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Lecture Notes – Geotechnics 1 Chapter 2 Lateral Earth Pressure

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Lateral earth pressure

An example of lateral earth pressure overturning a retaining wall

Lateral earth pressure is the pressure that soil exerts in the horizontal direction. The lateral earth pressure is important because it affects the consolidation behavior and strength of the soil and because it is considered in the design of geotechnical engineering structures such as retaining walls, basements, tunnels, deep foundations and braced excavations.

The coefficient of lateral earth pressure, K, is defined as the ratio of the horizontal effective stress, σ’h, to the vertical effective stress, σ’v. The effective stress is the intergranular stress calculated by subtracting the pore pressure from the total stress as described in soil mechanics. K for a particular soil deposit is a function of the soil properties and the stress history. The minimum stable value of K is called the active earth pressure coefficient, Ka; the active earth pressure is obtained, for example,when a retaining wall moves away from the soil. The maximum stable value of K is called the passive earth pressure coefficient, Kp; the passive earth pressure would develop, for example against a vertical plow that is pushing soil horizontally. For a level ground deposit with zero lateral strain in the soil, the “at-rest” coefficient of lateral earth pressure, K0 is obtained.

There are many theories for predicting lateral earth pressure; some are empirically based, and some are analytically derived.

At rest pressure

At rest lateral earth pressure, represented as K0, is the in situ lateral pressure. It can be measured directly by a dilatometer test (DMT) or a borehole pressuremeter test (PMT). As these are rather expensive tests, empirical relations have been created in order to predict at rest pressure with less involved soil testing, and relate to the angle of shearing resistance. Two of the more commonly used are presented below.

Jaky (1948)[1] for normally consolidated soils:

K_{0(NC)} = 1 - \sin \phi ' \

Mayne & Kulhawy (1982)[2] for overconsolidated soils:

K_{0(OC)} = K_{0(NC)} * OCR^{(\sin \phi ')} \

The latter requires the OCR profile with depth to be determined. OCR is the overconsolidation ratio and \phi ' is the effective stress friction angle.

To estimate K0 due to compaction pressures, refer Ingold (1979)[3]

Soil Lateral Active Pressure and Passive Resistance

Different types of wall structures can be designed to resist earth pressure.

The active state occurs when a retained soil mass is allowed to relax or deform laterally and outward (away from the soil mass) to the point of mobilizing its available full shear resistance (or engaged its shear strength) in trying to resist lateral deformation. That is, the soil is at the point of incipient failure by shearing due to unloading in the lateral direction. It is the minimum theoretical lateral pressure that a given soil mass will exert on a retaining that will move or rotate away from the soil until the soil active state is reached (not necessarily the actual in-service lateral pressure on walls that do not move when subjected to soil lateral pressures higher than the active pressure). The passive state occurs when a soil mass is externally forced laterally and inward (towards the soil mass) to the point of mobilizing its available full shear resistance in trying to resist further lateral deformation. That is, the soil mass is at the point of incipient failure by shearing due to loading in the lateral direction. It is the maximum lateral resistance that a given soil mass can offer to a retaining wall that is being pushed towards the soil mass. That is, the soil is at the point of incipient failure by shearing, but this time due to loading in the lateral direction. Thus active pressure and passive resistance define the minimum lateral pressure and the maximum lateral resistance possible from a given mass of soil.

