OF T OIJRFIABLE SOILS

BACKGROUND OF THE INVENTION

This invention relates generally to soil stabilization, and more particularly to liquefaction remediation of liquefiable soil to minimize damage to supported structures or works from earthquake-induced liquefaction.

Earthquakes are caused by sudden breaks in the earth's crust. In certain

portions of the world there appears to be a continuous movement between one section of the

earth's crust and an adjacent one, causing an accumulation of strain at these boundaries.

When the stresses developed by such strain reach the strength of the materials, a slip occurs

between the two portions of the crust and tremendous amounts of energy are released. This

energy propagates outward from the focus or origin of the earthquake in the form of elastic

stress waves which can carry destructive amounts of energy for hundreds of miles.

One of the most destructive effects of these stress waves results from their effect

on deposits of saturated loose fine sand or silty sand, causing a phenomenon known as

liquefaction. When liquefaction occurs the soil mass loses all shear strength and behaves

temporarily as a liquid. Such temporary loss of shear strength can have catastrophic effects

on earthworks or structures founded on these deposits. Major landslides, lateral movement

of bridge supports, settling or tilting of buildings, and failure of waterfront structures have all

been observed in recent years, and efforts have been increasingly directed toward development of methods to prevent or reduce such damage.

Any impact or shock on or within the upper portion of the earth's crust causes stress waves to be transmitted through the soil. Any or all of a number of different types of

waves are possible, and which of these waves actually occur depends on the location, type and

configuration of shock or impact. Seismologists have identified two classes of such earth waves; body waves which travel through the interior of a mass, and surface waves which

travel along the surface.

Body waves travel through the interior of a medium and radiate outward in all

directions from a disturbance. In an earthquake the original slip occurs in a relatively

localized vicinity in the bedrock below the earth's surface, and the wave front is essentially

spherical. As the waves travel farther and farther from the source the curvature of the wave

front becomes less and less, and at a great distances from the source the wave front will be

indistinguishable from a plane wave.

The two types of body waves are compressional or longitudinal, called P-waves,

and shear or transverse waves, called S- aves.

Surface waves occur at the surface of an elastic medium, or at the interface of

two elastic media of differing properties. Particle motions associated with this type of wave

are confined to a relatively thin region close to the surface or interface. Surface waves

propagate outward from the source with a circular wave front. Again, as the wave front

travels farther and farther from the source the curvature of the wave front becomes less and

less.

The surface waves of most interest are the Rayleigh wave and the Love wave.

Two other waves called the coupled wave and the hydrodynamic wave die out rapidly as they

proceed from the source.

The total energy transported is represented almost entirely by the Rayleigh, the

S-, and the P-waves, with the Rayleigh wave carrying the largest amount of energy, the S-

wave an intermediate amount, and the P-wave the least. The velocity of the P-wave is almost double that of the Rayleigh and S- waves, and the velocity of the S-wave is only slightly greater

than that of the Rayleigh wave.

At some distance from a disturbance a particle at the earth's surface first

experiences a displacement in the form of an oscillation at the arrival of the P-wave followed

by a relatively quiet period leading up to another oscillation at the arrival of the S-, and

Rayleigh waves. These events are referred to as the minor tremor, and major tremor at the time of arrival of the Rayleigh wave.

The time interval between arrivals becomes greater and the amplitude of

oscillation becomes smaller with increasing distance from the source. In addition, the minor

tremor decays more rapidly than the major tremor. It is evident, therefore, that the Rayleigh

wave is the most significant disturbance along the surface of the elastic half-space, and at large distances from the source may be the only clearly distinguishable wave.

Real earth motions are actually quite complex, due to the variation between a

homogeneous elastic medium and the real earth. When elastic waves impinge on an interface between differing elastic media, at least a part of the energy is reflected back from the interface in the form of a reflected wave. When multiple interfaces are present the wave

pattern can become extremely complex.

Further, considerable energy can be transmitted through the bedrock itself, and

it appears that in many cases the main forces acting on soil elements in the field during

earthquakes are those resulting from the upward propagation of shear motions from the

underlying rock formations. Although the actual wave pattern may be very complex, the

resulting repeated and reversing shearing deformations imposed on the soil by the shear wave

components are the principal cause of liquefaction in saturated fine sand or silty sand deposits.

When loose sand is subjected to repeated shear strain reversals, the volume of

the sand will decrease with each reversal, although the amount of volume decrease becomes

less with each cycle. If the sand is saturated and drainage out of the sand is prevented, it will

be understood that since the volume of the sand is decreasing, the pressure of the water must

increase. As the water pressure becomes greater the grain-to-grain contact pressure in the

sand must become smaller and smaller. When this grain-to-grain contact pressure becomes

zero, the entire sand mass will lose all shear strength and will act as a liquid. This

phenomenon is known as liquefaction and can occur in loose, saturated sand deposits as a

result of earthquakes, blasting, or other shocks.

The factors that effect the occurrence of liquefaction are soil type, compactness of the soil, soil permeability, magnitude of the strain reversals, and number of strain reversals.

Fine cohesionless soils (fine sands) or fine cohesionless soils containing moderate amounts of silt are most susceptible to liquefaction. There is some evidence to show

that uniformly graded materials are more susceptible to liquefaction than well graded

materials, and that for uniformly graded soils, fine sands tend to liquefy more easily than

coarse sands, or gravely soils. Moderate amounts of silt appear to increase the liquefaction susceptibility of fine sands. Although fine sand with larger amounts of silt are not as susceptible, liquefaction is still possible.

