Modeling and Design of Shallow Foundations

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Construction of structures involves setting up of foundation which is the lowest part of a building or a bridge and which transmits weight to underlying soil. There are two classes of foundations, these are: shallow and deep ones. The major subject of the paper is modeling and design of shallow foundations. A shallow foundation is a footing planned to take a shape of rectangle or square which supports columns, other structures and walls. As per the provision of civil engineering, a foundation is considered to be shallow when it is less than six feet in depth or when its depth equals its width.

According to Paolocci (1997), “a foundation supports the weight or load of any construction work such as building, bridges and roads. The design used to model a foundation depends on the type of soil, load of the building, materials used and the purpose of the construction,” (p.564). Modeling and design of shallow foundations includes the techniques and requirements of civil engineering that must be put in place while setting up a foundation.[1] There are various types of shallow foundation such as mat-slab, spread footing and slab- on – grade.

Spread footing foundation is mostly used in construction of commercial structures and basements. This type of shallow foundation includes strips of concrete that help in transfer of wall or column loads to bedrock. Several factors control spread footing such as penetration that results due to near surface layers, leading to changed volume because of shrink, swell or frost heave.

Mat-slab foundations are used in the distribution of heavy walls or column loads constructed across the whole building and help to reduce pressure created from construction materials. This type of shallow foundation is constructed at a close range with ground surface or in construction of lower part of basements. Mat-slab foundations can also be used in construction of high rise buildings where the foundation is thick and requires extensive reinforcement to ensure that there is uniform transfer of load.

Another type of shallow foundation is slab-on- grade that is used in structural engineering for structures formed from mold set ground. This foundation is elevated through a concrete slab placed in the mold, thus creating no space between the structure and bed rock. Slab-on-grade is common in construction works found in warmer climate where there is no need for heat ducting, ground freezing and thawing. The advantages of using this form of shallow foundation is that it is cheap, sturdy and less vulnerable to insects, such as termites for example.

In their argument, Zeng & Steadman (1998) have formulated that “shallow foundations are commonly used in structural constructions through the application of various models and designs. This creates an environment for providing strong construction work that lasts for a long period of time,” (p.247). Other forms of foundations such as deep, piles, caissons and piers are mainly used to establish strong foundation for prime structures.[2] The provisions of civil engineering do not provide overwhelming constructions that are threat to human life and the environment. The use of shallow foundations has advantages and disadvantages.

Advantages of shallow foundations are that

* It is cost effective hence affordable

* There is no need of experts to provide labor for shallow foundations

* Materials used are concrete and easily available.

* The construction procedure is simple.

Disadvantages of using shallow foundation

* Limitation capacity is soil structure

* Foundation is always subjected to torsion, moment and pullout

* Settlement is a major problem

* The ground surface is sometimes irregular making the structures sloppy.

When designing a shallow foundation, there are two common aspects that must be considered. Firstly, the pressure on applied foundation should not be more than the bearing capacity of the supporting soil. Secondly, foundation settlement should not be excessed due to the impact of pressure on applied foundation.

Chapter 1: The modes of failure depending on soil type, foundation size and depth.

There are only three specific modes of soil failure associated with soil type, foundation size and depth. These include general shear failure, local shear failure and punching shear failure.

General shear failure

It is a mode of failure in which ultimate strength of soil is associated with the entire surface of sliding before the entire structure underlying soil is affected by excessive movement. This mode of failure depending on soil type, foundation size and depth is commonly encountered in stiff clays and sand soil that is in dense underlying shallow foundation. When the load of the structure is increased, the foundation pressure on the shallow foundation increases.[3] Foundation settlement also increases with increased pressure until ultimate bearing capacity is reached.

Sudden foundation settlement increase is immediately noticed when bearing capacity has been reached. This is an indication of loss in support of the shallow foundation leading to failure of foundation. “Another impact of general shear failure mode is the inability of the foundation to maintain applied pressure. This is also accompanied by failure surface that is a threat to structural construction,” (Le Pape Sieffert, p.1404). Generally, in shear failure mode, there is always a difference between applied pressure and foundation settlement that corresponds to ultimate bearing capacity.

