a mortar blinding should be done on the prepared surface to receive the reinforcements. The width of the blinding should be such that the carpenter will be able to nail or mark his kicker (or whichever method that is adopted) on the blinding. The blinding should be easily broken off as soon as sinking starts.

Step 5: Setting out of kickers
From the established profile lines, the width of the tank walls should be transferred to the blinding on the ground (see Figure 3). The contractor can use laser, spirit levels, iron squares, or whatever instrument at his disposal to achieve this. Perfectly cut pieces of wood can be used as markers for the iron bender to position his rebars properly.

kicker for walls — Fig 3: Typical kicker for wall

Step 6: Installation of reinforcements
The iron bender should install the reinforcements according to the structural drawing (see example on Figure 4). The concrete cover to the surface facing the soil should typically be taken as 50 mm while the concrete cover to the water storage surface should be taken as 40 mm. The iron bender should ensure that the binding wires are neatly trimmed or pointed inwards after tying because roughly done binding wire can be a source of leakage in the tank. The reinforcement of the wall should be made to project into the base (in L-shape) before the formwork and concreting is done. The water bar (preferably stainless steel water bar) should be installed too as shown in Figure 5.

Typical tank wall reinforcement detail 2 — Fig. 4: Typical tank wall reinforcement details

Step 7: Formwork
The formwork should be properly done and braced as suitable for water retaining structures. Lost ties with hydrophilic water bars wrapped round them with suitable plugs can be adopted to hold the panels in place. The panels should be made with suitable materials such as reusable plastics or marine plywoods. Acrow props should be used to support the bracings to ensure perfect verticality. A small toe of about 150 mm should be provided inwards the tank (see Figure 5). The carpenter or other contractors should also prepare a good scaffold/platform for casting of the concrete.

Step 8: Concreting
A minimum of grade 30 concrete with water to cement ratio not exceeding 0.5 should be used. Read the specifications for concrete for water retaining structures here. Approved water proofing admixtures should be used also. The concreting should get to the level where the top slab should start. The reinforcement of the walls should be allowed to project into the top slab for proper shear connection. The toe and kickers could be cast first with water bars installed. This will aid the carpenters in achieving a perfect dimension. The first phase of casting is shown in Figure 5 while the full shell is shown in Figure 6. Contractors can adopt a different approach if they wish.

Initial casting — Fig 5: Typical kicker with toe showing all projecting reinforcements

Final casting of tank — Fig 6: Fully cast tank shell

Step 9: Curing and striking
The concrete should be cured and the formwork removed after an approved period of time by the structural engineer.

Step 10: Sinking
Labourers should climb into the tank and excavate the soil in order to sink the tank to the desired depth. This should be done as carefully as possible and two functional pumping machines (depending on the size of the tank) should be made available to enable the labourers excavate in the dry. The reinforcements projecting into the base should be bent upwards to enable the labourers do their excavation. The sinking is assisted by the weight of the tank which must overcome the frictional resistance from the soil.

sinking of tank — Fig 7: Sinking of tank shell

Step 11: Concreting the base
After sinking to the desired depth, the base surface should be prepared, cleaned, and properly blinded with concrete of high quality. The reinforcement should be straightened back, lapped properly, and the transverse reinforcements installed. All the water bars should be checked to ensure that they are perfect condition and the remaining portion of the base should be cast to the required thickness with waterproofing admixture. All through this process, there should be constant pumping out of the groundwater. The total weight of the tank at this point should be greater than the upthrust to avoid flotation.

Step 12: Check for water tightness
Typically after casting, you should check the following day to ensure that the tank is dry (note that pumping of groundwater to stay below the base should continue while the concrete gains strength). If the tank is observed to be dry after setting of concrete and pumping of groundwater stops, it means that water exclusion was achieved. The tank can then be flooded with water to check drop in level and to also encourage the autogenous healing of any possible cracks.

References:
(1) Lagos State Physical Planning and Development Regulations (2005): Lagos State Urban and Regional Planning Law. L.S.L.N. No 7
(2) Ubani O.U. (2018): Structural Design of Swimming Pools and Underground Water Tanks. Structville Integrated Services Limited, Lagos Nigeria. ISBN 9789-7869-5413

On the Natural Frequency of Multi-Storey Buildings

By

Ubani Obinna

-

September 3, 2021

A multi-storey building can develop lateral vibrations in the two principal directions and torsional vibration around its vertical shear centre axis. The natural frequency of a structure is the frequency at its free or natural vibration. For a simple mass-spring system, the natural frequency is given by Equation (1);

f = 1/2π √(k/m) —– (1)

Where f is the natural frequency (Hz), and k and m are the stiffness and mass respectively.

Low-rise buildings have high natural frequencies, while tall flexible buildings are characterized by their low natural frequencies. Resonance occurs when the frequency of excitation is close to a system’s natural frequency. Therefore low-rise buildings are more susceptible to earthquake-induced load than to wind loads.

Although tall buildings are flexible and are therefore further away from the peak in the spectral density function of earthquakes, they are susceptible to the low-frequency range of seismic action. Wind poses a special hazard to tall buildings since their fundamental frequencies move towards the wind-spectrum peaks with higher flexibility. Therefore, it is important to calculate the natural frequency of multi-storey buildings.

Zalka (2013) suggested manual procedures for calculating the natural frequency of multi-storey frames. The equations used for calculating the natural frequency of a multi-storey frame is based on the whole bracing system, which can be characterised by the shear stiffness of the frameworks and coupled shear walls, the global bending stiffness of the frameworks and coupled shear walls, and the local bending stiffness of the individual columns/wall sections, shear walls, and cores.