Rankine theory

Rankine’s theory, developed in 1857,[4] is a stress field solution that predicts active and passive earth pressure. It assumes that the soil is cohesionless, the wall is frictionless, the soil-wall interface is vertical, the failure surface on which the soil moves is planar, and the resultant force is angled parallel to the backfill surface. The equations for active and passive lateral earth pressure coefficients are given below. Note that φ’ is the angle of shearing resistance of the soil and the backfill is inclined at angle β to the horizontal

K_a = \cos\beta \frac{\cos \beta - \left(\cos ^2 \beta - \cos ^2 \phi \right)^{1/2}}{\cos \beta + \left(\cos ^2 \beta - \cos ^2 \phi \right)^{1/2}}
K_p = \cos\beta \frac{\cos \beta + \left(\cos ^2 \beta - \cos ^2 \phi \right)^{1/2}}{\cos \beta - \left(\cos ^2 \beta - \cos ^2 \phi \right)^{1/2}}

For the case where β is 0, the above equations simplify to

K_a = \tan ^2 \left( 45 - \frac{\phi}{2} \right) = \frac{ 1 - \sin(\phi) }{ 1 + \sin(\phi) }
K_p = \tan ^2 \left( 45 + \frac{\phi}{2} \right) = \frac{ 1 + \sin(\phi) }{ 1 - \sin(\phi) }

Coulomb theory

Coulomb (1776)[5] first studied the problem of lateral earth pressures on retaining structures. He used limit equilibrium theory, which considers the failing soil block as a free bodyin order to determine the limiting horizontal earth pressure. The limiting horizontal pressures at failure in extension or compression are used to determine the Ka and Kprespectively. Since the problem is indeterminate,[6] a number of potential failure surfaces must be analysed to identify the critical failure surface (i.e. the surface that produces the maximum or minimum thrust on the wall). Mayniel (1908)[7] later extended Coulomb’s equations to account for wall friction, symbolized by δ. Müller-Breslau (1906)[8] further generalized Mayniel’s equations for a non-horizontal backfill and a non-vertical soil-wall interface (represented by angle θ from the vertical).

K_a = \frac{ \cos ^2 \left( \phi - \theta \right)}{\cos ^2 \theta \cos \left( \delta + \theta \right) \left( 1 + \sqrt{ \frac{ \sin \left( \delta + \phi \right) \sin \left( \phi - \beta \right)}{\cos \left( \delta + \theta \right) \cos \left( \beta - \theta \right)}} \ \right) ^2}
K_p = \frac{ \cos ^2 \left( \phi + \theta \right)}{\cos ^2 \theta \cos \left( \delta - \theta \right) \left( 1 - \sqrt{ \frac{ \sin \left( \delta + \phi \right) \sin \left( \phi + \beta \right)}{\cos \left( \delta - \theta \right) \cos \left( \beta - \theta \right)}} \ \right) ^2}

Instead of evaluating the above equations or using commercial software applications for this, books of tables for the most common cases can be used. Generally instead of Ka, the horizontal part Kah is tabulated. It is the same as Ka times cos(δ+θ).

The actual earth pressure force Ea is the sum of a part Eag due to the weight of the earth, a part Eap due to extra loads such as traffic, minus a part Eac due to any cohesion present.

Eag is the integral of the pressure over the height of the wall, which equates to Ka times the specific gravity of the earth, times one half the wall height squared.

In the case of a uniform pressure loading on a terrace above a retaining wall, Eap equates to this pressure times Ka times the height of the wall. This applies if the terrace is horizontal or the wall vertical. Otherwise, Eap must be multiplied by cosθ cosβ / cos(θ − β).

Eac is generally assumed to be zero unless a value of cohesion can be maintained permanently.

Eag acts on the wall’s surface at one third of its height from the bottom and at an angle δ relative to a right angle at the wall. Eap acts at the same angle, but at one half the height.

Caquot and Kerisel

In 1948, Albert Caquot (1881–1976) and Jean Kerisel (1908–2005) developed an advanced theory that modified Muller-Breslau’s equations to account for a non-planar rupture surface. They used a logarithmic spiral to represent the rupture surface instead. This modification is extremely important for passive earth pressure where there is soil-wall friction. Mayniel and Muller-Breslau’s equations are unconservative in this situation and are dangerous to apply. For the active pressure coefficient, the logarithmic spiral rupture surface provides a negligible difference compared to Muller-Breslau. These equations are too complex to use, so tables or computers are used instead.