Recent evidence indicates that sands containing up to 20% clay may also be

liquefiable.

Typical values of soil permeability are shown in Table 1. The wide range of permeability for various materials is shown.

TABLE I. RELATIVE VALUES OF PERMEABILITY.

Relative permeability Values of k (cm/sec) Typical soil

Very Permeable Over 1 X 10 ' Coarse gravel

Medium permeability 1 X IO ^"1 to 1 X IO ^"3 Sand, fine sand

Low Permeability 1 X IO ³ to 1 X IO ^"5 Silty sand, dirty sand

Very low permeability 1 X IO ^"5 to 1 X IO ⁷ Silt

Impervious Less than 1 X IO ^"7 Clay

To correct to feet per minute, multiply the above values by 2; to convert to feet

per day, multiply the above by 3 X IO ³ .

During an earthquake, shear strain reversals in the soil result principally from

the passage of S-waves. The magmtude and number of these shear strain reversals depend on

the magnitude and duration of the earthquake.

As a result of the shear strain reversals cohesionless soils will experience

volume reduction. In deposits below the water table volume reduction will cause water to flow

out of the vicinity where the volume reduction is taking place. Depending on the permeability

of the soil, this flow will be impeded, with a resulting increase in pressure within the pore

water. As the pressure within the pore water becomes greater, the gain-to-grain contact

pressure will disappear, and the mass will lose all shear strength, i.e. liquefaction occurs.

In very coarse sands or gravels water can flow freely enough that pore water

pressures never become dangerously high. At greater depths grain-to-grain contact pressures

are initially greater, and pore water pressures must become greater for liquefaction to occur. In dense material more strain reversals must occur to provide sufficient volume decrease to

cause liquefaction.

Cohesive materials (clays) respond differently to shear strain, and in general are

not susceptible to liquefaction. Recent evidence indicates that under some conditions sands containing up to 20% clay may lose strength during an earthquake.

Treatments for controlling liquefaction consist of one of four general methods:

1. remove material subject to liquefaction and replace with sound material.

2. provide structural support to underlying firm soil strata, i.e. piling.

3. densify the material so as to render it less susceptible to liquefaction.

4. provide drainage to prevent build up of pore water pressures, and/or provide strength reinforcement to the soft liquefiable soils.

Physically removing the soil material susceptible to liquefaction and replacing

it with sound material is one of the most positive methods of controlling liquefaction.

Unfortunately it is also one of the most expensive, often prohibitively so. Complications arise because these deposits are always below the ground water table and often as deep as 50 to 60

feet.

Another solution to the liquefaction problem is to found the structure on piling driven through the susceptible soils to firm underlying material. However, such firm

underlying material is often quite deep. Besides being expensive this method is not entirely satisfactory because the soil between the piling can still liquefy. If such liquefaction occurs

the piling is left without lateral support and danger of buckling exists.

One of two methods are normally used for deep densification, namely, deep

vibratory compaction and dynamic compaction.

Deep vibratory soil compaction devices , which includes vibroflotation, Terra-

probe (Trademark), Vibro-wing (Trademark), and others, is most effective in clean sands, and under the proper conditions may be the most positive and cost effective method of controlling

liquefaction. Unfortunately, only a small percentage of the soils susceptible to liquefaction

are appropriate for treatment by deep vibratory compaction, because the presence of

appreciable amounts of silt or clay renders the process ineffective. The stone column method might be thought of as an extension of vibroflotation. This method will be discussed later.

Typical costs for deep vibratory compaction range from $1.00 to $5.00 per cubic yard of

material treated. Treatment has been accomplished to depths in excess of 100 feet.

Dynamic compaction is accomplished by repeatedly dropping heavy weights (4

to 35 tons) onto the ground surface from heights of 20 to 120 feet. Although this method is

effective in materials containing significant amounts of silt or clay, there are depth limitations.

The depth to which densification is achieved depends on the how large a weight is used. For

weights of 20 to 35 tons the process is limited to 30 to 35 feet in clean sands, and in materials

containing significant amounts of silt or clay may be limited to 20 feet or less. For weights

up to 20 tons the depth limitation in clean sands is on the order of 15 to 20 feet, and may be only 10 feet or so in dirty materials.

Very large and specialized equipment is required for weights greater than 20 tons, and both mobilization and production costs are drastically increased. These large

weights are practical for only very large projects.

If the soil to be treated is very soft or if the ground water table is near the

surface it is necessary to install a "buffer" pad of granular material 5 to 7 feet thick to drop

the weight on to. This buffer pad distributes the shock loads of the falling weight to the underlying soil to be densified, and also raises the operation to a level where the craters created remain above ground water level.

The process is also severely limited in congested areas because of the

detrimental effect on adjacent works from the impact of the weight as it strikes the ground.

Under the proper conditions this method is very cost effective and positive. Typical costs may range from $0.50 to $6.00 per cubic yard of material treated.

Stone columns, as the name implies, are simply vertical columns of compacted

stone extending through a deposit of soft soil. The most common method of installing stone

columns, developed in Germany in the late 1950's is a natural extension of the vibroflotation

process, and uses modified vibroflotation equipment. Another technique, developed

concurrently in Japan often utilizes sand instead of stone. Another recently developed method, ROTOCOLUMN (Service Mark), produces very clear and uncontaminated columns.

