Analysis Of Terzaghi's Equations For Soil Bearing Capacity

1. Carry out bearing capacity calculations for shallow foundations for the scheme, alongside calculations for deep and piled foundations, so that a comparison can be made of the relative dimensions of the shallow and piled foundation solutions.

2. Determine an appropriate arrangement of ground improvement techniques to deal with the need for ground raising on site above the soft alluvial deposits and hence provide recommendations on how to engineer the roads, services and drains so that they remain in a serviceable state (focus on the geotechnical processes occurring in the soft alluvial deposits and hence provide detailed calculations to support your solution to deal with any expected ground movements).

3. Outline the technical and practical problems likely to be experienced when implementing the solution to the ground problems at the given site.

Data for the Shallow Foundation

The Terzaghi’s Equations will be used in the analysis of the ultimate bearing capacity of the soils. However, the analysis is based on the fact that a shallow foundation is defined as one whose depth is lesser or equal to the width (Jamai, 2017).

The data for the shallow foundation

Taking a shallow foundation width is depth of 50m and the width 50m,

The unit weight of the soil is given (zone A):55kN/m2 to 80kN/m2

The unit surcharge imposed by the soil above the footing= 50*60=3000kN/m taking the unit weight as 60kN/m (on the assumption that it is in between 55 and 70 that is given). Taking the soil fiction angle as 0 and determining the coefficients of  cohesion, surcharge and  unit weight from the bearing capacity tables.

 (Kumbhojkar, 1993)

Depending on the type of footing to be used, Terzaghi suggested the following formulas to be used:

For the square and circular footing respectively. In this analysis, the footing will be assumed to be square.

The above formulas will need to be modified, as per terzaghi requirements with the eventual local shear formulas being:

This is the case for undrained soils and therefore, working on the firm spoil layer of the zone A site where Cu=55-70kN/m2

Strip footing:

Qu=5.7Cu+q which, assuming a Cu of 60 gives Qu=342kN/m2+q and calculating q

q Is given as .however, considering that we are working on stiff clay the table given by IS1904 (1978) indicate all the bearing capacities of some soils, but on a presumptive basis. The bearing capacity of the stiff clay soil can be taken as 100kN/m2.

Therefore: q=50*100=5000kN/m2

Therefore, the total general shear will be initiated when the total load exceeds 5000+234=5234Nm2 (strip footing)

On the other hand the ultimate load bearing capacity of the soil for local shear can be calculated-from the local shear formulas-as:

C’ is the contribution of cohesion’  

The contribution factor for cohesion c= (Bowles, 1997)

According to the field tests, the results indicate that N values were greater than 50.We may take 50 as the N value which means that the contribution of cohesion =300

All the coefficients have been determined while the breadth of the footing has been assumed to be 50m, therefore, the local shear that may be experienced for a square footing=2223+0+8000=10223

The analysis indicates that bearing capacity for the ultimate shear is less than the bearing capacity for the local shear.

Calculating for Zones 2 and 3

Calculating for zones 2 and 3

The development of the area 3 considers wall loads of between 35KN/m per meter run and 45kN/m per meter run.

The analysis will consider a shallow foundation whose depth will be about 1.0 to 7.10m.

Working on the same parameters as zone 1;

 (Kumbhojkar, 1993)

Soft clay has a bearing capacity of 100kN/m2 (IS1904, 1978)

However, the undrained bearing capacity of the soil is taken between 30kN/m2 to 35kN/m2.

Working on the average of these extremes, the assumption may work on Cu=33kN/m2.

q=

q=100*50=5000

Which is later on used to determine the bearing capacity of the strip foundation under general shear

 (5.7Cu=188.1)

Which translates to 5188.1kN/m2, significantly lower.

On the other hand, the ultimate bearing capacity under local shear can be calculated from the modified formulas:

The contribution of cohesion factor can be taken as 300, the same as in the first calculation.

Therefore, the bearing capacity of the shallow foundation can be taken as: 2223+0+660=2883

Comparing the two spoils, the soft clay has a lower bearing capacity than the firm clay.

Zone C

Zone C is to be used for the development of commercial development with the main concern the bearing capacity of about 8000kN to be attained.

The analysis will be based on the bearing capacity of the very stiff clay.

The data provided for the stiff clay: Cu=150kN/m2to 225kN/m2.We can assume the Cu to be 200kN/m2.

q=

The bearing capacity of the stiff clay is 100kN/m2 which gives q as 5000kN/m2

However, the ultimate bearing capacity can be calculated through:

Which gives 1140+5000=6140kN/m2 much more than that of the stiff and soft clay. This is the ultimate bearing capacity of the soil under general stress.