By combining the individual bracing elements, linked by the floor slabs, to form a single cantilever, an equivalent system can be established with shear stiffness K, global bending stiffness EI_g and local bending stiffness EI. The shear stiffness and the global bending stiffness are not independent of each other and can be incorporated into an effective shear stiffness, leading to a single equivalent column with effective shear stiffness K_e and bending stiffness EI.

Model for calculating the Natural Frequency of Multi-Storey Buildings — Fig 1: Model for the lateral vibration analysis. a) bracing system consisting of frames, coupled shear walls, shear walls and cores, b) equivalent column (Zalka, 2013)

We will show how this is done with a solved example. Let us consider the frame of a tall building shown in Figure 2. The properties of the building are as follows;

Total height of building H = 90 m
Number of storeys n = 30
Height of each storey h = 3 m
Width of each bay L = 5 m
Dimension of columns = 500 x 500 mm
Dimension of beams = 600 x 400 mm
Modulus of elasticity of concrete = 28 × 10⁶ = kN/m²
Mass at each level = 2100 kg/m

Multi storey frame — Fig 2: Frame of a 30 storey building

Solution
Second moment of area of beams I_B = (bd³)/12 = (0.4 × 0.6³)/12 = 0.0072 m⁴
Second moment of area of columns I_C = (bd³)/12 = (0.5 × 0.5³)/12 = 0.0052083 m⁴Flexural rigidity of beams EI_b = 28 × 10⁶ × 0.0072 = 201600 kN.m²
Flexural rigidity of columns EI_C = 28 × 10⁶ × 0.0052083 = 145833.33 kN.m²

The part of shear stiffness associated with beams = K_B = ∑(12EI_b)/(L_ih) = 2 × [(12 × 201600)/(5 × 3)] = 322560 kN

The part of the shear stiffness associated with the columns is;
K_C = ∑(12EI_C)/h² = 3 × [(12 × 145833.33)/3²] = 583333.32 kN

From the above, the reduction factor r can be defined as;
r = (K_C)/(K_B + K_C) = (583333.32)/(322560 + 583333.32) = 0.6439

The original shear stiffness of the frame work can now be defined as;
K = K_B× r = 322560 × 0.6439 = 207696.384 kN

With the above shear stiffness, the square of the fundamental frequency (f_s²) of the framework due to shear deformation can be calculated as;

f_s’² = [1/(4H)²] × [r_f².K/m]

Where r_f is the mass distribution factor given by:
r_f= √n/(n + 2.06) = √30/(30 + 2.06) = 0.967 (Note that n = number of storeys = 30)

f_s’² = [1/(4 × 90)²] × [(0.967² × 207696.384)/2100] = 7.136 x 10^-4 Hz²

I_g = ∑(A_c,it²_i)
I_g = (0.5 × 0.5) x (5² + 5²) = 12.5 m⁴

The square of the fundamental frequency that belongs to this global second moment of area is;

f_g² = (0.313.r_f².EI_g)/H⁴m = (0.313 × 0.967² × 28 × 10⁶ × 12.5)/(90⁴ x 2100) = 7.435 x 10^-4 Hz²

The effectiveness factor shows the extent the global bending deformation erodes the shear stiffness:

s_f = √[(f_g²)/(f_s’² + f_g²)] = √[(7.435 x 10^-4 )/(7.136 x 10^-4 + 7.435 x 10^-4)] = 0.714

With the effectiveness factor, the effective shear stiffness is;
K_e = s_f².K = 0.714² x 207696.384 = 105882.7858 kN

The square of the fundamental frequency that belongs to the effective shear stiffness can now be calculated:

f_s² = [1/(4H)²] × [r_f².K_e/m] = [1/(4 × 90)²] × [(0.967² × 105882.7858)/2100] = 3.638 x 10^-4 Hz²

For the local bending stiffness (EI = EI_cr), the sum of the second moments of area of the columns should be produced (and multiplied by reduction factor r). As the bays of the framework are identical, the second moment of area of one column is simply multiplied by n and r (the reduction factor):

I = r∑I_c= 0.6439 x 3 x 0.0052083 = 0.010 m⁴

The fundamental frequency which is associated with the local bending stiffness is defined by;

f_b² = (0.313.r_f².EI)/H⁴m = (0.313 × 0.967² × 28 × 10⁶ × 0.010)/(90⁴ x 2100) = 5.948 x 10^-7 Hz²

As a function of the non-dimensional parameter;

k = H√(K_e/EI) = 90√[105882.7858/(28 × 10⁶ × 0.010)] = 55.345

The frequency parameter η can be obtained from Table 1;

Table 1: Frequency parameters η as a function of k (Zalka, 2013)

By interpolation;

η = 12.76 + [(55.344 – 50)/(60 – 50)] x (15.26 – 12.76) = 14.096

Finally, the fundamental frequency is;

f = √{5.948 x 10^-7 + 3.638 x 10^-4 + [(14.096²/0.313) – (55.345²/5) – 1] x 0.714 x 5.948 x 10^-7} = 0.019 Hz

When this was modelled on Staad Pro, the natural frequency obtained was 0.014 Hz as shown in Figure 3.

Thank you for visiting today. Discussions on this post are welcome.

References
Zalka K. A. (2013): Structural Analysis of Regular Multi-storey Buildings. CRC Press – Taylor and Francis Group, USA

3D Soil-Structure Interaction of Cantilever Retaining Walls

By

Ubani Obinna

-

November 16, 2020

Retaining walls are structures constructed for the purpose of retaining earth fill. There are different types of retaining walls such as cantilever retaining walls, gravity retaining walls, counterfort retaining walls, buttress walls, etc. Each of these has found wide applications in various civil engineering construction works such as embankments, highways, basements, etc.

Traditionally, cantilever retaining walls are designed as line elements where the width of the cantilever is analysed per unit strip (usually per metre length). The base of the cantilever is usually considered rigid, and as a result, a linear pressure distribution under the base is usually assumed.