Local shear failure

This mode of failure is encountered in sand soil that is medium dense and medium stiff clay type of soils. Local shear failure is characterized by absence of distinct peak in pressure against foundation settlement. Determination of bearing capacity in local shear failure is based on excessive foundation settlement. Local shear failure is associated with progressive failure surface that extends to ground surface once bearing capacity has been reached.[4] In addition, it is a failure with ultimate shearing strength of soil that is usually mobilized locally along with the potential surface of sliding. This happens at a time when the structure supported by soil is affected by rapid movement.

Punching shear failure

This mode of failure usually occurs in loose sands and soft clays types of soil. It is accompanied by a surface that is triangular in shape and is directly under shallow foundation. One major characteristic of punching shear failure is the lack of distinctive ultimate bearing capacity. Ultimate bearing capacity in punching shear failure is considered to be the pressure that corresponds with excess foundation settlement. It involves failure of reinforced concrete slab that have been subjected to high local forces especially in flat slab structures and usually happens at column support points.

In their research project, Nova and Montrasio (1997) have established that “the strength of the concrete is influenced by intermediate principal shear stresses and normal stresses. Hydrostatic pressure is also another factor that influences the strength of concrete,” (p.50). A concrete consists of several layers that makes it to be strong and reinforcing steel is used to strengthen the slab. In material modeling, concrete is considered as isotropic material until a point when cracking happens. Once the concrete is cracked, it incorporates tension, reduces shear stiffness and stiffening. This helps to establish strong concrete that is necessary for shallow foundations.

Chapter 2: Using the right type of foundation on the right soil.

The type of soil on which a foundation is to be established contributes to the strength of structures constructed. However, to get the right type of soil that supports strong foundation is the major challenge faced by civil engineers. One important item that civil engineers need to put into consideration is establishment of a strong structural foundation. There are different types of building foundations such as raft, piling and footing that are considered when setting up a structure. It is necessary to check the condition of soil before putting up a structure. This helps to provide a strong surface that supports the load of the walls and roof.[5] The condition of soil is done through soil investigations carried out by soil engineers who provide a report that is used by architects to determine the type of foundation to be used in a particular area.

The soil engineer has the capacity to establish settlement characteristics of soil, depth to ground water and the necessary measures needed to upgrade a given site to the standard code. Two common factors should be put in place when determining the quality, substance and type of soil. It is important to establish virgin and fill type of soil that helps to determine how the right foundation is used on the best quality soil. A virgin soil is a type of soil that has never been disturbed and it is the best to set up building foundation. This is due to its compatibility and texture that is able to hold heavy weight of buildings and other structures. Fill type of soil also known as sandy loam on the other hand, means a piece of land that has been refilled and thereafter used as an area for construction. This type of soil is not best because in most cases, it is always loose and needs to be compacted for it to withstand applied pressure.[6] To convert fill soil into useful state, it requires the application of engineering knowledge which is very expensive.

According to Pool (1997), the right type of foundation that is used on the right soil is the major important element that should be put into consideration before construction work starts. The right type of foundation, whether shallow or deep, depends on the type of soil in a given construction site,” (p.35). Builders are advised not to set up structures in an area that is covered by expansive clays and if it becomes inevitable to construct structure, clay soil must be removed. The right foundation is also used to give builders the capacity to determine areas that are prone to earthquakes and land slides. This is because areas subjected to natural catastrophes like earthquakes have poor quality soils and hence builders should consider the type of foundation to be used.[7]

The type of soil is used to determine the type of foundation to be used in structural construction. For instance, clay type of soil is considered to expand during wet season and contract during dry period hence it is not recommended to be used on shallow foundation. The reason of a problem is because the active zone of expansive clay is always near the surface. Sandy loam soil does not change with moisture content or temperature and soil engineers recommend this type of soil. It is in a position to support slab foundation and applied pressure, but the major challenge is soil erosion. This happens when there is heavy rainfall that erodes the foundation and this calls for slab jacking that aims at repairing the slab to avoid further damage.

