Authors: Mostafa Rahal Lufan Zuo Atikah Baig 
Supervisors: Dr. Florian Schönborn, Dr. Christoph Winter

1. Introduction

The project involves the replacement of basement floor columns and foundations in a 120 year old multi-story building. The effects of creep and shrinkage will be considered, as well as, settlement due to unloading or reloading of the soil. To achieve a stable structure, all the old columns will be replaced by new columns with larger cross-sections and longer lengths. A 3D FEM models of 3 phases before, during and after construction were created. In model 3, the effects of creep and shrinkage was assessed. Finally, the influence of settlement in all 3 models was examined.

Figure 1.1 The planned procedure to replace the columns

2. FEM Models

A segment of the floor plan of the building will be assessed for the analysis. A 3 by 3 column distribution was taken from the middle part of the floor. The middle column of the 9 will examined for displacements, creep, shrinkage, and settlement. The floor plans and sections of the structure were provided by Prof. Feix Ingenieure GmbH.

Figure 2.1 Floor plan of the building

2.1.  Pre-Construction Model 1

The software Dlubal RFEM was used for creating and performing structural analysis for the structure. The first model was based on the original state of the building pe-construction of the new columns. The model consists of 6 floors with a height of 25.56 m. This model have the same cross section for all the columns which is 50 by 50 cm. The columns are reinforced concrete of type C20/25. The spacing between the columns is 5.15 m. The thickness of slab is 15 cm and the beams are 22*51 cm. The material beam and the slab are composed of reinforced concrete having the type C16/20.

Figure 2.2 Pre-construction model

The loading applied on the floors of the structure is the imposed dead load of 2.1 KN/m2 and live load of 5 KN/m2. The combination used is the service combination where there is no factors added to the load.

Figure 2.3 Applied dead load (left) and live load (right)Figure 2.4 Loading applied on model 1

A structural analysis was performed on the model. The displacement in the middle column was found to be 1.5 mm under service load. The stiffness of the column is:

K = EI / L = (30000× 10^-6 × 0.5^2) / 5.4 = 1.38 × 10^-3 N/m

2.5 Deformed shape of model 1Figure 2.6 Deformed behavior of model 1

A comparison was conducted to deduce the difference in the displacement by only applying the dead load which came to be 0.9 mm and 0.6 mm for live load.

Figure 2.7 Displacement due to dead load (left) and live load (right)

The reaction force on the support for the middle column came to be 2053.01 KN.

Figure 2.8 Normal forces (left) and reactions (right) of model 1

2.2.  During Construction Model 2

For the second model is the construction phase where the middle concrete column was replaced by a steel structure extending to two floors to carry the load of the building.

Figure 2.9 Transition of old column to steel structure

Figure 2.10 During Construction model 2

Figure 2.11 Steel structure detailing

In this model, the load was reduced to only self-weight as dead load and 1 KN/m2 live load since it’s in construction.

Figure 2.12 Applied Load on model 2

After performing the analysis, the displacement is the middle column increased to 3.5 mm. This can be described due to the absence of the old column.

2.13 Deformed shape of model 2

Figure 2.14 Deformed behavior of model 2

A comparison was conducted to deduce the difference in the displacement by only applying the dead load which came to be 3 mm and 0.5 mm for live load.

 Figure 2.15 Displacement due to dead load (left) and live load (right)

In this model the middle support was separated into 4 supports which reduced the reaction forces.

Figure 2.16 Normal forces (left) and reactions (right) of model 2

2.3.  After Construction Model 3

The third model is the post-construction phase where the new column has been cast. The new column is bigger than the old column having a section of 65 by 65 cm. In addition, the height of the column increased by 1 meter reaching 6.4 m. The new material of the column is C35/45.

Figure 2.17 Transition of old column to new column

Figure 2.18 After Construction model 3

The loading applied on the floors of the structure same as model 1 are the imposed dead load of 2.1 KN/m2 and live load of 5 KN/m2. The combination used is the service combination where there is no factors added to the load.

Figure 2.19 Applied dead load (left) and live load (right)

Figure 2.20 Applied Load on model 3

A structural analysis was performed on the model. The displacement reduced in the middle column compared to the first model which was found to be 1 mm under service load. This can be explained since the stiffness of the column increased compared to the first model. The stiffness of the new column is:

K = EI / L = (34000× 10^-6 × 0.65^2) / 6.4 = 2.244 × 10^-3 N/m > stiffness of the old column

2.21 Deformed shape of model 3

2.22 Deformed behavior of model 3

A comparison was conducted to deduce the difference in the displacement by only applying the dead load which came to be 0.6 mm and 0.4 mm for live load.