Stone columns are installed on a regular pattern over the area to be treated, and

provide reinforcement, resulting in increased vertical load capacity as well as improved composite shear resistance. Stone columns have been used to improve a wide range of soils,

from very soft clays to materials marginally suitable for vibroflotation or deep vibratory

compaction. In mixed soils improvement can be gained in the cleaner, cohesionless material, while the column provides reinforcement in those areas that do not respond to vibratory

compaction. The permeable vertical stone column also provides an effective drainage path for

dissipation of excess pore water pressures.

The concept of stone columns or gravel drains to prevent dangerous buildup of

pore water pressures in controlling liquefaction was first quantified by Seed and Booker (Seed,

H.B. and J. R. Booker, "Stabilization of Potentially Liquefiable Sand Deposits Using Gravel

Drains," Journal of the Soil Mechanics and Foundations Division, A.S.C.E. , Vol. 103, No.

GT7, July, 1977). Both gravel drains and stone columns are installed on a regular pattern

over the area to be treated, and to such a depth as to penetrate the liquefiable soils. An escape

path for drainage of pore water is provided from the top of the columns. This usually takes

the form of a stone layer which in turn drains into a sewer system or "daylights" to the ground

surface (See Fig. 1).

By this method the excess water pressures within the gravel columns or drains

are maintained at a very low level. Excess pore water pressures generated within the

intervening soil will dissipate rapidly because the drainage path to the nearest column or drain

is relatively short.

In the Seed-Booker analysis, excess pore pressures within the columns or drains

are assumed to be zero. This condition cannot strictly be met in practice because the water level within the column must rise above the ground water level for drainage out of the column

to occur. Further, vertical movement of water within the stone column or gravel drain

generates head losses with resulting back pressures.

The tributary area surrounding each column is idealized to a circle with a radius

chosen to produce a circle with area equivalent to the actual tributary area. The analysis then

considers the drainage and pressure conditions within a cylinder of soil contaimng a gravel

column at its center. In the analysis no drainage is allowed across the outside surface of this

cylinder of soil, and the excess pore water pressure is considered to be zero at its inside

radius, or at the interface with the gravel column. The Seed-Booker analysis is based on these

assumptions, and presents a series of charts and graphs convenient for design of gravel drains

to limit excess pore pressures to a desired level for earthquakes of various magnitudes and

durations. A computer program (PROGRAM LARF by trademark) is available for solution

of the equations.

Another computer program (EQDRAIN) has been written to study the effect of head losses produced by water flow within the drain, and the effect of a rising water level

within the drain. This program can handle variable thicknesses and depths below the surface

of the liquefiable soil. It is intended that this program will be refined to accommodate liquefiable soils with properties that vary with depth. This program will be available for

design use.

Typical stone column diameters range from 2 to 5 feet, and typical gravel drain diameters range from 8 inches to 18 inches. Typical spacings for stone columns range from

4 feet to 10 or 12 feet, and spacings of gravel drains ranges from 2 to 6 or 7 feet. This wide

range of values reflects the effect of varying soil materials and severity of earthquake designed

for.

The cost of stone columns ranges from about $15.00 to $30.00 or more per

foot. Gravel drains range from $2.50 to $5.00 per foot. This equates to a cost per cubic yard

of material treated of $3.50 to as much as $25.00 to $30.00 for stone columns, and $2.00 to

$15.00 for gravel drains. In addition a cost of from $1.00 to $3.00 per square foot of surface

area must be added for a surface drainage system for drains, or for a stress distribution mat

for stone columns.

SUMMARY OF THE INVENTION

The apparatus and method of the present invention for treating liquefiable soil

for earthquake liquefaction protection for a structure or work thereon, comprises a plurality

of substantially vertical prefabricated composite drains positioned at spaced intervals in the liquefiable soil, and a reservoir which is adapted for draining off water that is expelled from these composite drains. The object is to provide pore water pressure relief from a series of

spaced locations within a liquefiable soil by providing an open drainage path which operates

as efficiently as possible - i.e. requires as little pressure as possible to move the required

amount of water.

The liquefiable soils being treated, and most susceptible to liquefaction, are fine

cohesionless soils (fine sands) or fine cohesionless soils containing moderate amounts of silt.

More specifically such liquefiable soils have a permeability in the approximate range of 1 X

10" ² to 1 X 10"° cm/sec, as opposed to very permeable soils, such as coarse gravel which has

a permeability of over 1 X IO ^"1 cm/sec or impervious soils, such as clay, which have a permeability of less than 1 X IO ^"7 cm/sec.

The composite drains are comprised of an elongated plastic core providing

channels therein for channeling water therealong and this core is surrounded by a geofabric or filter fabric. An advantage of the geofabric is that it will not be subject to plugging or to

silt build-up since the drain is not used until an actual earthquake or other heavy shocks occur

to the liquefiable soil. This geofabric is provided with opening sizes such as to prevent the

entrance of soil particles but allows pore water to freely enter.

The elongated plastic core of the composite drain structure, in one form,

includes a flexible strip of material having lateral stand-off protrusions providing drainage

channels therebetween. In another version, the elongated plastic core may be constructed of

corrugated and perforated plastic pipe, which is surrounded by the geofabric. In some

instances the geofabric may be omitted from the corrugated, perforated plastic pipe.

Approximate dimensions range from 1/2 to 2 inches thick by 4 to 18 inches

wide in the case of the formed plastic core, and from 1-1/2 inches to 8 or 10 inches inside diameter in the case of the plastic pipe. These products can all convey large amounts of water at very low pressure gradients.