The right foundation is only constructed through evaluation of the type of soil in relation to moisture content and impact of temperature change. A good foundation should be set up to reach the bedrock for full support of the structure load and applied pressure. When the foundation is built to underlie the bedrock, soil erosion is reduced and shifting effect of the soil is also cancelled. A foundation that is built on a mixture of different types of soil is prone to serious damage that results from different ways upon which soil reacts. To resolve the issue of soil from reacting differently, soil engineers recommend that builders should replace weak soil with more strong textural soils.[8] For instance, in a construction site that has part of clay and sand, the clay soil is potentially replaced with sand soil. This yields uniform soil consistency that helps to support the right type of foundation.

In a case where a building or any other structure is constructed to underlie soil type with various conditions, the structures are deemed to move in different ways. For instance, in a case when one half of the foundation is built on expansive clay and the other is on fill, the amount of movement varies from one half to the other. In other instances, the foundation system may not be designed in a proper way, this results to differential movement that causes damage to structure and foundation. Therefore it becomes easy to establish the type of soil by considering the site upon which foundation is built. “When the foundation is shallow, the type of soil is considered to be the best and on the other hand, deep foundation is established on soils that are of poor quality, (p.Gazetas, 1991, p.39). Therefore, the right foundation is used to determine the right type of soil to support structural constructions.

Chapter 3: Water table level and bearing capacity

Bearing capacity refers to the maximum value of pressure that the foundation on which a structure stands can support. The depth of a foundation is dependent on the type of the soil under which the foundation stands. A good foundation has the capacity to transmit the load of a structure evenly below the ground surface. However, the ground surface is greatly influenced by the depth of the water table. “In construction and design, water table represents the surface that separates between saturated and unsaturated groundwater zones. Depending on the depth of the bed rock, the water table may be high or low,” (Carpenter, 2001, p.27). In some areas, the depth of water table keeps on shifting depending on the seasons of rain. When the rainfall is high, say during spring, water table rises nearer to the surface while on the other hand descending considerably to lower grounds during the summer.

The depth of water table at any given time affects the modeling design, especially in the case of the shallow foundations. In all cases, the ultimate depth to which one can put utilization of underground space is dependent on the depth of the water table.

In design, we have witnessed cases where the distance from the ground of the foot of foundation slab shifts above the water table. This has led to rejections of such plans by relevant safety authorities due to the concern of the resultant catastrophes that can emanate from unforeseen deformations on the surrounding soil due to the added weight.[9] When constructing structure with shallow foundations in places where water table is high, the preliminary plans involve dewatering of the grounds beneath using trenches so as to construct a firm foundation that will support the weight of the structure adequately. To avoid any problems in the soil supporting structure, most designs in these cases propose installation of a wall in the ground which stands over the overall breadth of the water table horizon. This acts as an enclosing structure that collects the accumulating water. This water can be directed to a draining system or a reservoir (Le Pape, Sieffert, p.1379). The next step is to develop a design for draining the accumulated water. In most cases, designers apply the methods of well-point-filter by use of submersible pumps and needle-filters for deeper foundations.

For shallow foundations like in our case, the most applicable method for draining water from building trenches is the use of an open end discharge system. The selection of a proper design and analysis of the best way to construct a feasible water collecting reservoir and draining mechanism is very crucial in minimizing the effect of dewatering on the structure. The most important factor to note is that, after a completion of a structure, the added weight exerts extra pressure on the ground. Since the original water seeping from the ground was in equilibrium with the atmospheric pressure, the added pressure might lead to more seepage of water from the ground adjacent to the new structure.[10] Presence of groundwater near to the surface may lead to deterioration of material used for construction. In case where steel is to be used for construction, it is wise to know that, the abundance of water and air provides a conducive environment for oxidation and ultimate corrosion of the steel.