However, when the dimensions of the retaining wall are such that a rigid behaviour cannot be obtained, or the soil is so soft or subjected to movement, then there will be significant soil-structure interaction. In this approach, the deformation of the soil and the structure itself contributes to the response of the structure to the externally applied load.

In this article, we are going to investigate the interaction of cantilever retaining walls with the soil supporting them in order to see how this affects the settlement, internal forces, and base pressure distribution. This will be carried out using Staad Pro software.

The factors usually checked out for in design of cantilever retaining walls are;

(1) Overturning
(2) Sliding
(3) Bearing capacity
(4) Uplift (rarely critical)
(5) Structural resistance

Methodology
We are going to consider the analysis and design of the retaining wall with the dimensions and soil properties shown in Figure 1.

cantilever retaining wall — **Figure 1**: Cantilever retaining wall on sand

The retaining wall was modelled using concrete plate elements of mesh size 0.5m x 0.5m on Staad Pro software. The unit weight of concrete was set to be 24 kN/m³for the computation of self-weight.

The soil elements were modelled using 8-noded solid element with the elastic properties indicated in Figure 1. Each soil element was modelled as a cuboid with a length and width of 0.5m, and thickness (depth) of 1m. The solid elements were stacked on each other to achieve the formation thickness of 7m. The rock layer was achieved by supporting the last nodes of the soil elements using pinned support. A width of 3m was adopted for modelling the retaining wall.

At ultimate limit state, the permanent actions (self-weight of concrete and earth fill) were factored with a partial factor of 1.35, while the variable action (surcharge) was multiplied by a partial factor of 1.5. The effect of groundwater was not considered in the analysis. The 3D rendering of the soil and retaining wall is shown in Figure 2. The concrete cantilever wall is shown in gold colour, while the soil element is shown in wine red colour (burgundy).

Soil-Structure Interaction of Cantilever Retaining Walls — **Figure 2**: 3D Soil-Retaining Wall Modelling on Staad Pro.

Results
(1) Settlement
The settlement profile and deflection of the retaining wall at the serviceability limit state are shown in Figure 3.

Figure 3: Deflection and Settlement Profile of the soil

The maximum elastic settlement at the toe (SLS) = 19.647 mm
Elastic settlement at the heel (SLS) = 14.856 mm
Deflection at the free end of the cantilever = 35.493 mm

(2) Pressure distribution
The pressure distribution under the retaining wall at the serviceability and ultimate limit states are shown in Figures 4 and 5 respectively. As expected, the maximum pressure occurred at the toe, while minimum pressure occurred at the heel. The pressure distribution was observed to be non-linear, but a little consideration will show that linear approximation can be adopted for design purposes. At SLS, a minimum pressure of 52.6 kPa was observed at the heel, and a maximum pressure of 184 kPa was found to be concentrated at the corners of the toe.

Pressure distribution SLS — **Figure 4**: Base pressure distribution (SLS)

Pressure distribution ULS — **Figure 5**: Base pressure distribution (ULS)

(3) Bending moment
The bending moments on the wall at ULS are shown in Figures 6 and 7.

3D Soil-Structure Interaction of Cantilever Retaining Walls 58 — **Figure 6**: Vertical bending moment on the retaining wall

**Figure 7**: Horizontal bending moment on the retaining wall

(4) Stability Analysis (SLS)

(a) Sliding
Summation of horizontal forces = 401.99 kN
Summation of vertical forces = 1876.8 kN

Let the coefficient of friction of the base against sliding be tan(2/3 x 30^o) = 0.363

Factor of safety against sliding = [1876.8 x 0.363] / 401.99 = 1.69 (Okay)

(b) Overturning
Overturning moment = 2612.6 kNm
Stabilising moment = 12356.42 kNm

Factor of safety against overturning = 12356.42/2612.6 = 4.729 (Okay)

The design for the reinforcements can be done accordingly. Kindly carry out the manual analysis of the same retaining wall and forward it to ubani@structville.com for consideration.

Analysis of Moving Load on Bridges Using Staad Pro

By

Ubani Obinna

-

March 2, 2020

Every code of practice for bridge design has provision for modelling of traffic action as moving loads. This is similar to the idea of influence lines, where the wheel load action effect at the critical location of the influence line/surface is used in design combination. In this post, we are going to show how you can model bridges, and apply moving load on Staad Pro according to the principles of Eurocodes.

In the past, we have made publications on how you can apply Load Model 1 of EN 1991-2 on highway bridges. You can also read on how you can carry out grillage analysis of bridges using Staad Pro. Other publications such analysis of bridge deck girders under Load Model 1 using Staad Pro can also be considered to enhance your knowledge on the topic.

Let us consider a bridge deck with the configuration shown in Figure 1;

Bridge deck Staad Pro 1 — Fig 1: Bridge deck configuration

We can apply the tandem load of EN 1991-2 on the bridge deck in order to obtain the critical bending moment and shear forces. We have prepared a 21 page manual on how you can model a complete simply supported one-span bridge on Staad Pro. This can help you model a bridge of this nature by yourself on Staad Pro with full support of our technical team peradventure you need further help in getting it done. To obtain the publication for a nominal fee click HERE.

How to Apply Moving Load on Staad Pro

Step 1: Define the load
Go to → Loads → Definitions → Moving
Using the procedure described in Chapter 1, define the tandem wheel load of Eurocode on the bridge deck;

Please note that the vehicle definition shown in Figure 2 is based on Eurocode Load Model 1 for tandem load on notional lane 1. The configuration of the wheel load is shown in Figure 3. You can define as many vehicle wheel load configurations as applicable.

