Uplift Capacity of Piles

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July 12, 2023

Table of Contents

In the design of pile foundations, it is usually very common to express the load carrying capacity in terms of axial compression. However in some cases, piles are subjected to uplift forces, and must be designed to resist such forces in order to avoid the pull out of the foundation or the structure. Piles that are subjected to uplift forces are also called tension or anchor piles. Uplift forces are developed due to hydrostatic pressure or overturning moments.

Forces due to earthquake, wind, or waves, are the major actions that can induce uplift forces in piles. Structures such as transmission towers, mooring systems for ocean surface or submerged platforms, tall chimneys, jetty constructions, etc., all have their foundations subject to uplift loads.

Factors Affecting Uplift Capacity

Several factors influence the uplift capacity of piles and they are briefly described below.

Soil Characteristics: Soil properties, including the cohesion and friction angle, significantly affect uplift capacity. Clay soils will rely on the cohesion or unit adhesion of the soil with the pile material for uplift resistance, while granular soils will rely on frictional forces (dependent on the angle of internal friction) for uplift resistance.
Pile Geometry: The shape, size, and length of the pile influence its uplift capacity. Longer piles provide a larger surface area in contact with the soil, thus increasing resistance against uplift forces. Additionally, the pile diameter and shape can affect the distribution of uplift forces along the pile shaft. It is also important to note that pile cap dimensions and group effects can also influence the uplift capacity of piles.
Pile Material: The material used for pile construction plays a role in uplift capacity. Steel piles are often preferred due to their high strength and ductility, providing better resistance against uplift. However, other factors, such as corrosion potential, must also be considered. Furthermore, scholars have also determined that the angle of wall friction between the pile and the surrounding soil is dependent on the pile material.
Pile Installation Method: The uplift capacity is typically higher in driven piles than bored piles.
Groundwater Conditions: The level of groundwater significantly affects uplift capacity. In saturated soil conditions, the presence of water can reduce the soil’s effective stress, potentially reducing the uplift resistance of piles. Conversely, dewatering or densification techniques can improve uplift capacity.

Methods for Determining Uplift Capacity

Uplift capacity of piles may be assessed using theoretical analyses (classical equations developed using soil properties), field tests, and numerical modeling. The following are commonly used approaches:

Analytical Methods: Several analytical methods, such as the Terzaghi’s equation and the Vesic’s method, provide simplified solutions to estimate uplift capacity. These methods typically consider soil parameters, pile geometry, and groundwater conditions to calculate the uplift resistance.
Field Load Tests: Load tests conducted in the field help validate the design assumptions and provide valuable data on the actual uplift capacity. Common load test methods include the pile load test, plate load test, and pile uplift test. These tests involve applying controlled loads to the pile and measuring its response to determine uplift capacity.
Numerical Modeling: Finite element analysis (FEA) and other numerical modeling techniques allow engineers to simulate complex soil-pile interactions and evaluate uplift capacity. Numerical models consider soil behavior, pile-soil interaction, and other relevant factors to provide detailed insights into the uplift response.

Generally, the equation for uplift capacity of a single pile may be written as;

P_ul = W_p + A_sf_r ——– (1)

where,
P_ul = uplift capacity of pile,
W_p = weight of pile,
f_r = unit resisting force
A_s= effective surface area of the embedded length of pile.

Uplift capacity of pile in clay

For piles embedded in clay, equation (1) may be written as;

P_ul = W_p + A_sαc_u ——– (2)

where,
c_u = average undrained shear strength of clay along the pile shaft,
α = adhesion factor (= c_a/c_u),
c_a = average adhesion

**Figure 1:** Relationship between adhesion factor α and undrained shear strength c_u

Figure 1 gives the relationship between α and c_u based on pull out test results as collected by Sowa (1970). As per Sowa (1970), the values of c_a agree reasonably well with the values for piles subjected to compression loadings.

Uplift capacity of pile in sand

The ultimate uplift capacity of a vertical pile for piles embedded in sandy soil depends on the skin resistance created between the pile shaft and the soil.

According to Murthy (2012), adequate confirmatory data are not available for evaluating the uplift resistance of piles embedded in cohesionless soils. Ireland (1957) reports that the average skin friction for piles under compression loading and uplift loading are equal, but data collected by Sowa (1970) indicate lower values for upward loading as compared to downward loading especially for cast-in-situ piles. A study by Ramasamy et al. (2004) showed that the pull out shaft friction is significantly less than the push in shaft friction.

Poulos and Davis (1980) suggest that the skin friction of upward loading may be taken as two-thirds of the calculated shaft resistance for downward loading.

According to Verma and Joshi (2010), the net uplift capacity of piles embedded in sand can be given by the equation (3) as:

Q_u = ½ K_s σ_v tanδ πdZ_c + K_s σ_v tanσ π(L – Z_c) ——– (3)

Where;
K_s = coefficient of earth pressure
σ_v = effective vertical stress at a depth of Zc = γ_dZ_c
d = diameter of pile
γ_d =dry unit weight of soil
δ = soil-pile friction angle
L = Length of pile
Z_cor L_cr = critical depth of embedment

According to Verma and Doshi (2010), the value of coefficient of earth pressure in Equation (3) has a large range of 0.3 to 4.0, which implies that there are many implications to the value of K_s.

Solved Example

A 450 mm diameter pile is embedded in a homogenous medium dense sand, determine the net pullout capacity (FOS = 3.0). Given: L = 12 m, φ = 38°, K_s = 1.5, and δ = 25°, γ_(average) = 17 kN/m³
The water table is at great depth, and take the critical depth to be 15D.

Solution

Critical depth = 15 × 0.45 = 6.75 m
σ_v = 6.75 × 17 = 114.75 kN/m²

f_s = 114.75 × 1.5 × tan 25 = 80.263 kN/m²

f_s1 = ½ f_sπdZ_c = ½ × 80.263 × π × 0.45 × 6.75 = 382.9 kN
f_s2 = f_sπd(L – Z_c) = 80.263 × π × 0.45 × (12 – 6.75) = 595.71 kN

Total skin resistance = f_s1 + f_s2 = 382.9 + 595.71 = 978.61 kN

Q_a = 978.61/3 = 326.2 kN (Factor of safety of 3)

After Poulos and Davis (1980), pull out capacity = 2/3 × 326.2 = 217.46 kN

Conclusion

The uplift capacity of piles is an important factor in the design of structures that are subjected to uplift loads. Geotechnical design of piles must ensure that the uplift capacity of the piles is sufficient to resist the expected loads. There are a number of equations that can be used to estimate the uplift capacity of piles, but the final design should be based on the specific soil conditions and the design requirements.

References

Ireland, H.O. (1957). “Pulling Tests on Piles in Sand,” Proc. 4th Int. Conf. SM and FE, Vol. 2.
Murthy V.N.S (2012): Geotechnical Engineering. Marcel Decker Inc. New York
Poulos, H.G., and Davis, E.H. (1980). Pile Foundation Analysis and Design, John Wiley & Sons, New York.
Ramasamy, G., Dey, B. and Indrawan, E. (2004): “Studies on skin friction in piles under tensile and compressive load”, Indian Geotechnical Journal, Vol. 34, No. 3, pp. 276-289.
Sowa, V.A. (1970). “Pulling Capacity of Concrete cast-in-situ Bored Pile,” Can. Geotech. J., Vol. 7.
Verma A. K. and Joshi R. K. (2010): Uplift Load Carrying Capacity of Piles in Sand. Indian Geotechnical Conference – 2010, GEOtrendz pp 857 – 860

Column Splice Connection Design

By

Ubani Obinna

-

July 10, 2023

Column splice connection design involves joining two or more column sections to create a longer column or to provide additional strength. It is used when the length of a column is too long to be fabricated as a single piece. They are also used for connecting columns of different sections as a building goes higher. Similar to beam splices, column splices are typically designed to transfer axial load, shear, and moment.

Properly designed column splice connections are important in ensuring easier buildability, transportation, handling, and maintaining the overall stability and safety of various construction projects in steel structures. The primary function of a column splice connection is to transfer axial loads and moments between the connected column sections. The design should effectively distribute the applied loads through the connection without compromising the structural integrity.

In this article, we will explore the design of bolted column splice connection.

Types of Column Splices

There are two main types of column splices: bearing splices and non-bearing splices. Bearing splices rely on full bearing contact between the two column sections to transfer the axial load. In this case, the loads from the upper column are directly transferred to the lower column through the use of division plates or direct contact between the two sections.

Non-bearing splices use bolts or welds to transfer the axial load. In this case, there is no bearing between the interconnected columns and they are usually detailed with a gap in between the column stacks.

Design of column Splices

The design of a column splice must consider the following factors:

The type of splice (bearing or non-bearing)
The size and strength of the column sections
The axial load, shear, and moment applied to the splice
The material properties of the column sections and the splice plates

Design Example

Design a column splice connection for two similar column sections (UC 254x254x89) subjected to an axial dead load of 528kN and a design moment of 178 kN. The ends are not prepared for contact in bearing.

Section Details
Upper Stanchion; UC 254x254x89 (S275)
Lower Stanchion; UC 254x254x89 (S275)
Flange splice plate; 120 mm × 690 mm × 15 mm (S275)
Flange plate bolts; M22 (Grade 8.8 Black Bolts)
Web splice plate; 137 mm × 390 mm × 15 mm (S275)
Web plate bolts; M22 (Grade 8.8 Black Bolts)

Splice Details

Flange plates
Number of bolt rows above and below splice; n_fpr = 4
Number of bolt columns above and below splice; n_fpc = 2
Dist from end of upper column to first row of bolts; e_ucfend = 60 mm
Dist from end of lower column to first row of bolts; e_lcfend = 60 mm
Bolt pitch; p_fpb = 75 mm
Distance from outer bolts to plate end; e_fpend = 60 mm

Web plates
number of bolt rows above and below splice; n_wpr = 2
number of bolt columns above and below splice; n_wpc = 2
Dist from end of upper column to first row of bolts; e_ucwend = 60 mm
Dist from end of lower column to first row of bolts; e_lcwend = 60 mm
Bolt pitch; p_wpb = 75 mm
Distance from outer bolts to plate end; e_wpend = 60 mm

Loading Details
Axial compressive force due to dead load; F_cd = 528.0 kN
Moment on splice; M = 178.0 kNm

Design Loading
Design load;
F_t = max(0 kN, abs(M) / min(D_u – 2T_u – t_fp, D_l – 2T_l – t_fp) – F_cd / 2) = 580.8 kN

Check 1 – recommended detailing requirements – column splice, flange plates on inside

Upper Column
Overall depth; D_u = 260 mm
Overall width; B_u = 256 mm
Flange thickness; T_u = 17.3 mm
Web thickness; t_u = 10.3 mm
Root radius; r_u = 12.7 mm

Lower Column
Overall depth; D_l = 260 mm
Overall width; B_l = 256 mm
Flange thickness; T_l = 17.3 mm
Web thickness; t_l = 10.3 mm
Root radius; r_l = 12.7 mm

Flange Plates
Upper projection;
L_fpu = e_ucfend + (n_fpr – 1) × p_fpb + e_fpend = 345 mm

Lower projection;
L_fpl = e_lcfend + (n_fpr – 1) × p_fpb + e_fpend = 345 mm

Detailing Requirements
The upper projection of the flange plate meets the detailing requirements
Lower projection of flange plate meets detailing requirements
The width of the flange plate meets the detailing requirements
The thickness of flange plates meets the detailing requirements
The width of web plates meets the detailing requirements

Flange plate packing;
t_fpack = abs((D_u / 2 – T_u) – (D_l/2 – T_l)) = 0.0 mm

Web plate packing;
t_wpack = abs(t_u – t_l) / 2 = 0.0 mm

Sufficient web plate bolts provided
Bearing plate not required

Check 2 – the presence of tension due to axial load and bending moment – internal