Figure 2.23 Displacement due to dead load (left) and live load (right)

The reaction force on the support for the middle column increased to 2167.45 KN.

Figure 2.24 Normal forces (left) and reactions (right) of model 3

2.4.  Bending Moment Comparison

2.4.1.  Model 1

In the first model, the bending moment (My) of the middle beam on the first level was examined where it reached -75.58 KN.m on top of the middle column.

Figure 2.25 Bending moment (My) of model 1

2.4.2.  Model 2

However, in the second model a significant change the behavior of the moment in the middle part ere it became positive of 36.98 KN.m

Figure 2.26 Bending moment (My) of model 2

2.4.3.  Model 3

For the third model, the bending moment (My) of the middle beam where it increased compared to first model -83.1 KN.m on top of the middle column.

Figure 2.27 Bending moment (My) of model 3

3. Creep and shrinkage

The main cause of concrete creep is self-desiccation resulting from the loss of water consumed during the hydration reaction. Loss of water from fresh concrete and moisture from hardened concrete are the reasons for shrinkage.  As creep and shrinkage occur in young concrete, we only consider them in the new column of the FEM model 3 from the previous section.

Regarding the creep and shrinkage model, even though we have selected concrete C35/45, we still need to determine the type of cement to be used. The table shows three options: SL, NR, and RS, which respectively refer to slow setting, normal or fast setting, and fast setting with high strength. Additionally, various relative humidities should be taken into account. The percentages were set at 50% and 80%. Subsequently, the creep and shrinkage effect was modelled using three types of cement and two relative humidities. 

Table 3.1 Feautures of three types of cement

3.1. Creep

With higher-strength concrete, the creep capacity is through the higher strength and the significantly reduced porosity in connection with the low w/z value are limited. The result is, among other things, drying creep significantly reduced.

$//<![CDATA[ \begin{array}{l}\varepsilon_c_c\end{array} //]]>$: creep strain

$//<![CDATA[ \begin{array}{l}\varphi_0\end{array} //]]>$: creep number

$//<![CDATA[ \begin{array}{l}\varepsilon_c_i_,_2_8\end{array} //]]>$: elastic short-term strain for a concrete age of 28 days

$//<![CDATA[ \begin{array}{l}E_c\end{array} //]]>$: modulus of elasticity

As the modulus of elasticity is linked to the strength development of the concrete and therefore generally increases with increasing concrete age, the creep strain is linked to the modulus of elasticity for a concrete age of 28 days, irrespective of the actual load age. The creep model anchored in DIN 1045-1 and EN 1992-1-1 is based on the tangent modulus at origin Ec0 as the reference value. Based on Eq.(1), elastic strains and creep strains can be combined to form the total stress-induced strain:

$//<![CDATA[ \begin{array}{l}I(t,t_0)\end{array} //]]>$: creep or compliance function

$//<![CDATA[ \begin{array}{l}n(t)\end{array} //]]>$ : reciprocal of the aging function

The creep or compliance function$//<![CDATA[ \begin{array}{l}I(t,t_0)\end{array} //]]>$according to Eq. (3) is a characteristic material property and indicates the total stress-induced strain under the effect of a constant unit load. $//<![CDATA[ \begin{array}{l}n(t)\end{array} //]]>$denotes the reciprocal of the aging function of the modulus of elasticity and takes into account the reduced elastic deformation with increasing initial load age.

The mathematical formulations of the creep function or creep coefficient developed in the past can be divided into summation and product approaches. In the superseded generation of standards, e.g. DIN 4227, a summation approach was anchored, for which the creep strains were divided into reversible components - the delayed elastic strains with the associated creep coefficient and irreversible components.