The vertical drains are spaced in the general range of 2 to 6 feet. This spacing depends not only upon the permeability and compressibility of the liquefiable soil, but also

upon head losses involved in moving the water from its point of entrance into the drain to its

final discharge into the reservoir. This obviously involves head losses incurred from vertical flow within drains. It also involves head losses incurred in entering the reservoir, as well as the head required to lift the water to the level of the reservoir, if this level is above that of the

static ground water table.

Suitable reservoirs may be in the form of an existing naturally available

reservoir or a man made reservoir as required. For example, the layer of liquefiable soil being

treated may possibly overlie a bed of highly permeable soil or course sand. In this instance,

the vertical composite drains are inserted in such a way that they entirely penetrate the

liquefiable soil and enter into the underlying bed of highly permeable soil. Accordingly, when

water pressure or head pressure within the drains builds up during an earthquake, it is quickly drained off to the underlying reservoir.

Another such reservoir which is readily available in many instances occurs

when the ground water surface exists within a highly permeable soil or aquifer overlying the liquefiable soil. The vertical drains may be so implanted to drain off into this naturally occurring aquifer. In both cases the ground water level will temporarily rise nominally when

discharge from the drains occurs.

When a suitable naturally occurring or available reservoir is not present, a

reservoir may often be constructed by placing a 1- to 4-foot layer of highly permeable soil or

gravel on the ground surface above the liquefiable soil. The structure or work is built over

this layer of permeable material. The vertical drains are placed so as to conduct the expelled

water to the surface, and the void spaces within the permeable layer provide the required

reservoir. The water deposited in these void spaces then gradually seeps away after a seismic

event.

The ground surface will normally be at some distance above the static ground

water level, and the pressure head required to lift the water from this level to the surface will

be applied as back pressure to pore water trying to enter the drains from the liquefiable soil.

This will obviously affect the amount of water expelled from the soil, and in turn the spacing

of the vertical drains required to maintain excess pore water pressures within the soil to a

desired level. The amount of back pressure that can be tolerated is interrelated with all of the

other factors involved in the design.

Soil permeability and compressibility, the magnitude and duration of the seismic

event designed for, and the factor of safety or the magnitude the excess pore water pressure

within the liquefiable soil will be allowed to attain, are generally given and dictate the design requirements. The actual remediation system design then specifies the vertical drain size or cross sectional area (affects head losses of water flow within the drain), drain spacing, and

reservoir requirements. These factors are chosen to attain the most cost-effective combination.

Normally, the practical limit that the pore water can economically be lifted to the reservoir

level is on the order of 2 to 5 or 6 feet.

A suitable, and often preferable, reservoir can also be constructed by augering

a hole at each drain location from the ground surface down to the water table surface, and

filling this hole with crushed stone or gravel, or other porous material. Under this

arrangement the elevation head difference between the static ground water level and the

reservoir is initially zero, and increases only nominally as water enters into the reservoir.

This rise of water level within the reservoir is accounted for in the design procedure. The

diameter of this augered hole may be in the range of 2 to 4 feet.

In another form this reservoir may consist of a section of pipe buried in a

vertical position, with its lower end at the ground water surface. The drains are arranged to

terminate at their upper ends inside the reservoir so created. The upper end of the reservoir

pipe is covered by a plug or end cap. Although several different materials could be used for such a reservoir, corrugated plastic is normally preferred. The inside diameter ranges from

8 inches to about 2 feet.

When vertical prefabricated drains are used for liquefaction remediation in combination with piling, the piling can be constructed to include reservoir space within its

interior. For example, steel pipe piling may be used. It is also a simple matter to construct precast concrete piling with internal void spaces.

In some cases, the vertical drains may contain within themselves sufficient void

space above the water table to suffice as a cost-effective reservoir.

As an added safety factor, the liquefiable soil may also be compacted by

conventional methods either before or after the vertical drains have been inserted; or, since

the drain installation equipment often utilizes a vibrating mandrel to facilitate penetration into

the earth, it is a simple matter to modify the mandrel to accomplish densification during drain

installation. To accomplish this 3 or 4 fins are added radially to the mandrel. Cleats or

protrusions are added to the fins to help transmit vibrations to the soil, and thus effect

densification. Alternatively, a series of holes cut into the fins can act to efficiently transmit

vibrations.

This probe arrangement, without the central installation mandrel, is similar to

various types of vibrating probes commonly used for soil densification. Soil densification

from a single probe insertion, or compaction point, is greatest near the probe and diminishes with radial distance. In normal vibrocompaction operations it is desirable that this area of

influence be as large as possible. Thus, fewer insertions can cover a given area and at a minimum cost. Very large probes with powerful vibrohammers are common for efficient

operations.

The time each insertion is left in the ground also affects the resulting

densification. The most efficient combination of probe size, compaction point spacing, and

time spent at each point is usually found through field tests for each project. Smaller spacings

result in a higher level of densification, but higher cost.

In the present case, compaction point spacing will be dictated by drainage

requirements, and will be much smaller than for a normal vibrocompaction project. Thus,

efficient compaction will be possible with smaller probes, and less time per compaction point.

As mentioned previously, this type of densification is effective in relatively clean cohesionless

soil only. It is expected that densification will not be effective in soils containing significant

amounts of silts or clay. However, drainage supplied by the composite drain will be effective

in the dirtier materials. This should be an advantage for sites with mixed soil conditions

_D ESCRIPTION OF RELATED WICK DRAIN PRIOR ART

The prefabricated drain soil remediation method and apparatus of the present

invention are similar in many respects to the vertical drain method (sometimes called "wick"

drains) commonly used to accelerate consolidation of soft clays. Such soft clays are not liquefiable soils or soils subject to earthquake liquefaction, and are therefore not applicable to

the teachings of the present invention. A brief discussion of "wick" drains follows.