Tension Force;
F_t = M / min(D_u – 2T_u – t_fp, D_l – 2T_l – t_fp) – F_cd / 2 = 580.8 kN

Check 3 – tensile capacity of flange cover plate – internal

Grade of cover plate;
p_yfp = 275 N/mm²

Net area of flange cover plates (one flange);
A_netfp = 2(d_fp – n_fpc / 2D_hfb ) × t_fp = 2880 mm²

Net area coefficient;
K_efp = 1.2

Gross area of flange cover plates (one flange);
A_grossfp = 2d_fpt_fp = 3600 mm²

Design area of flange cover plates (one flange);
A_fp = min(K_efp × A_netfp, A_grossfp) = 3456 mm²

Tensile capacity;
P_tfp = p_yfp × A_fp = 950.4 kN

Utilisation factor;
Ucheck₃ = F_t / P_tfp = 0.611

Tension capacity of flange cover plate: PASS

Check 4 – Shear capacity of bolt group connecting flange cover plate to column flange

Grade of bolts;
p_bsfp = 460 N/mm²

Shear capacity of top pair of bolts;
P_sfb1 = min(P_sfb, 0.5 × e_fpend × t_fp × p_bsfp) = 113.6 kN

Shear capacity of other bolts; P_sfb = 113.6 kN

Joint length; L_j = (n_fpr -1) × p_fpb = 225 mm

Amended bolt capacity;
P_sfba = 113.6 kN

Reduction factor;
R_f = min(9d_fb / (8d_fb + 3t_fpack), 1) = 1.000

Shear capacity of bolt group;
P_sfbsum = R_f × n_fpc × (P_sfb1 + (n_fpr – 1) × P_sfba) = 909.0 kN

Force on splice plate; F_t = 580.8 kN

Utilisation factor;
Ucheck₄ = F_t / P_sfbsum = 0.639

Shear capacity of flange plate bolt group : PASS

Check 5 – Bearing capacity of flange cover plate connected to column flange

Bearing strength of the end plate;
p_bsfp = 460 N/mm²

Bearing capacity of the flange plate per bolt (outer);
P_bsfp1 = min(d_fb × t_fp × p_bsfp, 0.5 × e_fpend × t_fp × p_bsfp) = 151.8 kN

bearing capacity of the end plate per bolt (other);
P_bsfp = d_fb × t_fp × p_bsfp = 151.8 kN

Capacity of bolt group;
P_bsfpsum = n_fpc × (P_bsfp1 + (n_fpr – 1) × P_bsfp) = 1214.4 kN

Bearing force on bolt group;
F_t = 580.8 kN

Utilisation factor;
Ucheck₅ = F_t / P_bsfpsum = 0.478

Bearing capacity of flange plate: PASS

What is the Correct Position for Column Rebar Laps?

By

Ubani Obinna

-

June 26, 2023

Columns are compression members used for transferring superstructure loads to the foundation. In reinforced concrete detailing and construction, the lapping of reinforcements is almost unavoidable due to logistics and handling issues during construction. As a result, design codes all over the world have guidelines on how to properly lap reinforcements in columns.

Improper detailing of reinforced concrete columns can lead to concrete spalling, cracking, and other forms of failure, which may compromise the structural integrity of a column. A poorly arranged reinforcement can also lead to premature buckling and bending that can reduce the load-carrying capacity of reinforced concrete columns.

Here are some important detailing guidelines provided for column laps;

(1) When the diameter of both bars at the lap exceeds 20mm and the cover is less than 1.5 times the size of the smaller bar, transverse links shall be provided throughout the lap length.

(2) At the lap, the least link diameter should be at least one-quarter the size of the smaller bar.

(3) Link spacing shall not exceed;
(a) 12 x diameter of the smallest bar
(b) 0.6 x dimension of the smallest side of the column
(c) 240 mm

(4) Compression lap length should be at least 25% greater than the compression anchorage length.

(4) For cranked bars, the minimum slope of the crank should be maintained at 1:10. However, this value may be increased up to 1:20 for smooth load transfer.

However, the code appears to be silent on the actual location where columns should be lapped. What do you think? Kindly comment below.

Analysis of Soil Liquefaction Potential

By

Ubani Obinna

-

February 20, 2024

Table of Contents

Liquefaction refers to the process in which a granular material changes from a solid to a liquid state due to increased pore-water pressure and decreased effective stress. This phenomenon occurs during ground shaking when loose or medium-compact granular soils experience pore space shrinkage, causing the pore water to be squeezed and leading to loss of bearing capacity.

If the pore water cannot easily drain, it leads to a significant increase in pore-water pressure (u) and a reduction in effective stress (𝜎′). The effective stress (𝜎′) is related to the total stress (𝜎) by the equation;

𝜎′ = 𝜎 − u —— (1)

When the effective stress drops below a certain value, the soil loses contact between grains and starts behaving like a liquid. This is very dangerous for structures supported on such soils.

**Figure 1:** Saturated sand condition during liquefaction (Xiao, 2015)

In effect, when loose or medium-compact granular soils experience ground shaking, the pore spaces shrink and squeeze the pore water. If the pore water cannot easily drain, the pore-water pressure significantly increases, leading to a reduction in effective stress. When the effective stress drops to a certain value, the soil loses its grain-to-grain contact and behaves like a liquid.

Liquefaction can have severe consequences for structures and the surrounding environment. It can result in reduced bearing capacity, causing buildings and infrastructure to sink or collapse. Lateral spreads of liquefied soils can cause large settlements and horizontal displacements. These effects can lead to significant damage and pose risks to human safety.

Figure 2 illustrates the mechanism of liquefaction, which can result in reduced bearing capacity, significant settlement, and horizontal displacement due to lateral spreads of liquefied soils. This can manifest as sand boils or lateral spread of surface soils.

Liquefaction has been observed in various earthquakes, including the 1964 Niigata, 1964 Alaska, 1971 San Fernando, 1985 Mexico City, 1994 Northridge, 1994 Kobe, 1999 Taiwan, 1999 Turkey, 2010 Baja California, 2011 Tōhoku, and 2018 Palu Sulawesi Indonesia earthquakes.

**Figure 3:** Building failure due to liquefaction

Certain conditions must be met for liquefaction to occur:

The soil deposit consists of sandy or silty soil.
The soil is saturated or nearly saturated (usually below the groundwater table).
The soil is loose or moderately compacted.
The soil is subjected to seismic action (e.g., from an earthquake).

Soils that are relatively well-drained, such as well or poorly graded gravels (GW, GP), are less susceptible to liquefaction compared to sand or silty sand (SW, SP, or SM). Denser granular soils are less prone to liquefaction than loose soils. Liquefaction is less likely to occur in granular soils under higher initial confining effective stress (e.g., deeper soils). Based on case histories, liquefaction typically occurs within a depth of 15 meters.

Cohesive soils generally do not experience liquefaction. To qualitatively evaluate cohesive soils, the Chinese criteria defined by Seed and Idriss (1982) can be used. Liquefaction in cohesive soils can only occur if all three of the following conditions are met:

The clay content (particles smaller than 75μm) is less than 15% by weight.
The liquid limit is less than 35%.
The natural moisture content is greater than 0.9 times the liquid limit.

Screening investigations should also consider the possibility of a locally perched groundwater table, which may occur due to changes in local or regional water management practices, leading to a significant rise in the groundwater table.

Assessment of Liquefaction Hazard

Liquefaction hazard assessments are commonly conducted by employing a factor of safety (Equation 2). This factor represents the relationship between the available resistance to liquefaction, measured in terms of the cyclic stresses required to induce liquefaction, and the cyclic stresses generated by the design earthquake.

Both of these stress parameters, the resistance and the generated stresses, are typically normalized with respect to the effective overburden stress at the specific depth under consideration. They are known as the cyclic resistance ratio (CRR) and cyclic stress ratio (CSR) respectively.

FS = CRR/CSR —— (2)

The recommended guidelines provide guidance on selecting an appropriate factor of safety. For instance, the National Earthquake Hazards Reduction Program (NEHRP) Recommended Provisions for Seismic Regulations for New Buildings and Other Structures (2004) suggest that a factor of safety ranging from 1.2 to 1.5 is generally suitable for building sites. The actual value chosen depends on factors such as the significance of the structure and the potential for ground displacement.

Other authorities also provide recommendations on acceptable levels of risk. The California Geological Survey (1997) proposes that a factor of safety greater than 1.3 can be considered an acceptable level of risk. The DOD Handbook on Soil Dynamics and Special Design Aspects (1997) specifies that a factor of safety of 1.2 is appropriate for engineering design. Empirical methods are commonly used in practice to calculate the factor of safety and are widely adopted.

Evaluation of CSR

Seed and Idriss (1971) presented the following equation for the calculation of the cyclic stress ratio (CSR), and this equation is still the most widely used empirical method:

CSR = 𝜏_av/𝜎′_vo = 0.65 (a_max/g)⋅(𝜎_vo/𝜎′_vo)⋅r_d —— (3)

where:
𝜏_av = average cyclic shear stress induced by design ground motion,
𝜎′_vo = initial vertical effective stress at the depth under consideration in static condition,
𝜎_vo = initial vertical total stress at the depth under consideration in static condition,
a_max = peak horizontal acceleration at the ground surface generated by the earthquake,
r_d = stress reduction coefficient.

The NCEER workshop (1997) recommended the following equations by Liao and Whitman (1986a) for routine practice and noncritical projects:

r_d = 1.0 − 0.00765z (for z ≤ 9.15m) ——-(4a)
r_d = 1.174 − 0.0267z (for 9.15m < z ≤ 23m) ——-(4b)

The NCEER workshop (1997) cautioned users that there is considerable variability in r_d, and the r_d calculated from Equation (4) is the mean of a wide range of possible r_d, and the range of rd increases with depth.

Evaluation of CRR

The standard penetration test (SPT), the cone penetration test (CPT), shear wave velocity measurements, and the Becker penetration test (BPT) are the four field tests that are typically utilized by empirical methods for the evaluation of the CRR.

The SPT and CPT methods are often favoured because of the more extensive database and previous experience, although the other tests may be done at sites underlain by gravelly sediment or where access to large equipment is limited. This preference is due to the fact that the SPT and CPT methods have been around longer.

SPT Method of CRR Assessment

The CRR is graphically determined from the SPT blow count as shown in Figure 4. This CRR curve – the SPT clean-sand base curve – is for fines content ≤ 5% under magnitude 7.5 earthquakes. The SPT blow count is first corrected to consider overburden stress, equipment used to conduct the SPT, and the fines content (>5%); then Figure 4 is used to derive the CRR, which in turn is corrected for other earthquake magnitudes.

**Figure 4:** SPT clean-sand (percent fines ≤ 5%) base curve for magnitude 7.5 earthquakes (Xiao, 2015)

Step 1: Corrections to overburden stress and various SPT equipment
To account for the effect of overburden stress and various equipment used for SPT, the following equation is used:

(N₁)₆₀ = N_mC_NC_EC_BC_RC_S ——– (5)

Nm = measured standard penetration blow count,
CN = correction factor based on the effective overburden stress, 𝜎′vo,
CE = correction for SPT hammer energy ratio (ER)
CB = correction factor for borehole diameter,
CR = correction factor for SPT rod length,
CS = correction factor for samplers with or without liners.

Step 2: Corrections to fines content
The corrected (N₁)₆₀ in Equation (5) is further corrected for the fines content (FC) in the soil.