Eurocode wheel load configuration — Fig 3: Wheel load configuration for Load Model 1

Step 2: Generate the moving load on the bridge
Go to → Load Case Details → Load Generation

When you click on Load Case details, click on Load Generation as circled in red pen in Figure 4, then click Add.

Go over to the right hand side of the screen (Load and Definitions) and click on the load generated, and click Add in order to define the exact details such as the starting point, location, and step increment. This is shown in Figure 5.

Load generation details — Fig 5: Details of the generated load

For this example, one of the loads generated is shown in Figure 6.

Wheel load on Bridge — Fig 6: Wheel load position on the bridge based on the definition given

Having gotten here, you can analyse the structure and see the variation of bending moment and shear forces as the vehicle travels through the bridge.

Moving load results — Fig 6: Bending moment on the girders due to moving load

Formulas for Calculating Different Properties of Concrete

By

Ubani Obinna

-

May 25, 2021

Table of Contents

The most basic test done on concrete is the compressive strength test. Sometimes, other properties of concrete such as tensile strength, modulus of elasticity, shrinkage values, etc are needed for design purposes.

Researchers and standards have come up with different relationships between the compressive strength of concrete and other properties. In this article, we are going to show the formulas which relate the compressive strength of concrete with other properties as applicable to the Eurocodes.

Characteristic strength of concrete (f_ck)

The characteristic strength is that strength below which 5% of results may be expected to fall during compressive strength test. Individual results below f_ck may be obtained but, in general, only need to be investigated if they fall more than 4 MPa below f_ck (BS EN 206-1, cl 8.2, table 14).

Design strength (f_cd)

The compressive design strength of concrete is given by;

f_cd= α_cc f_ck/γ_c ——– (1)

where;
f_ck = characteristic cylinder compressive strength of concrete at 28 days
γ_c = partial (safety) factor for concrete (taken as 1.5 for UK National Annex)
α_cc= a coefficient taking account of long-term effects on the compressive strength (which is reduced under sustained load) and unfavourable effects resulting from the way the load is applied (conservatively taken as 0.85).

Target mean strength (f_cm)

The target mean strength, f_cm, is also the value used to establish the mix design and is intended to take account of the normal variability that will occur in concrete production. This margin of 8MPa for cylinders is consistent with a normal distribution with a standard deviation (SD) of about 5MPa:

f_ck = f_cm– 1.64SD ——- (2)

Where 1.64SD = 8
Therefore SD = 8/1.64 ≈ 5MPa

N/B: For cubes, the margin is 10 MPa which gives a standard deviation of about of 6 MPa.

Development of compressive strength with time

While design is usually based on the 28-day strength, BS EN 1992-1-1, sub-clause 3.1.2(6) gives an expression for the development of the mean compressive strength of concrete with time at 20°C as follows:

f_cm(t) = [β_cc(t)]f_cm ——— (3)

where;
f_cm(t) is the mean compressive strength at age t days.
β_cc(t) = exp{s[1 – (28/t)^0.5]} ——— (3a)

where;
s is a coefficient which depends on cement type
= 0.20 for cement of strength classes CEM 42.5R, CEM 52.5N and CEM 52.5R (Class R)
= 0.25 for cement of strength classes CEM 32.5R, CEM 42.5N (Class N)
= 0.38 for cement of strength classes CEM 32.5N (Class S)
(where Class R = high early strength; Class N = normal early strength; Class S = slow early strength).

Tensile strength

Tensile strength is commonly defined in one of three ways: direct tensile strength, tensile splitting strength, or flexural strength. For normal structural uses, the mean tensile strength, f_ctm, is related to the cylinder strength by the expressions:

Strength classes ≤ C50/60
f_ctm = 0.30 f_ck^(2/3) MPa ——— (4)

Strength classes > C50/60
f_ctm = 2.12log_e [1 + (f_cm)/10] MPa ——— (5)

Flexural tensile strength

Flexural tensile strength can also be calculated from the mean tensile strength by the following expressions.

The flexural strength is the higher of:

f_ctm,fl = (1.6 – h/1000)f_ctm ——— (6)
or,
f_ctm,fl = f_ctm

where;
h is the total member depth in mm

Strength development of tensile strength

BS EN 1992-1-1 provides expressions for calculating tensile strength at different maturities:

f_ctm(t) = [β_cc(t)]^α f_ctm——— (7)

where:
β_cc(t) is as defined in Equation (3a)
α = 1 for t < 28 days
α = 2/3 for t ≥ 28 day

Modulus of elasticity

In design, the secant modulus, E_cm (in GPa), is derived from the mean compressive strength, f_cm (in MPa), from the expression:

E_cm = 22 [f_cm /10]^0.3 GPa ——— (8)

Variation of Modulus of Elasticity with age

The variation of modulus of elasticity with time is estimated using the expression:
E_cm(t) = [f_cm(t)/f_cm]^0.3 E_cm ——— (9)

This formulas and relationships in this post are culled from:
Bamforth P., Chisholm D., Gibbs J., Harrison T. (2008): Properties of concrete for use in Eurocode 2. The Concrete Centre, UK

Structural Design of Composite Columns

By

Ubani Obinna

-

February 6, 2023

Composite sections of concrete and steel have a lot of advantages, especially in the structural performance and fire resistance of a building. For columns and other compression members, they usually appear as steel-reinforced concrete columns (SRC) or as concrete-filled steel tubes. In this article, we are going to consider the structural design of concrete encased H-section subjected to concentric axial load using Eurocode 4 and BS 5950.

According to BS 5950, the steps to design composite steel columns are as follows;

Determine ultimate axial load F_c.
Select trial section and check if it is non-slender.
Determine r_x, r_y and A_g from steel tables.
Determine effective lengths, L_EX and L_EY
Calculate slenderness ratios, λ_EX (= L_EX/r_x) and λ_EY (= L_EX/r_y).
Select suitable strut curves from Table
Determine compressive strength, p_c
Calculate compression resistance of member, P_c = A_gp_c.
Check F_c≤ P_c . If unsatisfactory return to 2.

