Apparatus and methods for prediction of scour related information in soils

Methods are described for measurement and prediction of site specific scour around a structure obstructing a flow. Representative soil samples are collected from an area proximate the structure location and tests are conducted on the samples to determine the erosion rate and hydraulic shear stress imposed. The maximum shear stress and initial scour rates around the structure are also obtained. Next, the maximum depth of scour is calculated, and the depth of scour versus time curve for the structure is then predicted. In a preferred embodiment, the methods described are used to predict a scour depth versus time curve around a cylindrical bridge support standing in the way of a constant velocity flow and founded in a uniform cohesive soil. An erosion function apparatus is also described which can be used to test representative samples of soil in the area where a structure is located.

S
 TATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT Not
 Applicable.
 BACKGROUND OF THE INVENTION
 1. Field of the Invention
 The present invention relates generally to the measurement and prediction
 of scour rate in soils. It has been found that the invention has
 particular applicability to the measurement and prediction of scour rate
 in cohesive soils at bridge supports and other structures that obstruct
 the flow of a body of water.
 2. Description of the Related Art
 There are approximately 600,000 bridges in the United States, and 500,000
 of them are over water. During the last thirty years, over 1,000 of the
 600,000 bridges have failed, and 60% of those failures are due to scour of
 the soil surrounding bridge piers or other supports. Earthquakes, by
 comparison, account for only 2% of bridge failures. The average cost for
 flood damage repair of highways on the federal aid system is $50,000,000
 per year. Clearly, bridge scour is a significant problem deserving of
 significant study and attention.
 Bridge scour can be divided into general scour, local scour and channel
 migration. General scour is general erosion of a stream bed without
 obstacles. Local scour is generated by the presence of obstacles such as
 piers and abutments, while channel migration is lateral movement of the
 main stream channel.
 When bridges are designed, core samples are usually taken of the soil in
 the area where the bridge supports will be located. However, these samples
 are not typically tested to determine their susceptibility to local scour.
 Rather, a maximum scour depth is calculated and applied to the bridge
 design regardless of the actual soil present. The scour depth for sand is
 usually used and, if the soil is more scour resistant than sand, the
 bridge may be overdesigned, resulting in a significantly higher cost for
 the structure. If, on the other hand, scour is ignored, the bridge may be
 prone to failure earlier than planned. It is important, then to be able to
 accurately predict or forecast the actual rate of scour for a given
 location as well as the maximum depth of scour that can be expected for a
 given period of time.
 Current scour prediction practice is unable to account for different soil
 types. Current practice is heavily influenced by two FHWA hydraulic
 engineering circulars called HEC-18 and HEC-20 (Richarson and Davis, 1995;
 Lagasse et al., 1995). For pier scour, HEC-18 recommends the use of the
 following equation to predict the maximum depth of scour ("z.sub.max ")
 above which all soil resistance must be discounted:
EQU z.sub.max =2z.sub.0 K.sub.1 K.sub.2 K.sub.3 K.sub.4 (D/z.sub.0).sup.0.65
 F.sub.0.sup.0.43
 where z.sub.0 is the depth of flow just upstream of the bridge pier
 excluding local scour, K.sub.1, K.sub.2, K.sub.3, K.sub.4 are coefficients
 to take into account the shape of the pier, the angle between the
 direction of the flow and the direction of the pier, the stream bed
 topography, and the armoring effect. D is the pier diameter, and F.sub.0
 is the Froude number defined as v/(gz.sub.0).sup.0.5 where v is the mean
 flow velocity and g is the acceleration due to gravity.
 However, nothing in HEC-18 gives guidance to calculate the rate of scour in
 clays and it is implied that the HEC-18 equation should also be used for
 determining the final depth of scour for bridges on clays. Clays generally
 scour much more slowly than sand. Thus, using the HEC-18 equation for
 clays, regardless of the time period over which scour is considered, is
 probably overly conservative. As a result, bridges constructed based upon
 such an analysis may be excessively expensive.
 In addition, it is probably improper to try to extrapolate a single
 representative critical shear stress for all clays. Other phenomena, not
 present in most sands, give cohesion to clays, including water meniscus
 forces and diagenetic bonds due to aging, such as those developing when a
 clay turns to rock under pressure and over geologic time. Because of the
 number and complexity of these phenomena, it is very difficult to predict
 .tau..sub.c for clays on the basis of a few index properties. As a result,
 the inventors consider it preferable to measure .tau..sub.c directly for a
 proposed bridge site.