(N₁)_60CS= 𝛼 + 𝛽(N₁)₆₀ ——– (6)

where:
(N₁)_60CS= the (N₁)₆₀ for equivalent clean sand; (N₁)_60CS is used in Figure 4 to find the CRR under magnitude 7.5 earthquakes,
(N₁)₆₀ = corrected SPT blow count calculated in Equation (5),
𝛼 and 𝛽 = coefficients determined from the following relationships:

𝛼 = 0 for FC ≤ 5%
𝛼 = exp[1.76 − (190∕FC²)] for 5% < FC < 35%
𝛼 = 5.0 for FC ≥ 35%

𝛽 = 1.0 for FC≤ 5%
𝛽 = [0.99 + (FC^1.5∕1000)] for 5% < FC < 35%
𝛽 = 1.2 for FC ≥ 35%

Step 3: Magnitude scaling factors (MSFs)
A magnitude scaling factor (MSF) is used to correct the factor of safety (FS) when the earthquake magnitude is not 7.5:

FS =(CRR_7.5/CSR)⋅ MSF ——- (7)

where:
CRR_7.5 = the cyclic resistance ratio for a magnitude 7.5 earthquake.
The NCEER workshop (1997) summarized the MSFs proposed by various investigators (Figure 5).

**Figure 5:** Magnitude scaling factors derived by various investigators (Xiao, 2015)

Solved Example

Liquefaction Analysis Using SPT Method (After Xiao, 2015)

It is proposed to build a new bridge across a river. The construction site contains poorly graded sandy soil with fines content (passing #200 sieve) of 18%. The soil deposit of the riverbed is fully saturated with 𝛾_sat=19.5 kN/m³. The nearby Foot Hill fault system could generate a peak (horizontal) ground acceleration, a_max, of 0.25 g at this construction site. Caissons are used as the bridge foundation.

The bottom of the caissons is at a depth of 5m below the riverbed. SPT were performed in a 10.2-cm (4-inch) diameter borehole using a safety trip hammer with a blow count of 6 for the first 15 cm (6 inches), 7 blows for the second 15cm (6 inches), and 9 blows for the third 15cm (6 inches) of driving penetration.

During the design earthquake of magnitude 6.0, will the saturated sand located at the bottom of the caisson liquefy?

Solution:

(1) Calculate CSR:
CSR = 𝜏_av/𝜎′_vo = 0.65 (a_max/g)⋅(𝜎_vo/𝜎′_vo)⋅r_d
where:
Total overburden stress: 𝜎_vo = 19.5 × 5 = 97.5 kN/m²
Effective overburden stress: 𝜎′_vo = 97.5 − 9.81 × 5 = 48.5 kN/m²
Peak horizontal acceleration: a_max = 0.25 g
As z = 5m ≤ 9.15m,
Stress reduction resistance: r_d = 1.0 − 0.00765 × 5 = 0.965

So: CSR = 0.65 × 0.25g/g × 97.5/48.5 × 0.965 = 0.304

(2) Calculate CRR using the SPT method:
First, calculate the corrected SPT blow count:
(N₁)₆₀ = N_mC_NC_EC_BC_RC_S

N_m is the measured SPT blow count, which is the total blow count of the second and third six-inch penetrations.
So N_m = 7 + 9 = 16.
The correction factor on the basis of effective stress (note: Pa = 1 atm = 101.3 kN/m²):
C_N = 2.2/(1.2 + 𝜎′_vo/pa) = 2.2/(1.2 + 48.5/101.3) = 1.31

Given the automatic trip hammer, the borehole diameter of 102 mm (4 inch), and the rod length of 5m (15 ft),

the correction factor for SPT hammer energy ratio C_E =1.0,
the correction factor for borehole diameter C_B =1.0,
the correction factor for SPT rod length C_R = 0.85, and
the correction factor for samplers with liner C_S =1.0.

So ∶ (N₁)₆₀= 16 × 1.31 × 1.0 × 1.0 × 0.85 × 1.0 ≈ 18

Then calculate the equivalent clean-sand SPT blow count (N₁)₆₀:
(N₁)_60CS = 𝛼 + 𝛽(N₁)₆₀
As fines content (FC) = 18%,
𝛼 = exp[1.76 − (190∕FC²)] = exp [1.76 − (190∕18²)] = 3.234
𝛽 = [0.99 + (FC^1.5∕1000)] = [0.99 + (18^1.5∕1000)] = 1.066

(N₁)_60cs = 3.234 + 1.066 × 18 = 23

From Figure 4, find CRR_7.5 = 0.26.

(3) Calculate MSF:
From Figure 5, at M = 6.0, MSF is between 1.76 and 2.1. On the basis of the critical nature of the project (the foundation of a bridge), the MSF is chosen as the lower bound, 1.76.

(4) Factor of safety against liquefaction:
FS = (CRR_7.5/CSR) × MSF = (0.26/0.304) × 1.76 = 1.5 > 1.3

Conclusion: The SPT analysis concludes that the site will not liquefy under the design earthquake.

References:
Xiao M. (2015): Geotechnical Engineering Design (1st Edition). ISBN: 9780470632239 John Wiley & Sons, UK.

Embracing Tradition: Bringing the Traditional Style into Your Home

By

Ubani Obinna

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August 11, 2023

In an era dominated by modern designs and contemporary aesthetics, there is a timeless charm in incorporating traditional style into your home. The traditional style embodies a sense of elegance, sophistication, and a connection to the past. By blending classic elements and rich textures, you can create a warm and inviting space that pays homage to the past while still maintaining a sense of comfort and functionality.

In this article, we will explore the key aspects and strategies to help you achieve a traditional style in your home.

Understanding Traditional Style

Traditional style draws inspiration from various historical periods, including the Georgian, Victorian, and Colonial eras. It emphasizes symmetry, classic proportions, and intricate detailing.

Architecture plays a fundamental role in setting the stage for a traditional style home. Traditional homes often boast distinct architectural features that contribute to their timeless appeal. Here are some key architectural elements to consider:

Moulding and Millwork

Crown mouldings, baseboards, and chair rails are essential elements of traditional architecture. These decorative mouldings add depth and visual interest to walls, creating a sense of elegance. Look for intricate designs and profiles that suit the overall style of your home.

Wainscoting and Paneling

Wainscoting refers to the application of wooden panels along the lower portion of walls, typically topped with a chair rail. This traditional architectural feature adds sophistication and character to a room. Raised paneling is another option, where the panels are more intricately carved or recessed.

Coffered Ceilings

Coffered ceilings are a hallmark of traditional architecture. These ceilings feature a grid-like pattern of sunken panels bordered by beams or mouldings. They add depth and visual interest to a room while creating a sense of grandeur.

Archways and Columns

Incorporating archways and columns can add a touch of classical elegance to your home. Arched doorways, either leading from room to room or as grand entrances, evoke a sense of grandeur. Columns can be used to divide spaces, frame entryways, or as decorative elements in the interiors.

Window and Door Treatments

Traditional architecture often includes windows and doors with intricate detailing. Consider incorporating window casings with decorative trim, such as pediments or keystones. Traditional-style doors may feature panelling or glass inserts with ornate designs.

Fireplaces

Fireplaces are a quintessential feature of traditional homes, serving as focal points in living rooms or bedrooms. Opt for a fireplace with a mantel that boasts ornate carvings and classic lines. Surround it with decorative tiles or a traditional-style hearth. If you need a more modern approach to heating your home, then traditional column radiators are a good option.

traditional style fireplace design — Fireplace design

Exterior Details

The exterior of a traditional home can feature elements such as dormer windows, pitched roofs with rafters, gables, and decorative accents like dentil moulding or corbels. Incorporating these elements can help establish a cohesive traditional aesthetic from the outside in.

When selecting or renovating a home, look for properties that already possess traditional architectural features. However, if your current home lacks these elements, you can work with architects or contractors to incorporate them into your space. By adding architectural details, you can create a solid foundation for achieving a traditional style throughout your home.

Remember that architectural elements can be combined and tailored to suit your personal taste and the specific period of traditional style you wish to emulate. Whether you draw inspiration from Georgian, Victorian, or Colonial architecture, paying attention to these architectural features will go a long way in creating a traditional ambience in your home.

Colours and Patterns

Colours and patterns play a crucial role in establishing the traditional style in your home. By carefully selecting a warm and inviting colour palette and incorporating classic patterns, you can create a cohesive and timeless look. Here are some key considerations:

Colour Palette

Traditional interiors often feature a rich and warm colour palette that creates a cozy and inviting atmosphere. Earth tones, deep jewel tones, and muted hues work well in this style. Consider colours such as deep reds, warm browns, olive greens, and golden yellows. These colours evoke a sense of richness and elegance.

Neutrals

Neutrals are also essential in traditional interiors. Creams, beiges, and soft grays serve as a backdrop for the bolder colors in the space. These neutral tones provide balance and allow other elements, such as furniture and patterns, to stand out.

Upholstery Fabrics

Upholstery fabrics are an excellent opportunity to introduce patterns into your traditional space. Classic patterns such as floral, damask, toile, stripes, or plaids can be incorporated into sofas, armchairs, ottomans, and throw pillows. Choose fabrics with rich textures and a sense of luxury, such as silk, velvet, or brocade.

Draperies and Curtains

Window treatments play a significant role in traditional interiors. Opt for luxurious and heavy fabrics, such as velvet or silk, in solid colours or classic patterns. Consider long and flowing curtains with decorative tiebacks and valances. These elements add elegance and frame the windows beautifully.

Wallpaper

Wallpaper can be an excellent way to infuse pattern and depth into your traditional space. Look for wallpapers with intricate designs, damasks, or subtle prints. Consider using wallpaper in a dining room, or entryway, or as an accent wall in a bedroom or living room. It can instantly transform a space and add a sense of traditional charm.

Rugs and Carpets

Traditional-style rugs and carpets are essential for grounding a room and adding warmth. Look for Oriental, Persian, or Aubusson-style rugs with intricate patterns and rich colors. These rugs can be used in living rooms, dining rooms, bedrooms, or even hallways to tie the space together and provide visual interest.

Accent Colors

In addition to the foundational colour palette, accent colours can be introduced to highlight specific elements or add pops of colour. Consider incorporating accent colours through artwork, decorative accessories, or even painted furniture. Deep blues, burgundies, or emerald greens can be used sparingly to create visual interest and depth.

Remember to strike a balance when incorporating colours and patterns. Choose a dominant colour palette and use patterns strategically to avoid overwhelming the space. Mixing solid colours with patterns can create a visually appealing contrast.

By selecting a warm and inviting colour palette and integrating classic patterns, you can successfully achieve a traditional style in your home. The careful use of colours and patterns will contribute to the overall ambience and aesthetic, creating a space that exudes timeless charm and elegance.

Creating Traditional Spaces

a) Living Room: Arrange furniture symmetrically to establish a sense of balance. Opt for a plush sofa and matching armchairs surrounding a coffee table. Add a touch of formality with a grand chandelier or a set of classic table lamps. Incorporate a fireplace, if possible, as it is a hallmark of traditional living rooms.

b) Dining Room: Set the stage for elegant dinners with a large wooden dining table, complemented by upholstered chairs. Incorporate a statement chandelier above the table and adorn the walls with framed artwork or mirrors in ornate frames.

c) Bedroom: Select a four-poster or canopy bed to establish a focal point. Use layered bedding with luxurious fabrics and intricate patterns. Add a vanity table with an antique mirror and a cozy seating area for a touch of sophistication.

d) Kitchen: Incorporate traditional cabinetry with raised panel doors and decorative moldings. Opt for a farmhouse-style sink, classic hardware, and pendant lighting. Consider adding a kitchen island with seating to create a gathering space.

Finishing Touches

a) Accessories: Display decorative items such as porcelain vases, antique clocks, and framed artwork. Incorporate collections or heirlooms to add a personal touch and enhance the traditional aesthetic.

b) Flooring: Install hardwood floors with intricate detailing or consider classic patterns like herringbone or parquet. Rugs with oriental or Persian designs can add warmth and texture to your traditional space.

c) Lighting: Choose lighting fixtures that align with the traditional style, such as crystal chandeliers, brass sconces, or Tiffany-style lamps. Proper lighting will enhance the ambiance and showcase the architectural details.

