# Bearing capacity

In geotechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the maximum average contact pressure between the foundation and the soil which should not produce shear failure in the soil. Ultimate bearing capacity is the theoretical maximum pressure which can be supported without failure; allowable bearing capacity is the ultimate bearing capacity divided by a factor of safety. Sometimes, on soft soil sites, large settlements may occur under loaded foundations without actual shear failure occurring; in such cases, the allowable bearing capacity is based on the maximum allowable settlement.

There are three modes of failure that limit bearing capacity: general shear failure, local shear failure, and punching shear failure.

## Introduction

A foundation is the part of a structure which transmits the weight of the structure to the ground. All structures constructed on land are supported on foundations. A foundation is a connecting link between the structure proper and the ground which supports it. The bearing strength characteristics of foundation soil are major design criterion for civil engineering structures. In nontechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the maximum average contact pressure between the foundation and the soil which should not produce shear failure in the soil. Ultimate bearing capacity is the theoretical maximum pressure which can be supported without failure; allowable bearing capacity is the ultimate bearing capacity divided by a factor of safety. Sometimes, on soft soil sites, large settlements may occur under loaded foundations without actual shear failure occurring; in such cases, the allowable bearing capacity is based on the maximum allowable settlement.

## General bearing failure

A general bearing failure occurs when the load on the footing causes large movement of the soil on a shear failure surface which extends away from the footing and up to the soil surface. Calculation of the capacity of the footing in general bearing is based on the size of the footing and the soil properties. The basic method was developed by Terzaghi, with modifications and additional factors by Meyerhof and Vesić. The general shear failure case is the one normally analyzed. Prevention against other failure modes is accounted for implicitly in settlement calculations.[1] There are many different methods for computing when this failure will occur.

## Terzaghi's Bearing Capacity Theory

Karl von Terzaghi was the first to present a comprehensive theory for the evaluation of the ultimate bearing capacity of rough shallow foundations. This theory states that a foundation is shallow if its depth is less than or equal to its width.[2] Later investigations, however, have suggested that foundations with a depth, measured from the ground surface, equal to 3 to 4 times their width may be defined as shallow foundations.[2]

Terzaghi developed a method for determining bearing capacity for the general shear failure case in 1943. The equations, which take into account soil cohesion, soil friction, embedment, surcharge, and self-weight, are given below.[2]

For square foundations:

${\displaystyle q_{ult}=1.3c'N_{c}+\sigma '_{zD}N_{q}+0.4\gamma 'BN_{\gamma }\ }$

For continuous foundations:

${\displaystyle q_{ult}=c'N_{c}+\sigma '_{zD}N_{q}+0.5\gamma 'BN_{\gamma }\ }$

For circular foundations:

${\displaystyle q_{ult}=1.3c'N_{c}+\sigma '_{zD}N_{q}+0.3\gamma 'BN_{\gamma }\ }$

where

${\displaystyle N_{q}={\frac {e^{2\pi \left(0.75-\phi '/360\right)\tan \phi '}}{2\cos ^{2}\left(45+\phi '/2\right)}}}$
${\displaystyle N_{c}=5.14\ }$ for φ' = 0
${\displaystyle N_{c}={\frac {N_{q}-1}{\tan \phi '}}}$ for φ' > 0
${\displaystyle N_{\gamma }={\frac {\tan \phi '}{2}}\left({\frac {K_{p\gamma }}{\cos ^{2}\phi '}}-1\right)}$
c′ is the effective cohesion.
σzD′ is the vertical effective stress at the depth the foundation is laid.
γ′ is the effective unit weight when saturated or the total unit weight when not fully saturated.
B is the width or the diameter of the foundation.
φ′ is the effective internal angle of friction.
K is obtained graphically. Simplifications have been made to eliminate the need for K. One such was done by Coduto, given below, and it is accurate to within 10%.[1]
${\displaystyle N_{\gamma }={\frac {2\left(N_{q}+1\right)\tan \phi '}{1+0.4\sin 4\phi '}}}$

For foundations that exhibit the local shear failure mode in soils, Terzaghi suggested the following modifications to the previous equations. The equations are given below.