The local bearing capacity of the soil can be calculated from:

2223+0+4000=6223kN/m2

In all the above analyses, the bearing capacity of the soil can be estimated from the following equations is used to measure the load capacity of the pile at the tip:

 (Hannah & Meyerhorf, 1978)

On the other hand, the following equation is used to determine the fractional resistance of the soil and pile interface.

The two equations are combined to determine the bearing capacity of the soil under deep foundation.

In this analysis, the consideration is steel piles which have a friction angle of 20 degrees. Considering piles of 10m diameter.

Zone 1

Area of circular pile=78.53m2

Cu=assuming 175kN/m2 (stiff to very stiff clay)

Pile Foundation

Therefore

 =123.7MN/m2

This is just an indication of the bearing capacity of the soil when a pile is used as the foundation on very stiff clay. Shortage of data on for analysis indicates that the load capacity of the soil is very high.

A high bearing capacity of the soil is one of the most fundamental and important aspects that is considered during the design and construction of the foundation. An increase in the bearing strength of the soil means that the ground can accommodate a heavier load and stresses such as those associated with settlement are not highly pronounced (Fellenius, 2012). An increase in the strength of the soil results into economies when designing the foundation mainly due to the sizing as well as the depth. On the other hand, soils with lower bearing capacities require huge investment s and more to this, may be subjected to higher degrees of settlement and stresses. These soils usually require humongous investment either because of the extensive area that has to be covered by a shallow foundation or the increase in depth when the foundation is a deep one (Wrana, 2015).

Geotechnical investigations such as the standard penetration test are the basic building blocks of geotechnical engineering (Niazi & Mayne, 2013). These investigations are used to determine the properties of the soil and therefore ensure that the right foundation is designed and constructed. However, designing a foundation on the basics of soil properties as well as the loading may not be sufficient. Some areas are subjected to seismic activities while other soils have undesirable alluvial deposits.

Seismic loads vary from place to place and from time to time. Therefore, it is important to try and establish the relationship between seismic loads and the soil so as to ensure there is a proper framework in place to ensure that the loading does not affect the foundation by inducing too much stresses. Though not of the same context, the soils of alluvial deposits act in the same way as being subjected to seismic loading (Sitharam, 2013). The soil particles can easily be displaced and as such, provide a major challenge to structural design.
There are two regions which experience stresses die to foundation loading: the radial shear zones and the Rankine passive zones (Cai, et al., 2012). These are the regions that are adjacent to the footing and therefore experience the stress. However, these areas are more pronounced in alluvial deposits because of the increased angle of friction.

Conclusion

Settlement will occur on the alluvial site and as such, it is important to establish a methodology through which the settlement will be reduced and more to this, mitigated. However, the process will have to be conducted in accordance to the site test methodology. Site tests is used to determine the amount of settlement that has occurred and therefore may be employed to monitor the extent of settlement in the alluvial deposits.

The extent to which the settlement has occurred can be measured by the use of a single point settlement gauge which is usually fixed along the length of the foundation ( Chunhui, et al., 2014). It can be used for both the deep as well as the shallow foundation. Working with the settlement gauge, the formula that may be used is:  

S’ is the level of measurement, s is the measured level of settlement by the liquid and d stands for the measured compression. However, there are many locations where the settlement may occur and it is therefore imperative to consider a single point settlement pattern (Gabrielaitis, et al., 2013). In this, the design has to consider the layer that has been compressed and it is usually the soil that is directly underneath the pile. In designing a building or a road, the single point sensor has to be placed at strategic points whereby settlement is likely to have detrimental or profound effect on the overall structure.

The size of the layer that will be formed after loading can be determined through two methods; the control of strain method and the control of stress method (Wrana , 2014). The control of stress method is founded on the principle of maximum stress and basically, the control formula is as follows:

Whereby additional stress can be calculated from the following formula:

 Where aj stands for the coefficient of stress while poj is the additional pressure.

Moreover, this can be calculated by the use of the control of strain method. It has been widely applied in the road as well as construction industry in order to determine the depth at which there is a likelihood that there will be a deformation on the foundation (Pinasti, et al., 2015). The underlying mathematical equation is: 

However, the analysis should be based on layer by layer deformation with the final level of deformation determined by the coefficient of settlement. After determining the type of deformation, the methods that may be used in the rectification process in order to ensure stability to both roads and other structures may be employed.Some of these methods are indicated below. These technologies will be used to improve the compactness as well as the solidification levels of the soil (Wrana , 2015)

To begin with, vibrio compaction may be used to increase the density of the soil and reduce the spacing between the particles. The major purpose of the machinery is to pack the soil particles into a smaller space and therefore rearrange the configuration. However, the principle of this technology is based on the injection of water as well as vibration in order to rearrange soil particles.

