The document discusses analytical and numerical approaches to studying consolidation settlement of foundations built on sand drains. The analytical part reviews existing literature on settlement, structure, installation and monitoring of sand drains. Popular theories on free strain and equal strain cases with and without smear are covered. The numerical part uses PLAXIS 2D to model a drain unit cell and address the reduction in consolidation time from sand drains under varying loads, the relationship between ultimate settlement and loading, and the relationship between ultimate settlement and drain diameter.
Effect of expansive soils on buildings and its preventionSailish Cephas
This document discusses expansive soils and their effects on building structures. It defines expansive soils as soils that swell when water is added and shrink when drying out, due to minerals like montmorillonite that absorb water. Common expansive soils in India include black cotton soils. When the moisture content of expansive soils changes, it can cause problems like cracking in buildings due to uneven swelling or shrinkage. Solutions discussed include replacing expansive soil, compacting or chemically stabilizing soil to reduce swelling, and using moisture barriers to control moisture variation.
The document discusses soil consolidation and laboratory consolidation testing. It begins with an introduction to consolidation and describes the three types of soil settlement: immediate elastic settlement, primary consolidation settlement, and secondary consolidation settlement. It then discusses consolidation in more detail, including the spring-cylinder model used to demonstrate consolidation principles. Finally, it describes the process and components of a laboratory oedometer consolidation test.
This document discusses permeability and seepage in soils. It begins with an overview of permeability, noting that it is a measure of how easily water can flow through soil. Darcy's law is then presented, which relates permeability to flow velocity. Several laboratory tests for measuring permeability are also described, including constant head, falling head, and determination from consolidation or capillary tests. Real-world applications where permeability is important are mentioned, such as seepage through dams or behind retaining walls.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Detailed content on shear strength of soils, principles of effective stresses, tests conducted to determine the shear strength of soils and its applications, dilatancy, thixotropy and sensitivity.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Effect of expansive soils on buildings and its preventionSailish Cephas
This document discusses expansive soils and their effects on building structures. It defines expansive soils as soils that swell when water is added and shrink when drying out, due to minerals like montmorillonite that absorb water. Common expansive soils in India include black cotton soils. When the moisture content of expansive soils changes, it can cause problems like cracking in buildings due to uneven swelling or shrinkage. Solutions discussed include replacing expansive soil, compacting or chemically stabilizing soil to reduce swelling, and using moisture barriers to control moisture variation.
The document discusses soil consolidation and laboratory consolidation testing. It begins with an introduction to consolidation and describes the three types of soil settlement: immediate elastic settlement, primary consolidation settlement, and secondary consolidation settlement. It then discusses consolidation in more detail, including the spring-cylinder model used to demonstrate consolidation principles. Finally, it describes the process and components of a laboratory oedometer consolidation test.
This document discusses permeability and seepage in soils. It begins with an overview of permeability, noting that it is a measure of how easily water can flow through soil. Darcy's law is then presented, which relates permeability to flow velocity. Several laboratory tests for measuring permeability are also described, including constant head, falling head, and determination from consolidation or capillary tests. Real-world applications where permeability is important are mentioned, such as seepage through dams or behind retaining walls.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Detailed content on shear strength of soils, principles of effective stresses, tests conducted to determine the shear strength of soils and its applications, dilatancy, thixotropy and sensitivity.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
The document provides information about shear strength of soil. It defines shear strength and its components of cohesion and internal friction. It discusses Mohr's circle of stress and Mohr-Coulomb theory for shear strength. The types of soil are classified based on drainage conditions during shear testing. Common shear strength tests like direct shear test, triaxial test, unconfined compression test and vane shear test are also explained. Sample calculations for shear strength determination from test results are presented.
Lecture 11 Shear Strength of Soil CE240Wajahat Ullah
Shear Strength of Soil
Shear strength in soils
Introduction
Definitions
Mohr-Coulomb criterion
Introduction
Lab tests for getting the shear strength
Direct shear test
Introduction
Procedure & calculation
Critical void ratio
This document provides information about soil permeability and hydraulic conductivity. It discusses three key points:
1) It defines permeability and hydraulic conductivity as a soil's capacity to allow water to pass through it. Darcy's law establishes that flow is proportional to hydraulic gradient.
2) It identifies factors that affect permeability, including particle size, void ratio, properties of pore fluid, shape of particles, soil structure, degree of saturation, and more.
3) It describes methods to determine hydraulic conductivity in the lab, including constant-head and falling-head permeability tests, and how hydraulic conductivity is calculated based on water flow through a soil sample.
Soils and rocks have unique and distinct engineering properties.
Engineering properties of soils and rocks are very essential parameters to be analysed for several technical reasons.
Properties of these materials may not only pose problems but also give solutions to solve the problems.
Introduction.
Some definitions.
Mohr circle of stress.
Mohr-coulomb’s strength theory.
Tests for shear strength.
Shear tests based on drainage conditions.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
In situ permeability testing in boreholesMartin Preene
This document discusses in-situ hydraulic testing methods for low permeability materials. It defines hydraulic conductivity and permeability, and describes current UK testing practices like packer injection tests. More sophisticated pulse tests and deconvolution analysis methods are presented, which are useful for very low permeability environments. These specialist techniques allow reliable determination of flow models and permeability for applications like nuclear waste repositories.
The document provides information about stress distribution in soil due to self-weight and surface loads. It discusses Boussinesq's formula for calculating vertical stress in soil due to a concentrated surface load. The formula shows that vertical stress is directly proportional to the load, inversely proportional to depth squared, and depends on the ratio of radius to depth. A table of coefficient values used in the formula for different ratios of radius to depth is also provided.
BOUSSINESQ THEORY
VERTICAL STRESS DUE TO POINT LOAD
TABLE FOR VALUES OF BOUSSINESQ’S COEFFICIENT (퐼_퐵)
SOME POINTS FOR USING THE BOUSSINESQ’S EQUATION.
LIMITATIONS OF BOUSSINESQ’S SOLUTION.
This document summarizes the liquid limit and plastic limit tests conducted on a soil sample. The liquid limit was found to be 51.679% using two different methods that produced similar results. The plastic limit was 24.525%. Based on these Atterberg limits, the soil was classified as clay with high plasticity. The limits help characterize the soil's engineering properties and behavior when wet or dry. The experiment showed the soil behaves plastically when wet and becomes hard when dry, typical of clays.
This document discusses the shear strength of soils. It begins with an abstract describing shear strength and factors that influence it, such as particle interactions and stresses. It then outlines different methods to measure shear strength in the laboratory and field, including direct shear tests, triaxial shear tests, and vane shear tests. The Mohr-Coulomb failure criteria is also explained as a way to analyze shear strength based on normal and shear stresses. Key parameters that govern shear strength are identified as cohesion and the friction angle.
A method of testing soils by pressing a cone of standard dimensions into the soil under a known load and measuring the penetration. (extensive investigation and research in construction site).