When loads are placed on the surface of soft saturated clay deposits large settlements often result because of compression of the clay material . This settlement can take

place only as pore water is expelled, and since the permeability of the clay is very low this

process takes place very slowly. Total settlements of several meters are common and often

take years to occur. This time-dependent process is called consolidation. A process called

sand drains and surcharging has been used in these cases since the early 1920' s. See D. E.

Moran, Patent No. 1,598,300 (1926). In this process sand drains or columns are installed through the soft clay layer to be treated. These sand drains are placed on a regular pattern in

the same manner as the gravel drain layout shown on Figure 1. Typical spacings range from

4 to 12 feet and sand drain diameters are typically 1 foot and occasionally as much as 2 feet.

After the sand drains are installed a sand drainage blanket 1 to 3 feet thick is

placed over the drains to permit water flow out of the drains. An earth embankment is placed

over this sand blanket. The thickness of this embankment or surcharge is calculated to produce loading roughly 10% greater than the anticipated final design load planned for the

project. Since drainage out of the clay can now flow into the sand drains, the drainage path

is much shortened and consolidation occurs much more rapidly. The surcharge is left in place

until the consolidation process is nearly complete, typically 6 months or less. The surcharge is then removed and the project proceeds.

In the late 1960's and early 1970's vertical wick drains were developed as an

alternative to sand drains. Vertical wick drains are not truly wicks but are composite drains composed of an extruded plastic core, shaped to provide drainage channels when this core is

wrapped in a special geofabric. The geofabric is a filter fabric constructed with opening sizes

such as to prevent the entrance of soil particles, but allow pore water to enter freely. The finished wick material is band-shaped about 1/8 to 1/4 inches thick and typically 4 inches

wide. It is provided in rolls containing 800 to 1000 feet of drain. An example manufacturer of wick drains is American Wick Drain Corporation of Matthews, North Carolina, U.S.A.

(AMERDRAIN tm).

Installation is accomplished by means of specialized equipment, consisting of

a crane mounted vertical mast housing a special installation mandrel (See FIG. 6). The

mandrel, containing the drain, is intruded directly into the ground from the bottom of the

mast. After reaching the desired depth, the mandrel is withdrawn back into the mast, leaving

the undamaged drain in place within the soil. For example, see U.S. Patent No. 5,213,449.

Typical spacings for vertical wick drains are from 3 to 9 or 10 feet. This

method is very cost effective and has virtually replaced the older sand drain method.

Typical per foot costs of vertical wick drains installed ranges from $0.35 to

$1.00. This amounts to a cost per cubic yard of material treated of from $0.15 to $2.00. The

cost of a surface or horizontal drainage system and surcharge must be added.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects and advantages appear in the following description and claims.

The accompanying drawings show, for the purpose of exemplification, without

limiting the invention or claims thereto, certain practical embodiments illustrating the principals of this invention, wherein:

FIG. 1 is a schematic view in front elevation and vertical cross section illustrating a building structure supported on liquefiable soil which has been remediated with gravel drain or stone column techniques of the prior art;

FIG. 2 is a schematic view in front elevation and vertical cross section

illustrating a building structure supported on liquefiable soil which has been treated or

remediated with the use of prefabricated vertical composite drains in accordance with the teachings of the present invention;

FIG. 3 is a schematic view in vertical cross section of a reservoir constructed

by filling an augered hole with stone or other granular material;

FIG. 4 is a schematic view in vertical cross section of an alternate reservoir construction consisting of a section of corrugated plastic, or other, pipe;

FIG. 5 is a schematic view in vertical cross section and frontal elevation

illustrating remediation treatment of liquefiable soil in accordance with the teachings of the

present invention with vertical composite drains in combination with reservoirs which are

naturally present;

FIG. 6 is a schematic view of a typical wick drain installation rig adapted for

installation of vertical prefabricated drains for liquefaction remediation; and

FIG. 7 is a cross section showing an installation mandrel fitted with "fins" for

compaction of soil simultaneously with drain installation.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Referring to FIG. 2, liquefiable soil 10 having a permeability in the

approximate range of 1 X IO ² to 1 X IO ^"6 cm/sec, is treated in accordance with the teachings

of the present invention for earthquake liquefaction protection prior to erecting the building

structure 11 or work thereon.

A plurality of substantially vertical prefabricated composite drains 12 penetrate

the entire depth 13 of the liquefiable soil 10.

Prefabricated composite drains 12 are comprised of elongated plastic cores

providing channels therein for channeling water therealong and which are surrounded by filter

fabric or geofabric. These composite drains are readily available on the market for purposes

other than soil liquefaction remediation.

A number of composite drainage products similar in construction to vertical

wick drains have been developed since the early 1980's and are also usable in suitable form

in the apparatus and method of the present invention. These products are also constructed of a plastic core surrounded by a geofabric, but have larger cross sectional area than ordinary

wick drains. Uses range from drainage around basements to edge drains for highways. One

such composite drain is manufactured by the previously cited American Wick Drain

Corporation, under the trademark AKWADRAIN. The elongated plastic core of the AKWADRAIN is constructed of a flexible plastic strip having lateral standoff protrusions

which provide drainage channels therebetween. Another manufacturer is Burcan

Manufacturing Inc. of Whitby, Ontario, Canada, who manufactures a similar product under

the trademark "HITEK".