The current generation of standards, including DIN 1045-1 and EN 1992-1-1, is based on a multiplicative combination of individual functions (product approach) that describe the effects of the influencing parameters and the creep strain over time. The creep coefficient $//<![CDATA[ \begin{array}{l}\varphi(t, t_0)\end{array} //]]>$ is calculated according to Eq. (4) from the basic creep coefficient $//<![CDATA[ \begin{array}{l}\varphi_0\end{array} //]]>$, i.e. the final value for $//<![CDATA[ \begin{array}{l}t\to\infty\end{array} //]]>$, and the function of the time history $//<![CDATA[ \begin{array}{l}\beta_c(t, t_0)\end{array} //]]>$. At time$//<![CDATA[ \begin{array}{l}t_0\end{array} //]]>$ , for$//<![CDATA[ \begin{array}{l}\beta_c(t, t_0)\end{array} //]]>$ assumes the value of 0, at time t for$//<![CDATA[ \begin{array}{l}\beta_c(t, t_0)\end{array} //]]>$ assumes the value of 1.

$//<![CDATA[ \begin{array}{l}\varphi_0\end{array} //]]>$ : basic creep coefficient (final creep number)

$//<![CDATA[ \begin{array}{l}\beta_c(t, t_0)\end{array} //]]>$ : function of the time history

 The effective component thickness h0 as a measure of the speed and intensity of the drying process corresponds to the ratio between the cross-sectional area Ac in mm2 and the

exposed to the environment u in mm

h0: effective component thickness

Ac: cross-sectional area (mm^2)

u: environment exposed extent (mm)

h1: reference value 100 mm

t1: reference value 1 day

RH : relative humidity of the environment (%)

RH0: reference value 100%

The equation for the effective thickness of a column with a square cross-section can be obtained from the literature, as illustrated in Figure 3.1.

Figure 3.1 Effective thickness of a rectangular cross section

Table 3.2 presents the parameters required for the creep and shrinkage models. It contains the material properties of concrete C35/45, geometrical characteristics of the column and final creep numbers of different cement types and relative humidities.

 Table 3.2 Parameters of creep and shrinkage model

The equation below shows the final creep model. It uses the force (F) acting on the column using the results from the third FEM model in the previous chapter and the final creep number$//<![CDATA[ \begin{array}{l}\varphi_0\end{array} //]]>$ from the reference excel calculation.

The first aspect to consider is the influence of cement type and relative humidity on the start of loading day (day 7). As demonstrated in Figure 3.2, the creep strain increases gradually over time. Furthermore, it has been observed that for the same concrete type, an increase in relative humidity leads to a decrease in creep strain. In general, under the same relative humidity conditions, rapid setting and high strength (RS) cement shows the lowest creep strain compared to the other two types, while slow setting cement (SL) exhibits the highest creep strain. However, there is negligible difference in displacements between different types of cement and relative humidities, with only a 0.39 millimetre variation. Therefore, the effect of cement types and relative humidities on creep strain can be disregarded.

Figure 3.2 Creep strain over time

The second aspect to consider is the effect of the timing of loading initiation. Loading start dates were established from day 1 to day 49, and Figure 3.3 displays the creep strain at day 50. All creep strains decrease as loading is delayed. In addition, it was found that higher relative humidity and the use of cement type RS lead to lower creep strain. Similarly to the previous graph, the difference in displacement is small enough to be neglected, at only 0.781 millimetres. Therefore, we will maintain the start of loading at day 7.

Figure 3.3 Creep strian over start of loading days

In conclusion, although the types of cement, relative humidity, and start of loading timing can influence creep strain, their effects on our study case are negligible. Therefore, we have chosen the normal cement (N,R) and have scheduled the start of loading for day 7. Using 80% relative humidity as an example, the calculation shows a displacement of 1.52mm. Compared with the length of the new column, the impact of creep is very small and therfore neglegible.

3.2. Shrinkage

The parameters from Table 3.2 are also utilized in the shrinkage model. The following equation presents the shrinkage model, which consists of two parts: shrinkage strain and dry shrinkage strain. Shrinkage strain (epsilon cas) is a function of time (t), while drying shrinkage strain (epsilon cds) is a function of time (t), concrete age at the start of drying (ts), and relative humidity (RH).

The equations below demonstrate the detailed calculation.

Apart from the fact that all shrinkage strains are negative and the choice of cement type, the results are similar to the creep strain. Both shrinkage and drying strains increase over time. There is no influence of relative humidity on shrinkage strain, which is dependent on the type of cement and time. The graph illustrates that rapid setting with high strength cement (RS) exhibits the lowest absolute value of shrinkage strain, while slow setting cement (SL) displays the highest value. Normal or rapid setting cement (N,R) falls in the middle. However, the displacement difference between these three types of cement is very small (0.0151 mm), and therefore its impact can be considered negligible.

