INTRODUCTION
Background
Throughout the world, due to rapid urbanization and development, construction projects are rapidly built on fine-grained soils Natural soils in their original condition may be inappropriate for short or long term structure activities and so must be enhanced before use In particular, many coastal areas contain deep multi-layers of compressible clay initially deposited by sedimentation from lakes, rivers, and seas These fine-grained soils have poor bearing capacity and indicate excessive settlements under the load One of the most broadly and successfully used techniques to boost soft soils is preloading with vertical drains to consolidate the soil and expedite strength growth My thesis mainly builds on the understanding of consolidation by both vertical and horizontal drains developed in the last decades
This chapter illustrates the perception of consolidation and how surcharge with vertical drains can accelerate the water expulsion process The progress of vertical and horizontal drain concepts is discussed.
Consolidation
Figure 1.1: Soil phase diagram (Das, 2008)
Soil formed from two or three phase composition (see Figure 1.1) The space inside the soil particles are replaced by water, air or a combination of both Consolidation associates the contraction of voids under load It develops in three stages (see Figure 1.3) Immediate settlement happens instantly after loading with zero volume change, i.e shape change only In saturated soil (i.e no air) the expansion in pressure emerging from the load is immediately carried out by the liquid which is incompressible Such excess pore-water pressure regularly disappears as water seeps out of the soil and the stress is transferred to the soil skeleton This is defined as primary consolidation (see Figure 1.2)
Primary consolidation may last year’s depending on soil permeability When additional pore-water pressure has expelled, the soil remains to consolidate continually as the soil particles rearranges to fill into voids
Figure 1.3: Typical oedometer settlement (Das, 2008)
Consolidation of soils can lead to serious problems for constructions like embankments founded on them If structures settle uniformly little damage is experienced except perhaps to services feeding it However, settlement is rarely uniform
Varied loading and the nonhomogeneous characteristic of soil lead to differential settlement This produces added loads that often create cracking in the structure If soils have insufficient strength to withstand the applied loads it may be difficult to build such structures in the first place Soil density largely affects shear strength in soil The densification of soil due to consolidation thus results in considerable strength gain, allowing increased loads to be subjected to the soil
1.2.1 Settlement with Prefabricated Vertical Drains (PVD)
Pre-consolidation is a method adopted to reduce the consequence of consolidation on structures and enhance the strength of the ground Basically, a surcharge is applied to the ground, usually in the form of an embankment, where a structure located on This embankment induces the foundation soil to consolidate Once the required primary consolidation is attained the pre-consolidation load is discharged and the structure built
Thus after construction, the soil foundation experiences the slow gradual process of secondary compression Differential settlements are reduced so the structure is less likely to crash or collapse
The rate at which preloading attains the required consolidation is accelerated by increasing the magnitude of the surcharge The magnitude of surcharge is restricted by soil failure criteria Thus preloading surcharges are raised in periods as the shear strength of soil enhances and is able to prevent increased loads without failure To hasten the consolidation process so surcharges can be set up more quickly (or not built up as high in the first place), one must speed the egress of water from the soil frame The establishment of vertical drains reduce the leakage path for water to seep out under the additional pore-water pressure (see Figure 1.5) In particular, they equip both a radial outflow path in addition to vertical outflow path Clays have greater horizontal permeability than in the vertical permeability Usually, water only seeps out in the vertical direction due to the large extent of the clay body Vertical drains allow the increased horizontal permeability to be exploited.