Another recently developed product is corrugated plastic pipe. This product

is perforated or slotted and wrapped in a geofabric. In cases where water is expected to flow into the drain only during a seismic event the geofabric may be omitted. The small amount

of soil fines carried into the drain during the seismic event will simply settle out later and clog

only a few inches of the bottom of the drain. Several events would need to occur to produce

significant blockage. Two examples are manufactured by Hancor, Inc. of Findlay, Ohio, U.S.A. and Advanced Drainage Systems, Inc. of Columbus, Ohio, U.S.A. (ADS®).

Existing vertical drain installation equipment may be modified to install either of these products as vertical drainage elements.

The prefabricated composite drains 12 as schematically illustrated in FIG. 2 are intended to represent any one of the aforedescribed conventional prefabricated composite drains, or any new designs thereof.

The prefabricated drains 12 in FIG. 2 are uniformly spaced throughout the entire area of liquefiable soil 10 which underlies building structure 11. This spacing will vary

anywhere from approximately 2 to 6 feet, depending upon the permeability and compressibility

of liquefiable soil 10, the magnitude and duration of the earthquake designed for, the factor

of safety, and the type of prefabricated- drain 12 employed. Soil 8 is a nonliquefiable soil layer

which overlies the liquefiable soil 10.

With the treating apparatus or method of the present invention, a reservoir must

also be employed in combination with the vertical prefabricated drains and adapted to drain

off water which is expelled from the composite drains. The reservoir may be man made or

a naturally occurring reservoir may be utilized when available. In FIG. 2, a man made

reservoir 14 is illustrated and is constructed of a layer of compacted gravel. The void space

within the gravel forms the reservoir. Drainage pipes 15 are provided to maintain the gravel

in a drained condition so that if an earthquake should occur reservoir space will be available.

In some cases it will be advantageous to place an impermeable membrane (plastic film or

other) over the reservoir to prevent the entrance of outside water.

Thus when an earthquake occurs and water head pressure builds up within the

composite drains 12, the water has an immediate free draining means of escape and is permitted to drain off to reservoir 14.

The initial static water level 19 is shown. The distance 20 represents an

elevation head that must be overcome in order for water to enter reservoir 14 from the drains 12. The pressure to accomplish this lift must be provided by additional excess pore water

pressure within the liquefiable soil 10. The detrimental effect of this added excess pore water

pressure can be, within limits, compensated by decreasing the spacing of the drains 12. However, if the distance 20 is too great, the required spacing may become so small as to be

impractical, or uneconomical because of the large number of drains. Indeed, the required

additional excess pressure may even be greater than the maximum allowable pore water

pressure within the liquefiable soil.

Figure 3 shows an alternative form of man-made reservoir, an augered hole

21 at each drain 12 is filled with crushed rock or other porous material. The interstices of this

porous material form the reservoir 14. The overlying structure or work 11 can be founded directly on top of these created reservoirs or placed on top of a layer of fill covering the

reservoirs. In this case an impermeable membrane is placed over the top of the reservoirs to

prevent contamination of the porous material.

In the event of an earthquake initial conditions will start with the water level

in the reservoirs 14 at the initial static ground water level 19, and there will be zero added

excess pore water pressure required to lift the expelled water. During the earthquake, flow into the reservoir will exceed the amount of water that can be dissipated out, and the level

within the reservoir will rise. Further, the static ground water level will generally vary

seasonally and with other factors. The requisite amount of reservoir volume must be provided

above the highest expected ground water level. This, along with the required diameter of the augered hole 21 , is deteπriined in the design process. After the earthquake the water deposited

in the reservoir will gradually drain out and eventually return to the level 19.

Figure 4 shows a similarly created man-made reservoir. In this case a section

of pipe 22 is embedded within the ground at each drain location. The drains 12 are arranged

to terminate at their upper ends in the interior of this pipe. The top of the pipe is provided with an end cap or plug 23. The overlying structure or work 11 can be either placed on an

intervening layer of fill 24 or placed directly on the tops of the embedded pipes 22. The pipes

22 could be of any number of materials, but normally would be constructed of corrugated plastic. The operation of this reservoir is identical in all other respects as described

previously.

As previously indicated, a naturally occurring reservoir may be used in

substitution of the man-made reservoir 14 of FIGS. 2, 3 and 4. This is schematically

illustrated in FIG. 5.

FIG. 5 illustrates a naturally occurring reservoir form of a highly permeable soil

layer or aquifer 16 which underlies the treated liquefiable soil 10, or alternatively a highly

permeable soil layer or aquifer 17 may overly the treated liquefiable soil. FIG. 5 is intended to represent either one of these naturally occurring reservoirs in the alternative, as it is not

always likely that both such naturally occurring reservoirs would simultaneously be available for use at a given site. One or more impermeable soil layers 18 may exist between the treated

liquefiable soil 10 and either an underlying aquifer 16 or an overlying aquifer 17. The static ground water level may or may not be located within an overlying aquifer.

The prefabricated composite drains 12 penetrate the liquefiable soil 10 and

continue on to additionally penetrate the top of an underlying aquifer 16, such as coarse sand, thereunder. Thus, when excess pore water pressures are generated in the liquefiable soil 10

during an earthquake these pressures are readily relieved by water flow downwardly into the

naturally occurring reservoir 16, thus preventing extreme excess pore water pressure buildup leading to liquefaction.

In a similar fashion, when the underlying reservoir 16 is not available, a highly

permeable soil layer 17 may occur naturally above the liquefiable soil 10, and the pore water is permitted to drain upwardly through prefabricated drains 12.