This document provides lecture notes on soil mechanics from Einstein College of Engineering. It covers the objectives of the soil mechanics course, which is to provide knowledge of engineering properties of soil. The document then outlines the topics that will be covered, including introduction to soil properties, soil water and flow, stress distribution and compression, shear strength, and slope stability. It lists reference textbooks and provides an in-depth section on soil classification systems, properties, particle size distribution, consistency limits, and the Indian Standard Soil Classification System.
1. The document discusses slope stability analysis using the Swedish slip circle method for analyzing finite slopes made of cohesive soils.
2. It describes the assumptions of the method and calculates the factors of safety for circular failure surfaces with and without tension cracks.
3. The document also covers other methods like the ordinary method of slices for c-f soils and discusses locating the critical slip circle using empirical relationships.
This document discusses direct shear tests which are used to determine the shear strength of soils. It provides definitions of key terms like shear strength and failure. It explains that shear strength depends on interactions between soil particles and failures occurs when particles slide past each other. It describes the direct shear test procedure which involves applying normal and shear stresses to a soil sample in a shear box to cause failure. The document provides equations to calculate normal stress, shear stress, dry unit weight and void ratio from direct shear test data.
This document provides information on two soil classification systems: the AASHTO and USCS systems. The AASHTO system classifies soils into eight groups (A-1 through A-8) based on particle size distribution, liquid limit, and plasticity index. The USCS system classifies soils into four categories (coarse-grained, fine-grained, organic, and peat) based on grain size, plasticity, and compressibility. Both systems use laboratory tests like sieve analysis and Atterberg limits to determine the soil classification group. The document describes the classification criteria and symbols used in detail for each system.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
This document presents information about static cone penetration tests. It discusses the principles and applications of cone penetration testing. The principles section explains that a metal cone is penetrated into the subsurface at a constant rate, and the cone tip resistance, sleeve friction, and friction ratio are recorded to determine soil stratigraphy and properties. The applications section notes that data is used to estimate parameters like undrained shear strength and stress history, and that results can be directly applied to soil profiling and engineering designs.
Geotechnical Engineering-II [Lec #1: Shear Strength of Soil]Muhammad Irfan
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Prefabricated vertical drains (PVDs) are synthetic drains used to accelerate consolidation of soft soils. PVDs shorten drainage paths, reducing consolidation time from over 15 years to 1 year. PVDs are more efficiently installed than sand drains, with lower risk of breakage or shear failure during installation or settlement. PVDs have higher discharge capacities than sand drains and cause less soil disturbance during installation, resulting in smaller smear zones. Properly designed and installed PVD systems can reduce a 90% consolidation time from 42 years to 12 months.
The document provides information about shear strength of soil. It defines shear strength and its components of cohesion and internal friction. It discusses Mohr's circle of stress and Mohr-Coulomb theory for shear strength. The types of soil are classified based on drainage conditions during shear testing. Common shear strength tests like direct shear test, triaxial test, unconfined compression test and vane shear test are also explained. Sample calculations for shear strength determination from test results are presented.
Lecture 11 Shear Strength of Soil CE240Wajahat Ullah
Shear Strength of Soil
Shear strength in soils
Introduction
Definitions
Mohr-Coulomb criterion
Introduction
Lab tests for getting the shear strength
Direct shear test
Introduction
Procedure & calculation
Critical void ratio
This document provides information about soil permeability and hydraulic conductivity. It discusses three key points:
1) It defines permeability and hydraulic conductivity as a soil's capacity to allow water to pass through it. Darcy's law establishes that flow is proportional to hydraulic gradient.
2) It identifies factors that affect permeability, including particle size, void ratio, properties of pore fluid, shape of particles, soil structure, degree of saturation, and more.
3) It describes methods to determine hydraulic conductivity in the lab, including constant-head and falling-head permeability tests, and how hydraulic conductivity is calculated based on water flow through a soil sample.
Soils and rocks have unique and distinct engineering properties.
Engineering properties of soils and rocks are very essential parameters to be analysed for several technical reasons.
Properties of these materials may not only pose problems but also give solutions to solve the problems.
Introduction.
Some definitions.
Mohr circle of stress.
Mohr-coulomb’s strength theory.
Tests for shear strength.
Shear tests based on drainage conditions.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
In situ permeability testing in boreholesMartin Preene
This document discusses in-situ hydraulic testing methods for low permeability materials. It defines hydraulic conductivity and permeability, and describes current UK testing practices like packer injection tests. More sophisticated pulse tests and deconvolution analysis methods are presented, which are useful for very low permeability environments. These specialist techniques allow reliable determination of flow models and permeability for applications like nuclear waste repositories.
The document provides information about stress distribution in soil due to self-weight and surface loads. It discusses Boussinesq's formula for calculating vertical stress in soil due to a concentrated surface load. The formula shows that vertical stress is directly proportional to the load, inversely proportional to depth squared, and depends on the ratio of radius to depth. A table of coefficient values used in the formula for different ratios of radius to depth is also provided.
BOUSSINESQ THEORY
VERTICAL STRESS DUE TO POINT LOAD
TABLE FOR VALUES OF BOUSSINESQ’S COEFFICIENT (퐼_퐵)
SOME POINTS FOR USING THE BOUSSINESQ’S EQUATION.
LIMITATIONS OF BOUSSINESQ’S SOLUTION.
This document summarizes the liquid limit and plastic limit tests conducted on a soil sample. The liquid limit was found to be 51.679% using two different methods that produced similar results. The plastic limit was 24.525%. Based on these Atterberg limits, the soil was classified as clay with high plasticity. The limits help characterize the soil's engineering properties and behavior when wet or dry. The experiment showed the soil behaves plastically when wet and becomes hard when dry, typical of clays.
This document discusses the shear strength of soils. It begins with an abstract describing shear strength and factors that influence it, such as particle interactions and stresses. It then outlines different methods to measure shear strength in the laboratory and field, including direct shear tests, triaxial shear tests, and vane shear tests. The Mohr-Coulomb failure criteria is also explained as a way to analyze shear strength based on normal and shear stresses. Key parameters that govern shear strength are identified as cohesion and the friction angle.
A method of testing soils by pressing a cone of standard dimensions into the soil under a known load and measuring the penetration. (extensive investigation and research in construction site).
This document provides lecture notes on soil mechanics from Einstein College of Engineering. It covers the objectives of the soil mechanics course, which is to provide knowledge of engineering properties of soil. The document then outlines the topics that will be covered, including introduction to soil properties, soil water and flow, stress distribution and compression, shear strength, and slope stability. It lists reference textbooks and provides an in-depth section on soil classification systems, properties, particle size distribution, consistency limits, and the Indian Standard Soil Classification System.
1. The document discusses slope stability analysis using the Swedish slip circle method for analyzing finite slopes made of cohesive soils.
2. It describes the assumptions of the method and calculates the factors of safety for circular failure surfaces with and without tension cracks.
3. The document also covers other methods like the ordinary method of slices for c-f soils and discusses locating the critical slip circle using empirical relationships.
This document discusses direct shear tests which are used to determine the shear strength of soils. It provides definitions of key terms like shear strength and failure. It explains that shear strength depends on interactions between soil particles and failures occurs when particles slide past each other. It describes the direct shear test procedure which involves applying normal and shear stresses to a soil sample in a shear box to cause failure. The document provides equations to calculate normal stress, shear stress, dry unit weight and void ratio from direct shear test data.