Figure 3.4 Shrinkage strain over time

Additionally, the influence of cement type and relative humidity on the start of drying day (day 7) is the second aspect to consider. As shown in Figure 3.5, the magnitude of drying shrinkage strain also gradually increases over time. It has been observed that an increase in relative humidity leads to a decrease in drying shrinkage strain for the same concrete type. Comparing the three types of cement under the same relative humidity conditions, it can be observed that rapid setting and high strength (RS) cement has the highest drying shrinkage strain, while slow setting cement (SL) exhibits the lowest drying shrinkage strain. It is important to note that this evaluation is based solely on objective measurements and not subjective evaluations. However, there is no significant difference in displacements among different types of cement and relative humidities, with only a 0.237 millimetre variation. Thus, the influence of cement types and relative humidities on drying shrinkage strain can be disregarded.

The timing of the start of the drying process is the third aspect to consider. Drying start dates were established between day 1 and day 49. Figure 3.6 displays the drying shrinkage strain on day 50. The drying shrinkage strain's absolute value decreases as we delay the drying process.  Furthermore, it was discovered that higher relative humidity and the use of SL cement type result in a decrease in the absolute value of drying shrinkage strain, which differs from the creep model cement type. However, the displacement difference is negligible, measuring only 0.447 millimetres. Therefore, we will initiate the drying process on day 7.

Figure 3.5 Drying shrinkage strain over timeFigure 3.6 Drying shrinkage strain over start of drying days

In conclusion, the shrinkage strain in our study case is not significantly affected by the types of cement, relative humidity or start of drying timing. Therefore, we have chosen normal cement (N,R) and scheduled the start of drying for day 7. Taking 80% relative humidity as an example, the calculation indicates a displacement of -0.486mm. Compared to the length of the new column, the impact of shrinkage is very small and therefore negligible.

4. Settlements

Settlement refers to the vertical displacement or sinking of the ground, primarily due to the consolidation and compaction of soil under applied loads. It's a critical aspect in geotechnical engineering, as excessive settlement can lead to structural damage, misalignment's, or even failure of built structures.Shallow foundations built on cohesive soils need to be secure against the soil's shear failure and ensure that the settlement is within acceptable limits for the specific superstructure. Typically, the design of such foundations is more influenced by settlement considerations than by the risk of shear failure. Design standards often limit both total and differential settlements to prevent functional issues, varying according to the structure type. Thus, accurately predicting settlement is crucial in the design process of shallow foundations.

The total settlement of a foundation is categorized into two types: immediate (or elastic) settlement and consolidation settlement. Immediate settlement is the initial elastic deformation or change in volume in the soil caused by the foundation load, occurring without significant pore-water pressure dissipation. This type of settlement is generally minor compared to consolidation settlement in clay soils, but in certain cases, especially in highly plastic or organic soils, it can be substantial. Immediate settlement is vital for several reasons: it can form a significant part of the total settlement, it's integral to understanding the overall time-dependent settlement behavior, and it's related to the undrained stability of a foundation, with excessive immediate settlement potentially indicating imminent failure.[1]

The soil testing report reveals a comprehensive breakdown of the soil composition into four distinct types. Layer 1 comprises Filling Floors/Auffüllböden, Layer 2 consists of Quaternary Gravels/Quartäre Kiese, Layer 3 comprises Tertiary Sand/Tertiäre Sande, and Layer 4 encompasses Tertiary silts, clays, and marls/Tertiäre Schluffe, Tone und Mergel.

The foundation was approximately 6.35 meters deep, it's crucial to recognize that the foundation interacts predominantly with the soil properties of Layer 4, which consists of tertiary silts, clays, and marls of semi-solid consistency, which pose unique considerations for construction and stability. Understanding the specific soil type is crucial for implementing appropriate foundation design and construction techniques, ensuring the longevity and safety of the structure.This layer's geotechnical characteristics significantly influence the design and performance of the foundation.