In both cases, since hydrodynamic equilibrium will exist at the begirinmg of an

earthquake, zero additional excess pressure will initially be required to deposit water in the

reservoir. As water enters either reservoir 16 or 17 back pressures will be generated and a

nominal amount of added pressure must be supplied to sustain the flow of water into the

reservoirs. The amount of added pressure will depend of the amount of water flowing into the

reservoir, and on the storage coefficient of the reservoir. This storage coefficient should be

determined or estimated and considered in the design process.

The prefabricated composite drains of FIGS. 2, 3, 4 and 5 may also be utilized

in combination with conventional concrete or steel piles which fully are at least partially

coextend with the composite drains 12. For example, the composite drains may be laid into the side channels of piles with an I-beam cross section configuration, or they may be embedded into preformed concrete piles or positioned in cement or concrete. They may also

be embedded in stone columns which are formed in situ. Various piling configurations may

be utilized to provide either complete or partial reservoir requirements. The interior of steel

pipe piling might be used for this purpose. Also specially designed precast concrete piling

might contain void spaces for this purpose.

In order to further enhance the liquefaction remediation of the liquefiable soil,

the liquefiable soil may also be compacted by conventional means either before or after the

vertical drains 12 are installed. Compaction may also be carried out simultaneously with drain

installation. Illustrated in FIG. 6 is a conventional wick drain installation rig 25 adapted for

installation of vertical composite drains for liquefaction remediation. As illustrated, an

installation mast 31 is carried on some conventional piece of construction equipment 32. The

mast 31 is fitted with a continuous loop of roller chain 26 on each side of the mast. These

loops of roller chain are activated by a motor 27. A conventional vibratory driver 28 is

attached to slide vertically on the front of the mast 31. This vibratory driver is coupled to the

loops of roller chain 26 through special elastomers 36. These elastomers apply force to the

vibratory driver to cause it to move vertically, but isolate vibrations from reaching the chain, mast and carrier equipment. The installation mandrel 29 is attached directly to the vibratory

driver 28.

The drain 12 is carried inside the mandrel or insertion tube 29, and is driven downwardly into the earth to the desired depth. When this depth is reached the mandrel is

withdrawn. A special sacrificial tip at the bottom of the mandrel 35 stays in place in the earth and is attached to and retains the composite drain 12 in place. As the mandrel is withdrawn,

additional drain material feeds over a roller 34 and into an opening 33 to the interior of the

mandrel 29. When the bottom of the mandrel is withdrawn from the earth, the exposed drain

material 12 is cut, another sacrificial point is put in place, and the process is repeated at the

next location.

In conventional wick drain installation the vibratory driver may or may not be

used in the installation process. If the soil receiving the drains is soft enough, penetration can

be accomplished by static crowd of the mandrel 29. Often hard layers are interbedded with

or overly the soft soil, and penetration is difficult or impossible. In these cases the vibratory

driver may be turned on to facilitate penetration of these hard layers.

In the present invention fins 30 have been added to the mandrel 29. This is

shown in cross section in FIG. 7. Three fins are shown but two or more could be utilized.

The purpose of these fins is to transmit vibratory motion to the soil and thereby provide densification simultaneously with drain installation.

To facilitate transmission of vibratory motion to the soil, "cleats" or protrusions 37 may be added to the fins. Alternatively, holes 38 may be cut into the fins for this purpose

as shown in FIG. 6.

PERFORMANCE ANALYSIS

Previously described prior art prefabricated wick drains are designed for, and

perform very well in providing drainage that takes place slowly. Even under this slow

drainage, head loss from movement of water within the drain may be a problem in drains that

extend through very thick deposits of soft soil.

Consider a drain spacing of 7 feet. If 4 foot of settlement occurs in 3 months, the average flow rate through the drains will be about 0.0013 ft ³ /min.

In order to gain some idea of the head loss within the drain under these

conditions, reference may be taken from the Federal Highway Administration publication

FHWA/RD-86/168. From this reference it can be seen that, for an "average" wick drain, at

a confining pressure of 30 psi a discharge or flow of about 600 cubic meters per year will

produce an hydraulic gradient of about unity. For the case of slow consolidation drainage,

0.0013 ftVmin equates to about 19 Vyear, and for most wick drains the hydraulic gradient

would be roughly 0.03 ft/ft.

During an earthquake a settlement of say 1 inch may occur in 60 seconds (if the induced pore pressure ratio is approximately 0.6 to 0.7, the volumetric strain will be on the

order of 0.3% to 0.4%). For a thickness of 30 feet, this amounts to about 1 inch of

settlement.

For the case of the earthquake condition if the drains are spaced at 7 feet, the

average flow rate through the drain is roughly 3.5 ftVmin. This equates to about 52,000 mVyear, and the hydraulic gradient would be roughly 87 ft/ft. Such head losses are obviously intolerable, and the use of any of the conventional wick drains is not feasible.

To gain some idea how the advanced prefabricated drain products

(AKWADRAIN, HITEK, ADS, etc.) might function as vertical drains for liquefaction

protection in accordance with the teachings of the present invention, as compared with gravel

drains or stone columns, consider the example problem presented by Seed and Booker. This

example considers a soil layer having permeability k = 10 ⁵ m/s (3.25 X IO ^-5 ft/s, which

corresponds to very fine sand or silty sand - see Table I), and m _v3 (coefficient of volume

compressibility) = 2 X 10° ft ² /lb (corresponds to loose soil). This soil is subjected to an

earthquake which can be considered as applying 24 uniform stress cycles in a period of 70

seconds. The characteristics of the soil are such that liquefaction would occur after 12 cycles

if no drainage were provided.

