Conceptual Introduction:

The task involves designing a foundation for towers located in areas with soft silty clay deposits using steel pipe piles. The design criteria specify that the piles must support an axial compressive load of

at the Ultimate Limit State and must not settle more than $10$ mm under a Serviceability Limit State axial compressive load of $50$ kN$.$ Lateral or uplift loads due to winds are not considered in this scenario. The geotechnical information from cone penetration tests helps in understanding the subsoil characteristics, which are crucial for designing the piles to meet the specified requirements.

Explanation:

In this step, we establish the fundamental requirements and objectives for designing the foundation of towers in soft silty clay soil using steel pipe piles. The key considerations are the load the pile must support and the allowable settlement under loading conditions as specified by the Ultimate Limit State and Serviceability Limit State. This step also involves understanding the geotechnical characteristics of the site, which is essential for determining the feasibility and design parameters of the foundation solution. It sets the stage for the technical calculations that follow by framing the design problem within its real$-$world application constraints.

Step $2$

Provide Formulas

Ultimate Limit State $($

$)$ and Serviceability Limit State $($

$)$ Analysis

$1.$ Axial Bearing Capacity Formula:

For Ultimate Limit State:

Here,

is the ultimate axial load capacity,

is the cross$-$sectional area of the pile tip, and

is the ultimate bearing capacity per unit area from the soil.

For Serviceability Limit State:

Here,

is the allowable bearing capacity considering the allowable settlement $($generally lower than

$).$

$2.$ Settlement Calculation:

The settlement under service load can be approximated using:

Where

is the modulus of elasticity of the soil, which can be determined from soil tests or estimated from empirical correlations.

Explanation:

This step is critical for translating the design requirements into quantifiable engineering tasks. The formulas provided are foundational for calculating the bearing capacity of the piles $($both ultimate and service$)$ and the expected settlement under load. The axial bearing capacity formulas help determine whether the soil can support the loads without failure, while the settlement formula assesses the deformation of the soil under load, ensuring the structure's long$-$term performance and safety. These formulas are derived from soil mechanics principles and are essential for preliminary design and assessment of pile foundations.

Step $3$

Step$-$by$-$step Calculation Part:

Example Calculation for a Single Pile:

$1.$ Determine Soil Parameters: From cone penetration test data and empirical correlations:

at different depths

Modulus of elasticity of soil

$2.$ Calculate the Cross$-$Sectional Area of the Pile $($

$)$:

Assume a diameter

for the pile.

$3.$ Calculate Ultimate and Service Loads:

Using appropriate

and

values from the soil data.

$4.$ Check for Settlement under Service Load:

Ensure

is less than the allowable settlement $(10$ mm$).$

Detailed Calculations:

Using typical values of

m $($to be adjusted based on actual requirements$),$

MPa:

Explanation:

This step involves applying the earlier discussed formulas to perform detailed calculations based on the specific project data $($e$.$g$.,$ soil properties, pile dimensions$).$ It includes calculating the bearing capacity of the pile for both ultimate and service limits and checking if the pile's settlement under the service load is within acceptable limits$.$ This is a crucial step that involves iterative problem$-$solving to align the design with the practical and safety requirements. By executing these calculations, we can verify the feasibility of the proposed pile dimensions and make necessary adjustments to ensure compliance with design standards and project specifications. This step exemplifies the practical application of theoretical knowledge to solve real$-$world engineering problems.

Answer

Final Answer:

After re$-$evaluating the diameter and possibly the pile length to adjust the bearing area and modulus, the calculation would need to confirm that

and

meet the specified limits of $100$ kN and $10$ mm respectively. This process involves iteration and adjustments based on the detailed design requirements and soil characteristics.

I need detailed hand calculation for Diameter of pile and leght of pile