In eventuality where there are salts in the ground water, the rusting process would still be accelerated hence reducing the life of a structure. Salts, especially compounds of sulfur, are known to attack compound of cement used to construct cement structures. Attack on cement may lead to disintegration and weakening of a foundation structure. “To reduce such adverse effects, a designer is always advised to provide some protection on the reinforcing system or ensure that there is use of high grade of cement, a high cement ratio in mixing which is well compacted during the layering stage,” (Rhoden, Gordon, 2000, p.43). It is possible that any foundation of a structure may be at one time of their life get to an exposure to a swampy condition due to a rise on water table or seasonal flooding. In this respect, presence of high water table levels greatly influences the ultimate bearing capacity of a building. Water is seen to influence the internal influence between soil particles. For shallow foundations, the negative effects of high water table on the added pressure to the soil can be compensated by ensuring that the foundation is wide enough to distribute the resultant force evenly on the ground. The influence of water table on the bearing capacity of a structure is reduced. The worst scenario arises when the soil supporting a structure becomes completely saturated.

When the level of water table is considered to be directly at the base of a foundation in comparison to the slip lines, the water table influences the stability lines by extending them deeper in lateral direction.

Chapter 4: The Effect of Bearing Capacity

Pacheco and his colleagues (2008) have formulated that “the bearing capacity of shallow foundations is determined by the way it is designed to take on the load. In order to determine the bearing capacity, various calculations are done to acquire the inclination,” (234). Shallow foundations have to be designed in such a way to be able to take care of inclined load action. The formula used in determining the design structure considers the admissible velocity as well the seismic coefficient. Seismic coefficient takes care of the seismic movement. Shallow foundations permeate a certain admissible velocity.[11] Most of the formulas applied in bearing capacity take care of load inclination influence. The occurrence of earthquakes has shown weaknesses to some of the formulas applied in bearing capacity. The scale of foundation has been a major effect of bearing capacity. The granular soils found in areas where shallow foundations are laid have certain effects.

The effects of bearing capacity of shallow foundations are caused by the progressive failure which might be influenced by the soil type. The granular soils acquire the behavior of nonlinear strength. Its strength is not uniformly distributed. Granular soils acquire the property of progressive failure. The non linear strength of granular soils can be determined by the relationship strength-dilatancy. This relationship gives the dilatancy index which is used to describe the bearing capacity. The dilatancy index is determined by considering the progressive failure. These parameters are considered in designing shallow foundations since they determine their strength. In order to design shallow foundations to take the required load, data is collected for the performance of others foundations. This enables the ability to include all strength parameters which take care of shear forces.

According to Cremer, Pecker & Devenne (2001), “shallow foundations are normally affected by ground shaking which causes some weaknesses in the designed structure. Grounding shaking may occur as a result of various phenomena such as earthquakes,” (p.1266). Earthquakes occur as a result of adjustments in the earth’s crust. Shallow foundations are affected by ground shaking in several ways. Earthquakes lead to re-arrangement of pore pressures. These pore pressures determine the ground strength. Ground failure occurs when these pores are in redistribution affecting the distribution of shear forces. Granular soils are not highly affected by this effect. They offer resistance to the distribution of pressure pores. The process of consolidation which involves cohesive soils may take a couple of years. This process may include indulgence of surplus pore pressures.

Ground shaking may trigger inertial forces. The failure mechanism can be influenced by the inertial forces caused by earthquakes. Inertial forces cause a failure mode defined by overturning forces. Sliding resistance is affected by the inertial forces triggered by ground shaking. The sliding resistance determines the bearing capacity of shallow foundations. This is because any slight movement affects the strength of the inclination slope. The inclination slope is designed considering various forces such as shear. Many of the designs do not take concern of the effects of earthquakes. This has been a contributing factor to failure of shallow foundations.

Another way in which earthquakes affect shallow foundation is cyclic degradation. Soil strength can be affected by cyclic degradation which contributes to the formation of surplus pore pressures. Plastification is also one of the parameters related to cyclic degradation. These orientations lead to bearing capacity failure. Some of the failure modes contributed by cyclic degradation include rotational failures. The shear strength of soil may be lost through the process known as liquefaction.[12] The shear stiffness of soil determines the holding capacity of shallow foundations. A foundation is normally supported by soil on all sides and also beneath. This means that any change in shear stiffness of soil affects the foundations.