According to Eurocode 4, the simplified steps to design encased steel columns subjected to axial load are as follows;

Determine the ultimate axial load on the column N_Ed
Select a trial section and determine its properties
Obtain the buckling length of the column L
Obtain the effective flexural stiffness (EI)_eff of the composite section
Calculate the plastic resistance to compression of the composite section N_pl,Rk
Calculate the relative slenderness of the section (λ) using Euler’s critical load
Choose the appropriate buckling curve and calculate the corresponding reduction factor χ
Multiply the plastic resistance to compression with the reduction factor to obtain the buckling resistance of the section N_b,Rd
Check if N_Ed< N_b,Rdelse return to step 2.

Solved Example
Verify the capacity of UC 254 x 254 x 107 in grade S275 steel encased in a concrete section of 380 x 380 mm to resist a characteristic permanent axial force of 1900 kN and variable axial force of 800 kN using concrete grade C25/30. Column is 3m long and considered pinned at both ends (Area of reinforcement provided = 4H16 (804 mm² , f_yk = 500 N/ mm²).

Solution by BS 5950
The ultimate axial load on the column is given by;
Fc = 1.4Gk + 1.6Qk = 1.4(1900) + 1.6(800) = 3940 kN

Properties of the UC section from Blue Book
Area of UC section (A_g) = 13600 mm²
Radius of gyration (r_x) = 113 mm
Radius of gyration (r_y) = 65.9 mm
Design strength (p_y) = 265 N/mm² (since thickness of flange T = 20.5 mm)
Effective length (L_E) = 3.0 m

Effective length
Check that the effective length of column (L = 3000 mm) does not exceed the least of:
(i) 40b_c = 40 × 380 = 15200 mm
(ii) 100b_c²/d_c = (100 × 380²)/380 = 38000 mm
(iii) 250r_y = 250 × 65.9 = 16475 mm OK

Radii of gyration for the cased section
For the cased section r_x is the same as for UC section = 113 mm
For the cased section r_y = 0.2b_c = 0.2 × 380 = 76 mm but not greater than 0.2(B + 150) = 0.2(258.8 + 150) = 81.76 mm and not less than that for the uncased section (= 65.9 mm)
Hence r_y = 76 mm and r_x = 113 mm

Slenderness ratio
λ_EX = L_EX/r_x = (3000/113) = 26.548
λ_EY = L_EY/r_y = (3000/76) = 39.47

Compressive strength
The relevant compressive strength values for buckling about the x–x axis are obtained from Table 24(b)
of BS 5950 and from Table 24(c) of BS 5950 for bending about the y–y axis.

For λ_EX = 26.548 and p_y = 265 N/mm², p_c = 256.45 N/mm²For λ_EY = 39.47 and p_y = 265 N/mm², p_c = 230.848 N/mm²
The compression resistance of the column is therefore given by;

P_c = (A_g + 0.45f_cuA_c/p_y)p_c

Where:
A_g = 13600 mm²
f_cu = 30 N/mm²
A_c = b_cd_c = 380 x 380 = 144400 mm²
p_c = 265 N/mm²
p_c = 230.848 N/mm²

P_c = [13600 + (0.45 x 30 x 144400)/265] x 230.848 x 10^-3 = 4837.703 kN

Check that P_c is not greater than the short strut capacity, P_cs , given by;
P_cs = (A_g + 0.25f_cuA_c /p_y)p_y = [13600 + (0.25 x 30 x 144400)/265] x 265 x 10^-3 = 4687 kN (this is less than P_c , therefore, take P_cs)

F_c /P_c = 3940 /4687 = 0.840 < 1.0 Okay

Design by Eurocode 4
At ultimate limit state;
N_Ed = 1.35Gk + 1.5Qk = 1.35(1900) + 1.5(800) = 3765 kN

Effective length of the column L = 3000 mm
Area of UC section (A_a) = 13600 mm²
Radius of gyration (i_y) = 113 mm
Radius of gyration (i_z) = 65.9 mm
Design strength (f_y) = 265 N/mm² (since thickness of flange T = 20.5 mm)
I_y = 17500 cm⁴
I_z = 5930 cm⁴
E = 210000 N/mm²

The plastic resistance to compression N_pl,Rk = A_a.f_y + 0.85A_cf_ck + A_sf_yk
A_a = 13600 mm²
f_y = 265 N/mm²
A_c = 380 x 380= 144400 mm²
f_ck = 25 N/mm²
A_s = 804 mm²
f_yk = 500 N/mm²

N_pl,Rk = [(13600 x 265) + (0.85 x 144400 x 25) + (804 x 500)] x 10^-3 = 7074.5 kN
The relative slenderness λ_i = ( N_pl,Rk / N_cr )^0.5
N_cr,i = π²(EI)_eff,i/L²

(EI)_eff,i = E_aI_a + 0.6E_cmI_c + E_sI_s

E_a = E_s = Elastic modulus of the structural steel and reinforcement respectively = 210000 N/mm²
I_a = Moment of inertia of structural steel in the relevant axis
E_cm = Modulus of elasticity of concrete = 22(f_ck/10)^0.3 (GPa) = 28960 N/mm² (see Table 3.1 of Eurocode 2)
I_c = moment of inertia of the uncracked concrete section = bd³/12 = (380 x 380³)/12 = 17376.133 x 10⁵ mm⁴
I_s = moment of inertia of the reinforcement = πD⁴/64 = (π x 16⁴)/64 = 3216.99 mm⁴ (for four bars = 4 x 3216.99) = 12867.96 mm⁴