This document provides information on two soil classification systems: the AASHTO and USCS systems. The AASHTO system classifies soils into eight groups (A-1 through A-8) based on particle size distribution, liquid limit, and plasticity index. The USCS system classifies soils into four categories (coarse-grained, fine-grained, organic, and peat) based on grain size, plasticity, and compressibility. Both systems use laboratory tests like sieve analysis and Atterberg limits to determine the soil classification group. The document describes the classification criteria and symbols used in detail for each system.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
This document presents information about static cone penetration tests. It discusses the principles and applications of cone penetration testing. The principles section explains that a metal cone is penetrated into the subsurface at a constant rate, and the cone tip resistance, sleeve friction, and friction ratio are recorded to determine soil stratigraphy and properties. The applications section notes that data is used to estimate parameters like undrained shear strength and stress history, and that results can be directly applied to soil profiling and engineering designs.
Geotechnical Engineering-II [Lec #1: Shear Strength of Soil]Muhammad Irfan
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Prefabricated vertical drains (PVDs) are synthetic drains used to accelerate consolidation of soft soils. PVDs shorten drainage paths, reducing consolidation time from over 15 years to 1 year. PVDs are more efficiently installed than sand drains, with lower risk of breakage or shear failure during installation or settlement. PVDs have higher discharge capacities than sand drains and cause less soil disturbance during installation, resulting in smaller smear zones. Properly designed and installed PVD systems can reduce a 90% consolidation time from 42 years to 12 months.
This document discusses analytical and numerical approaches to modeling consolidation of clay soils installed with vertical sand drains. It first reviews the literature on analytical models and recent improvements. It then describes setting up a finite element model in PLAXIS to numerically analyze how sand drains improve consolidation time and how time and settlement vary with drain properties and loading. The model considers stiff and soft clay layers and calculates consolidation curves for each based on drain diameter and applied stress. Sand drains were found to significantly reduce consolidation time, especially for stiff clays, while final settlement was unaffected by drain diameter.
1) The document discusses ground improvement techniques of preloading and vertical drainage. Preloading involves applying a surcharge load to improve soil strength and reduce settlements before construction.
2) Vertical drains are often used with preloading to accelerate consolidation by shortening the drainage path. Common types are sand drains and prefabricated vertical drains.
3) Vacuum preloading is described as an alternative to conventional preloading using surcharge loads, applying atmospheric pressure via a membrane system instead. This requires an effective drainage and vacuum maintenance system.
This document discusses consolidation settlement, which occurs when saturated soil is loaded and squeezed, causing water to be expelled over time (years depending on soil permeability) and the soil volume to decrease. As water flows out, the soil settles vertically in direct proportion to the volume decrease. Two methods estimate consolidation settlement: using the coefficient of volume compressibility (mv) or the void ratio-effective stress (e-logσ'v) relationship. Practical applications include using prefabricated vertical drains to accelerate consolidation in clay soils.
Multistoried buildings should be designed such that they offer sufficient stiffness against
lateral displacement and should have the strength to resist inertial forces imposed by the ground
motion arising from earth quakes. Seismic forces in buildings are greatest at the base of the building.
Hence one of the key factors to be considered in designing seismic resistant buildings is the base
shear. Base shear is an estimate of the maximum expected lateral force that will occur due to seismic
ground motion at the base of a structure. In this manuscript we perform a detailed study of the values
of base shear for bare frame as well as infilled frame multi bay, multistoried structures using Free
Vibration analysis in SAP 2000 as well as pseudostatic analysis presented in I.S. 1893(Part I)-2002
Multi story building construction anshulAnshul Shakya
Multi-storey buildings aim to increase the floor area of the building without increasing the area of the land the building is built on, hence saving land and, in most cases, money (depending on material used and land prices in the area). The building with the most storeys is the Jaypee green garden isles is 2B+G+38.
This document provides an overview of consolidation in clays. It defines consolidation as the process where saturated clay is loaded externally and water is slowly squeezed out over a long period of time due to the low permeability of clay. This leads to long-term settlements occurring over several years. The document discusses concepts such as one-dimensional consolidation, coefficient of volume compressibility, consolidation testing, preconsolidation pressure, overconsolidation ratio, and using consolidation test data and plots to estimate settlement. It also briefly describes methods to accelerate consolidation using preloading and prefabricated vertical drains.
The document summarizes an industrial training report on the construction of a multistoried building. It describes two multistoried residential projects - Verna and Tana constructed by SI Property. Key details include the foundations using pile foundations and raft foundations, concrete mixes used, and reinforcement details of columns, beams and slabs. Amenities provided in the projects like parking, fitness center, kids play area are also mentioned. The report also provides information on new building materials seen during a visit to another project GIE Asteria, including Siporex blocks, Weber glue and fiberglass mesh.
This document contains lecture notes from Asst. Prof. Khalid R. Mahmood (PhD.) on stresses in soil masses. It discusses various topics related to stresses, including normal and shear stresses on a plane, stress distribution in soils, stresses caused by point loads, line loads, strip loads, embankment loading, and loading on circular and rectangular areas. It also presents the Mohr's circle method, principle stresses, and approximate methods like the influence chart method to calculate stresses at different depths below loaded areas.
Consolidation is the process where water drains from saturated soil pores, transferring the load from water to soil particles and causing volume change. There are three types of consolidation: immediate, primary, and secondary. One-dimensional consolidation assumes vertical drainage, making the process primarily vertical. Terzaghi's theory of one-dimensional consolidation models this using parameters like permeability, compressibility, and effective stress. The coefficient of consolidation describes the rate of compression, while compression and swelling indices characterize the void ratio-effective stress relationship. The oedometer test experimentally determines consolidation properties from soil specimen compression under incremental loads.
The document outlines the Lowndes County Board of Education's support for the Valdosta City School System in opposing consolidation. It provides background on consolidation issues and research showing little achievement gains and increased costs from consolidation. The presentation aims to give facts on consolidation and questions the economic feasibility and challenges of consolidating the two school systems.
The document discusses soil strength and different methods for measuring it. The Mohr-Coulomb failure criterion describes soil strength in terms of effective stresses. Laboratory tests like shear box and triaxial tests are used to measure soil strength parameters. The triaxial test can measure both drained (effective) and undrained strengths under controlled stress conditions. Interpretation of test results requires using concepts like effective and total stress Mohr circles.
This document discusses various aspects of designing and installing subsoil drainage systems. It provides guidance on determining pipe sizing and placement, choosing the proper filter material, and common installation mistakes to avoid. Key points covered include designing the system from the discharge point upward with uniform fall, using washed sand rather than gravel as the filter material to prevent particle migration, and ensuring proper trench grading and slope.