Equivalent fluid pressure

Terzaghi and Peck, in 1948, developed empirical charts for predicting lateral pressures. Only the soil’s classification and backfill slope angle are necessary to use the charts.

Bell’s relationship

For soils with cohesion, Bell developed an analytical solution that uses the square root of the pressure coefficient to predict the cohesion’s contribution to the overall resulting pressure. These equations represent the total lateral earth pressure. The first term represents the non-cohesive contribution and the second term the cohesive contribution. The first equation is for an active situation and the second for passive situations.

\sigma_h = K_a \sigma_v - 2c \sqrt{K_a} \
\sigma_h = K_p \sigma_v + 2c \sqrt{K_p} \

Coefficients of earth pressure

Coefficient of active earth pressure at rest

Coefficient of active earth pressure

Coefficient of passive earth pressure

 

CLICK LINK BELOW FOR FULL LECTURE NOTES

Chapter 2 – Lateral Stresses

 

Source: 1. https://en.wikipedia.org/wiki/Lateral_earth_pressure

2. http://www.diyadvice.com/

3. http://www.gabion1.co.uk/

 

My First Engineering education grant

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Alhamdulillah.. Survey Unit FKA granted research grant on EVALUTION ON PROJECT BASED LEARNING IMPLEMENTATION FOR CIVIL ENGINEERING STUDENTS IN MALAYSIAN UNIVERSITY by Universiti Teknologi Malaysia. Following is the executive summary of the research grant.

EXECUTIVE SUMMARY

“Implementation of Project Based Learning (PtBL) in Universiti Teknologi Malaysia  (UTM) as part of Outcome Based Education (OBE) framework have faced various challenges (i.e revamp on the undergraduate co-curricullum, required high commitments from academicians & faculty and facilities to cater  PtBL activities). This research focused on the effectiveness of PtBL teaching method in an effort to develop the students’ soft skills in tandem with the technical or professional competencies; and problems, challenges and potential improvement in the course. The Survey Camp course which  is offered at year one of a four years civil engineering degree programme in the Faculty of Civil Engineering (FKA), UTM and Faculty of Civil Engineering and Enviroment (FKAAS), Universiti Teknologi Tun Hussein Onn (UTHM) was chosen for this study. It  is a ten days fieldwork  in which the students  will carry out an engineering survey project from field to finish in groups of five to six students supervised by the academic staff. Assessment of the technical aspects was based on the students ability to meet the minimum engineering surveying’s standard whereas the assesment of soft skills was conducted during various sessions of  the survey projects. Survey questionaires were given at the beginning and the end of the course as part of evaluation of the course effectiveness. The research is  expected to evaluate the effectiveness of PtBL in Civil Engineering courses. Soft skills improvement should be seen through the implementation. However, the implementation will be not easy. The problems and difficulties will be guidance on the improvement of teaching methods. This will enable the researcher to established appropirate manual, standard of procedure and quality assessments either in the technical or soft skills on the implementation of course.”

 

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Introduction to Geotechnical Engineering

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Geotechnical engineering is the branch of civil engineering concerned with the engineering behavior of earth materials. Geotechnical engineering is important in civil engineering, but is also used by military, mining, petroleum, or any other engineering concerned with construction on or in 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 structurefoundations; and monitor site conditions, earthwork and foundation construction.[1][2]

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 androckfalls.

Ground Improvement refers to a technique that improves the engineering properties of the soil mass treated. Usually, the properties that are modified are shear strength, stiffness and permeability. Ground improvement has developed into a sophisticated tool to support foundations for a wide variety of structures. Properly applied, i.e. after giving due consideration to the nature of the ground being improved and the type and sensitivity of the structures being built, ground improvement often reduces direct costs and saves time.[3]

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, levees,channels, reservoirs, deposition of hazardous waste and sanitary landfills.

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.