Conclusion

Embracing the traditional style in your home allows you to create an environment that exudes timeless elegance and comfort. By incorporating architectural details, selecting classic furniture pieces, and paying attention to colors, fabrics, and textures, you can create a space that embraces the traditional style.

ChatGPT and Civil Engineering Calculations

By

Ubani Obinna

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June 7, 2023

Within the last few months, ChatGPT has caused a disruption in the way information is accessed on the internet. It appears that artificial intelligence is becoming capable of doing virtually everything, and the civil engineering/construction industry is not left out.

ChatGPT is an AI-based language model designed to engage in natural language conversations with users. It is part of the GPT (Generative Pre-trained Transformer) family of models developed by OpenAI. GPT models are trained on a vast amount of text data from the internet, allowing them to generate human-like responses to a wide range of prompts.

ChatGPT utilizes deep learning techniques, particularly Transformer architectures, to understand and generate text based on the context provided. It can process and generate coherent and contextually relevant responses by analyzing the patterns and structures of the input text.

In this article, we are going to review the response of ChatGPT to various calculations and examples relating to civil engineering.

QUESTION 1: A 4m span beam is simply supported at both ends and subjected to a uniformly distributed load of 10 kN/m at the midspan. What are the support reactions and the maximum bending moment?

CHATGPT:
To determine the support reactions and the maximum bending moment for the given beam, we can apply the principles of statics and beam analysis.

First, let’s consider the support reactions:

Vertical Reaction at Each Support: Since the beam is simply supported at both ends, each support will provide an equal and opposite vertical reaction. Let’s denote the upward reaction at each support as Rv.

The total load on the beam is the uniformly distributed load of 10 kN/m over the entire span. As the load is symmetrical, the load acting at the midspan is half of the total load, i.e., (10 kN/m) * (4 m) / 2 = 20 kN.

According to the principle of equilibrium, the sum of the vertical forces must be zero:
2Rv = 20 kN
Rv = 10 kN

Therefore, each support reaction is 10 kN vertically upward.

Next, let’s calculate the maximum bending moment:

The maximum bending moment occurs at the midspan of the beam when it is subjected to a uniformly distributed load. In this case, the maximum bending moment can be determined using the formula:

Mmax = (wL^2) / 8

Where:
Mmax is the maximum bending moment,
w is the uniformly distributed load (10 kN/m),
L is the span length (4 m).

Substituting the values into the formula, we get:

Mmax = (10 kN/m) * (4 m)^2 / 8
Mmax = 20 kNm

Therefore, the maximum bending moment in the beam is 20 kNm.

To summarize:

The support reactions at each end are 10 kN vertically upward.
The maximum bending moment in the beam is 20 kNm.

VERDICT: CHATGPT is correct with the bending moment, but wrong with the support reaction. The total load acting on the beam is not half of the total load, but simply the total area of the load (10 x 4 = 40 kN). So the total load on the beam is 40 kN, making the support reactions 20 kN at each support.

QUESTION 2: For the beam described above, what is the deflection at 1.5m from the left-hand side support?

CHATGPT Response:
To calculate the deflection at a specific point along the beam, such as 1.5m from the left-hand side support, we can use the formula for deflection of a simply supported beam under a uniformly distributed load.

The formula for the deflection at a distance x from the left support of a simply supported beam with a uniformly distributed load can be given as:

δ = (5 * w * x^4) / (384 * E * I)

Where:
δ is the deflection at the given point (1.5m in this case),
w is the uniformly distributed load (10 kN/m),
x is the distance from the left support to the point where the deflection is calculated (1.5m),
E is the modulus of elasticity of the material the beam is made of,
I is the moment of inertia of the beam’s cross-section.

The modulus of elasticity (E) and moment of inertia (I) depend on the properties and dimensions of the beam. Without that information, it is not possible to calculate the deflection accurately. The specific values for E and I would need to be known or provided to determine the deflection at a specific point on the beam.

Please note that calculating beam deflection involves additional assumptions, such as the beam being linearly elastic and having a constant cross-section throughout its length. Different beam materials and configurations may require different deflection formulas and considerations.

VERDICT: CHATGPT’s response is wrong. The AI model used a general equation for calculating the deflection at the mid-span of a simply supported beam subjected to a uniformly distributed load to calculate the deflection at a point that is not the mid-span. You cannot merely substitute any value of x into the famous deflection equation [δ = (5wx⁴) / (384EI)] if x is not the midspan.

The general equation for calculating the deflection at any point on a simply supported beam subjected to a uniformly distributed load is;

EIδ = -wLx³/12 + wx⁴/24 + (wL³/24)x

at x = L/2 (mid-span)
δ = [-wL(L/2)³/96 + w(L/2)⁴/24 + (wL³/24)L/2]/EI
δ = [-wL⁴/96+ wL⁴/384 + wL⁴/48]/EI = 5wL⁴/384EI

At x = 3L/8 (1.5m from the left-hand side), the value of the deflection can also be calculated.

QUESTION 3: Your approach to the above question is wrong. The formula is only valid for the mid-span of the beam and not anywhere else.

CHATGPT:
I apologize for the confusion caused by my previous response. You are correct, the formula I mentioned is applicable only for the deflection at the mid-span of the beam under a uniformly distributed load.

To determine the deflection at a specific point other than the mid-span, we need to use a different approach. In this case, we can calculate the deflection using the double integration method.

The deflection at a distance x from the left support can be calculated using the following steps:

Calculate the reaction forces at the supports using the total load and beam span as explained in the previous response. In this case, each support reaction is 10 kN vertically upward.
Determine the equations for the elastic curve in each segment of the beam. The beam can be divided into two segments: one from the left support to the point of interest (1.5m), and the other from the point of interest to the right support.
Integrate the equations of the elastic curve twice to obtain the deflection equation for each segment.
Apply the appropriate boundary conditions to determine the constants of integration.
Evaluate the deflection equation at the point of interest (1.5m) to obtain the deflection at that location.

Without specific information about the beam’s material, cross-section, and other relevant details, it is not possible to provide an accurate calculation of the deflection at 1.5m from the left support. To determine the deflection accurately, you would need to know the properties of the beam and use the appropriate equations and calculations based on those properties.

VERDICT: CHATGPT’s response is correct.

QUESTION 4: A rectangular reinforced concrete beam with a depth of 500mm and a width of 250mm is subjected to an ultimate bending moment of 95 kNm. What is the area of steel required if the yield strength of steel is 500 MPa, the characteristic compressive strength of concrete is 30 MPa, and the concrete cover is 35 mm.

CHATGPT:
To determine the area of steel required in a reinforced concrete beam, we need to consider the equilibrium of forces and the stress limits of both the concrete and steel.

Calculate the section modulus: The section modulus (Z) of a rectangular beam can be calculated using the formula: Z = (b * d^2) / 6 Where: b is the width of the beam (250 mm), d is the effective depth of the beam (depth – cover – steel diameter).

Given:
Depth of the beam (d) = 500 mm
Concrete cover (c) = 35 mm
Assuming the diameter of the steel reinforcement as 8 mm (commonly used size),
Effective depth (d) = Depth – Cover – Steel diameter = 500 mm – 35 mm – 8 mm = 457 mm

Now, calculate the section modulus:
Z = (250 mm * (457 mm)^2) / 6
Z = 20,610,417 mm^3

Calculate the stress in the concrete: The stress in the concrete (σ_c) can be calculated using the formula:
σ_c = M / Z
Where: M is the ultimate bending moment (95 kNm).

Given: Ultimate bending moment (M) = 95 kNm

Convert the moment to Nmm: M = 95 kNm * 10^6 Nm/kNm M = 95,000,000 Nmm

Now, calculate the stress in the concrete:
σ_c = 95,000,000 Nmm / 20,610,417 mm^3
σ_c = 4.61 MPa

Calculate the required area of steel: The required area of steel (A_s) can be determined using the formula:
A_s = (σc * Z) / σs
Where: σ_s is the yield strength of the steel reinforcement (500 MPa).

Given: Yield strength of steel (σ_s) = 500 MPa

Now, calculate the required area of steel:
A_s = (4.61 MPa * 20,610,417 mm^3) / (500 MPa)
A_s = 189.23 mm^2

Therefore, the required area of steel in the reinforced concrete beam is approximately 189.23 mm^2.

Verdict: Uhmmmmm ???

QUESTION 5: Can you carry out the calculation again according to the requirements of the Eurocode?

CHATGPT: Certainly! I apologize for the oversight. Here’s the calculation based on the requirements of the Eurocode for reinforced concrete design.

Calculate the design bending moment (M_d): The design bending moment (M_d) is calculated by dividing the ultimate bending moment by a factor of safety, typically taken as 1.5 for ultimate limit state design.
M_d = 95 kNm / 1.5 M_d = 63.33 kNm
Calculate the effective depth (d): The effective depth (d) is calculated as the overall depth minus the concrete cover and half the diameter of the reinforcement.
d = Depth – Cover – (Steel diameter / 2)
d = 500 mm – 35 mm – (8 mm / 2)
d = 457 mm
Determine the design compressive strength of concrete (f_cd): The design compressive strength of concrete (f_cd) is calculated by dividing the characteristic compressive strength of concrete (f_ck) by a factor of safety, typically taken as 1.5 for normal strength concrete.
f_ck = 30 MPa / 1.5 f_ck = 20 MPa
Calculate the design tensile strength of steel (f_td): The design tensile strength of steel (f_td) is calculated by dividing the characteristic yield strength of the reinforcement (f_yk) by a factor of safety, typically taken as 1.15.
f_yk = 500 MPa / 1.15 f_yk = 434.78 MPa
Determine the design moment capacity (M_rd): The design moment capacity (M_rd) is calculated using the following formula:
M_rd = (f_td * A_s * (d – a_s / 2)) / γ_M

Where:
A_s is the area of steel,
a_s is the distance from the centroid of the steel to the extreme compression fiber,
γ_M is the partial factor for moment resistance (taken as 1.0 for the ultimate limit state design).

Since the beam is under-reinforced according to Eurocode, the limiting value of a_s is the smaller of:
a_s = β_1 * (d – a_s / 2) or a_s = β2 * (d – xu)

For rectangular beams, β_1 = 0.5 and β_2 = 0.8.

Assuming a_s = 35 mm (same as the concrete cover), we can calculate the value of x_u (the depth of the neutral axis):
x_u = β_2 * d x_u = 0.8 * 457 mm
x_u = 365.6 mm

Now we can substitute the values into the formula:
M_rd = (f_td * A_s * (d – a_s / 2)) / γ_M
63.33 kNm = (434.78 MPa * A_s * (457 mm – 35 mm / 2)) / 1.0

Solving for A_s:
A_s = (63.33 kNm * 1.0) / (434.78 MPa * (457 mm – 35 mm / 2))
A_s ≈ 50.57 mm^2

Therefore, according to the Eurocode requirements, the required area of steel in the reinforced concrete beam is approximately 50.57 mm^2.

VERDICT: WRONG

QUESTION 6: Your solution is a bit strange. The bending moment provided was stated as an ultimate moment. Furthermore, even if the bending moment is ‘unfactored’, are you supposed to multiply or divide action effects with the partial factor of safety?

CHATGPT: I apologize for the confusion in my previous response. You are correct, for ultimate limit state design according to Eurocode, the ‘unfactored’ ultimate bending moment should be used directly in the calculations. Additionally, the action effects should be multiplied by the appropriate partial factor of safety.