This document discusses foundations for buildings. Foundations spread the load of the building to the ground to limit soil settlement. Foundations must be located safely and distribute dead, live, and wind loads appropriately. There are shallow and deep foundations. Good foundation design ensures loads are distributed economically, safely, and without movement during/after construction. Methods for foundation design include site investigation, load analysis, foundation material selection, and working drawings. Load bearing capacity depends on soil analysis and testing. Techniques to increase capacity include deeper foundations and soil compaction. Settlement and differential settlement can occur and techniques aim to reduce them, like raft foundations. Foundation type selection considers soil conditions, building type/loads, costs, and surroundings.
This document discusses various methods of ground improvement including dry soil mixing, wet soil mixing, dynamic compaction, injection systems for expansive soils, vibro compaction, vibro piers, and vibro replacement. Dry soil mixing is the most common method and involves mechanically mixing weak soils like clays with dry cement to create soilcrete. Wet soil mixing similarly mixes soils with cement slurry and is best for soils with up to 60% moisture content. Vibro compaction, vibro piers, and vibro replacement all involve vibrating aggregates like stone into the ground to improve load-bearing capacity.
Rapid urban and industrial growth demands more land for further development, to meet this demand land reclamation and utilization of unsuitable and environmentally affected lands have been taken up and converted to useful ones by adopting one or more Ground Improvement Techniques
This document discusses different methods for soil stabilization, including mechanical, physical, chemical, and bituminous stabilization. Mechanical stabilization involves compacting soil to increase density and strength. Physical stabilization involves blending soils or adding admixtures to improve properties. Chemical stabilization uses lime, cement, or other chemicals like calcium chloride to react with soils and modify their characteristics. Bituminous stabilization involves adding bitumen or asphalt to seal soil pores and increase cohesion between particles. The document provides details on appropriate soil types, required quantities, and construction methods for each stabilization technique.
There are several techniques for improving the mechanical properties of soil, including densification, reinforcement, and stabilization methods. Densification techniques like vibro-compaction, vibro-flotation, dynamic compaction, and blasting work to compact soil particles into a denser configuration, increasing strength and stiffness. Reinforcement techniques include installing discrete inclusions like compaction piles to reinforce weak soils. Stabilization techniques chemically alter the soil, such as jet grouting which mixes soil with cement grout under high pressure to form columns of treated soil.
Class 8 Triaxial Test ( Geotechnical Engineering )Hossam Shafiq I
The document summarizes laboratory tests conducted on sand and clay soils, including triaxial compression tests and unconfined compression tests. It describes the test procedures, equipment used, and how to analyze the results to determine soil shear strength parameters. Specifically, it outlines how to conduct a consolidated drained triaxial test on sand under three confining pressures and an unconfined compression test on clay to measure the undrained shear strength. Graphs and calculations of stress, strain, and shear strength are presented.
Field and Theoretical Analysis of Accelerated Consolidation Using Vertical Dr...inventionjournals
Mumbai is the region consisting of soft compressible marine clay deposits. There are several construction problems on such soils and thus ground improvement is need to be carried out. Vertical drains is generally preferred technique as accelerated settlement is achieved during the construction phase itself if planned accordingly. The concept of vertical drains is based on the theory of three dimensional consolidation as described by Terzaghi (1943). Based on this concept, a consolidation programme is developed and an attempt is made to determine the field to laboratory coefficient of vertical consolidation ratio by Taylor’s Square Root of Time Method and Casagrande’s Logarithm of Time Fitting Method for this region. Based on this, the rate of consolidation and time required for consolidation in the field can be determined knowing the consolidation parameters. Equations are developed by using output of the programme and it is explained.
FIELD AND THEORETICAL ANALYSIS OF ACCELERATED CONSOLIDATION USING VERTICAL DR...P singh
Mumbai is the region consisting of soft compressible marine clay deposits. There are several construction problems on such soils and thus ground improvement is need to be carried out. Vertical drains is generally preferred technique as accelerated settlement is achieved during the construction phase itself if planned accordingly. The concept of vertical drains is based on the theory of three dimensional consolidation as described by Terzaghi (1943). Based on this concept, a consolidation programme is developed and an attempt is made to determine the field to laboratory coefficient of vertical consolidation ratio by Taylor’s Square Root of Time Method and Casagrande’s Logarithm of Time Fitting Method for this region by considering the case study of Bhandup Lagoon Works Embankment. Based on this ratio, the rate of consolidation and time required for consolidation in the field can be determined knowing the consolidation parameters. Equations are developed by using output of the programme and it is explained.
FIELD AND THEORETICAL ANALYSIS OF ACCELERATED SETTLEMENT USING VERTICAL DRAINS ijiert bestjournal
This document discusses accelerated settlement of soft soils using vertical drains. It provides background on consolidation theories proposed by Terzaghi and Biot. It also reviews literature on three-dimensional consolidation analysis and the use of vertical drains to reduce drainage paths and accelerate settlement. Case studies evaluating methods to determine field-to-laboratory coefficients of consolidation are presented. The ratio of field to lab coefficients of consolidation has been found to range widely from 15 to 55 depending on site-specific soil properties and drainage conditions.
1. The document discusses Karl Terzaghi's principle of effective stress, which states that the stress on a soil is equal to the total stress minus the pore water pressure.
2. It then provides objectives and scope for a case study on evaluating Terzaghi's theory through consolidation tests. Materials used include remolded soil samples from various locations.
3. The document outlines Terzaghi's assumptions for his consolidation theory and provides his equations for calculating bearing capacity of strip, square, and circular footings. It also briefly reviews several literature sources analyzing consolidation and settlement prediction.
This document provides information about consolidation in soils. It begins with an introduction to soil mechanics and how consolidation is an important process when designing foundations. Consolidation occurs when saturated clay soils expel water from their pores due to applied stresses, resulting in volume decrease over time. The document discusses the theories behind one-dimensional consolidation, including the spring analogy and coefficients of consolidation, compression, and volume change. It provides details on performing oedometer consolidation tests and interpreting the results, including preconsolidation pressures. Terzaghi's theory of consolidation is also summarized.
This document discusses soil mechanics and consolidation. It provides background on soil mechanics, explaining that it involves determining soil parameters and properties based on mechanical laws. It then focuses on consolidation, defining it as the process where saturated soil decreases in volume due to expulsion of pore water under pressure. The document outlines the theory of one-dimensional consolidation proposed by Terzaghi, describing how it can be used to determine rates of volume change, settlement, and pore pressure dissipation over time in saturated soils. It also discusses laboratory testing methods like oedometer tests that are used to characterize consolidation properties.
9 17 fujisawa et al -seags e journal 2013-06chakfarmer
The document discusses an experimental study that investigated the relationship between seepage force and the velocity of sand particles during sand boiling. The study used silica sand and measured the migration velocities of seepage water and sand particles by calculating discharge amounts. The results revealed that:
1) The equilibrium of forces (gravity, buoyancy, fluid-particle interaction) can be used to estimate velocities of sand particles subjected to upward seepage flow.
2) The seepage force needed for horizontal transport of sand tends to decrease as the velocity of sand particles increases.