Layer 4 - Tertiary Soil, (Tertiary Silts, Clays, and Marls, At Least Semi-Solid Consistency)

• Angle of Internal Friction : 27.5°
• Unit Weight : 21 kN/m³
• Effective Unit Weight : 11 kN/m³
• Cohesion  : 20 kN/m²
• Stiffness Modulus (ES): 80 MN/m²
• Vertical Subgrade Modulus (ksv): 40 MN/m³

4.1.  Bearing Resistance

Bearing resistance refers to the ability of the ground to support the loads applied to it by structures such as buildings, bridges, and other civil engineering works. This concept is essential in ensuring that structures not only remain stable and secure under their own weight but also under the additional loads they may encounter throughout their lifespan, including environmental stresses and human activities. The analysis of bearing resistance involves evaluating the strength and deformation characteristics of soil or rock beneath the foundation, taking into account factors like soil type, density, moisture content, and load distribution. Understanding and accurately assessing bearing resistance is crucial for designing foundations that are both safe and cost-effective, preventing issues like excessive settlement or foundation failure, which can lead to significant structural damage and safety hazards.

The Eurocode provides guidelines for calculating the bearing resistance of foundations under two different soil conditions: undrained and drained. The appropriate method depends on the soil type and its drainage characteristics.

4.1.1.  Undrained Conditions

Applicability: Commonly used for saturated fine-grained soils like clays and silts where drainage is poor or the loading is so fast that the soil doesn't have time to consolidate (water within the soil doesn't have time to dissipate).

Primary Parameter: Shear strength of the soil in undrained conditions .

Formula: The design bearing resistance is calculated using the undrained shear strength and factors accounting for the shape of the foundation, the inclination of the load, and the foundation base. The formula considers these factors to modify the bearing capacity influenced by [3]

4.1.2.  Drained Conditions

Applicability: Suitable for coarse-grained soils like sands and gravels, or fine-grained soils where drainage is possible over time. It's used when the loading rate is slow enough to allow for consolidation and drainage.

Primary Parameters: Soil friction angle and cohesion.

Formula: The design bearing resistance is calculated using bearing capacity factors related to the soil friction angle, and factors that consider the shape and inclination of the foundation and load. These formulas are more complex and account for the drained strength parameters of the soil.[4]

For the specific case of silts, clays, and marls with a semi-solid consistency, the undrained condition is likely more applicable. These soil types typically exhibit significant cohesive strength and lower permeability, which implies that under typical loading scenarios, they are more likely to behave in an undrained manner.[4] 

Formula Breakdown - Design Bearing Resistance Formula:

Where:

:Design bearing resistance

: Effective area of the foundation

: Undrained shear strength of the soil

: Factor for the inclination of the foundation base

: Shape factor for the foundation

: Factor for the inclination of the load

: Surcharge (typically the weight of the soil above the foundation level or any additional load)

Factors & Application Soil Parameters:

1. Inclination of the Foundation Base : A factor that accounts for the base inclination. Since the base is horizontal, .
2. Shape of the Foundation : For a square foundation
3. Inclination of the Load  = 1 for vertical loads

4. We know that, Cohesion = 200 kN/m²  (Given that the soil type is clays, and marls, with semi-solid consistency, as per the ranges provided in the soil testing report,  typically falls between 200 kN/m² and 400 kN/m². Since the soil is described as at least semi-solid, we considerd the lower end of this range as a starting point for conservative design purposes, i.e. 200 kN/m². )       

5. Effective area of the foundation, = 5.76 m².

6. Surcharge = Depth of soil above the foundation × Unit weight = 1 m × 21 kN/m³ = 21 kN/m²

                                                                                                                                                                                                                                                                                                                             

Calculating Design Bearing Resistance

 Subsituting the values:

Rd=7226.496kN

Since, we have developed three distinct models representing various stages of construction for analytical purposes.

- Model 1 illustrating the existing building situation.

- Model 2  illustrating the scenario where concrete columns are replaced with steel columns.

- Model 3 depicts the post-construction phase with columns featuring increased cross-sectional area and height.

Our objective necessitates conducting settlement analysis on all three models to facilitate comparative evaluation.

4.2. Immediate Settlement

Immediate settlement is conventionally calculated using elasticity theory, which treats soil as a linear elastic material deforming according to Hooke's law. It refers to the initial deformation or compression of the soil immediately beneath a foundation due to the applied loads. This type of settlement occurs as soon as the load is applied and typically completes within a short period, often before any significant consolidation settlement begins. This is why it's sometimes referred to as "elastic settlement." The standard formula for immediate settlement, derived from elasticity theory, can be adjusted with certain factors for surface foundations. [1]

Various influence factors in the literature help estimate immediate settlement for both perfectly flexible and rigid shallow foundations. Depending on the foundation type (circular, rectangular, or strip), the average settlement is calculated differently, as indicated by Davis and Poulos (1968) and later by Mayne and Poulos (1999). They also proposed relationships to approximate settlements at different points of flexible foundations.