Let’s recalculate the required area of steel according to the Eurocode requirements:

Calculate the effective depth (d) as before:
d = Depth – Cover – (Steel diameter / 2)
d = 500 mm – 35 mm – (8 mm / 2) d = 457 mm
Determine the design compressive strength of concrete (f_cd): The design compressive strength of concrete (f_cd) is calculated by dividing the characteristic compressive strength of concrete (f_ck) by the appropriate partial factor of safety for concrete. For normal-strength concrete, this factor is taken as 1.5.
f_cd = 30 MPa / 1.5
f_cd = 20 MPa
Calculate the design tensile strength of steel (f_td): The design tensile strength of steel (f_td) is calculated by dividing the characteristic yield strength of the reinforcement (f_yk) by the appropriate partial factor of safety for steel. For reinforcing steel, this factor is typically taken as 1.15.
f_td = 500 MPa / 1.15
f_td = 434.78 MPa
Determine the required area of steel (A_s): The required area of steel (A_s) can be calculated using the formula:
A_s = (M_d * 10^6) / (f_td * (d – a_s / 2))

Where: M_d is the ‘unfactored’ ultimate bending moment (95 kNm),
f_td is the design tensile strength of steel (434.78 MPa),
d is the effective depth of the beam (457 mm),
a_s is the distance from the centroid of the reinforcement to the extreme compression fiber.

Assuming a_s = 35 mm (same as the concrete cover), we can substitute the values into the formula:
A_s = (95 kNm * 10^6) / (434.78 MPa * (457 mm – 35 mm / 2))
A_s ≈ 515.88 mm^2

Therefore, according to the Eurocode requirements, the required area of steel in the reinforced concrete beam is approximately 515.88 mm^2.

VERDICT: This particular solution is very close to being acceptable, even though the approach used in the calculation of the lever arm is a bit crude (considering the EC2 stress block). We know that for singly reinforced sections, the approach used by ChatGPT shouldn’t make any much difference in the design results (using the effective depth of 457mm, the area of steel required is 503 mm²).

Furthermore, ChatGPT made its own assumptions (such as selecting its own diameter of reinforcement), but it didn’t consider the diameter of links in calculating the effective depth. It was also able to pick the material partial factors of safety correctly. However, it erroneously used the term ‘unfactored moment’ which it picked from the question I posed to it. It probably assumed ‘unfactored moment’ to mean ‘design moment’.

QUESTION 7: A 500 mm diameter concrete pile is driven 12m deep into a homogenous pure clay soil with an effective cohesion of 18 kPa. What is the load-carrying capacity of the pile as a result of shaft friction?

CHATGPT:

To determine the load-carrying capacity of the pile due to shaft friction, we can use the principles of soil mechanics and the formula for calculating the ultimate shaft resistance in cohesive soils. The ultimate shaft resistance can be calculated using the following equation:

Qs = π * D * L * c’

Where:
Qs is the ultimate shaft resistance,
D is the diameter of the pile,
L is the depth of penetration,
c’ is the effective cohesion of the soil.

Given: Diameter of the pile (D) = 500 mm Depth of penetration (L) = 12 m Effective cohesion of the soil (c’) = 18 kPa

Converting the diameter to meters: D = 500 mm / 1000 D = 0.5 m
Converting the effective cohesion to kN/m²: c’ = 18 kPa * 1 kN/m² / 1000 Pa
c’ = 0.018 kN/m²

Substituting the values into the formula: Qs = π * 0.5 m * 12 m * 0.018 kN/m²
Qs ≈ 3.83 kN

Therefore, the load carrying capacity of the pile due to shaft friction is approximately 3.83 kN.

VERDICT: WRONG

QUESTION 8: But kPa is the same thing as kN/m^2

ChatGPT: You’re absolutely right, I apologize for the confusion in my response. kPa (kilopascal) is indeed equivalent to kN/m² (kilonewton per square meter), representing the unit of pressure or stress.

Given that the effective cohesion (c’) is already in kPa, we can directly substitute the values into the formula:

Qs = π * D * L * c’
Qs = π * 0.5 m * 12 m * 18 kPa
Qs ≈ 34.56 kN

Therefore, the load-carrying capacity of the pile due to shaft friction is approximately 34.56 kN.

VERDICT: This particular solution is correct. But out of curiosity, it is important to find out if the AI model picked the right equation.

QUESTION 9: Did you consider the adhesion factor (α) in your calculation?

I apologize for not considering the adhesion factor (α) in the calculation. The adhesion factor takes into account the reduction in the effective cohesion along the pile shaft due to factors such as pile installation method and soil characteristics.

The equation to calculate the ultimate shaft resistance considering the adhesion factor is:

Qs = α * π * D * L * c’

The adhesion factor (α) typically ranges between 0.5 and 1.0, depending on the soil conditions and installation method. Without specific information regarding the adhesion factor for your case, it is challenging to provide an accurate value. However, for a conservative estimate, let’s assume α = 0.5.

Using this assumption, we can calculate the load-carrying capacity of the pile due to shaft friction:

Qs = 0.5 * π * 0.5 m * 12 m * 18 kPa
Qs ≈ 8.14 kN

Therefore, considering an adhesion factor (α) of 0.5, the load carrying capacity of the pile due to shaft friction is approximately 8.14 kN.

VERDICT: For driven piles in clay soils with effective cohesion less than 40 kPa, the recommended value of the adhesion factor is 1.0. I guess we can forgive ChatGPT.

Conclusion

In conclusion, ChatGPT can be a useful tool for carrying out civil engineering calculations. However, it can only get better. As can be seen from this article, it can quickly perform calculations, especially for problems involving popular equations and well-known theories. For other advanced calculations, extreme caution should be used.

It is important to note that ChatGPT is an AI language model and does not have access to specific project details or real-time data. Therefore, its responses are based solely on the information provided and the knowledge it has been trained on.

While ChatGPT can provide valuable assistance in performing calculations, it is essential to exercise caution and independently verify the results as can be seen in this article. It appears that it is heavily influenced by the input data, and the expertise of the engineer is required to drive it in the right direction.

Engineering calculations often require careful consideration of various factors, including applicable codes, standards, material properties, and site-specific conditions. Therefore, it is always recommended to consult with qualified engineers and professionals to ensure accurate and reliable results.

Critical Depth for Skin Friction in Piles

By

Ubani Obinna

-

June 19, 2023

Table of Contents

Skin friction is the resistance developed along the sides of the pile shaft due to the interaction between the pile and the surrounding soil. It is one of the primary mechanisms by which piles transfer load to the soil. The magnitude of skin friction is influenced by various factors, including soil type, pile geometry, installation method, and load conditions.

In geotechnical engineering, the vertical effective stress, denoted by σ’, normally increases with depth. As a result, it should be logical that the magnitude of skin friction in piles should increase infinitely with increasing depth. In reality, the magnitude of skin friction will not continue to increase infinitely with increasing depth. It was formerly thought that at a certain depth, the value of skin friction in piles would become constant. This particular depth is called the ‘critical depth’.

The critical depth for skin friction is the depth below the ground surface at which the increase in pile diameter does not contribute significantly to the overall capacity of the pile. In other words, beyond this critical depth, the additional skin friction developed due to an increase in pile diameter becomes negligible. Determining the critical depth is crucial because it helps optimize the design and construction of piles, considering both cost-effectiveness and structural efficiency.

**Figure 1:** The theory of critical depth (Rajapakse, 2008)

As shown in Figure 1, skin friction was assumed to increase up to the critical depth and then maintain a constant value.

d_c = critical depth
S_c= skin friction at the critical depth (K.σ’_c.tanδ)
σ’_c= effective stress at critical depth

The following approximations were assumed for the critical depth

Critical depth for loose sand = 10d (d is the pile diameter or the width)
Critical depth for medium-dense sand = 15d
Critical depth for dense sand = 20d

However, this theory does not explain recent observations made from precise pile load test data. According to recent experiments, skin friction will not become absolutely constant as was once believed.

Experimental Evidence of Critical Depth

A typical variation in skin friction that occurs with increasing pile depth is shown in Figure 2. As can be seen in Figure 2, the assumption proposing constant skin friction below the critical depth is not supported by the results obtained from the experiments.

**Figure 2:** Variation of skin friction. (Source: Randolph et al., 1994)

The skin friction has a tendency to increase with depth, and it reaches its maximum value right above the tip of the pile. After then, there would be a significant reduction in skin friction. At the moment, there is no theory that can adequately explain the observations made in the field. The critical depth theory is still widely used in engineering today because there is no more advanced alternative.

Reasons for limiting skin friction in Piles

In order to explain why the skin friction does not increase infinitely with depth as the skin friction equation suggested, the following explanations have been presented.

Unit Skin Friction = K∙σ’∙tanδ
σ’ = γd

The value of K presented above is determined by the soil angle of friction, denoted by φ’. As one goes deeper, the angle of internal friction angle typically reduces. As a result, the K value reduces as depth increases (Kulhawy 1983).
The aforementioned equation for skin friction does not hold true at high-stress levels because the sand particles have to adjust their orientation.
A reduction in the magnitude of friction is experienced by the shaft as the pile depth increases. (See Figure 3) (Randolph et al. 1994).

**Figure 3:** Variation of skin friction in relation to depth (Rajapakse, 2008)

Let’s assume a pile was driven to a depth of 3m (10 ft), and the unit skin friction was measured at a depth of 1.5m (5 ft). If we also assume that the pile was driven further to a depth of 4.5m (15 ft) and that the unit skin friction was measured at the same depth of 1.5m( 5 ft). It has been reported that the second scenario has a lower unit skin friction at a distance of 1.5m.

Figure 3 demonstrates that as the pile is driven further into the earth, the local skin friction experiences a reduction. According to NAVFAC DM 7.2, the maximum value of skin friction and end bearing capacity is attained after 20 diameters within the bearing zone. This is the case regardless of the bearing material.

Solved Example on Critical Depth

(Calculation after Rajapakse, 2008)

Find the skin friction and end-bearing capacity of the pile shown. Assume that critical depth is achieved at 20 ft into the bearing layer. The pile diameter is 1 ft, and other soil parameters are as shown in the figure.

Solution
The skin friction is calculated in the overburden soil. In this case, skin friction is calculated in the soft clay. Then the skin friction is calculated in the bearing layer (medium sand) assuming the skin friction attains a limiting value after 20 diameters (critical depth).

STEP 1: Find the skin friction from A to B.
Skin friction in soft clay = α × c × perimeter surface area
= 0.4 × 700 × πdL = 0.4 × 700 × π × 1 × 12 = 10,560 lbs = 46.9 kN

STEP 2: Find the skin friction from B to C.
Skin friction in sandy soils S = K∙σ’∙tanδ × A_p

S = skin friction of the pile
σ’ = average effective stress along the pile shaft
Average effective stress along pile shaft from B to C = (σ_B + σ_C)/2
σ_B = effective stress at B
σ_C = effective stress at C

To obtain the average effective stress from B to C, find the effective stresses at B and C and obtain the average of those two values.
σ_B = 100 × 4 (100 – 62.4) × 8 = 700.8 lb/ft² (33.6 kPa)
σ_C = 100 × 4 (100 – 62.4) × 8 + (110 – 62.4) × 20 = 1452.8 lb/ft² (69.5 kPa)
Average effective stress along pile shaft from B to C = (700.8 + 1452.8)/2 = 1076.8 lb/ft²

Skin friction from B to C = K∙σ’∙tanδ × A_p = 0.9 × 1076.8 × tan 25 × (π × 1 × 20) = 28,407 lbs

STEP 3: Find the skin friction from C to D.
Skin friction reaches a constant value at point C, 20 diameters into the bearing layer.
Skin friction at point C = K∙σ’_v∙tanδ × A_p

σ’_v at point C = 100 × 4 (100 – 62.4) × 8 (110 – 62.4) × 20 = 1,452.8 lb/ft²
Unit skin friction at point C = 0.9 × 1,452.8 × tan 25 = 609.7 lb/ft² (29 kPa)
Unit skin friction is constant from C to D. This is because skin friction does not increase after the critical depth.
Skin friction from C to D = 609.7 × surface perimeter area = 609.7 × (π × 1 × 8) = 15,323.4 lbs (68.2 kN)

Summary
Skin friction in soft clay (A to B) = 10,560 lbs
Skin friction in sand (B to C) = 28,407 lbs
Skin friction in sand (C to D) = 15,323 lbs
Total = 54,290 lbs (241 kN)

STEP 4: Compute the end bearing capacity.
End bearing capacity also reaches a constant value below the critical depth.
End bearing capacity = q × N_q × A

q = effective stress at pile tip
N_q = bearing capacity factor (given to be 15)
A = cross-sectional area of the pile

If the pile tip is below the critical depth, q should be taken at critical depth. In this example, the pile tip is below the critical depth, which is 20 diameters into the bearing layer. Hence, q is equal to the effective stress at the critical depth (point C).