3) Previous studies on seepage failure focused on critical hydraulic gradients or velocities, but this study provides insights into how sand transport develops during
This document presents a semi-analytical solution for the two-dimensional plane strain consolidation process of unsaturated soil with vertical impeded drainage boundaries. The solution is derived using eigenfunction expansion and Laplace transform techniques to transform the partial differential equations for the air and water phases into ordinary equations. Comparisons are made to verify the accuracy of the solution, and computations are conducted to illustrate the consolidation process under different drainage efficiencies and investigate the influences of permeability ratios and spacing-depth ratios.
This document discusses one-dimensional consolidation in layered soils. It presents four idealized soil profiles with two layers each to analyze how permeability and compressibility affect consolidation rates. The correct approach considers both parameters, while assuming a single coefficient of consolidation can mislead. Results show consolidation is fastest when the more compressible soil is by the drained boundary, and slowest when the less permeable soil overlies the more compressible layer, similar to how heat transfers in baked Alaska. Neglecting layer properties can significantly underestimate or overestimate settlement rates.
1. Terzaghi's one-dimensional consolidation theory models saturated soil as a spring-loaded mass of water, with water flow allowing stress to transfer gradually to the spring over time.
2. A lab consolidation test subjects an undisturbed soil sample to increments of load, measuring settlement over time to determine coefficients of consolidation and compressibility.
3. Coefficient of consolidation (cv) is calculated from settlement curves using square root of time or log time methods, informing predictions of field settlement rates and times.
1. Terzaghi's one-dimensional consolidation theory uses the spring-mass analogy to model the behavior of saturated soil under loading. Pore water pressure dissipates over time as the soil skeleton gains effective stress and the spring compresses.
2. A lab consolidation test subjects an undisturbed soil sample to incremental loading in an oedometer apparatus. Dial gauge readings over time are used to determine consolidation properties like coefficient of consolidation (cv) and compression index (Cc).
3. Soil compressibility is evaluated from void ratio-effective stress plots. The preconsolidation pressure σ'pc indicates the soil's maximum past stress and influences its compression path. Normally consolidated soils follow the normal compression line
This document discusses consolidation properties and prefabricated vertical drains. It begins by outlining Terzaghi's theory of one-dimensional consolidation, including the assumptions, equations describing pore water flow and changes in void ratio over time. It then discusses how consolidation affects drained and undrained conditions. Prefabricated vertical drains are introduced as a way to accelerate consolidation settlement by improving drainage, shown in a settlement versus time graph comparing performance with and without PVDs.
The document discusses soil mechanics topics related to consolidation and settlement. It covers three types of settlement (immediate, primary consolidation, and secondary consolidation). It also explains the fundamental concept of consolidation using a piston-spring model and describes how a one-dimensional consolidation test (oedometer test) is conducted in the laboratory to determine soil compressibility.
The document discusses velocity distribution in diverging channels. It summarizes previous research on modeling flow in non-prismatic channels and the effects of roughness. The author then describes their study simulating flow in a diverging channel with smooth and gravel beds using ANSYS. The simulation results matched experimental data well. Velocity was found to decrease with increasing diverging angle and distance from the channel centerline.
This document discusses consolidation of soil using sand drains. It begins with an introduction to consolidation and how sand drains can accelerate the consolidation process. It then summarizes recent research on modeling consolidation with vertical and horizontal drains. The document presents numerical modeling objectives of comparing consolidation times with and without drains, relating settlement to applied stress, and relating consolidation time to drain diameter. Results show that sand drains reduce consolidation time significantly, settlement increases with applied load, and consolidation time decreases with larger drain diameter. In conclusion, sand drains effectively accelerate consolidation for both stiff and soft clays.
This document summarizes a numerical investigation into the effects of roughness on near-bed turbulence characteristics in oscillatory flows. Direct numerical simulations were performed for two particle sizes corresponding to large gravel and small sand particles. A double-averaging technique was used to study the wake field spatial inhomogeneities introduced by the roughness. Preliminary results showed additional production and transport terms in the double-averaged Reynolds stress budgets, indicating alternate turbulent energy transfer pathways. Budgets of normal Reynolds stress components revealed redistribution of energy from the streamwise to other components due to pressure work. The large gravel particles significantly modulated near-bed flow structures and isotropization, while elongated horseshoe structures formed for the sand case due to high shear. Redistribution of energy
1. Studies of Rainfall-induced Slope Failure.pdfSaktiIdrus1
This document summarizes the procedures for assessing the stability of residual soil slopes involving saturated-unsaturated soils. It outlines the relevant theory, including stress state variables, soil-water characteristic curves, shear strength, permeability, and seepage analysis. It discusses characterizing soil properties through field investigations and laboratory testing. It provides examples of applying the procedures to study rainfall-induced slope failures in Singapore, including establishing soil profiles, measuring soil properties, and instrumenting slopes to monitor pore-water pressures.
The document presents an analytical solution for modeling groundwater flow in a multi-aquifer system considering vertical flow in the wellbore and well loss due to friction. It extends a previous single aquifer solution to consider two interconnected aquifers separated by an aquiclude. Simultaneous equations are formulated using Bernoulli's theorem under hydrostatic conditions to compute water flow between the two aquifers and well for both steady and unsteady well water level conditions. The solution technique aims to more scientifically and economically characterize parameters in multi-aquifer systems compared to previous approaches that treated interconnected aquifers as isolated.
This document discusses circular slope failures and provides information on:
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- Assumptions and analysis procedures for circular failure, including homogeneous soil properties, shear strength relationships, and limit equilibrium analysis using slices.
- Groundwater flow assumptions and models used in the analysis, including phreatic surface positions.
- How to use the circular failure charts presented, which provide factor of safety values for different slope geometries and groundwater conditions.
- Examples of using the charts and determining critical failure surfaces and tension crack locations.
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Consolidation settlement with sand drains – analytical and numerical approaches
1. “Consolidation Settlement with Sand Drains – Analytical
and Numerical Approaches”
Department of Civil Engineering, IIT Kanpur
CE 632
By –
Kundan Tripathi (10327365)
Rajeev Verma (10572)
Saurav Shekhar (10660)
Shashank Kumar (10327670)
Umed Paliwal (10327774)
Dated: 5th
April, 2014
2. Abstract & Objective
Sand drains are often used in important construction projects in order to accelerate the process of
consolidation settlement for the construction of some structures. Sand drains increase the rate of
consolidation such that the settlement that would occur in years can be hastened to occur in
months. When a surcharge is applied at ground surface, the pore water pressure in the clay will
increase, and there will be drainage in the vertical and horizontal directions. The horizontal
drainage is induced by the sand drains. Hence the process of dissipation of excess pore water
pressure created by the loading (and hence the settlement) is accelerated.
The objectives of this study are two-fold. Analytical and numerical approaches have been studied
herein. The analytical part includes a review of the existing literature and presents useful extracts
in regards to settlement, structure, installation and monitoring of sand drains. Popular subjects
such as free strain and equal strain cases with and without smear have been glanced at. The
numerical part is the result of finite element analysis of a drain unit cell using Plaxis 2d version
8.2. It addresses –
1. Reduction in time of consolidation by use of sand drains and also the changes in this
reduction as the loading is changed.
2. Relationship between ultimate settlement and loading.
3. Relationship between ultimate settlement and drain diameter.
*****
3. Table of Contents
S.No Topic Page No.