The general form of the immediate settlement formula based on the theory of elasticity is shown in the equation below [2]

Where,

   -:Immediate (elastic) settlement

   -:Applied foundation pressure

   - :Width or diameter of the foundation

   - :Modulus of elasticity of the soil

   -:Influence factor, depending on the shape of the foundation and depth

4.2.1.  Immediate Settlement - Model 1

1. Bearing Pressure : This is the load per unit area applied by the foundation. Mathematically, it's expressed as: 

where:

• P is the total load transmitted to the foundation (in kN or kg),                                                                                                                                                                                                                                                                                       
• A is the area of the foundation in contact with the soil (in m²).

This value is crucial for assessing the load-bearing capacity of the soil and for determining how much the soil will compress or settle when the structure is built on it.

      2. Width of the Foundation : Given as 2.4m.

      3. Modulus of Elasticity of the Soil : From soil testing report,                                                                                                                                                                                                                                                                  

For settlement analysis, particularly when dealing with immediate or elastic settlement, the modulus of elasticity of the soil is a crucial parameter.As per the soil testing report, where several modulus values are given for different loading conditions,we selected the modulus that best represents the soil behavior under the type of load causing the settlement.

      4. Influence Factor : This depends on the shape of the foundation and the depth. For a square foundation on the surface, it is taken as 1.0.

Using these values, the formula for immediate settlement becomes:

Converting units for consistency (1 MN/m² = 1000 kN/m²):

To ensure the precision of the manually computed immediate settlement, we opted to verify it using GGU-Settle software.

4.2.1 Immediate Settlement - Model 1

The findings reveal that the immediate settlement reaches a maximum of 9.1mm for Model 1.

4.2.2. Immediate Settlement - Model 2

1. Bearing Pressure : This is the load per unit area applied by the foundation. Mathematically, it's expressed as:

      2. Width of the Foundation : Given as 2.4m

      3. Modulus of Elasticity of the Soil:

      4. Influence Factor : 1.0

Using these values, the formula for immediate settlement becomes:

Converting units for consistency (1 MN/m² = 1000 kN/m²):

In the figure below, we can see the results obtained from the software GGU-Settle.

4.2.2 Immediate Settlement - Model 2

The findings reveal that the immediate settlement reaches a maximum of 3.5mm for Model 2.

4.2.3. Immediate Settlement - Model 3

1. Bearing Pressure : This is the load per unit area applied by the foundation. Mathematically, it's expressed as:

      2. Width of the Foundation : Given as 2.4m

      3. Modulus of Elasticity of the Soil:

      4. Influence Factor : 1.0

Using these values, the formula for immediate settlement becomes:

Converting units for consistency (1 MN/m² = 1000 kN/m²):

In the figure below, we can see the results obtained from the software GGU-Settle

4.2.3 Immediate Settlement - Model 3

The findings reveal that the immediate settlement reaches a maximum of 9.6mm for Model 2.

4.3.  Consolidated Settlement 

Consolidated settlement of soil refers to the gradual reduction in volume and the associated vertical displacement that occurs when soil is subjected to an increase in stress over time. This phenomenon is a result of the rearrangement of soil particles and the expulsion of water from the void spaces within the soil mass.Over time, the water within the soil begins to drain and the soil particles further compact, causing additional settlement known as secondary consolidation.

This process is governed by factors such as the soil's composition, its initial void ratio, the applied stress, and the permeability of the soil. The consolidation settlement behavior of soil is typically characterized using laboratory tests such as oedometer tests or through field observations and monitoring. However, we can find the consolidated settlement through formulas mentioned in the Eurocode.Understanding the consolidated settlement of soil is crucial in various engineering applications, including the design and construction of foundations, embankments, and retaining structures. [5]

Since, we have developed three distinct models representing various stages of construction for analytical purposes.

- Model 1 illustrating the existing building situation.

- Model 2  illustrating the scenario where concrete columns are replaced with steel columns.

- Model 3 depicts the post-construction phase with columns featuring increased cross-sectional area and height.

Our objective necessitates conducting settlement analysis on all three models to facilitate comparative evaluation.