For square foundations:

${\displaystyle q_{ult}=0.867c'N'_{c}+\sigma '_{zD}N'_{q}+0.4\gamma 'BN'_{\gamma }\ }$

For continuous foundations:

${\displaystyle q_{ult}={\frac {2}{3}}c'N'_{c}+\sigma '_{zD}N'_{q}+0.5\gamma 'BN'_{\gamma }\ }$

For circular foundations:

${\displaystyle q_{ult}=0.867c'N'_{c}+\sigma '_{zD}N'_{q}+0.3\gamma 'BN'_{\gamma }\ }$

${\displaystyle N'_{c},N'_{q}andN'_{y}}$, the modified bearing capacity factors, can be calculated by using the bearing capacity factors equations(for ${\displaystyle N_{c},N_{q},andN_{y}}$, respectively) by replacing the effective internal angle of friction${\displaystyle (\phi ')}$ by a value equal to ${\displaystyle :tan^{-1}\,({\frac {2}{3}}tan\phi ')}$ [2]

## Meyerhof's Bearing Capacity theory

In 1951, Meyerhof published a bearing capacity theory which could be applied to rough shallow and deep foundations.[3] Meyerhof (1951, 1963) proposed a bearing-capacity equation similar to that of Terzaghi's but included a shape factor s-q with the depth term Nq. He also included depth factors and inclination factors.

## Factor of safety

Calculating the gross allowable-load bearing capacity of shallow foundations requires the application of a factor of safety (FS) to the gross ultimate bearing capacity, or;

${\displaystyle q_{all}={\frac {q_{ult}}{FS}}}$ [2]

## References

1. ^ a b Coduto, Donald P. (2001). Foundation design : principles and practices (2nd ed.). Upper Saddle River, N.J.: Prentice Hall. ISBN 0135897068. OCLC 43864336.
2. Das, Braja M (2007). Principles of foundation engineering (6th ed.). Toronto, Ontario, Canada: Thomson. ISBN 0495082465. OCLC 71226518.
3. ^ Das, Braja M (1999). Shallow foundations : bearing capacity and settlement. Boca Raton, FL: CRC Press. ISBN 0849311357. OCLC 41137730.
Cellular confinement

Cellular confinement systems (CCS)—also known as geocells—are widely used in construction for erosion control, soil stabilization on flat ground and steep slopes, channel protection, and structural reinforcement for load support and earth retention. Typical cellular confinement systems are geosynthetics made with ultrasonically welded high-density polyethylene (HDPE) strips or novel polymeric alloy (NPA)—and expanded on-site to form a honeycomb-like structure—and filled with sand, soil, rock, gravel or concrete.

Danish pile-driving formula

The Danish pile-driving formula is a formula which enables one to have a good gauge of the bearing capacity of a driven pile.

Deep foundation

A deep foundation is a type of foundation that transfers building loads to the earth farther down from the surface than a shallow foundation does to a subsurface layer or a range of depths. A pile or piling is a vertical structural element of a deep foundation, driven or drilled deep into the ground at the building site.

There are many reasons that a geotechnical engineer would recommend a deep foundation over a shallow foundation, such as for a skyscraper. Some of the common reasons are very large design loads, a poor soil at shallow depth, or site constraints like property lines. There are different terms used to describe different types of deep foundations including the pile (which is analogous to a pole), the pier (which is analogous to a column), drilled shafts, and caissons. Piles are generally driven into the ground in situ; other deep foundations are typically put in place using excavation and drilling. The naming conventions may vary between engineering disciplines and firms. Deep foundations can be made out of timber, steel, reinforced concrete or prestressed concrete.

Dynamic load testing (or dynamic loading) is a method to assess a pile's bearing capacity by applying a dynamic load to the pile head (a falling mass) while recording acceleration and strain on the pile head. Dynamic load testing is a high strain dynamic test which can be applied after pile installation for concrete piles. For steel or timber piles, dynamic load testing can be done during installation or after installation.