 Some devices are known that have been used to test the scour resistance of
 cohesive soils. One such device is described by Walter L. Moore and Frank
 D. Masch, Jr. in "Experiments on the Scour Resistance of Cohesive
 Sediments," vol. 67, no. 4, Journal of Geophysical Research, pp. 1437-1449
 (1962). The device described there is a "rotating cylinder apparatus"
 wherein a cylinder of cohesive soil 3 inches in diameter and 3 inches long
 is mounted coaxially inside a slightly larger transparent cylinder that
 can be rotated at any desired speed up to 2500 rpm. The annular space
 between the cylindrical soil sample and the rotating cylinder is filled
 with a fluid to transmit shear from the rotating cylinder to the surface
 of the soil sample. The soil samples are mounted in the machine with
 enough water to fill the annular space to the top. The speed of rotation
 of the outer cylinder is gradually increased until visual observation
 indicates the presence of scour on the surface of the sample. At this
 point, a reading is made by a torque indicator. The measured torque is
 then converted into a shear stress on the soil surface.
 There are a number of drawbacks to this type of device. First, the
 cylindrical soil samples used are mixed to a certain consistency and
 molded to form the sample. The mixing and molding can materially change
 the erosion characteristics of the soil being tested since the soil may
 not be representative of the compaction and consistency of in-place soil.
 Further, the method of testing using the rotatable cylinder apparatus
 requires the sample to be rotated at progressively more rapid rates until
 erosion or scour is observed. The rate of scour is not tested at a
 specific velocity and over a specific length of time to provide an erosion
 rate.
 A need exists for devices and methods that can accurately measure and
 predict scour, scour rates and related information, near bridge piers and
 the like.
 SUMMARY OF THE INVENTION
 In the present invention, methods are described for measurement and
 prediction of site specific scour. Representative soil samples are
 collected from an area proximate the bridge support location and tests are
 conducted on the samples to determine the erosion rate and hydraulic shear
 stress imposed. The maximum shear stress and initial scour rate are also
 obtained. Next, the maximum depth of scour is calculated, and the depth of
 scour is then predicted. In a preferred embodiment, the methods described
 are used to predict a scour depth versus time curve around a cylindrical
 bridge support standing in the way of a constant velocity flow and founded
 in a uniform cohesive soil.
 An erosion function apparatus is also described which can be used to test
 representative samples of soil in the area where a bridge support will be
 located.
 Thus, the present invention comprises a combination of features and
 advantages which enable it to overcome various problems of prior devices.
 The various characteristics described above, as well as other features,
 will be readily apparent to those skilled in the art upon reading the
 following detailed description of the preferred embodiments of the
 invention, and by referring to the accompanying drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
 The invention will be described herein with specific reference to bridge
 supports, such as piers. It will be understood, however, by those of skill
 in the art that the invention also has applicability to all other
 obstructions to flow within a body of water around which scour might
 potentially occur. Bridge supports and the like are constructed and seated
 in all types of soils and materials, including sand, clay, limestone and
 other rock formations, cements and so forth. Therefore, the term "soil,"
 as used herein, is meant to refer to all of these different types of
 materials.
 The methods and devices of the present invention do not require the use of
 probes or periodic underwater monitoring. The present invention is
 generally intended as a site specific scour prediction method because
 representative soil samples from a bridge site are collected and tested.
 Referring first to FIG. 1, an exemplary bridge support 10 is shown which is
 vertically disposed within water 12 and into the bed 14 beneath the water
 12. The support 10 has a diameter "D" and supports a bridge (not shown).
 The water 12 has a current that moves the water 12 generally in the
 direction shown by the arrow 16. FIG. 1 also depicts a scour hole 18 with
 a depth of "Z" that has developed around the bridge support 10. The bridge
 support 10 includes a central vertical member 20 that is seated on a
 horizontal platform 22 that in turn is supported by a plurality of
 subpiers 24. It should be understood that this particular construction for
 a bridge support is exemplary only and is not intended to limit the
 claimed invention.
 FIG. 2 is a diagram depicting an exemplary erosion function apparatus 100
 which can be used to determine the actual erosion rates, or scour rates,
 and hydraulic shear stresses imposed upon soil samples obtained near the
 bridge support 10. The erosion function apparatus 100 includes a water
 flow conduit 102 that is operationally interconnected with a pump 104 and
 water source 106 at the inlet 108 of the water flow conduit 102 for
 flowing water therethrough. A collection receptacle 110 is operationally
 associated with the outlet 112 of the water flow conduit 102.
 A flowmeter 114 is operationally interconnected with the conduit 102 such
 that the velocity of water flowed through the conduit is measured. The
 flowmeter 114 may comprise a spinner-type flowmeter of a type known in the
 art. However, other designs for flowmeters and other types of flow
 measurement can be used as well. A soil sample aperture 116 is cut into
 the lower side of the water flow conduit 102, and viewing windows 118 are
 located on the top and two sides of the water flow conduit 102 adjacent
 the soil sample aperture 116. It is currently preferred that the water
 flow conduit 102 be substantially rectangular in cross-section as the
 substantially flat bottom of the conduit 102 will simulate the
 substantially flat bottom of the bed 14.