According to EN 1997-1 §F.2(1), the total settlement of a foundation on cohesive or non-cohesive soil can be evaluated using elasticity theory and an equation of the form:

[6]

where:

Em = the design value of the modulus of elasticity.

p = bearing pressure

f = the settlement coefficient

B = width of the foundation

4.3.1.  Consolidated Settlement for Model 1

1. Design Value of the Modulus of Elasticity (Em) : Typical values of Young's modulus for cohessive soil(MPa) (based on Obrzud & Truty 2012 compiled from Kezdi 1974 and Prat et al. 1995) [7]

Table 4.3.1

As per the soil testing report, the soil falls under Clays with low-medium plasticity since the plasticity number I_p is ≤ 4, the design value for modulus of elasticity falls between 5-8 Mpa.  Considering, Em=8 MPa

           2. The Settlement Coefficient (f): The Eurocode does not specify a method for determining the f coefficient,leaving the choice of the method to the engineers. The existing literature describes many methods, but they are all similar.  [8]  

According to EN 1997-1 §F.2(2), The value of the settlement coefficient f depends on the shape and dimensions of the foundation area, the variation of stiffness with depth, the thickness of the compressible formation, Poisson's ratio, the distribution of the bearing pressure, and the point for which the settlement is calculated.

ν = Poisson’s ratio of soil

From the below table, we assume the value of ν = 0.3, since the soild is partially saturated undrained soil.

4.3.1 Poisson's Ratio

ω = shape and rigidity factor; for a rigid foundation the factor.

The formula for calculating the shape and rigidity factor ω is as follows:

where:

- B is the width of the footing.

- L is the length of the footing.

 ω = 0.88

Now calculating  the settlement coefficient f:

f = 0.8008

         3. Bearing Pressure(p): This is the load per unit area applied by the foundation. Mathematically, it's expressed as:

where:

-P is the total load transmitted to the foundation (in kN or kg),

- A is the area of the foundation in contact with the soil (in m²).

This value is crucial for assessing the load-bearing capacity of the soil and for determining how much the soil will compress or settle when the structure is built on it.

or  

4.3.2.  Consolidated Settlement for Model 2

1. Design Value of the Modulus of Elasticity (Em) : Em=8 MPa

      2. The Settlement Coefficient (f): 

f = 0.8008

        3. Bearing Pressure(p):

Consolidated Settlement:

or

4.3.3.  Consolidated Settlement for Model 3

1. Design Value of the Modulus of Elasticity (Em) : Em=8 MPa

       2. The Settlement Coefficient (f): f=0-8008

       3. Bearing Pressure(p):

Consolidated Settlement:

or

4.4. Total Settlement

Model 1:

T = Si + S = 7.52 + 90.3 = 97.82 mm

Model 2:

T = Si + S = 2.612 + 31.23 = 33.84mm

Model 3:

T = Si + S = 7.128 + 85.52 = 92.648 mm

We wanted to compare the results for total settlement with the results from a FEM software, hence we used GGU-Consoliadted, and obtained the following results:

4.4.1.  Total Settlement for Model 1

The table below shows the settlement in cm in a span of 365 days, we can see that at the 365^th day the total settlement will be 8.9cm.

4.4.1.1 Settlement in 365 days    4.4.1.2 Degree if Consolidation Vs Time

4.4.2.  Total Settlement for Model 2

The table below shows the settlement in cm in a span of 365 days, we can see that at the 365^th day the total settlement will be 3.3cm.

4.4.2.1 Settlement in 365 days    4.4.2.2 Degree if Consolidation Vs Time

4.4.3.  Total Settlement for Model 3

The table below shows the settlement in cm in a span of 365 days, we can see that at the 365^th day the total settlement will be 9.9cm.

4.4.3.1 Settlement in 365 days   4.4.3.2 Degree if Consolidation Vs Time

5.  Conclusion

5.1.  FEM Displacement

The displacement in the middle column of the pre-construction model 1 was determined to be 1.5 mm under service load. However, because the original column has been removed in model 2, which is during construction, it increased to 3.5 mm. After installing the replacement column in the third model, the displacement dropped to 1 mm because the new column is more stiffer than previous.

5.2. Creep and shrinkage

The effects of creep and shrinkage is only on the new column in Model 3. Although cement type, relative humidity and loading start time can influence creep and shrinkage strain, their effects on our study case are negligible. Therefore, we have chosen the normal cement (N,R) and scheduled the start of loading for day 7. Using 80% relative humidity as an example, the calculation shows a displacement of 1.52 mm due to creep and -0.486 mm due to shrinkage. Compared to the length of the new column, the effects of creep and shrinkage are very small and therefore negligible.