The procedure is standardized by ASTM D4945-00 Standard Test Method for High Strain Dynamic Testing of Piles. It may be performed on all piles, regardless of their installation method. In addition to bearing capacity, Dynamic Load Testing gives information on resistance distribution (shaft resistance and end bearing) and evaluates the shape and integrity of the foundation element.

The foundation bearing capacity results obtained with dynamic load tests correlate well with the results of static load tests performed on the same foundation element.

Geotechnical engineering

Geotechnical engineering is the branch of civil engineering concerned with the engineering behavior of earth materials. Geotechnical engineering is important in civil engineering, but also has applications in military, mining, petroleum and other engineering disciplines that are concerned with construction occurring on the surface or within the ground. Geotechnical engineering uses principles of soil mechanics and rock mechanics to investigate subsurface conditions and materials; determine the relevant physical/mechanical and chemical properties of these materials; evaluate stability of natural slopes and man-made soil deposits; assess risks posed by site conditions; design earthworks and structure foundations; and monitor site conditions, earthwork and foundation construction.A typical geotechnical engineering project begins with a review of project needs to define the required material properties. Then follows a site investigation of soil, rock, fault distribution and bedrock properties on and below an area of interest to determine their engineering properties including how they will interact with, on or in a proposed construction. Site investigations are needed to gain an understanding of the area in or on which the engineering will take place. Investigations can include the assessment of the risk to humans, property and the environment from natural hazards such as earthquakes, landslides, sinkholes, soil liquefaction, debris flows and rockfalls.

A geotechnical engineer then determines and designs the type of foundations, earthworks, and/or pavement subgrades required for the intended man-made structures to be built. Foundations are designed and constructed for structures of various sizes such as high-rise buildings, bridges, medium to large commercial buildings, and smaller structures where the soil conditions do not allow code-based design.

Foundations built for above-ground structures include shallow and deep foundations. Retaining structures include earth-filled dams and retaining walls. Earthworks include embankments, tunnels, dikes and levees, channels, reservoirs, deposition of hazardous waste and sanitary landfills. Geotechnical engineers are extensively involved in earthen and concrete dam projects, evaluating the subsurface conditions at the dam site and the side slopes of the reservoir, the seepage conditions under and around the dam and the stability of the dam under a range of normal and extreme loading conditions.

Geotechnical engineering is also related to coastal and ocean engineering. Coastal engineering can involve the design and construction of wharves, marinas, and jetties. Ocean engineering can involve foundation and anchor systems for offshore structures such as oil platforms.

The fields of geotechnical engineering and engineering geology are closely related, and have large areas of overlap. However, the field of geotechnical engineering is a specialty of engineering, where the field of engineering geology is a specialty of geology. Coming from the fields of engineering and science, respectively, the two may approach the same subject, such as soil classification, with different methods.

Glossary of structural engineering

Most of the terms listed in Wikipedia glossaries are already defined and explained within Wikipedia itself. However, glossaries like this one are useful for looking up, comparing and reviewing large numbers of terms together. You can help enhance this page by adding new terms or writing definitions for existing ones.

This glossary of structural engineering terms pertains specifically to structural engineering and its sub-disciplines. Please see glossary of engineering for a broad overview of the major concepts of engineering.

A grade beam or grade beam footing is a component of a building's foundation. It consists of a reinforced concrete beam that transmits the load from a bearing wall into spaced foundations such as pile caps or caissons. It is used in conditions where the surface soil’s load-bearing capacity is less than the anticipated design loads.

A grade beam differs from a wall footing because a grade beam is designed for bending and typically spans between pile caps or caissons, while a wall footing bears on soil and transmits the weight of the wall directly into the ground. It also differs from a strap beam because a grade beam is reinforced to distribute the weight of a wall to separate foundations, while a strap beam is designed to redistribute the weight of a column between footings.

Grade beams may also be used in conjunction with spread footings, in a case with large moments from lateral loads, in order to reduce the size of each spread footing.

Interference of the footings

The Interference of the footings is a phenomenon that is observed when two footings are closely spaced. The buildings when are to be constructed nearby to each other, the architectural requirements or the less availability of space for the construction forces the engineers to place the foundation footings close to each other, and when foundations are placed close to each other with similar soil conditions, the Ultimate Bearing Capacity of each foundation may change due to the interference effect of the failure surface in the soil.