1. Part 1 - Analytical Approach 4
1.1 Popular Theory 4
1.2 Recent Research 9
2. Part 2 – Numerical Approach 12
2.1 Objective 12
2.2 General Settings 12
2.3 Soil Properties 12
2.4 Boundary Conditions 15
2.5 Initial Conditions 15
2.6 Calculations 15
2.7 Observations 15
2.8 Results & Discussion 17
2.9 Conclusions 23
3. References 24
*****
4. Part 1. Settlement of Foundations built on Sand
Drains - Analytical Approach"
The consolidation settlement of soft clay subsoil creates a lot of problems in foundation and
infrastructure engineering. Because of the very low clay permeability, the primary consolidation
takes a long time to complete. To shorten this consolidation time, sand drains can be used. Sand
drains are constructed by driving down casings or hollow mandrels into the soil. The holes are
then filled with sand, after which the casings are pulled out. When a surcharge is applied at
ground surface, the pore water pressure in the clay will increase, and there will be drainage in the
vertical and horizontal directions. Hence the process of dissipation of excess pore water pressure
created by the loading (and hence the settlement) is accelerated. The basic theory of sand drains
was presented by Rendulic (1935) and Barron (1948) and later summarized by Richart (1959)
and in the development of these theories; it is assumed that drainage takes place only in the
radial direction, i.e., no dissipation of excess pore water pressure in the vertical direction. In the
study of sand drains, two fundamental cases:
1. Free-strain case- When the surcharge applied at the ground surface is of a flexible nature, there
will be equal distribution of surface load. This will result in an uneven settlement at the surface.
2. Equal-strain case.-When the surcharge applied at the ground surface is rigid, the surface
settlement will be the same all over. However, this will result in an unequal distribution of stress.
1.1 Adapted from advanced soil mechanics from B.M Das
1.1.1Free-strain consolidation with no smear
Figure 6.37bshows the general pattern of the layout of sand drains. For triangular spacing of the
sand drains, the zone of influence of each drain is hexagonal in plan. This hexagon can be
approximated as an equivalent circle of diameter de. Other notations used in this section are as
follows:
1. re = radius of the equivalent circle = de/2.
2. rw= radius of the sand drain well.
3. rs= radial distance from the centerline of the drain well to the farthest point of the smear zone.
Note that, in the no-smear case, rw= rs.
The basic differential equation of Terzaghi’s consolidation theory for flow in the vertical
direction is given in Eq. (1).
5. ……………….(1)
For radial drainage, this equation can be written as
Where
u=excess pore water pressure
r=radial distance measured from center of drain well
Cvr =coefficient of consolidation in radial direction
6. For solution of above Eq., the following boundary conditions are used:
1. At time t=0, u=ui
2. At time t>0, u=0 at r=rw.
3. At r=re, du=dr.
With the above boundary conditions, above Eq. yields the solution for excess pore water pressure
at any time t and radial distance r:
where
J0=Bessel function of first kind of zero order
J1=Bessel function of first kind of first order
Y0=Bessel function of second kind of zero order
Y1=Bessel function of second kind of first order
Where kh is the coefficient of permeability in the horizontal direction. The average pore water
pressure uav throughout the soil mass may now be obtained from as
7. 1.1.2 Equal-strain consolidation with no smear
The problem of equal-strain consolidation with no smear (rw=rs) was solved by Barron (1948).
The excess pore water pressure at any time t and radial distance r is given by
Uav=average value of pore water pressure throughout clay layer.
The average degree of consolidation due to radial drainage is
For re/rw>5 the free-strain and equal-strain solutions give approximately the same results for the
average degree of consolidation.
Olson (1977) gave a solution for the average degree of consolidation Ur for time-dependent
loading (ramp load) similar to that for vertical drainage. The surcharge increases from zero at
time t=0 and q at time t=tc. For t ≥ tc, the surcharge is equal to q. For this case
8. 1.1.3 Effect of smear zone on radial consolidation
Barron (1948) also extended the analysis of equal-strain consolidation by sand drains to account
for the smear zone. The analysis is based on the assumption that the clay in the smear zone will
have one boundary with zero excess pore water pressure and the other boundary with an excess
pore water pressure that will be time dependent. Based on this assumption.
9. 1.2 Recent Research
Recently several analytical and experimental studies have reported on sand drain consolidation
of clayey soils, some of them are listed below:
1.2.1 TOYOAKI NAGOMI, AND MAOXIN LI, (2003) CONSOLIDATION OF CLAY
WITH A SYSTEM OF VERTICAL AND HORIZONTAL DRAINS -
Consolidation behavior with the drain system is formulated using the transfer matrix method.
Special care is given to formulation of thin pervious layers for efficient computation. The
developed formulation is verified using available numerical and field information. Parametric
studies are conducted to study the consolidation characteristics of clay with the drain system.
Based on the findings, a design method for an optimum system of horizontal and vertical drains
is proposed and design charts are presented for such a design. The consolidation behavior of clay
with a system of horizontal drains and vertical cylindrical drains is formulated using the transfer
matrix approach. The developed formulation can handle the inhomogeneous profile in clay and
multiple horizontal drains made of either thin sand layers or geotexstile sheets. The number of
terms used in series is five terms in the r direction, and five to ten terms in the z direction
depending on the behavior in the series expression. As Terzaghi’s consolidation solution, only
one or two terms in the expansion in the z direction are sufficient to compute the consolidation
behavior in the later stage of consolidation but the upper-side number of terms is required in the
early stage of consolidation. The formulation is found to be very efficient and convenient for
computation.
1.2.2. K.R.LEKHA, N.R.KRISHNASWAMY, AND P.BASAK, (1998) CONSOLIDATION
OF CLAY BY SAND DRAIN UNDERTIME-DEPENDENT LOADING -
The literature contains a nonlinear theory of sand drain consolidation under time-dependent
loading that can take into account any effective stress/void ratio/permeability variations. A
generalized governing equation, capable of yielding a large class of analytical solutions for these
variations is derived in this paper. Closed-form solutions are presented for the variation of pore
water pressure with a time factor and load increment ratio under time-dependent loading. The
analytical formulation is validated by comparing the solution with the standard results available
in the literature for instantaneous loading, constant permeability, and constant compressibility.
Governing equation for equal strains and drain problems in time-dependent loading is given in its
10. most general form, which can conveniently account for any effective stress/void
ratio/permeability variation. This equation is linear and requires evaluation of only one integral
to yield the solution for a large class of problems in time-dependent loading with variable
permeability and compressibility. The theory is an extension of the solution by Basakand
Madhav(1970), for the case of instantaneous loading and variation of compressibility and
permeability. The analytical formulation is validated by comparing the solution with the standard
results available for instantaneous loading, constant permeability, and constant compressibility.
The results are presented for the variation of pore water pressure with a time factor and load
increment ratio.