Yield design theory is used in determining the symmetry of foundations. The bearing capacity of foundations with axial symmetry is calculated using this theory. “The thickness and the rigidity of the wall determine the carrying capacity. The bearing capacity depends on the type of footings,” (Reese, Isenhower & Wang, (2005, p.41). The various types of footing include: axial footings, inclined footings, horizontal footings and circular footings amongst other types. The diameter of shallow foundations also affects the bearing capacity. The effect of bearing capacity depends on the type of footing. The bearing capacity of circular footing is not the same as strip footing.

The effects of bearing capacity are also influenced by soil types. The bearing capacity of un-reinforced sand is as the bearing capacity of shallow foundation laid on reinforced sand. The soil particles also affect the bearing capacity. The soil participles influence distribution of pore pressures. The width of the foundation is used in determining the bearing capacity ratio. This means that the bearing capacity is affected by the width of the foundation. Layers of geogrid can be reinforced with sand in order to acquire maximum bearing capacity.

In conclusion, the effect of bearing capacity of shallow foundations is influenced by various variables. These include: soil types, ground shaking, type of footing, and foundation orientation. Ground shaking occurs as a result earthquakes as these influence the bearing capacity of shallow foundation in several ways. These include: change in shear soil stiffness, cyclic degradation and liquefaction amongst other ways.

Chapter: 5 Calculations of shallow foundation settlements

In construction theory, designers use equations to calculate the foundation settlements and the resultant rates of deformations on the bed soil under the pressure of the structure. The performance of bed calculations follows under two limiting states. First is the state of performance and the second limiting state is the state of safety. In the second state, a predicted finite deformation is not supposed to exceed those established in the condition under which structures and other buildings are only meant to support normal habitation.[13] This state is in most times used as the basic criteria to measure the safety of a structure. In cases of bed calculations, an extra constraint is included under which the average pressure exerted by the structure on the ground is not supposed to be greater than the computed value of resistance of the supporting soil to the pressure exerted on it. A common resolution has been that, in order to raise the limit of safety by 20%, the calculated limiting deformations should be less than 40% of the limiting values.[14] This occurrence is explainable by use of the facts that acknowledge the presence of patches which experience plastic deformation.

These regions develop with the progressive increase in the loading. Such developments form beneath the edges of foundations until a point where the linear relationship between the load from the structure and resistance from the ground beneath it fails. This linear union between the load and resistance stands in the situation of application of elasticity theory. According to Hooks law of deformation of linearly elastic material, stress (load) and strain (resistance) are applied. Application of layer by layer accumulation of resistance values enables a designer to account for lack of uniformity in soils in reference to deformity across the allowable limits of a compressible soil layer. “Designers also apply other engineering methods of settlement computation. When we apply the law relating to stress and strain for a given constant thickness that is compressible, the increase in settlement becomes proportional to the increase in the loading,” (Grimes, et al, 2006, p.681). Beyond a point of limit, the settlement tends to increase more rapidly than the load. The formation of regions with plastic deformations increases the rate of accumulation of settlement with increase in loading. This leads to the exhaustion of fatigue of the supporting bed hence interfering with its bearing capacity. Further loading from the structure becomes absolutely impossible as the soil or ground have reached its deformation level from the shear strains in it. Computations have gone further to prove that, by limiting pressure or structural load to the level of resistance, predictable settlements are maintained at lower levels than their limiting values. The extra allowable loading is left to cater for any eventuality of inadvertent loading.

In Calculation, the derivation of the ultimate bearing capacity of a foundation is based on soil constraints which include the soil strength, the shear strength and the weight per unit mass. Other factors considered include the shape, size and depth. In 1943, Tengazi developed a formula to define the ultimate bearing capacity of a narrow piece footing using three-term expression by use of bearing capacity factors of Nc, Nq, and Ng all of which have a relation to the friction angle (f)

qf =c.Nc +qo.Nq + ½g.B .Ng

Where c= apparent cohesion intercept,

qo = the product of the density and depth

D = the depth of the foundation

B = the breadth of the foundation

g = the unit weight of the soil removed from the soil at the time of creating the foundation.