5.3.  Settlements

Based on the analysis conducted and the results presented in Table below, it is evident that consolidation settlement significantly exceeds immediate settlement in clayey soils. This observation aligns with the inherent characteristics of weak clay soils, which typically contain a high water content, thereby leading to prolonged and substantial consolidation settlement. [9]

Upon comparing the settlement results obtained from software analysis and manual calculations, we find a generally consistent trend, albeit with slight variations. In the software analysis, Model 1 exhibits an immediate settlement of 9.1 mm and a total settlement of 89 mm, while Model 2 shows 3.5 mm immediate settlement and 33 mm total settlement, and Model 3 indicates 9.6 mm immediate settlement and 99 mm total settlement. Conversely, the manually calculated values for Model 1, Model 2, and Model 3 demonstrate immediate settlements of 7.128 mm, 2.612 mm, and 7.52 mm, respectively, with corresponding total settlements of 92.64 mm, 33.84 mm, and 97.82 mm. These discrepancies, while minor, likely stem from differences in computational approaches, assumptions, and input parameters between the two methods. Nonetheless, both sets of results offer valuable insights into the settlement behavior of the structural models, aiding in informed decision-making for design and construction considerations.

Considering the maximum allowable settlement criteria for framed buildings and reinforced load-bearing walls, which range from 75 to 135 mm for clay, or 5% of D (4 cm), the following results were obtained for the three models: [10]

- Model 1: Immediate Settlement - 9.1 mm, Total Settlement - 89 mm

- Model 2: Immediate Settlement - 3.5 mm, Total Settlement - 33 mm

- Model 3: Immediate Settlement - 9.6 mm, Total Settlement - 99 mm

These values indicate that according to the first criterion, the structures are deemed safe. However, adhering to the second criterion of 5% of D (40 mm), the structures would fail, necessitating design changes such as increasing the depth of the foundation.

It is noteworthy that Model 2 exhibits the most efficient and optimal performance, as its settlement values comply with both criteria mentioned. Therefore, considering the settlement constraints, Model 2 emerges as the preferred choice, demonstrating superior stability and adherence to safety standards. Adjusting the design parameters, particularly by increasing the foundation depth, would enhance the structural integrity and mitigate settlement-related risks.

6.  References

1. "Comparing Methods for Predicting Immediate Settlement of Shallow Foundations on Cohesive Soils Based on Hypothetical and Real Cases." Department of Civil Engineering, Faculty of Technology, Gazi University, 06500 Teknikokullar-Ankara, Turkey.
2. Davis, E. H., & Poulos, H. G. (1968). The use of elastic theory for settlement prediction under three-dimensional conditions. Ge´otechnique, 18(1), 67–91.
3. BS EN 1997-1:2004, "Eurocode 7: Geotechnical design - Part 1: General rules, Annex D, D3, pg 158.
4. BS EN 1997-1:2004, "Eurocode 7: Geotechnical design - Part 1: General rules, Annex D, D4, pg 158.
5. TANG, B. - CHEN, X. - ZHANG, W. (2004). Consider the rheological properties of soft Consolidation finite element analysis. Rock and Soil Mechanics, Vol. 25(4), pp. 583-586.
6. BS EN 1997-1:2004, "Eurocode 7: Geotechnical design - Part 1: General rules, Annex F, D2, pg 162.
7. Obrzud & Truty (2012), compiled from Kezdi (1974) and Prat et al. (1995).
8. Kezdi, A. (1974). Handbook of Soil Mechanics. Elsevier, Amsterdam.
9. Waheed, M., & Asmael, N. (2023). Study Immediate and Consolidation Settlement of Shallow Foundations. Civil and Environmental Engineering, 19(1), 318-327.
10. Choudhuri, K., & Chakraborty, D. (2022). Probabilistic analyses of three-dimensional circular footing resting on two-layer cohesive soil system considering soil spatial variability. Bulletin of Engineering Geology and the Environment, 1–20.
11. K. Zilch, G. Zehetmaier. (2010). Werkstoffkennwerte und Verbundverhalten. Bemessung im konstruktiven Betonbau DOI 10.1007/978-3-540-70638-0. Springer