Landscape products

Landscape products refers to a group of building industry products used by garden designers and landscape architects and exhibited at trade fairs devoted to these industries. It includes: walls, fences, paving, gardening tools, outdoor lighting, water features, fountains, garden furniture, garden ornaments, gazebos, garden buildings, pond liners.

Geosynthetics are another group of products used extensively in landscape construction for drainage, filtration, reinforcement and separation. Geotextiles are used for drainage to either convey or allow water penetration and to prevent the mixing of two different materials; geomembranes are used to contain liquids in ponds or wastes in landfills; geogrids and geocells are used for load support and to increase the bearing capacity of weak soils; and geocells are used for slope and channel protection and erosion control.The skills of combining these products to produce places are known as landscape design and landscape detailing.

Plymouth Municipal Airport (Massachusetts)

Plymouth Municipal Airport (IATA: PYM, ICAO: KPYM, FAA LID: PYM) is a town-owned, public-use airport located four nautical miles (7 km) southwest of the central business district of Plymouth, a town in Plymouth County, Massachusetts, United States. According to the FAA's National Plan of Integrated Airport Systems for 2009–2013, it is categorized as a general aviation airport. Due to space issues, the airport has 2 gates in Carver, Massachusetts.

The field was originally Outlying Landing Field Plymouth, a Naval Outlying Landing Field located in Plymouth, Massachusetts operational from 1942 to 1945. It existed as an outlying field of Naval Air Station Squantum (as well as nearby Naval Air Station Quonset Point in December 1944) and was used by student pilots to gain flight experience on its two 4,300-foot turf runways.

RAF Fairford

Royal Air Force Fairford or more simply RAF Fairford (IATA: FFD, ICAO: EGVA) is a Royal Air Force (RAF) station in Gloucestershire, England which is currently a standby airfield and therefore not in everyday use. Its most prominent use in recent years has been as an airfield for United States Air Force B-52s during the 2003 Iraq War, Operation Allied Force in 1999, and the first Gulf War in 1991. It is the US Air Force's only European airfield for heavy bombers.RAF Fairford was the only TransOceanic Abort Landing site for NASA's Space Shuttle in the UK. As well as having a sufficiently long runway for a shuttle landing (the runway is 3,046 m (9,993 ft) long), it also had NASA-trained fire and medical crews stationed on the airfield. The runway is rated with an unrestricted load-bearing capacity, meaning that it can support any aircraft with any type of load.

RAF Fairford is also the home of the Royal International Air Tattoo (RIAT), an annual air display. RIAT is one of the largest airshows in the world, with the 2003 show recognised by Guinness World Records as the largest military airshow ever, with an attendance of 535 aircraft.

Reinsurance sidecar

Reinsurance sidecars, conventionally referred to as "sidecars", are financial structures that are created to allow investors to take on the risk and return of a group of insurance policies (a "book of business") written by an insurer or reinsurer (henceforth re/insurer) and earn the risk and return that arises from that business. A re/insurer will only pay ("cede") the premiums associated with a book of business to such an entity if the investors place sufficient funds in the vehicle to ensure that it can meet claims if they arise. Typically, the liability of investors is limited to these funds. These structures have become quite prominent in the aftermath of Hurricane Katrina as a vehicle for re/insurers to add risk-bearing capacity, and for investors to participate in the potential profits resulting from sharp price increases in re/insurance over the four quarters following Katrina. An earlier and smaller generation of sidecars were created after 9/11 for the same purpose.

Ship launching airbag

Ship launching airbags are specialized air bags that are used for launching marine vessels. This method of launching ships is called airbag launching. These air bags are made of synthetic-tire-cord reinforcement layers and rubber layers, and are also known as marine airbags. They were invented in 1980. The first known use of marine airbags occurred on January 20, 1981 with the launch of a tank barge from the Xiao Qinghe shipyard. From then on, more and more shipyards, especially in China and Southeast Asia, began to use air bags to launch small and medium-sized vessels.