Effective stress σ’_v at point C = 100 × 4 (100 – 62.4) × 8 (110 – 62.4) × 20 = 1,452.8 lb/ft²
End bearing capacity = qN_qA = 1,452.8 × 15 × (πd²/4) = 17,115 lbs

Total ultimate capacity of the pile = total skin friction + end bearing = 54,290 + 17,115 = 71,405 lbs (317.6 kN)

Conclusion

The critical depth for skin friction in piles is a crucial parameter for the design of piles in sand. It is believed to depend on factors such as soil type, pile diameter, and installation techniques. The determination of the critical depth is very important to ensure that the shaft friction of the pile is not overestimated, thereby ensuring the stability and safety of structures supported by piles. Ongoing research and advancements in geotechnical engineering continue to enhance our understanding of the critical depth and its significance in pile foundation design.

Reference

Rajapakse R. (2008): Pile Design for Structural and Geotechnical Engineers. ISBN: 978-0-08-055916-2 Butterworth-Heinemann

Influence Lines

By

Ubani Obinna

-

June 1, 2023

Table of Contents

In bridge design, it is very necessary that bridge decks support both static and moving loads. Every component of a bridge needs to be designed to withstand the worst loading effect that could possibly arise in that part. In effect, traffic live loads should be placed where they will cause the most onerous effect on the structure. ‘Influence lines’ are a helpful tool for assessing the most severe loading condition.

An influence line represents the response of a specific element of a bridge to the effect of a moving load, such as reaction, shear force, bending moment, or axial force. It is a diagram where the value of the response at any point is equal to the effect caused by a unit load applied at that point. Influence lines provide a systematic approach for determining how the force, moment, or shear in a specific part of a structure changes as the applied load moves across the structure.

Influence lines for statically determinate structures consist of straight lines, but for indeterminate structures, they can have more complex shapes. The primary purpose of influence lines is to identify where to place live loads to achieve maximum effect.

Influence Lines for Shear in Simple Beams

Influence lines for shear at two sections of a simply supported beam are shown in Figure 1. When the summation of transverse forces to the left of a section is in the upward direction or when the summation of transverse forces to the right of the section are in the downward direction, positive shear is said to occur. For each position of the unit load, the shear force at sections 1-1 and 2-2 is determined by placing the unit force at various points.

**Figure 1:** Influence line for shear (Shanmugam and Narayanan, 2008)

The values provide the ordinate of the influence line, which may be used to draw the influence line diagrams for the shear force at sections 1-1 and 2-2. It should be noted that the slope of the influence line for shear on the left of the section is similar to the slope of the line on the right of the section. In other circumstances, this information can be used to draw the influence lines for shear force.

Influence Lines for Bending Moments in Simple Beams

Figure 2 shows the influence lines for the bending moment at the same sections, 1-1 and 2-2, of the simple beam under consideration in Figure 1. For a section, the moment is considered positive when the total of all the moments of the forces to the left is clockwise or when the sum to the right is counterclockwise. For various places of unit load, the values of the bending moment at sections 1-1 and 2-2 are obtained and plotted as shown in Figure 2.

**Figure 2:** Influence line for bending moment (Shanmugam and Narayanan, 2008)

It should be noted that a shear or bending moment diagram shows how shear or moment values change throughout the entire structure when loads are fixed in a specific position. Conversely, an influence line for shear or moment depicts how that response varies at a specific section of the structure due to the movement of a unit load from one end to the other. Influence lines are helpful in determining the magnitude of a specific response at the section where it is drawn, when the beam is subjected to various types of loading.

For instance, the shear force at section 1-1 is determined by the product of the load intensity, q_o, and the net area under the influence line diagram assuming a uniform load of intensity q_o per unit length operates throughout the full length of the basic beam depicted in Figure 22.

Since the net area at section 1-1 is 0.3P, the shear force there is 0.3q_oP as well. The bending moment at the section is calculated from the area of the appropriate influence line diagram times the intensity of loading, q_o. Therefore, the section’s bending moment is 0.08q_oP².

Solved Example

Let us consider the beam loaded as shown below. It is desirous to obtain the influence line for the support reactions, and for the internal stresses with respect to section 1-1.

In all cases, we will be taking P as unity (i.e 1.0)

(1) Influence line for support reactions

Support A
Support reaction at point A (F_A) = (L – x)/L
At x = -L₁;
F_A = (L + L₁)/L

At x = 0;
F_A = 1.0

At x = L + L₂;
F_A = (L – L – L₂)/L = – L₂/L

Support B
Support reaction at point B (F_B) = x/L
At x = -L₁;
F_B = -L₁/L

At x = 0;
F_B = 0

At x = L;
F_B = 1.0

At x = L + L₂;
F_B = (L + L₂)/L

(2) Influence line for bending moment with respect to section 1-1

(0 ≤ x ≤ a)
M_1-1 = F_A.a – P(a – x)
M_1-1= [P(L – x).a]/L – P(a – x)
But taking P = 1.0;
= [(L – x).a]/L – (a – x)

At x = -L₁;
M_1-1 = [(L + L₁).a]/L – (a + L₁) = [L₁(a – L)/L] = -L₁.b/L

At x = 0;
M_1-1 = [(L – 0).a]/L – (a – 0) = [L₁(a – L)/L] = 0

At x = a;
M_1-1 = [(L – a).a]/L – (a – a) = [L₁(a – L)/L] = a.b/L

(a ≤ x ≤ L)
M_1-1 = [P(L – x)a]/L

At x = a;
M_1-1 = [(L – a)a]/L = a.b/L

At x = L;
M_1-1 = [(L – L)a]/L = 0

At x = L + L₂;
M_1-1 = [(L – L – L₂)a]/L = – L₂a/L

(2) Influence line for shear with respect to section 1-1

(0 ≤ x ≤ a)
Q_1-1 = P(L – x)/L – P = – F_B = –x/L

At x = -L₁;
Q_1-1 = L₁/L

At x = 0;
Q_1-1 = 0

At x = a;
Q_1-1 = -a/L

(a ≤ x ≤ L)
Q_1-1 = -(P.x)/L + P = (L – x)/L

At x = a;
Q_1-1 = b/L

At x = L;
Q_1-1 = 0

At x = L + L₂;
Q_1-1 = [(L – L – L₂)]/L = -L₂/L

Influence Lines for Trusses

Influence lines for support reactions and member forces can be constructed using the same approach as influence lines for various beam functions. They provide valuable information for determining the maximum load that can be applied to a truss. By analyzing the movement of a unit load across the truss, we can calculate the responses of interest at each panel point.

However, it is not necessary to calculate the member forces at every panel point, as certain parts of the influence lines can be identified as straight lines for multiple panels. Method of sections can be used to obtain the member forces in any panel of interest.

**Figure 3:** Influence line for trusses

The truss shown above is used as an example to explain how to construct influence lines for trusses. Passing a section 1-1 and taking into account the equilibrium of the free body diagram of one of the truss segments yields the member forces in BD, CE, and BE.

First, a unit load is applied to node C, and the force in BD is calculated by calculating the moment about node E of all forces acting on the right-hand segment of the truss, then dividing that moment by the lever arm (the distance at which the force in BD is perpendicular to node E).

The resultant value provides the influence diagram’s ordinate at C in the truss. Similar to how the force in BD for a unit load imposed at E is represented by the obtained ordinate at E. Two additional points, one at each of the supports, can be added to the influence line to complete it. The relevant influence line diagram can be finished by obtaining the force in the member CE due to the unit load applied at C and E.

The influence line for force in BE can be obtained by taking into account the horizontal component of force in the diagonal of the panel. The influence diagrams for the member forces in BD, CE, and BE are shown in Figure 3. By running an imaginary vertical section through the panel and taking moments at the junction of the diagonal and the other chord, it is possible to estimate the influence line ordinates for the force in a chord member of a ‘curved-chord’ truss.

Qualitative influence lines: Müller–Breslau principle

One of the most effective methods of obtaining influence lines is by the use of the Müller–Breslau principle, which states that ‘the ordinates of the influence line for any response in a structure are equal to those of the deflection curve obtained by releasing the restraint corresponding to this response and introducing a corresponding unit displacement in the remaining structure’.

In this way, the shape of the influence lines for both statically determinate and indeterminate structures can be easily obtained, especially for beams.

Some methods for drawing influence lines are as follows:

Support reaction
Remove the support and introduce a unit displacement in the direction of the corresponding reaction to the remaining structure as shown in Figure 4 for a symmetrical overhang beam.

**Figure 4:** Influence line for support reaction (Shanmugam and Narayanan, 2008)

Shear
Make a cut at the section and introduce a unit relative translation (in the direction of positive shear) without relative rotation of the two ends at the section as shown in Figure 5.

**Figure 5:** Influence line for mid-span shear force (Shanmugam and Narayanan, 2008)

Bending moment
Introduce a hinge at the section (releasing the bending moment) and apply bending (in the direction corresponding to positive moment) to produce a unit relative rotation of the two beam ends at the hinged section as shown in Figure 6.

**Figure 6:** Influence line for mid-span bending moment (Shanmugam and Narayanan, 2008)

Influence lines for continuous beams

Using the Muller–Breslau principle, the shape of the influence line of any response of a continuous beam can be sketched easily. One of the methods for beam deflection can then be used for determining the ordinates of the influence line at critical points.

Conclusion

In summary, influence lines are valuable tools in structural analysis, providing insights into the behaviour of structures under varying loads. They aid in determining critical locations, optimizing designs, evaluating load effects, and ensuring structural integrity. By utilizing influence lines, engineers can make informed decisions and design structures that are safe, efficient, and capable of withstanding the intended loads.

Reference

Shanmugam N. E. and Narayanan R. (2008). ‘Structural Analysis’ in ICE Manual of Bridge Engineering, Eds by Gerard Parke and Nigel Hewson. Thomas Telford Ltd, UK

Incrementally Launched Box Girder Bridges

By

Ubani Obinna

-

June 3, 2023

Table of Contents

Launched single-cell box girders are employed in situations where the bridge alignment is straight or on a constant radius curve, either vertically or horizontally. It is particularly useful for overcoming access issues or avoiding obstructions at ground level.

Typically, this method is used for bridge spans up to 60 meters, but in some cases, it has been utilized for longer spans up to 100 meters by using temporary piers to reduce the effective span length during launching. The depth of the deck must remain constant during the launching process, with a typical ratio to the launched span of 1:16 or less.

The process involves casting segments behind the abutment and pushing or pulling the deck over the piers. A designated casting area is prepared behind the abutment, where the reinforcement is assembled, concrete is poured, and launching takes place. The segments used for the bridge are usually standardized and have lengths of 20-30 meters.

Procedure for Incremental Launching of Box-girder Bridges

The launching process begins with the casting of the first segment, which is then moved forward on temporary bearings. The second segment is cast against the first, and both are incrementally moved forward. This process continues with subsequent segments being cast and the deck being moved until it reaches the opposite abutments and reaches its final position.