Problem statement
In practice, clay layers are often thick and drain spacing is small enough so that the vertical drainage becomes insignificant and it might be ignorable (Chung et al., 2009)
The horizontal drainage, in which the radial (or horizontal) coefficient of consolidation (cr) is an important factor, therefore plays a critical role in the total consolidation of the PVD-improved grounds The cr value can be interpreted from field tests (e.g., CPTU dissipation test), from laboratory tests (e.g., radial consolidation tests (RCT)), or from some empirical correlations, in which the RCT on undisturbed sample should provide the most reliable value Similar to methods for vertical consolidation test (VCT) (ASTM D2435; ASTM D4186), an RCT might be conducted using either incremental loading (IL) method (hereafter referred to as RCTIL) or constant rate of strain (CRS) method (hereafter referred to as RCTCRS) However, both RCTIL and RCTCRS have not been standardized in any formal standards For the same soil material and same range of applied pressure, the CRS method might be completed in a shorter time than the IL method and it provides continuous profiles of consolidation parameters (e.g., cv or cr) with applied pressure However, key limitations of the CRS method are that it is very complicated for routine performances and the consolidation parameters vary with varied strain rate applied The IL method is simple to carry out in practice, and in fact most existing methods for determining the consolidation parameters were proposed for the IL method This research focuses on the CRSIL
The RCTIL can be conducted using either a central drain (CD) (i.e., inward drainage) or a peripheral drain (PD) (i.e., outward drainage) Existing methods for determining cr value are mainly focused on the test with a CD rather than a PD This is because the test results can conveniently be interpreted using the well-known theoretical solutions of Barron (Barron, Lane, Keene, & Kjellman, 2002) However, the test with a CD is often associated with three typical problems: (1) the interpreted cr value is a function of n
=de/dw, where de is radius of soil specimen and dw is the radius of the central drain; (2) soil disturbance resulted from preparation of the central drain affects the test results significantly; and (3) the attainment of the test depends greatly on the central placement of the central drain (if it is a porous stone), which is quite difficult in routine test For a given soil under the same magnitude of applied pressure, the RCTIL of both drainage types should result in the same value of cr, but the problems associated with the test using a CD can be avoided by using a PD Since not much attention has been paid to explore the advantages of the test with a PD, an in-depth study on this drainage condition is therefore very necessary to take its advantages in routine performances.
Objectives and scope of present study
The key goals of the research are to investigate the effectiveness of the RCTIL using a PD compared with the test using a CD and to propose a comprehensive method to evaluate cr value of clays from the test so that the method can conveniently be applied in routine performances The particular objectives of the research are:
- To design and manufacture a multi-directional flow consolidation cell that should be able to perform the RCTIL using either a CD or a PD
- To highlight the advantages of the test using a PD over the test using a CD in testing procedures
- To make a comparative study on the cr values obtained from the RCTIL using a PD and a CD on the same clay, equipment and procedures
- To make a comparative study on the cr values obtained lab-based method and CPTu based methods
This research focuses on the RCTIL, not on the RCTCRS To depict the advantages of the test using a PD over that using a CD, both drainage types will be used for pairs of specimens of the same depths In order to fulfil the targets described above, the research would cover field tests (sampling and CPTu) at a site in Dinh Vu Port, Hai Phong City, Vietnam and laboratory tests on undisturbed samples obtained from the sites Extensive analytical analyses will be carried out to depict the test results The following are main activities of the research:
- At research site, boring and sampling was conducted for one borehole up to 23.0 m
A total of 06 sampling tubes (at 06 sampling depths) as obtained The sampling tubes were brought to the laboratory and preserved for laboratory test
- One CPTu sounding in association with CPTu dissipation test was conducted nearby the sampling borehole location The CPTu test results are used characterize the soil at the site and the CPTU dissipation test results are used to determine the coefficient of radial consolidation (cr) which will be compared with that with that obtained from radial consolidation test in the lab In total, 06 dissipation points at the centers of 06 sampling depths, respectively, were conducted at the site At each test depth the penetration was halted to conduct the dissipation test until at least 50% of excess pore water pressure has been dissipated
- Designed and manufactured a consolidation cell that could be able to perform the RCTIL using either a CD or a PD, and more importantly the cell could be able to function using the standard loading frame and monitoring system of the conventional oedometer test (ASTM D2435 / D2435M - 11, 2011)
- Perform all basic laboratory tests (e.g., Atterberg limits, water content, unit weight, specific gravity, and conventional consolidation test) to characterize the soil, and RCTIL using a CD and a PD
- Analyze test data and compare the cr values obtained from laboratory and field tests.