Problem geometry as shown on FIG. 2 was assumed. The thickness 13 of the liquefiable soil 10 was taken to be 30 feet. An overlying nonliquefiable layer 8 was assumed

with a thickness 9 of 5 feet, and the static ground water table 19 was assumed to be 2 feet above the liquefiable soil (i.e. thickness 20 is 3 feet). The initial effective overburden at the top of the soft soil was taken as 800 lb/ft ² .

Results were obtained using the computer program EQDRAIN. The method utilized by this program is to break the liquefiable soil layer into sublayers. Generation of pore water pressures due to seismic shaking is computed for each sublayer according to the

same scheme used in program LARF (as proposed by Seed & Booker). The flow into the

drains from each sublayer is monitored, and head losses from cumulative vertical flow within

the drains are calculated. Also head losses in the portions of the drains above the liquefiable

layer are monitored, as well as the water level in the drains or reservoir. The cumulative

effect of these sources of back pressure is computed, and applied for each sublayer. Time zero is assumed at the beginning of seismic activity. Static ground water conditions are assumed

initially, and the water level in the drains is at the level 19. The above calculations are

performed at time zero, and repeated for some predetermined time interval. The process is

continued for any desired length of time.

Results from program EQDRAIN were checked with those from program LARF

to the extent possible. Agreement was excellent.

Head losses from water flow in the drains are computed according to Darcy's

law for stone columns or gravel drains, according to Manning's equation for corrugated pipe,

and for AKWADRAIN according to

1 = 0,0"

where C, and n are experimentally determined constants. Head losses from flow through the

geotextiles are computed according to the manufacturer's published permitivity values. Head loss through slits or perforations, in the case of perforated pipe, are computed as v ²

2g where v is the flow velocity through the slit or perforation and g is the gravitational constant.

For the corrugated pipe, Manning's n-value was taken as 0.015. For all cases the geofabric

was considered to be Amoco Style 4545 geofabric with a permitivity of .333 ft ³ /sec/ft ² /ft. For

4-inch diameter corrugated pipe the orifice area of the slits was taken as 1.90 in ² /ft of pipe.

For 2" x 12 " AKWADRAIN the equivalent diameter was taken as the diameter of a circle

with circumference equal to that of the drain, 0.74 feet, and the empirical flow constants

according to the manufacturer are

/ = 19.30(? ^{1 8}

where Q is in cfs. For wick drains, parameters were estimated based on the aforementioned

Federal Highway Administration publication FHWA/RD-86/168. The permeability of clean,

gravel can range from about 1 to 100 cm/sec. Depending on the installation method,

considerable contamination of the gravel material is possible during the construction of either

stone columns or gravel drains. Thus, choosing an appropriate permeability for these

materials is difficult. For comparison purposes, calculations were performed for permeabilites

of 1 , 10, and 100 cm/sec.

Vertical drain spacing is normally designed to limit maximum pore pressure

ratios, r _ω to a value of 0.6. The pore presure ratio at any point is defined as the pore water pressure, u, divided by the initial effective overburden stress, σ _v '

Table II. Drain Spacings to Produce (r _u ) _max of 0.6.

Earthquake: Equivalent No. Cycles = 24 Soil: k=0.325xl0 ^" ft/sec Duration = 70 seconds m _v =0.2xl0- ⁵ ft ² /sec No. cycles to liquefaction = 12

Table II lists the results of these calculations. The per square foot treatment costs were based on typical costs as follows:

Three-foot diameter stone columns Typical cost $17.00/foot

One-foot diameter gravel drain 3.00/foot Four-inch I. D. corrugated pipe 1.30/foot

2" X 12" AKWA drain 1.60/foot

Wick drains 0.40/foot

The drastic effect of changes in the permeability of gravel material for stone

columns and gravel drains is obvious, particularly for the 1-foot diameter gravel drains. The

cost of treatment per square foot for this case varies from $10.35 to $8.67 for 3-foot diameter

stone columns, and from $9.63 to $3.93 for 1-foot diameter gravel drains. Quality control in

the construction of these products is important, but often difficult to achieve in practice.

Installing a composite drain centrally in either a stone column or gravel drain would assure

that the required flow capacity is achieved. For instance, if a 4-inch corrugated plastic pipe

were installed in a 1-foot diameter gravel drain the spacing could be increased to

approximately 5.2 feet, even if the stone material had a permeability of 1 cm sec or less.

The efficiency of the advanced drainage products is also evident, with a cost

treatment of $2.53 per square foot for AKWA drain and $2.62 per square foot for corrugated

pipe. The extremely high cost for wick drains is because of their very low flow capacity,

necessitating a small spacing.

Table II presents a comparison of results of one particular case only, and results

for other conditions could be expected to vary drastically. For instance, if the distance 20 is

greater than roughly 3 to 6 feet the water rise in the prefabricated drainage products becomes relatively larger. This exerts more back pressure on pore water trying to enter the drain, and smaller drain spacings are necessary. In this case the use of a reservoir of the type shown on

FIGS. 3 or 4 may be cost effective.

Novelties of this approach include the concept of using composite drains for liquefaction remediation, the concept of a reservoir (man-made or natural), applicable to both

composite and gravel or sand drains, the possible use of a composite drain with either gravel

or sand drains, and combining soil densification through vertical vibration of a modified probe

with drain installation.