In the case of a drained loading, the calculations are based on the effective stresses where the value of (f) is > 0 and Nc, Nq Ng are all >0. While in reference to swampy regions, the swampy strength resulting from shear (su); Nq = 1.0 and Ng = 0 in relation to cumulative stresses.[15]

The Skempton’s equation employed in calculation of the bearing capacity for swampy or undrained areas for example swampy soils is;

qf = su .Ncu + qo

Where the Ncu = the Skempton’s bearing capacity factor, which is obtainable from a chart. Otherwise the Skempton’s bearing capacity factor can be derived by use of the following expression.

Ncu =

In this equation, the value sc represents the shape factor while the dc is the depth factor.

Nq = 1, Ng = 0, Nc = 5.14

Where; sc = 1 + 0.2 (B/L) for B<=L

dc = 1+ Ö(0.053 D/B ) for D/B < 4

In the same respect, the bearing capacity factor for drained, or soils with a deep water table. The following equation was developed for a long narrow piece footing.

qf =c.Nc +qo.Nq + ½g.B .Ng

However this equation gains applicability only on the use of shallow footings exposed to vertical non eccentric loads.

In case of rectangular and circular foundations, shape factor is considered.

qf = c .Nc .sc + qo .Nq .sq + ½ g .B .Ng .sg

Additional factors can be used to give allowance for depth, distributed loading, inclined loading and the slope of the ground. In actual fact, depth of a structure is only significant if it exceeds the breadth of the structure.[16]

The following equation is used to calculate the bearing capacity factor.

When considering the depth factor the following equation is applied.

qf = c.Nc.dc + qo.Nq.dq + ½ B.gNg.dg

for D>B:

dc = 1 + 0.4 arc tan(D/B)

dq = 1 + 2 tan(f'(1-sinf’)² arctan(B/D)

dg = 1.0

for D=

dc = 1 + 0.4(D/B)

dq = 1 + 2 tan(f'(1-sinf’)² (B/D)

dg = 1.0

In case of an inclusion of safety factor, we employ;

Fs is to compute the bearing capacity qa from ultimate bearing pressure qf. The value of Fs is expected to fall between 2.5-3.0.


Carpenter, T. (2001). Environmental, Construction and Sustainable Development-Vol.1. New York: John Wiley & Sons

Cremer C., Pecker A., Davenne L. (2001). “Cyclic macro-element for soil-structure interaction: material and geometrical non-linearities”, International Journal for Numerical and Analytical Methods in Geomechanics,Vol. 25: 1257-1284.

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Negro P., Paolucci R., Pedretti S., Faccioli E. (2000). “Large-scale soil-structure interaction experiments on sand under cyclic loading”, Proc. 12th World Conference on Earthquake Engineering, Auckland, New Zealand.

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Pacheco, M., Danziger, F. & Pinto, C. (2008). “Design of Shallow Foundations under Tensile Loading for Transmission Line Towers: An Overview.” Engineering Geology, Vol.101, pp.226-235

Paolucci R. (1997). “Simplified evaluation of earthquake induced permanent displacements of shallow foundations”, Journal of Earthquake Engineering, Vol. 1, pp. 563-579.

Pool, R. (1997). Beyond Engineering: How Society Shapes Technology. Oxford: Oxford University Press

Priestley M.J.N., Kowalsky M.J. (2000). “Direct Displacement-Based Design of concrete buildings”, Bulletin of the New Zealand National Society for Earthquake Engineering, Vol. 33, pp. 421-444.

Reese, L., Isenhower, W. & Wang, S. (2005). Analysis and Design of Shallow and Deep Foundations. New York: John Wiley & Sons

Rhoden, C. & Gordon, C. (2000). Studying

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