LITERATURE REVIEW
Fundamentals of One Dimensional Consolidation
A soil may be known to be a skeleton of solid particles enclosing voids which may be filled with combination of gas and liquid If a sample of soil subjected to sustained pressure so that its volume is reduced in a drained manner
As the compression happens, the pore water is seeped out based on Darcy’s law, (Taylor 1948) At the same time, a slow expulsion of water accompanied by the reduction in the volume of the soil mass, which results in settlement
(a) Initial loading, water takes load, soil (i.e spring) has no load
(b) Dissipation of excess water pressure, water seeping out and soil starts to take load
(c) Final loading water dissipated and soil has load Figure 2.1: Mechanism of consolidation
The consolidation of clay under a surcharge does not occur instantaneously; clays are impermeable that the water is relatively trapped into the pores When an increment of load is subjected the pore water cannot seep out promptly Since clay particles have a tendency to approach one another and pressure increases in the pore water which is known the excess pore pressure The hydraulic gradients appear due to this excess pressure lead the fluid to escape from the soil As drainage continuous, the excess pressures dissipate and later the externally constant applied stress is gradually transferred to the soil frame The part of pressure carried by soil frame is defined as effective stress
Soil skeleton then changes under the rise in effective stresses This is called consolidation
2.1.1 Consolidation Theory with Vertical Drainage The soil property designated by cv is called the coefficient of consolidation:
In the consolidation understanding, the drainage path length is evaluated downward from the surface of the clay sample The thickness of the sample is nominated by 2H, the distance H thus being the length of the longest drainage path
A dimensionless time factor is illustrated as:
H (2.2) and average degree of consolidation
The relation between Uavg and Tv can be observed from Figure 2.2
Figure 2.2: Uv versus Tv relationship (Head, 1994) 2.1.2 Consolidation Theory with Horizontal Drainage
Case for Equal Vertical Strain – For the case where loading and compression are as in the standard test, but where pore water flow is restricted to the radial direction only, it has been shown in Eq (2.4) that the differential equation of consolidation is:
The consolidation of the soil specimen in an RCT, as schematically shown in Figure 2.3, is an excellent case for represent the consolidation condition expressed by Eq (2.4)
Figure 2.3: Schematic diagram of an RCT with central drain and peripheral drain
2.1.2.1 For the case of a peripheral drain (PD)
By isolating an element of the sample to a distance r from the axis (Figure 2.4, if we call u=u(r,t) the pore pressure at a time t, then the difference between the volume of water flowing into and out of the element will be:
Figure 2.4: (a) Scheme of arrangement of the consolidation test in the triaxial apparatus, with drainage towards the cylindrical surface; (b) Cylindrical element of the sample
If ε is the strain per unit length along the z axis, the change in volume may also be expressed by
Equating both values, we get
Since the value of the vertica l strain ε is independent of r and only a function of time (equal strain), we have
At any given time, t after loading, diagram of u (hypothesis) changes as following:
Figure 2.5: Distribution of pore pressures within the soil sample related to r and t Solving this equation is achieved by applying the following boundary conditions:
LOADING PLATE (IMPERVIOUS) u PD (t)= u max /2
Eq (2.9) may be thus expressed:
This equation represents a distribution of pore pressures in the form of a paraboloid (Figure 2.5) with a maximum in the axis of a sample of
Where u0 = initial excess pore pressure at t = 0, T r c t d r / e 2 is time factor
2.1.2.2 For the case of a center drain (CD)
The answer of Eq (2.4) for the equal vertical strain condition (Barron, 1948) is described by
(2.14) where de is the length of influence (i.e., double the effective radial drainage path), and n is the drain spacing ratio, given by
/ n d d (2.15) where dw is the length of the drain The following equation is obtained:
If the real time t corresponding to Ur is determined, then the value of cr for any given value of n may be obtained from Eq (2.16), which can be written as
Consolidation Tests in Laboratory
In this test, the undisturbed specimen is undergoing axially in increment of subjected stress Each stress increment is loaded constantly until finishing primary consolidation
During this transform, water is expelled, leading to a reduced in size which is assessed at reasonable intervals
Figure 2.6: Schematic of oedometer test (Head, 1994)
2.2.2 Horizontal Consolidation Test 2.2.2.1 Horizontal consolidation test with center drain
Radial drainage inwards to a sand column drain was achieved in a conventional oedometer by Rowe (1959) Apparatus with radial drainage were performed on remolded soil samples was amended to perform conventional consolidation test (Sridhar &
Robinson, 2011) A description of the consolidation cell, after modification, is shown in Fig 2.7
Figure 2.7: Schematic of the apparatus used for conducting radial consolidation test
(Sridhar & Robinson, 2011)2.2.2.2 Horizontal consolidation test with peripheral drain Horizontal (radial) drainage to a pervious boundary at the perimeter with the top and bottom faces sealed; equal strain loading is described in Figure 2.8.