1.2.3. IEW-ANN TAN, (1993) ULTIMATE SETTLEMENT BY HYPERBOLIC PLOT
FOR CLAYS WITH VERTICAL DRAINS
The rectangular hyperbola method (Tv/U versus Tv) is extended to the case of drains and
surcharge by considering the hyperbolic plots for combined vertical and radial flow
consolidation in clays of varying thickness and drain spacing ratio for typical soil
properties of Cv of 1-5 m2
/yr. The results indicate that the hyperbolic plots are linear
between U50% and U90%. For the lines radiating from the origin to U50% point , the slope is
(1/0.5 = 2.0), and to the U90% point, the slope is (1/0.9 = 1.11). Thus, the ratio of the
slopes of these radiating lines to the slope of the linear portion of the hyperbolic plots
identifies the U50% and U90% for any settlement record using drains and surcharge. It is found
that the estimate of ultimate settlement from the U50% and U90% is more accurate than the
conventional inverse slope .approach of the hyperbolic method, especially for data between
the 50% and 90% consolidation points. The hyperbolic method of settlement analysis can be
extended to the practical case of vertical drains and surcharge. The use of the inverse of
the slope of the first straight-line portion of the hyperbolic plot of settlement data tends
to overestimate the amount of ultimate primary compression. To some extent, this
overestimation compensates for the effects of secondary compression, but in field
applications the amount of secondary compression is uncertain. However, when the
hyperbolic method is used to obtain the 50% and 90% points of the settlement record,
the ultimate compression obtained from these points agrees reasonably well with long-term
compression data of the Skh-Edeby test fill. Therefore, this method can provide a useful
and practical check on the progress of consolidation in field applications using vertical
drains and surcharge, especially in the absence of reliable soil properties data.
11. 1.2.4. CHIN JIAN LEO, (2004) EQUAL STRAIN CONSOLIDATION BY VERTICAL
DRAINS-
Closed-form analytic solutions of equal strain consolidation by a vertical drain with smear and
well resistance have been developed in the present paper. Solutions in this paper, however, have
been derived for coupled radial and vertical drainage and covered a step-loading or a ramp-
loading situation. Comparisons made with the corresponding analytic solutions of Hansbo and
Barron showed that the differences between the solutions of the present paper and the solutions
of Hansbo and/or Barron are generally quite small. In keeping with Barron (1948), consolidation
is considered in the undisturbed soil mass only, not in the vertical drain or the smeared zone, and
only radial drainage is assumed in smeared zone.
1.2.5 BUDDHIMA INDRARATNA, ALA AlIJORANY ANS CHOLACHAT
RUJIKATKARNOM, ANALYTICAL AND NUMERICAL MODELLING OF
CONSOLIDATION BY VERTICAL DRAIN BENEATH A CIRCULAR EMBANKMENT
While analyzing the axisymmetric problems, it is tried that aspects of geometry, material
properties, and loading characteristics are either maintained as constants or represented by
continuous functions in the circumferential direction. In the case of radial consolidation beneath
a circular embankment by vertical drains i.e., circular oil tanks or silos, the discrete system of
vertical drains can be substituted by continuous concentric rings of equivalent drain walls. An
equivalent value for the coefficient of permeability of the soil is obtained by matching the degree
of consolidation of a unit cell model. A rigorous solution to the continuity equation of radial
drainage towards cylindrical drain walls is presented and verified by comparing its results with
the existing unit cell model. The proposed model is then adopted to analyze the consolidation
process by vertical drains at the Skå-Edeby circular test embankment. The calculated values of
settlement, lateral displacement, and excess pore-water pressure indicate good agreement with
the field measurements.
1.2.6. TUNG WEN SHU and HUI_JYE LU, (2013) CONSOLIDATION FOR RADIAL
DRAINAGE UNDER TIME-DEPENDENT LOADING
It represents the details of consolidation for radial drainage under linear time-dependent
loading with varying loading dependent coefficients of radial consolidation by using a visco
elastic approach. By extending Barron’s solution for radial consolidation of small strain
sustained constant load, the convolution integral with time as the variable was used to analyze
the consolidation under time-dependent loading. Four different loading rates were applied in the
consolidation tests on three types of remolded clay with various plasticity indices to study the
behavior of radial consolidation. The findings indicate that the predicted consolidation
settlements accounting for the loading rate-dependent Cr values more closely match the
experimental results than the predictions using an assumed constant Cr.
12. PART 2. Numerical Approach toward study of Sand
Drains
2.1 Objective:
1. Comparative analysis of consolidation times with and without sand drains.
2. Find variation of ultimate consolidation settlement with applied stress.
3. Find variation of consolidation time with sand drain diameter at constant applied stress.
The finite element software Plaxis 8.2 was used for the modeling of vertical sand drains through
a layer of saturated clay. The goal was to discover the qualitative relationship between the
ultimate consolidation settlement and time taken vs. the load applied and the diameter of sand
drains. The time required for consolidation with and without drains was compared. The geometry
of the unit cell modelled is given in figures 2.1. and 2.2.
2.2 General Settings:
The following general settings were used for the modeling-
Model: Axisymmetry
Elements: 15 noded
x-acceleration: 0
y-acceleration: 0
Earth gravity : 9.8 m/s^2
Length: metre
Force: kN
Time: day
2.3 Soil Properties:
Three material sets were created for this problem- Dense Sand, Stiff Clay and Soft Clay.
Sand Drain: The sand used for making the drain was accorded the following properties-
Material Set: Dense Sand
Unsaturated unit weight = 17 kN/m3
13. Saturated unit weight = 20 kN/m3
Permeability Kx = ky = 1 m/day
Cohesion = 1 kpa
Internal angle of friction = 35 degrees
Angle of dilatancy = 3 degrees
Young’s Modulus = 40000 Kpa
Poisson’s ratio = 0.30
Fig. 2.1 Sample geometry of unit
cell without sand drain. Plaxis
8.2
Height
of
the
unit
cell
=
15m
Clay
layer
14. Clay layer: Two different types of clay were studied-
Clay 1 material set: Stiff Clay
Unsaturated unit weight = 18 kN/m3
Saturated unit weight = 19 kN/m3
Permeability Kx = ky = 0.001 m/day
Cohesion = 50 kPa
Internal angle of friction = 0 degrees
Angle of dilatancy = 0 degrees
Young’s Modulus = 50000 Kpa
Fig. 2.2 Sample geometry of the unit cell with
sand drain. Plaxis 8.2
Height
of
clay
layer
=
15m
Clay
surrounding
the
sand
drain
in
a
unit
cell
Sand
Drain
15. Poisson’s ratio = 0.35
Clay 2 material set: Soft clay
Unsaturated unit weight = 15 kN/m3
Saturated unit weight = 17 kN/m3
Permeability Kx = ky = 0.01 m/day
Cohesion = 15 kpa
Internal angle of friction = 25 degrees
Angle of dilatancy = 0 degrees
Young’s Modulus = 10000 Kpa
Poisson’s ratio = 0.25
2.4 Boundary Conditions:
The two vertical sides of the unit cell and one bottom side were accorded the standard fixities
boundary condition (no displacements) and closed consolidation boundary condition. In short,
settlement and consolidation both were allowed only through the top surface.
2.5 Initial conditions:
The effective stresses and ground water pore pressure were generated in the standard way (K0
procedure and phreatic surface respectively).