Hence;
(EI)_eff,y = (210000 x 17500 x 10⁴) + (0.6 x 28960 x 17376.133 x 10⁵) + (210000 x 12876.96) = 6.69455 x 10¹³ N.mm²
(EI)_eff,z = (210000 x 5930 x 10⁴) + (0.6 x 28960 x 17376.133 x 10⁵) + (210000 x 12876.96) = 4.26485 x 10¹³ N.mm²

N_cr,y = [(π² x 6.69455 x 10¹³)/3000²] x 10^-3 = 73413.955 kN
N_cr,z = [(π² x 4.26485 x 10¹³)/3000²] x 10^-3 = 46769.313 kN

λ_y = (N_pl,Rk / N_cr,y)^0.5 = (7074.5/73413.955)^0.5 = 0.310
λ_z = (N_pl,Rk / N_cr,z)^0.5 = (7074.5/46769.313)^0.5 = 0.389

Check h/b ratio = 266.7/258.8 = 1.0305 < 1.2, and t_f < 100 mm (Table 6.2 EN 1993-1-1:2005)

Therefore buckling curve b is appropriate for y-y axis, and buckling curve c for z-z axis. The imperfection factor for buckling curve b α = 0.34 and curve c = 0.49 (Table 6.1)

Φ = 0.5 [1 + α(λ – 0.2) + λ²]

Φ_y = 0.5 [1 + 0.34 (0.310 – 0.2) + 0.310²] = 0.567
Φ_z = 0.5 [1 + 0.49 (0.389 – 0.2) + 0.389² ] = 0.622

X = 1/[Φ + √(Φ² – λ²)]
X_y = 1/[0.567 + √(0.567² – 0.310²)] = 0.959
X_z = 1/( 0.622 + √(0.622² – 0.389²)) = 0.903

Therefore N_b,Rd = (X_zN_pl,Rk)= (0.903 x 7074.5) = 6388.685 kN

N_Ed /N_b,Rd = 3765/6388.685 = 0.589 < 1.0 kN Okay

Difference between Autogenous and Drying Shrinkage of Concrete

By

Ubani Obinna

-

June 15, 2023

Shrinkage in concrete refers to the volume reduction or contraction that occurs in concrete as it dries and ages. It is a natural and inevitable process caused by several factors, including the loss of water from the concrete matrix and the chemical reactions that take place during hydration.

The magnitude of shrinkage in concrete depends on various factors, including the water-to-cement ratio, cement type, aggregate properties, temperature, relative humidity, and curing conditions. Higher water-to-cement ratios generally lead to increased shrinkage, as there is more water available for evaporation and drying. Additionally, certain types of cement, such as high-early-strength (R) or low-alkali cement, can exhibit higher shrinkage characteristics.

For instance, grade 42.5R cement is expected to exhibit higher shrinkage characteristics than grade 42.5N cement.

Shrinkage in concrete can have several consequences and implications for construction. It can cause cracking, which not only affects the aesthetic appearance of the concrete but also compromises its structural integrity and durability. Cracks can provide pathways for the ingress of harmful substances, such as water, chlorides, and other aggressive chemicals, leading to the corrosion of reinforcing steel and the deterioration of the concrete.

There are different types of shrinkage in concrete such as drying shrinkage, plastic shrinkage, carbonation shrinkage, and autogenous shrinkage. However, shrinkage in concrete is usually the sum of autogenous shrinkage and drying shrinkage. In this article, we will be reviewing the difference between autogenous and drying shrinkage in concrete.

Autogenous shrinkage is caused by self-desiccation in young concrete as water is consumed during the hydration reaction. This occurs majorly within the early days of casting the concrete. However, drying shrinkage is the reduction in volume caused mainly by the loss of water during the drying process and this continues perhaps for years after the concrete is placed. This means that drying shrinkage commences after curing.

Autogenous Shrinkage

Autogenous shrinkage is a phenomenon that occurs in concrete without any external drying or thermal effects. It refers to the volume reduction or contraction of concrete due to the self-desiccation process, which is caused by the chemical reactions between cement and water during hydration.

When cement reacts with water, it forms a gel-like substance called C-S-H (calcium silicate hydrate), which gives concrete its strength. As the hydration process continues, this gel continues to absorb water, leading to a decrease in the water content within the concrete matrix. As a result, the volume of the gel decreases, causing autogenous shrinkage.

Autogenous shrinkage can be influenced by various factors, including the water-to-cement ratio, cement composition, temperature, relative humidity, and the presence of supplementary cementitious materials. Higher water-to-cement ratios generally lead to greater autogenous shrinkage because more water is available for hydration. Additionally, higher temperatures and lower relative humidity can accelerate the rate of shrinkage.

Autogenous shrinkage can have several consequences for concrete structures. First, it can lead to cracking if the concrete is restrained from freely contracting. These cracks can impair the durability and structural integrity of the concrete. Furthermore, shrinkage-induced cracks can provide pathways for the ingress of harmful substances such as water, chloride ions, and other aggressive agents, which can result in deterioration over time.

Mechanism of Autogenous Shrinkage
(1) During the hardening process of concrete, water from the mix accumulates into the pores, voids, and capillaries of the mixture.
(2) Water binds itself into the grains of the binder, as well as moving into the surroundings whose relative humidity is usually less than that of the concrete.
(3) In order to move water from the tiny voids, considerable forces are required to overcome the surface tension, as well as the forces of adhesion which binds the water to the voids.
(4) These forces act on the load-bearing structure of the concrete which at that time has low stiffness, can cause deformations in the concrete which can lead to cracking.

Autogenous shrinkage cracks can be largely avoided by keeping the surface of the concrete continuously wet; conventional curing by sealing the surface to prevent evaporation is not enough and water curing is essential. With wet curing, water is drawn into the capillaries and the shrinkage does not occur.