Determination of Coefficient of Consolidation
2.3.1 Analysis of Time-Compression Curve
Figure 2.9 illustrates three differently shapes of consolidation curve obtained from conventional consolidation experiment on different types of soil (Leonards and Girault,
1961) Type I curve is the most typical one and described by Terzaghi’s theory with S- shaped curve
C rigid porous stone soil sample
Figure 2.9: Shapes of consolidation curve gained from oedometer test
(Leonards and Girault, 1961) 2.3.2 Graphical Method
In the graphical methods, the coefficient of consolidation in conventional oedometer experiment can be derived by curve fitting methods The characteristics feature of Tr versus Ur association is analyzed The same association is then implemented to the time (t) versus settlement (S) linkage to determine cr Sridharan (Sridharan, Prakash, & Asha,
1996) proposed a √t method, where t is the time, for the determination of cr These empirical approaches were created to fit approximately the observed laboratory test data to the Terzaghi’s theory of consolidation The following procedure was approved by
Step 1: Extent the straight line part of the curve to reach the ordinate (t = 0) at point D0 The point shows the initial reading (D0) P is the intersection of this line with the abscissa
Step 2: Draw Q with OQ = 1.15 OP in the case of vertical drain (Figure 2.7); OQ 1.167 OP in the case of horizontal consolidation with both central drainage and peripheral drain (Figure 2.8)
Step 3: DQ and the curve intersect at point G
Step 4: Horizontal line stretches from G to the ordinate (D90) The point illustrates the value of √t90 The value of T corresponds to U = 90% is 0.848 in the case of vertical drain; 0.288 in the case of radial drainage to periphery, equal strain loading
Figure 2.10: Theoretical curve linkage square-root time factor to degree of consolidation for vertical drainage (Taylor, 1942)
Figure 2.11: Consolidation curve relating square-root time factor to for drainage radially outwards to periphery with equal strain loading (Head, 1994)
Robinson (Robinson & Allam, 1998) proposed the inflection point method that the point of inflection, which is the point where the slope is maximum in an Ur- logTr plot, happen at a degree of consolidation of 63.2 % as shown in Figure 2.13(a) and Figure 2.13(b) The time, t63.2, matching to the point of inflection can be derived from a plot of (dS/dlogt) versus t plot, from which cr can be determined The inflection point method explained above can be simply plotted to derive the time corresponding to the point of inflection from a set of S-t data from a conventional consolidation test, without performing a graphical construction
Robinson and Allam (Robinson & Allam, 1998) suggested a non-graphical matching method for interpreting the time corresponding compression data The settlement (S) collateral t is expressed as
Where S0 and S100 are the settlement corresponding to the beginning and end of primary consolidation
Substituting Eq (2.12) in Eq (2.22), we get
A minimum of approximately consolidation curve are sufficient to calculate the values of S0, S100 and cr However, a non-linear regression may be implemented for obtaining better results
Figure 2.12: (a) Theoretical Ur-log Tr curve for n = 5; (b) (dUr/d log Tr)-log Tr plot showing the inflection point (Sridhar & Robinson, 2011)
Falling Head Permeability Test
Figure 2.14 shows a schematic drawing of a falling head test setup For practical engineering purposes, the coefficient of permeability of clay is often depicted from one dimensional incremental loading oedometer compression tests (IL tests) The vertical coefficient of consolidation cv is obtained from the vertical compression modulus Mv and the vertical hydraulic conductivity kv (Larsson and Sa¨llfors, 1986):
(2.24) where ɣw is the unit weight of water Applying the standard procedures for oedometer testing of clays, only the properties in the vertical direction are evaluated (Mv, kv and cv)
Figure 2.13: Falling-head permeability test (Das & Sobhan, 2008)
However, in projects using prefabricated vertical drains (PVDs), consolidation is mainly carried out by the horizontal flow through the soil towards the drains, so it is preferable to conduct tests allowing for evaluation of horizontal coefficient of permeability kr and the horizontal coefficient of consolidation cr Figure 2.15 described method for trimming horizontal soil specimen to conduct permeability test In other expression, cr is defined as a function of Mr and kr:
Vertical trimming for determining vertical coefficient of permeability
Horizontal trimming for determining horizontal coefficient of permeability
Figure 2.14: Principal sketch of horizontal and vertical trimming of samples from determining vertical and horizontal coefficient of permeability
Natural soils are usually anisotropic in which the hydraulic conductivity in horizontal direction (kh) is often larger than that in vertical direction (kv) This characteristic is due to the fact that soils are deposited in layers Table 2.4 shows typical ratios of kh/kv from some natural soil types The hydraulic conductivity (k) of any given soil is function of void ratio, grain size distribution, viscosity of water, and in-situ temperature In cases of involving effective stress changes, the void ratio changes with the changes of effective stress Thus, k depends on changes of effective stress Range of possible field values of kh/kv for fine-grained soil are ranged from 2 to 4 (Jamiolkowski, Ladd, Germaine, &
If the soil compressibility is isotropic (i.e.,M v M r ), the interrelationship between the horizontal and vertical permeability can be expressed as: v v r r k k c
The piezocone penetration test (CPTu)
The piezocone penetration test (CPTu) is an in-situ testing method used to identify the geotechnical characteristics of soils and evaluate subsurface stratigraphy, relative density, strength and equilibrium groundwater pressures By using ASTM and international standards, tip resistance (qc), sleeve friction (fs), and pore-water pressure (u) are derived at different depth, as described in Figure 2.16
Figure 2.15: Overview of the cone penetration test per ASTM D 5778 procedures
(P.W Mayne, 2007) 2.5.2 Pore-water Dissipation Tests
Dissipation testing monitors pore water pressures as they dissipate with time A full- displacement device such as a cone penetrometer evaluates the appearance of additional pore water pressures (Δu) locally around the head of probe In clean sands, the Δu will decay rapidly because of the high hydraulic conductivity of sands, whereas in clays and silts of low hydraulic conductivity the measured Δu will take a noticeable time to equilibrate The static pore-water will eventually record to u0 Thus, the obtained porewater pressures (um) are a combination of transient and hydrostatic pressures, such that:
During the permanent stop, the rate at which Δu declines with time It can be monitored and used to depict the coefficient of consolidation and permeability of the soil media Dissipation readings are regularly plotted on log scales; therefore, in clays with low hydraulic conductivity it becomes impractical to wait for full equilibrium that corresponds to Δu = 0 and um = u0 A standard of practice is to record the time to achieve 50% dissipation, designated t50
2.5.3 Coefficient of Consolidation 2.5.3.1 Monotonic Dissipation
For these cases, the strain path method (Teh, 1991) may be used to determine ch from the expression:
T a I c t (2.28) where t = corresponding measured time during dissipation (usually taken at 50% equalization), T* = modified time factor, IR = G/su = rigidity index soil and a = probe radius
The strain path solutions (Teh, 1991) are described in Figure 2.18(a) and (b) for both midface and shoulder type elements in the case of monotonic dissipation response, respectively
For clays, the rigidity index (IR) is the ratio of shear modulus (G) and shear strength (su) and may be calculated from different means including: (a) measured triaxial stress- strain curve, (b) measured pressuremeter tests, and (c) empirical correlation One correlation based on the index: r f
(2.29) where τf (= su in undrained case) is shear strength at failure, was originally suggested by Vesic (Vesic, 1973) and it was associated with the assumed elastic ideal plastic behavior of soil That is, G is a constant value until plastic failure happens However, in modern soil mechanics G has been well recognized to degrade nonlinearly with the increment of induced shear strains Around a penetrometer, G varies from the maximum value (G0) at some distance from the penetrometer to much smaller value (G