2.6 Calculations:
Calculations were run till the excess pore pressure developed reached 1 kPa or below at all points
in the unit cell.
2.7 Observations:
The observations are summarized in the tables below-
2.7.1 U (settlement) vs. Δσ (Applied Stress)
Taking diameter of sand drain = 0.4 m
16. Table 2.4 Clay 1
Δσ (kPa) Total Consolidation
Settlement (m)
Total Time with Sand
drain, t1 (days)
Total Time without
Sand Drain, t2 (days)
100
200
300
400
500
600
700
800
900
1000
0.019
0.038
0.063
0.09
0.117
0.144
0.171
0.198
0.225
0.253
11.484
22.972
19.619
17.234
18.006
20.912
20.688
28.395
30.295
30.345
122.5
183.75
153.13
157.92
169.4
149.3
172.87
179.69
175.62
181.9
Table 2.5 Clay 2
Δσ (kPa) Total Consolidation
Settlement (m)
Total Time with Sand
drain, t1 (days)
Total Time without
Sand Drain, t2 (days)
100
200
300
400
500
600
700
800
900
1000
0.077
0.169
0.261
0.353
0.445
0.537
0.629
0.721
0.814
0.906
22.968
45.938
45.938
45.938
45.938
45.938
45.938
45.938
61.251
61.251
61.25
91.876
91.876
91.876
91.876
91.876
91.876
91.876
91.876
91.876
2.7.2 U (Settlement) vs. Diameter (of drain)
Keeping applied stress at 300 kPa
Table 2.6 Clay 1
d (m) Total Consolidation
Settlement (m)
Total Time (days)
17. 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.063
0.063
0.063
0.064
0.064
0.064
0.063
11.875
42.109
31.582
15.312
12.919
10.287
8.373
Table 2.7 Clay 2
d (m) Total Consolidation
Settlement (m)
Total Time (days)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.265
0.265
0.263
0.261
0.259
0.261
0.253
93.876
61.251
45.938
46.057
30.626
28.261
23.088
2.8 Results and Discussion:
2.8.1 Time vs. Time
From Tables 2.4 and 2.5, it is clear that sand drains effectively reduce the time taken for
consolidation of saturated clay for both stiff and soft clays. As expected, this reduction is much
more pronounced in case of stiff clays where the time taken reduces by about 6 to 11 times.
While in the case of soft clays, the reduction factor is 1.5 to 3 times.
It is noticeable that as the applied stress increases and the final settlement (U) and time taken (t1
and t2) increase with it, the reduction factor is seen to decrease. Sand drains become less and less
effective as the time of consolidation increases. All these results may be noticed in Tables 2.8
and 2.9.
18. Clay 1 Table 2.8
Time with sand drain, t1
(days)
Time without sand drain, t2
(days)
Reduction Ratio t2/t1
11.484
22.972
19.619
17.234
18.006
20.912
20.688
28.395
30.295
30.345
122.5
183.75
153.13
157.92
169.4
149.3
172.87
179.69
175.62
181.9
10.66701
7.998868
7.805189
9.163282
9.407975
7.139441
8.356052
6.328227
5.796996
5.994398
Clay 2 Table 2.9
Time with sand drain, t1
(days)
Time without sand drain, t2
(days)
Reduction Ratio t2/t1
22.968
45.938
45.938
45.938
45.938
45.938
45.938
45.938
61.251
61.251
61.25
91.876
91.876
91.876
91.876
91.876
91.876
91.876
91.876
91.876
2.666754
2
2
2
2
2
2
2
1.499992
1.499992
2.8.2 U vs Δσ
For both stiff and soft clays, settlement steadily increases with applied load. This is in
accordance with theory and intuition.
20. 2.8.3 Settlement vs. Diameter of Sand Drain
As expected, the final settlement did not vary with the diameter of sand drain. And the time of
consolidation steadily decreases with increase in the diameter of drains. This is also in
accordance with theory.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
100
200
300
400
500
600
700
800
900
1000
RaOo
Applied
Stress
(kPa)
Fig.
2.5
RaOo
of
SeDlement
SoP
Clay
to
SOff
Clay
21. 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Total
SeDlement
(m)
Diameter
of
Sand
Drain
(m)
Fig.
2.6
SeDlement
vs.
Drain
Dia
for
Clay
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Total
SeDlement
(m)
Diameter
of
Sand
Drain
(m)
Fig.
2.6
SeDlement
vs.
Drain
Dia
for
Clay
2
22. 0
10
20
30
40
50
60
70
80
90
100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
ConsolidaOon
Time
(days)
Diameter
of
Sand
Drain
(m)
Fig.
2.7
Total
Time
vs.
Drain
Diameter
for
Clay
1
0
10
20
30
40
50
60
70
80
90
100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
ConsolidaOon
Time
(days)
Diameter
of
Sand
Drain
(m)
Fig.
2.7
Total
Time
vs.
Drain
Diameter
for
Clay
2
23. 2.9 Conclusions
1. Sand drains effectively reduce the time taken for consolidation of saturated clay for both
stiff and soft clays.
2. This reduction is much more pronounced in case of stiff clays where the time taken
reduces by about 6 to 11 times.
3. Sand drains become less and less effective as the time of consolidation increases.
4. For both stiff and soft clays, settlement steadily increases with applied load.
5. The settlement of soft clay was found to be 3 to 5 times more than that for stiff clay.
6. The final settlement does not vary with the diameter of sand drain.
7. And the time of consolidation steadily decreases with increase in the diameter of drains.
*****
24. References:
1. Leo, C. (2004). ”Equal Strain Consolidation by Vertical Drains.” J. Geotech. Geoenviron.
Eng., 130(3), 316–327.
2. Xiao, D., Yang, H., and Xi, N. (2011) Effect of Smear on Radial Consolidation with
Vertical Drains. Geo-Frontiers 2011: pp. 4339-4348. doi: 10.1061/41165(397)444
3. Hsu, T. and Liu, H. (2013). ”Consolidation for Radial Drainage under Time-Dependent
Loading.” J. Geotech. Geoenviron. Eng., 139(12), 2096–2103.
4. Indraratna, B., Aljorany, A., and Rujikiatkamjorn, C. (2008). ”Analytical and Numerical
Modeling of Consolidation by Vertical Drain beneath a Circular Embankment.” Int. J.
Geomech., 8(3), 199–206.
5. Nogami, T. and Li, M. (2003). ”Consolidation of Clay with a System of Vertical and
Horizontal Drains.” J. Geotech. Geoenviron. Eng.,129(9), 838–848.
6. Lekha, K., Krishnaswamy, N., and Basak, P. (1998). ”Consolidation of Clay by Sand
Drain under Time-Dependent Loading.” J. Geotech. Geoenviron. Eng., 124(1), 91–94.
7. Tan, S. (1993). ”Ultimate Settlement by Hyperbolic Plot for Clays with Vertical
Drains.” J. Geotech. Engrg., 119(5), 950–956.
8. Das, B. M. (2008). “Advanced Soil Mechanics”, 3rd Ed., Taylor and Francis, London and
New York.