The area behind the casting bay is used for steel fixing and placing prestressing ducts, which can progress simultaneously with other operations. When the deck is launched, the steel cage is attached to the concrete and pulled into position for concreting. The formwork system is designed to be lowered, leaving the deck on temporary supports ready for launching.

Temporary bearings, consisting of steel plates with stainless steel surfaces and laminated rubber pads, are used on each pier and in the casting area to facilitate the deck launching process. A low-friction sliding surface is created by inserting a Teflon pad between the bearing and concrete deck.

Launching devices, typically fixed to the abutments, are employed to provide the necessary thrust resistance. These devices jack up the deck slightly to grip the structure, push or pull it forward, and then drop down to release the structure and move back for another stroke.

During the launching process, the pushing force needs to increase to overcome the frictional force on the temporary bearings, which can range from 2% to 6% of the vertical load. Greater pushing forces are required when launching a deck up a slope, while a braking device is needed when launching it down a slope. The abutment is primarily responsible for resisting the launching force and must be designed to prevent sliding or overturning.

You can watch the video for the incremental launching of box girder bridges below.

Additional resistance can be achieved by providing the casting area with a ground slab as a working platform and connecting it with the abutment. Guides are fixed to the piers to ensure the deck remains properly aligned during the launching operation. Once the launching is complete, the deck is raised, and the temporary bearings are replaced by permanent bearings.

To reduce cantilever moments occurring as the deck is launched over a pier, a temporary lightweight steel launching nose can be attached to the front of the box. The length and stiffness of the launching nose are critical factors in its effectiveness, and a balance must be struck between its cost and the cost of accommodating additional moments in the deck. Typically, the launching nose length is about 60% of the span length, and its stiffness (EI) is approximately 10-15% of the concrete deck.

Alternatively, a temporary tower and stay-cables can be utilized over the front portion of the deck instead of a launching nose to reduce bending moments. The tension in the stays is adjusted as the deck passes over a pier to control the moments and forces imposed on the structure. As the deck moves over the piers, each section experiences changes in moment and shear, and the prestress design needs to account for the full range of these forces.

During the launching process, the deck needs to be strong enough to resist shear forces and the temporary bearing load under the webs as it passes over the piers. The webs are typically kept at a constant thickness, and the corners where the web meets the bottom slab are reinforced to distribute the local loads from the temporary bearings. Design considerations must also account for unevenness in the concrete surface and differential settlement of the piers and temporary supports, which generate additional moments and shears in the deck during launching.

Launching the deck creates friction in the temporary bearings, resulting in a load being applied to the top of the piers. The temporary bearings are aligned parallel to the deck, inducing a horizontal load on the piers in addition to the vertical loads. Therefore, the piers must be designed to withstand these combined horizontal and vertical loads. Providing stays or guys to the top of the piers can help reduce the effects of these horizontal loads.

Summary of procedure for incremental launching of box girder bridges

The construction methodology for incrementally launched box girder bridges involves a systematic process that can be summarized in the following steps:

Design and Planning: The initial stage involves detailed design and planning of the bridge structure, considering factors such as span lengths, segment sizes, construction sequence, and launching forces. Engineering calculations and structural analysis are performed to ensure the feasibility and integrity of the design.
Fabrication of Segments: The bridge segments, typically box-shaped girders, are prefabricated offsite. This includes the fabrication of individual segments or segments in smaller assemblies, depending on their size and transportation constraints. Quality control measures are implemented to ensure that the segments meet the required specifications and tolerances.
Construction of Piers and Abutments: The piers and abutments that will support the bridge are constructed first. These elements provide the necessary foundation and stability for the bridge structure. Precise alignment and positioning of the piers and abutments are crucial to ensure the accuracy of the bridge alignment during the launching process.
Installation of Bearings and Temporary Supports: Bearings and temporary supports are installed on the piers and abutments. Bearings allow for controlled movement and transfer of loads between the bridge and its supports. Temporary supports, such as launching nose beams and sliding bearings, are positioned to facilitate the launching process.
Incremental Launching: The prefabricated segments are transported to the construction site and assembled in a sequence along the bridge alignment. The launching process involves sliding each segment into its final position using hydraulic jacks, pushing the bridge incrementally forward. The temporary supports facilitate the sliding movement and provide stability during launching.
Post-Launch Adjustments: Once a segment is launched, adjustments may be made to ensure proper alignment, fit, and connection between segments. These adjustments may involve fine-tuning the position and alignment of the segment, as well as making necessary modifications to the temporary supports or sliding mechanisms.
Segment Connection and Completion: Once all segments are in place, they are securely connected and integrated to form a continuous bridge structure. This includes welding or bolting connections, as well as completing any required post-tensioning or grouting activities. Additional construction activities, such as deck placement, barrier installation, and finishing touches, are carried out to finalize the bridge construction.

Throughout the construction process, careful monitoring, quality control, and safety measures are implemented to ensure the structural integrity and safety of the bridge. Engineering expertise and coordination among various stakeholders, including designers, fabricators, contractors, and inspectors, are essential to successfully execute the incremental launching method for box girder bridges.

Advantages of incrementally launched box girder bridges

Access and Obstruction Avoidance: Incrementally launched box girder bridges are beneficial when there are access limitations or obstructions at ground level. By constructing the bridge in segments and launching them over piers, it allows for easier navigation around obstacles or challenging terrain.
Efficient Construction Process: The incremental launching method allows for continuous construction without the need for temporary support in the middle of the span. This can save time and reduce construction costs compared to other bridge construction methods.
Reduced Disruption: Incrementally launched box girder bridges minimize disruption to traffic and water flow during construction. The launching process avoids the need for temporary detours or interruptions in the flow of vehicles or water under the bridge.
Standardized Segments: The use of standardized segments simplifies the construction process, as the same segment lengths can be used for multiple bridge projects. This standardized approach improves efficiency and reduces design and fabrication costs.

Disadvantages of incrementally launched box girder bridges

Limited Span Length: Incrementally launched box girder bridges are typically suitable for shorter to medium spans, up to approximately 100 meters. For longer spans, additional temporary piers may be required to reduce the effective span length during launching, increasing complexity and cost.
Structural Integrity during Launching: The launching process can subject the bridge segments to increased bending moments and shear forces. Proper design and engineering are crucial to ensure the structural integrity of the bridge during the launching phase.
Specialized Equipment and Expertise: Incrementally launched box girder bridges require specialized launching equipment and expertise. The construction process demands careful coordination and precise engineering to ensure safe and successful launches.
Additional Design Considerations: Incrementally launched bridges require specific design considerations, such as accommodating differential settlement of piers and temporary supports, mitigating frictional forces on temporary bearings, and addressing variations in concrete surface. These factors increase the complexity of the design process.

Conclusion

In summary, the incremental launching of bridges involves casting the deck segments behind the abutment and pushing or pulling the deck over the piers.t This method offers a range of advantages, including reduced traffic disruption, enhanced safety, cost-effectiveness, and improved quality control.

By embracing this innovative construction technique, engineers and contractors can achieve efficient and successful outcomes in the construction of box girder bridges. As technology and construction practices continue to evolve, the incremental launching method will likely play a pivotal role in the development of future infrastructure, enabling the efficient and sustainable growth of transportation networks around the world.

Foundation for Bridges Over Water

By

Ubani Obinna

-

May 29, 2023

Table of Contents

An engineer may face significant challenges while designing the foundations for bridges over water, jetties, and offshore marine facilities. In the case of over-water bridges, the environment (water body) can pose more design challenges than the ground conditions (sea bed) at the bridge location. However, for bridges on land, the ground condition is the major deciding factor for the foundation design.

The loading on the foundation for bridges differs greatly from the loading for building foundations. Imposed loads are more prominent in the design of bridges than they are for buildings. They can be as much as half the dead load on highway bridges and two-thirds of the dead load on railway bridges (Tomlinson, 2001).

Traffic-related imposed loads are moving loads that can cause the bridge deck to experience strong longitudinal traction forces. Transverse forces can be induced by wind loadings, as well as by current drag, wave forces, and ship collisions in the case of river or estuary crossings. Longitudinal forces are also induced by shrinkage and temperature changes in the bridge deck.

Earthquake forces can be transmitted by the ground to bridge supports from any direction, especially when it comes to piers in deep water or high-level constructions where the mass of the displaced water must be added to that of the pier body. When whole spans are erected at ground level and hoisted or rolled onto the piers, for example, there might be a quick application of load to the foundations in addition to working loads from traffic.

Continuous-span bridges are particularly susceptible to the effects of differential foundation settlements. The determined total and differential settlements must also be taken into account in relation to the good rideability of the road surface. The intersection of the bridge and embanked approaches, as well as the joints connecting fixed and link spans, are critical places.

Factors affecting the choice of foundation for bridges over water

The following list of environmental factors explains how to choose an appropriate foundation type and construction approach.

Conditions of exposure and water depths

Bridges on open waterways of a vast estuary or bay crossing are in a hostile environment from winds and wave action, which may limit the operational period of floating construction equipment and potentially damage partially completed structures. This encourages the use of massive prefabricated components that can be quickly sunk onto a prepared bed or piled platform after being towed or transported by barges to the bridge site.

When the water level is sufficient for the unit to float, a box caisson is an appropriate design. However, weather conditions are crucial during the initial stages of towing the caisson to the site and sinking it in position. Weather-related delays should be taken into account while planning the overall construction schedule.

towing of box caissons — Towing of box caisson (source: https://www.aomi.co.jp/en/tech/cason.html)

The shallow draft bottom part of open-well caissons is floated to the construction site and buried by removing the soil from the open wells while the walls are sunk gradually. These caissons are employed in shallow water. Compared to box caissons, which can be sunk during a very brief window of favourable weather, open-well sinking construction processes are more weather-dependent.

However, it is possible to sink caissons at exposed sites by sinking the caissons from an artificial island or by deploying a jack-up barge to provide a solid working platform. The advent of heavy-lifting cranes capable of lifting a bridge pier caisson as a single item in various regions of the world has significantly reduced delays and dangers caused by weather conditions in recent years.

The use of simple and single-skin cofferdams is only appropriate for sheltered waterways. However, more efficient forms of cofferdams can be employed in conditions of moderate exposure.

Water Currents and Tides

River currents and tidal streams create scour holes when the soil at bed level is vulnerable to erosion, thereby inducing drag forces on the piers or piles. In the vicinity of cofferdams, where eddies are caused by transient factors like partially driven sheet piles, scour can be a very crucial design factor. As a caisson is lowered through the final few meters of water, mattressing can be necessary on an erodible bed to stop erosion under restricted flow circumstances.

BRIDGE SCOUR — Scouring of bridge piers/piles

When pitching bearing piles or sheet piles, the current drag forces can cause problems. Before the piles are held in place at the head by the pile cap or temporary girts, damaging oscillations of the piles may occur at some flow rates.

Rivers in flood pose a major threat to bridges Both from the perspective of lateral pressures on the abutments, piers, and superstructures as well as the potential undermining of the foundations due to the scouring impact of the water. The lateral hydrodynamic forces are calculated in a similar manner to those due to wind. Thus from;

q = ρv_c²/2

(where v_c is the velocity of flow in m/s), if the density of water is taken as 1000 N/m³ then the water pressure:

q = 500v_c²/10³ [kN/m²]
and
P = qAC_D [kN]

Values of C_D for various shaped piers in the USA are given in AASHTO LRFD (3rd edition) and in the UK are found in BA 59 (Highways Agency, 1994). The degree of scour depends upon many factors such as the geometry of the pier, the speed of flow and the type of soil.

Ship Collision

The cost of the foundations may increase significantly if measures are taken to reduce the possibility of bridge piers collapsing due to ship collisions. Not just the designated navigation channel is at risk. Collisions are equally likely to happen if a ship drifts outside of the designated channel. In certain large estuaries, the deep-water channel can quickly move from one side of the river to the other. Nearly every pier of a multi-span bridge may be in danger if there is a significant variation in tides.