Practically, autogenous shrinkage happens in the interior of a concrete mass. According to BS EN 1992-1-1, autogenous shrinkage occurs in all concretes and has a linear relationship to the concrete strength.

According to EN 1992-1-1, autogenous shrinkage is given by Equation (1)

ε_ca(t) = β_as(t)ε_ca(∞) ————————— (1)

Where;
ε_ca(∞) = 2.5(f_ck – 10) x 10^-6
β_as(t) = 1 – e^(√0.2t)f_ck = characteristic strength of concrete (MPa)
Where t is given in days.

Drying Shrinkage

As concrete matures, moisture is gradually lost from the concrete mass to the atmosphere. This moisture loss is accompanied by volume change which is referred to as drying shrinkage.

Drying shrinkage, therefore, depends on the relative humidity (for instance, indoor concrete will shrink more readily when compared with external concrete), the quantity and class of cement (rich concrete mixes will shrink more than leaner mixes), and the member size (thinner sections will shrink more quickly than thicker sections). According to EN 1992-1-1, drying shrinkage strain develops slowly, since it is a function of the migration of the water through the hardened concrete.

Expression 3.9 in EN 1992-1-1 gives the development of drying shrinkage strain with time as given in Equation (2);

ε_cd(t) = β_ds(t, t_s).k_h.ε_cd,0 ———————- (2)

Where k_h is a coefficient depending on the notional size h₀ (see Table 1).

β_ds(t, t_s) = (t – t_s)/[(t – t_s) + 0.04√(h₀³)]

Where;
t is the age of the concrete at the moment considered (in days)
t_s is the age of the concrete (in days) at the beginning of drying shrinkage (normally this is at the end of curing)
h₀ is the notional size (in mm) of the cross-section = 2A_c/u

Where;
A_c is the concrete cross sectional area (for slabs, Ac = thickness x 1000 mm)
U is the perimeter of that part of the cross-section exposed to drying (for slabs, take u = 2000 mm)

ε_cd,0 is the basic drying shrinkage strain. This is given in Annex B of EN 1992-1-1 as Equation (3);

ε_cd,0 = 0.85[(220 + 110.α_ds1).e^{(-α_ds2.0.1f_cm)}] x 10^-6 x β_RH ——— (3)
β_RH = 1.55[1- (RH/RH₀)³] ————- (4)

Where;
f_cm is the mean compressive strength (Mpa)
α_ds1 is a coefficient which depends on the type of cement
= 3 for cement class S
= 4 for cement class N
= 6 for cement class R

α_ds2 is a coefficient which depends on the type of cement
= 0.13 for cement class S
= 0.12 for cement class N
= 0.11 for cement class R

RH is the ambient relative humidity (%)
RH₀ = 100%

Specification of Concrete for Water Retaining Structures

By

Ubani Obinna

-

February 19, 2024

Table of Contents

Water retaining structures, from dams to swimming pools and water tanks, demand concrete that adheres to strict performance criteria. Beyond structural integrity, the concrete must exhibit exceptional durability in an aqueous environment, resisting water penetration (leakage), chemical attack, and freeze-thaw cycles. Specifying appropriate concrete for these applications requires balancing multiple factors, ensuring both long-term functionality and cost-effectiveness.

In the year 2018, we made a successful publication on the Analysis and Design of Swimming Pools and Underground Water Tanks. In this article, we will briefly review some construction aspects of water retaining structures with emphasis on the specification of concrete to be used for the construction of water retaining structures. To download the textbook on the design of swimming pools, with Staad Pro video tutorials and an Excel spreadsheet for the calculation of crack widths, click HERE.

After carrying out the structural analysis and design of a water retaining structure, the next step is to ensure that the construction is properly executed such that the water tightness and strength of the element will not be compromised. A good design and a bad construction are as good as a failed project. The recommendations given in the following sections can be followed to ensure good results in the construction of water retaining structures.

Key Considerations in Concrete for Water Retaining Structures

Strength and Durability

Strength class: Minimum compressive strength is typically in the range of 30-50 MPa, depending on structure type and design loads. Consider future expansions or hydrostatic pressure when selecting a strength class. However, the characteristic compressive strength of concrete for water-retaining structures should not be less than 30 MPa (C30/37) after 28 days of curing.

Permeability: Low permeability minimizes water ingress, reducing the potential for leaching and reinforcement corrosion. Specify a maximum water-to-cement ratio (typically 0.50) and use dense, well-graded aggregates.

Air content: Adequate air content (4-7%) improves freeze-thaw resistance and reduces internal stresses.

Cracking: Minimize by proper joint design, reinforcement detailing, and shrinkage-reducing admixtures.

Material Selection

For the construction of water retaining/excluding structures, class N (normal hardening) cement is recommended and should be used ahead of Class R (rapid hardening) due to shrinkage issues. In general, the concrete should be specified according to BS EN 206 and BS 8500 Parts 1 and 2. For water tanks, all materials in contact with potable water will need to comply with specific regulations and should be non-toxic. This is why all admixtures that will be used must be approved.

Cement: Portland cement types N (normal) or NA (normal air-entrained) are common choices. For severe environments, consider sulfate-resistant cement or supplementary cementitious materials (SCMs) like fly ash or slag.
Aggregates: Dense, well-graded, and clean aggregates minimize voids and permeability. Specify maximum size based on wall thickness and reinforcement spacing.
Admixtures: Utilize admixtures judiciously. Air-entraining admixtures enhance freeze-thaw resistance, while water reducers improve workability without compromising strength. Ensure compatibility with other ingredients and potable water regulations if applicable.