In recent years, higher strength materials have been used in air bag production, allowing them to have much more bearing capacity. Hence, they have begun to be used at the launchings of larger vessels. In October 2011, the successful launch of one vessel with a deadweight tonnage (DWT) of 75000 tonnes set a world record for ship launches utilizing air bags. The following year, on June 6, 2012, the ship "He Ming" (IMO number 9657105), with a DWT of 73541 tonnes, total length of 224.8m, breadth of 34m, and depth of 18.5m, also launched successfully using air bags.

Soil mechanics

Soil mechanics is a branch of soil physics and applied mechanics that describes the behavior of soils. It differs from fluid mechanics and solid mechanics in the sense that soils consist of a heterogeneous mixture of fluids (usually air and water) and particles (usually clay, silt, sand, and gravel) but soil may also contain organic solids and other matter. Along with rock mechanics, soil mechanics provides the theoretical basis for analysis in geotechnical engineering, a subdiscipline of civil engineering, and engineering geology, a subdiscipline of geology. Soil mechanics is used to analyze the deformations of and flow of fluids within natural and man-made structures that are supported on or made of soil, or structures that are buried in soils. Example applications are building and bridge foundations, retaining walls, dams, and buried pipeline systems. Principles of soil mechanics are also used in related disciplines such as engineering geology, geophysical engineering, coastal engineering, agricultural engineering, hydrology and soil physics.

This article describes the genesis and composition of soil, the distinction between pore water pressure and inter-granular effective stress, capillary action of fluids in the soil pore spaces, soil classification, seepage and permeability, time dependent change of volume due to squeezing water out of tiny pore spaces, also known as consolidation, shear strength and stiffness of soils. The shear strength of soils is primarily derived from friction between the particles and interlocking, which are very sensitive to the effective stress. The article concludes with some examples of applications of the principles of soil mechanics such as slope stability, lateral earth pressure on retaining walls, and bearing capacity of foundations.

Soil stabilization

Soil stabilization a general term for any physical, chemical, mechanical, biological or combined method of changing a natural soil to meet an engineering purpose. Improvements include increasing the weight bearing capabilities, tensile strength, and overall performance of in-situ subsoils, sands, and waste materials in order to strengthen road pavements.

Some of the renewable technologies are: enzymes, surfactants, biopolymers, synthetic polymers, co-polymer based products, cross-linking styrene acrylic polymers, tree resins, ionic stabilizers, fiber reinforcement, calcium chloride, calcite, sodium chloride, magnesium chloride and more. Some of these new stabilizing techniques create hydrophobic surfaces and mass that prevent road failure from water penetration or heavy frosts by inhibiting the ingress of water into the treated layer.

However, recent technology has increased the number of traditional additives used for soil stabilization purposes. Such non-traditional stabilizers include: Polymer based products (e.g. cross-linking water-based styrene acrylic polymers that significantly improves the load-bearing capacity and tensile strength of treated soils), Copolymer Based Products, fiber reinforcement, calcium chloride, and Sodium Chloride.

Soil can also be stabilized mechanically with stabilization geosynthetics, for example, geogrids or geocells, a 3D mechanical soil stabilization technique. Stabilization is achieved via confinement of particle movement to improve the strength of the entire layer. Confinement in geogrids is by means of interlock between the aggregate and grid (and tensioned membrane), and in geocells, by cell wall confinement (hoop) stress on the aggregate.Traditionally and widely accepted types of soil stabilization techniques use products such as bitumen emulsions which can be used as a binding agents for producing a road base. However, bitumen is not environmentally friendly and becomes brittle when it dries out. Portland cement has been used as an alternative to soil stabilization. However, this can often be expensive and is not a very good "green" alternative. Cement fly ash, lime fly ash (separately, or with cement or lime), bitumen, tar, cement kiln dust (CKD), tree resin and ionic stabilizers are all commonly used stabilizing agents. Other stabilization techniques include using on-site materials including sub-soils, sands, mining waste, natural stone industry waste and crushed construction waste to provide stable, dust free local roads for complete dust control and soil stabilization.