A ring of skirt piles surrounding a group of large diameter piles to prevent ships from getting wedged between individual units, an independent ring fender, or enclosing the pier by a man-made island can all be used as forms of protection for piers. Impact at any angle to the axis of the pier must be considered. The pier body can experience torsional shear from vessel collision.

protection of bridge piers using fenders — Protection of bridge piers using fenders

Artificial islands should only be used in shallow water because the area around the pier needs to be big enough to allow the moving ship to ride up the slope and come to rest before the overhanging bow may hit the pier. The amount of fill material, boulder stone for wave protection, and mattressing for scour protection become unreasonably big in deep water, and the islands may block the navigation channel.

Earthquakes

Because the forces acting at a high level on the bridge superstructure combine with the forces acting on the pier body to produce strong overturning moments at the base level, earthquakes pose serious design challenges for deep-water piles. The mass of the pier itself must be multiplied by the volume of water it displaces.

In deep water, the eccentric loading on the pier base can be very high, favouring once more a long, narrow pier. Because earthquake forces can be oriented in any direction, including vertically, a circular structure may be necessary.

The liquefaction of loose to medium-dense granular soils is a result of ground shaking. With information on the soil deposit’s in-situ density and particle-size distribution, the liquefaction depth can be determined. To support the pier, piled foundations or ground treatment to densify a loose soil deposit may be necessary.

Bridge Pier Construction in Cofferdams

Shallow-water locations with sheltered or moderately exposed conditions are appropriate for the construction of bridge piers within cofferdams. Simple earth bank cofferdams can be used to build the piers in sites with very shallow water or at half-tide.

Although an overall depth of 32 m from high water to the base of the excavation was practical for the Thames Bamer foundations, sheet pile cofferdams can be built in water as deep as 15 m without too much difficulty, but the challenges increase as the depth of the water increases.

Wave action can cause damage to single-skin sheet pile cofferdams, and repeated wave impact can lead to fatigue failure of welded connections. Interconnected cells can be used to create strong cofferdams. To prevent ship collisions, the ring of cells can be left in place.

The locations where sheet piling is most advantageously used are those where there is an impermeable stratum at or below excavation level that serves as a cut-off for groundwater ingress, allowing the excavation to be pumped out and the pier foundation to be built in dry conditions. The excavation and construction of the concrete base are done underwater when a cut-off is not an option.

Bridge Pier Construction with Box Caissons

Box caissons are closed-bottomed hollow constructions that are buoyant when being towed to a bridge site and then buried onto a prepared bed by flooding valves. The top can be left open in sheltered conditions while sinking and ballasting are being done, or a closed top can be provided for towing in turbulent waters. Box caissons should not be used for foundations on weak soils or in locations where erosion might compromise the base.

They are particularly well suited for foundations on compact granular soils resistant to scour erosion or on a rock surface that has been dredged to remove loose material, levelled, and covered in a layer of crushed rock. A cement-sand grout is injected to fill the area between the bottom of the box and the blanket, and skirts are provided to allow the caisson to bed into the blanket. Due to weather conditions at an exposed site, bed preparation of a rock surface in deep water may be prone to lengthy delays.

CAISSON 2 — Typical protection techniques and preparation of seafloor for box caissons (source: https://www.aomi.co.jp/en/tech/cason.html)

A stacked raft can be constructed to support the caisson in situations when the depth of the mud or loose material is too great for dredging. When lowering a huge box caisson, the final few meters are crucial. The structure’s foundation displaces a huge amount of water, and if the caisson is dropped too quickly, it may slide from its desired position. Slack water is preferred during tidal circumstances to reduce the flow velocity producing erosion in the constricting area between the caisson bottom and the bed.

Sinking can be conveniently accomplished by temporarily fastening the caisson to a moored barge and lowering the unit onto the rock blanket during a single tide. After ballasting, grout can be injected through pipes inserted in the exterior and interior walls between the caisson’s base and the blanket. A 300mm deep peripheral skirt can prevent grout from escaping the blanket’s region.

sinking of caisson — Schematics of sinking of box caisson by flooding with water (source: https://www.aomi.co.jp/en/tech/cason.html)

With the exception of the row of cells next to the shallow-water sides of the piers, where the impact from large ships was not feasible, mass concrete can be utilized to fill the cells up to the level of the capping slab. Sand could be used to fill these cells. The pier can then be constructed from the capping slab.

Bridge Pier Construction with Open-well Caissons

Open caissons (including monoliths) are suitable for foundations in rivers and waterways since soft clays, silts, sands, or gravels are easily excavated by grabbing from open wells and do not present a significant skin friction resistance to the sinking of the caissons. Since men are unable to work under compressed air at pressures higher than 350 kN/m², open caissons are necessary when the required sinking depth exceeds the pressure of that magnitude.

Foundation for bridges: Open-well caisson — Foundation for bridges: Open-well Caisson (Tomlinson, 2001)

Open caissons are inappropriate for sinking through soils containing huge rocks, tree trunks, and other obstructions. A great difficulty is encountered when it is sunk to an uneven bedrock surface. Furthermore, when they are buried in steeply sloped bedrock, they are likely to move physically out of the vertical. For bridge foundations, open caissons are useful in rivers where there is a significant seasonal level variation.

Beginning in the low-water period, caisson sinking is finished to the design founding level prior to the annual flood. When no work can be done on the bridge superstructure, the caisson can be permitted to be completely or partially covered by flood water without suffering any damage.

Open caissons are sealed after they reach the founding level by pouring a layer of concrete into the bottom of the wells. After pumping the wells empty and adding more concrete, the caissons can be filled with either clean sand or concrete or, in cases where their dead weight must be maintained low, with clean fresh water.

schematics of bridge construction on open well caisson — Support of a bridge using open-well caisson

Open caissons have the drawback that the soil or rock at the foundation level cannot typically be inspected before putting the sealing concrete because the sealing is done underwater. The wells can only occasionally be pumped dry to allow for a bottom inspection.

Another drawback is that the act of grasping loose, soft materials beneath the water causes the material to surge and inflow beneath the cutting edge, leading to significant subsidence of the ground around the caisson. Open caissons are therefore inappropriate for usage on sites where nearby structure sinking could result in damage.

Bridge Pier Construction with Pneumatic Caissons

When dredging from open wells would result in loss of ground surrounding the caisson, causing the settlement of nearby structures, pneumatic caissons are utilized instead of open-well caissons. They are also employed for sinking through uneven ground or obstruction-filled ground, where an open caisson would be more likely to tilt or refuse to continue sinking.

The ‘dry’ working chamber of pneumatic caissons has the benefit that excavation can be done by hand, and obstructions like tree trunks or boulders can be removed from under the cutting edge. Additionally, the soil beneath the foundation can be examined, and if necessary, bearing tests can be conducted in-situ. In contrast to open-well caissons, where the final excavation and sealing concrete are nearly usually completed underwater, the foundation concrete is poured in the dry.

Compared to open-well caissons, pneumatic caissons have the drawback of requiring more equipment and labour during the sinking, and the rate of sinking is often slower. Unless another method of ground-water lowering is utilized externally to the caisson, the depth of sinking is limited to 36 m below the water table due to the important restriction that men cannot work in air pressures much greater than 3.5 bar.

Dewatering wells must be situated far enough away from the caisson to be unaffected by ground movement brought on by the caisson sinking if such measures are employed to lower air pressures in the working chamber.

Bridge piers supported by piling

Bridge piers that are situated in water can also be supported by using precast piles that have been driven into the ocean floor. The typical approach is to position the pile heads at or above the level of the high water mark, and then to employ standard pile caps to provide support for the piers.

Typically, barges are used to transport the piles and pile drivers to the desired location in the water. The diameter and embedment length of the piles must be obtained from the geotechnical and structural design using the sea bed soil information and the anticipated loading condition. When the barge floats the piles to the required location, they are placed on the underwater surface and then driven down by the pile driver.

To ensure stability and resistance against water currents, the piles are inclined outward (battered piles), enabling them to support the lateral load of the bridge structure and withstand the forces of the water. The piles are installed in groups, with wider spacing at the bottom and closer spacing at the top, (similar to a triangular shape).

Following the pile installation, the next step involves placing pile caps on the top of the grouped piles. Pile caps serve to create a stable foundation and provide a larger surface area for the distribution of the load onto the piles. Once this is completed, the construction of the bridge pier structure can commence from the pile cap.

An additional possibility is to erect the pile caps inside of a cofferdam. Either the combined mass and bending resistance of the pile group and cap, or a separate fender structure, can provide protection against the possibility of a ship colliding with the structure.

Conclusion

Bridge foundations constructed in water require specialized techniques to ensure stability and structural integrity. These foundations are typically built using one of the following methods: cofferdams, caissons, or drilled shafts/piles.

Cofferdams are temporary structures built in the water to create a dry work area. They are often constructed using sheet piles driven into the riverbed or seabed. Once the cofferdam is in place, the water is pumped out, allowing workers to excavate the foundation and pour concrete. After the foundation is complete, the cofferdam can be removed.

Caissons are large watertight structures that are built on land and then floated into position. They are then sunk to the riverbed or seabed, creating a dry workspace. Caissons are commonly used for building bridge piers or abutments. The caisson is filled with heavy material such as concrete or stone to provide stability. Once the caisson is in place, the foundation is constructed within it.

Precast piles or drilled shafts are another method used for constructing bridge foundations in water. This technique involves drilling deep holes into the riverbed or seabed and then filling them with concrete or reinforcing steel. Alternatively, precast piles can be driven into the seabed and then joined using pile caps.

Regardless of the method used, bridge foundations in water must be designed to withstand the forces exerted by water currents, waves, and changing water levels. They often require additional measures such as scour protection to prevent erosion around the foundation.

Overall, constructing bridge foundations in water is a complex and challenging task that requires careful planning, specialized equipment, and experienced professionals. By employing the appropriate construction techniques and accounting for environmental factors, engineers can ensure the stability and longevity of the bridge structure.

References
Tomlinson M. J. (2001). Foundation Design and Construction (7th Edition). Pearson Education Ltd.

Factors Affecting Uplift Capacity

Methods for Determining Uplift Capacity

Uplift capacity of pile in clay

Uplift capacity of pile in sand

Solved Example

Conclusion

References

Types of Column Splices

Design of column Splices

Design Example

Assessment of Liquefaction Hazard

Evaluation of CSR

Evaluation of CRR

SPT Method of CRR Assessment

Solved Example

Understanding Traditional Style

Moulding and Millwork

Wainscoting and Paneling

Coffered Ceilings

Archways and Columns

Window and Door Treatments

Fireplaces

Exterior Details

Colours and Patterns

Colour Palette

Neutrals

Upholstery Fabrics

Draperies and Curtains

Wallpaper

Rugs and Carpets

Accent Colors

Creating Traditional Spaces

Finishing Touches

Conclusion

Conclusion

Experimental Evidence of Critical Depth

Reasons for limiting skin friction in Piles

Solved Example on Critical Depth

Conclusion

Reference

Influence Lines for Shear in Simple Beams

Influence Lines for Bending Moments in Simple Beams

Influence Lines for Trusses

Qualitative influence lines: Müller–Breslau principle

Influence lines for continuous beams

Conclusion

Procedure for Incremental Launching of Box-girder Bridges

Advantages of incrementally launched box girder bridges

Disadvantages of incrementally launched box girder bridges

Conclusion

Factors affecting the choice of foundation for bridges over water

Conditions of exposure and water depths

Water Currents and Tides

Ship Collision

Earthquakes

Bridge Pier Construction in Cofferdams

Bridge Pier Construction with Box Caissons

Bridge Pier Construction with Open-well Caissons

Bridge Pier Construction with Pneumatic Caissons

Bridge piers supported by piling

Conclusion

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