Construction Practices

Mixing and placing: Employ proper mixing procedures and equipment to achieve uniform consistency. Place concrete promptly and avoid segregation.
Curing: Implement effective curing practices, such as water spraying or curing compounds, to ensure proper hydration and minimize shrinkage cracking.
Joints: Design and construct joints to accommodate movement and prevent water leakage. Utilize waterstops (water bars) where necessary.

Additional Considerations

Chemical exposure: For structures exposed to aggressive chemicals, specify cement and additives with appropriate resistance.
Water quality: If the structure holds potable water, ensure all materials comply with relevant regulations for safety and non-toxicity.
Sustainability: Explore options like SCMs or recycled materials to reduce environmental impact while maintaining performance.

Standards and Codes

Refer to relevant national or international standards like ACI 318 (Building Code Requirements for Structural Concrete) or BS EN 206 (Concrete – Specification, performance, production and conformity) for detailed guidance and specific requirements.

Olympic swimming pool — **Figure 2:** Olympic standard swimming pool

Permeability Considerations

Concrete for water-retaining structures must have low permeability. Water tightness refers to the ability of concrete to hold back or retain water without visible leakage (Kosmatka et al., 2003). It is common knowledge that the permeability of concrete is related to the water/cement ratio because the mix design factor is directly related to the permeability of the hardened cement paste. After the hydration reaction is completed, the remaining water leaves the concrete slowly, thereby leaving pores which reduce the strength of the concrete and the durability.

It is widely believed that a water/cement ratio of 0.2 (about 10 litres of water to 50 kg bag of cement) is needed to complete the hydration reaction, while the rest is to improve the workability of the concrete. However according to Mather et al. (2006), for a given volume of cement to hydrate completely, the quantity of original mixing water required is 1.2 times the solid volume of the cement.

The reason for this is that water should be available to fill up the 30% pore space that must be present after the hydration reaction. Ultimately, the authors opined that not all the cement will hydrate if the water/cement ratio is less than 0.4, even though only half of the water will go into a chemical combination. Research carried out by Kim et al. (2014) showed that porosity in concrete increased by 150% when the water/cement ratio was increased from 0.45 to 0.6.

**Fig 2**: Experimental Relationship Between Hydraulic Permeability and Water/Cement Ratio Under Different Curing Conditions (Whiting 1989, cited by Kosmatka et al, 2003)

According to Powers et al., (1954) cited by Kosmatka et al. (2003), the permeability of mature hardened cement paste kept continuously moist ranges from 0.1 x 10^-12 to 120 x 10^-12 cm/sec for water-cement ratios ranging from 0.3 to 0.7 (see Figure 2). Also, in a leakage test conducted by Portland Cement Association on cement mortar disks of 25 mm thickness subjected to a water pressure of 140 kN/m2; the disks made with a water/cement ratio of 0.5 or less showed no sign of leakage after being moist cured for seven days.

However, the disks made with a water/cement ratio of 0.8 showed leakage after being cured for the same period of time. Research has also shown that concrete cured in water is less permeable than concrete that hardened in air, therefore it is recommended that immediately after removing the formwork of tank walls, the tank should be flooded with water. This also helps in autogenous healing of cracks.

Furthermore, the permeability and gradation of the aggregates, the quality of the aggregate/cement paste interface, and the ratio between cement paste and aggregates affect the overall permeability of concrete. Workability is usually an issue when we try to keep the water/cement ratio low. The best way out is to use water-reducing admixtures to make the concrete workable.

This is a better option than using waterproofing admixtures and a high water/cement ratio. Waterproofing admixtures reduce absorption and water permeability by acting on the capillary structure of the cement paste. They will not significantly reduce water penetrating through cracks or through poorly compacted concrete which are two of the more common reasons for water leakage in concrete structures.

Summary

Table 1 gives the recommended concrete material requirements for water-retaining structures. A concrete specified and prepared as given in Table 1 should not give problems for water retaining structures provided it is well placed and compacted.

Table 1: Recommendation for concrete to be used water retaining structure

Recommended Concrete Specification for Water Retaining Structures

In effect, cracking can only be controlled by structural design based on the structural arrangement adopted: introducing movement joints, or by reinforcing the structure properly to limit the crack widths. Otherwise, Type A water protection should be specified. For water-retaining structures, the recommended minimum thickness for water tightness is 250 mm, unless the hydrostatic pressure in the tank walls is very low.

Specifying concrete for water retaining structures requires a comprehensive understanding of performance demands, material properties, and construction practices. By carefully considering strength, durability, material selection, and construction techniques, engineers can ensure long-lasting, leak-free structures that fulfil their intended purpose for decades to come.

References
Kim Yun-Yong , Kwang-Myung Lee, Jin-Wook Bang, and Seung-Jun Kwon (2014): Effect of W/C Ratio on Durability and Porosity in Cement Mortar with Constant Cement Amount. Advances in Materials Science and Engineering Volume 2014, Article ID 273460, 11 pages http://dx.doi.org/10.1155/2014/273460

Kosmatka, S. H., Kerkhoff B., and Panarese, W. C. (2003): Design and Control of Concrete Mixtures, EB001, 14th edition, Portland Cement Association, Skokie, Illinois, USA

Mather, B. and Hime, W. G. (2002): Amount of Water Required For Complete Hydration of Portland Cement. American Concrete Institute (ACI) Volume: 2 Issue Number: 6 ISSN: 0162-4075 pp 56 -58 http://worldcat.org/oclc/4163061

Powers, T. C.; Copeland, L. E.; Hayes, J. C.; and Mann, H. M (1954): Permeability of Portland Cement Pastes, Research Department Bulletin RX053, Portland Cement Association, http://www.portcement.org/pdf_files/RX053.pdf

Whiting, D. (1989): “Permeability of Selected Concretes,” Permeability of Concrete, SP108, American Concrete Institute, Farmington Hills, Michigan, pp 195 -222.

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