Many of the "green" products have essentially the same formula as soap powders, merely lubricating and realigning the soil with no effective binding property. Many of the new approaches rely on large amounts of clay with its inherent binding properties.

Bitumen,tar emulsions, asphalt, cement, lime can be used as a binding agents for producing a road base. When using such products issues such as safety, health and the environment must be considered.

The National Society of Professional Engineers (NSPE) has explored some of the newer types of soil stabilization technology, specifically looking for "effective and green" alternatives. One of the examples utilizes new soil stabilization technology, a process based on cross-linking styrene acrylic polymer. Another example uses long crystals to create a closed cell formation that is impermeable to water and is frost, acid, and salt resistant.

Utilizing new soil stabilization technology, a process of cross-linking within the polymeric formulation can replace traditional road/house construction methods in an environmentally friendly and effective way.

There is another soil stabilization method called the Deep Mixing method that is non-destructive and effective at improving load bearing capacity of weak or loose soil strata. This method uses a small, penny-sized injection probe and minimizes debris. This method is ideal for re-compaction and consolidation of weak soil strata, increasing and improving load bearing capacity under structures and the remediation of shallow and deep sinkhole problems. This is particular efficient when there is a need to support deficient public and private infrastructure.

Stabilization (architecture)

Stabilization is the retrofitting of platforms or foundations as constructed for the purpose of improving the bearing capacity and levelness of the supported building.

Soil failure can occur on a slope, a slope failure or landslide, or in a flat area due to liquefaction of water-saturated sand and/or mud. Generally, deep pilings or foundations must be driven into solid soil (typically hard mud or sand) or to underlying bedrock.

Static load testing is an in situ type of load testing used in geotechnical investigation to determine the bearing capacity of deep foundations prior to the construction of a building. It differs from the statnamic load test and dynamic load testing in that the pressure applied to the pile is slower.

Structural support

Structural support is a part of a building or structure providing the necessary stiffness and strength in order to resist the internal forces (vertical forces of gravity and lateral forces due to wind and earthquakes) and guide them safely to the ground. External loads (actions of other bodies) that act on buildings cause internal forces (forces and couples by the rest of the structure) in building support structures. Supports can be either at the end or at any intermediate point along a structural member or a constituent part of a building and they are referred to as connections, joints or restraints.Building support structures, no matter the materials, have to give accurate and safe results. A structure depends less on the weight and stiffness of a material and more on its geometry for stability. Whatever the condition is, a specific rigidity is necessary for connection designs. The support connection type has effects on the load bearing capacity of each element, which makes up a structural system. Each support condition influences the behaviour of the elements and therefore, the system. Structures can be either Horizontal-span support systems (floor and roof structures) or Vertical building structure systems (walls, frames cores, etc.)

Vibro stone column

Vibro stone columns or aggregate piers are an array of crushed stone pillars placed with a vibrating tool into the soil below a proposed structure. This method of ground improvement is also called vibro replacement. Such techniques increase the load bearing capacity and drainage of the soil while reducing settlement and liquefaction potential. Stone columns are made across the area to be improved in a triangular or rectangular grid pattern. They have been used in Europe since the 1950s, and in the United States since the 1970s. Column depth depends on local soil strata, and usually penetrates weak soil.

During construction, a vibrating tool suspended from a crane penetrates to the design depth by means of its own weight and vibrations. Predrilling may be required in dense soil or may be used to reduce the amount of ground displacement during installation. Crushed stone is introduced into the hole by one of two methods. In the dry bottom method, a pipe attached to the vibrator supplies stone directly to it. In the wet top method, water jets located in the vibrator’s tip create an annular space around the vibrator through which stone is introduced from the top.

The vibrating probe breaks down the pores of the surrounding soil, thereby densifying the soil. The stone that is poured in takes the place of the soil and keeps up the pressure on the soil that was created by the vibrating probe. The stone consists of crushed coarse aggregates of various sizes. The ratio in which the stones of different sizes will be mixed is decided by design criteria. Spacing and diameter of columns are also determined by design criteria.

Soil
Foundations
Retaining walls
Stability
Earthquakes
Geosynthetics
Numerical analysis

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