Secondly, vacuum consolidation may be used to increase the compactness of the alluvial deposits. By surrounding the area with a membrane and creating a vacuum, the soil particles will settle into a more consolidated form. The vacuum loading maintains the pore pressure within the soil particles but increases the stress therefore providing a platform for consolidation.

Finally, grouting may be used to improve the density of the soil so as to reduce the extent of settlement. It involves pumping of materials into the soil so as to change the charactreristics.The method may increase the strength of the soil, reduce the rate of movement and increase the density of the soil.It will have remarkable improvements and the alluvial deposits will be more compact and less susceptible to settlement as well as movement.

Implementing the actual solutions to the site may be challenging. Site specific problems need to be managed and implemented in a specific manner. The problems need to be addressed in an object oriented manner and failure to do so will result into an inefficient process. As such, it is important to identify some of the challenges likely to be faced during the implementation of ground solutions.

To begin with, there are challenges that will be faced regarding environmental pollution as well as effects on the environment. Some of the solutions such as grouting lead to the introduction of foreign substances into the ground and this may be faced by rebellion from environmentalists and conservatism. Therefore, there needs to be proper impact assessment of the environmental impacts of the proposed solution prior to the actual implementation process.

Secondly, varying soil properties are likely to lead to inefficiency in the process employed. The soil strata have different properties and the implementation of some methods consider the properties of  one particular soil.it is difficult to consider the properties of the different soils and this leads to a problem in the efficiency of the process.it is a problem that has faced many ground solutions. However, with the change in technology, the proper solutions are being implemented.

Thirdly, there is a likelihood that some of the solutions are likely to affect the general environment and therefore health concerns. The vacuum consolidation is aimed at creating a vacuum which improves the consolidation process but this is likely to lead to a change in the level of the water table. Change in the level of water table may have serious implications on the health of the locals especially because of contamination by ground metals. Moreover, the ground freezing methodology has an effect of reducing the amount of water in the ground by using freezing techniques to convert the water into a glue.

Finally, the use of these technologies has an effect of changing the natural structure of the soil. Change in the soil structure has far more consequent al results than when in the original state. One of the problems may be as a result of geological changes. A change in the geological structure of the soil during natural events such as earthquakes may result to chemical reactions which may have overall effect on the surrounding.

References

Chunhui, S., Jun, Z. & Jianlin, M., 2014. Settlement Calculation Method for Over-length Piles Foundation Based on Field Test in The Beijing high speed railway. Volume 19.

Bowles, J. E., 1997. Foundation Analysis and Design. Singapore:: McGraw-Hill, Inc.,.

Cai, G., LIU, S. & PUPPALA, A. J., 2012. Reliability assessment of CPTu-based pile capacity predictions in soft clay deposits,. Engineering Geology.

Fellenius, B. H., 2012. Basics of Foundation Design. Calgary, Alberta, Canada: s.n.

Gabrielaitis, L., Žaržojus, G. & Papinigis, V., 2013. Estimation of Settlements of Bored Piles Foundation. procedia Engineering.

Hannah, A. M. & Meyerhorf, G. G., 1978. "Ultimate Bearing capacity of Foundations on Layered Soil under Inclined Load. Canatlian Geotechnical journar.

IS1904, 1978. s.l.:s.n.

Jamai, H., 2017. Methods of Pile Installation. [Online]
Available at: https://www.aboutcivil.org/deep-pile-foundation.html
[Accessed 17 06 2018].

Niazi, F. & Mayne, P. W., 2013. Cone Penetration Test Based Direct Methods for Evaluating Static Axial Capacity of Singlepiles. geotechniocal and geological engineering, pp. 979-1007.

Pinasti, I., Muslim, D. & Fajar, f., 2015. Suitable calciulation of shallow foundation bearing capacity by comparing the calculation of terzaghi and meyerhorf's concept in jatanangor,west java province,indonesia. s.l., s.n.

Sitharam, T. G., 2013. Advanced foundation engineering. s.l.:s.n.

Wrana , B., 2014. Lectures on Soil Mechanics,Wydawnictwo Politechniki Krakowskiej. s.l.:s.n.

Wrana , B., 2015. PILE LOAD CAPACITY – CALCULATION METHODS. Studia Geotechnica et Mechanica,, 37(4).

Wrana, B., 2015. Lectures on Foundations, Wydawnictwo. s.l.:s.n.