 Pressure sensors 120, 122 are located on the upstream and downstream sides
 of the soil sample aperture 116. As will be explained shortly, the use of
 the pressure sensors 120, 122 are used to help determine the shear stress
 .tau. and maximum shear stress .tau..sub.max proximate the bridge support
 10. The sensors 120, 122 preferably comprise pressure sensitive
 transducers, and they are operatively associated with a computer or other
 device that is capable of detecting the differential pressure .DELTA.p of
 the pressures detected by the two sensors 120, 122. Such devices are well
 known in the art.
 A soil sample apparatus 124 is affixed to the lower side of the water flow
 conduit 102 so that soil may be selectively pushed or urged into the
 conduit 102. The soil sample apparatus 124 includes a soil containing
 cylinder 126 which is shown having a soil sample 128 contained therein. It
 is presently preferred that the soil containing cylinder 126 comprise a
 76.2 mm diameter Shelby tube of a type known in the art. The upper end of
 the cylinder 126 is fitted within or otherwise affixed to the soil sample
 aperture 116 so that the soil sample 128 can be selectively moved through
 the aperture 116 and into the conduit 102. A reciprocable piston 130 is
 located proximate the lower end of the cylinder 126 below the soil sample
 128. The piston 130 should be movable within the cylinder 126 in small
 increments, such that a small amounts of the soil sample 128, i.e.
 cylindrical portions approximately 0.1 mm in height, can be selectively
 moved into the conduit 102 and subject to erosion by the flow of water
 through the conduit 102. A motor 129 is used to actuate the piston and
 move it upward or downward within the cylinder. The motor 129 is
 preferably a step-type motor that will move the piston 130 upwardly in
 small, measured increments.
 The erosion function apparatus 100 is used to test a representative soil
 sample and allow, using those tests, prediction of the scour depths and
 rates of scour for areas in the bed 14 around a particular bridge support,
 such as support 10 using projected velocity rates and selected time
 periods. As a result, more realistic planning may be done as a bridge is
 designed to ensure that the bridge is neither overdesigned nor
 underdesigned for scour.
 Determination of Scour Rates
 According to the methods of the present invention, at least one
 representative soil sample, such as sample 128, is taken from the area
 proximate the proposed or existing location for a bridge support such as a
 pier. The soil sample is preferably taken in an area of shallow water
 within the river. If desired, a barge may be used and the soil sample
 obtained from the barge. Alternatively, the soil sample may be taken from
 an on-shore location near the river. The soil sample is captured in a
 cylinder which is driven into the soil by a drill rig of a type known in
 the art. The cylinder is then removed from the soil with a sample retained
 therein. As noted previously, the preferred cylinder for use in collecting
 and testing such samples is presently a 76.2 mm Shelby tube. The use of
 the cylinder permits a sample of the soil to be collected that is
 substantially representative of the soil in-place. The soil is not
 compacted or reshaped in order to provide a sample for testing.
 Once the soil sample is obtained, the soil containing cylinder is placed
 into the erosion function apparatus 100, as described earlier. The piston
 130 is actuated to urge a protruded portion 132 of the soil sample 128
 through the aperture 116 and into the flow bore of the water flow conduit
 102. The protruded portion 132 extends a preferred linear distance, or
 height, above the lower surface of and into the conduit 102, thereby
 becoming subject to erosion by water flowed through the conduit 102.
 Suitable heights for the sample portions protruded into the conduit 102
 are 0.1 mm, 0.5 mm and 1 mm above the inner lower surface of the conduit
 102. A presently preferred height for the protruded portion 132 is 1 mm as
 such appears to provide a sufficient amount of soil within the conduit 102
 in order to determine erosion rates for the soil through visual
 observation at different flow rates and for different types of soils.
 Sands, for example, erode very quickly while compacted clays and
 limestone-based soils erode more slowly.
 When a protruded portion 132 of the soil sample 128 has been pushed into
 the conduit 102, as described, the pump 104 is then actuated to flow water
 from the water supply 106 through the water flow conduit 102 and into the
 collection receptacle 110. Water is flowed by the pump 104 at a
 predetermined velocity v as measured by the flowmeter 114. An observer
 visually observes the protruded portion 132 of the soil sample 128 through
 the transparent viewing windows 118 and records the amount of time
 required for the protruded portion 132 of the soil sample 128 to erode,
 thus providing the measured rate of scour z for the sample 128 at that
 water velocity v.
 Following erosion, the soil sample 128 can then be advanced by the piston
 130 to project another protruded portion 132 into the conduit 102. Several
 successive tests are performed in this manner. The process is repeated for
 at least one hour and leads to an average erosion rate z for the velocity
 v.
 Next, erosion tests of this type are performed for a range of water flow
 velocities v varying between 0.1 meters per second to 6 meters per second,
 as this range of flow velocities should include the expected flow
 velocities for most bodies of water under natural conditions.
 Determination of Shear Stresses
 The inventors have recognized that the scour process is highly dependent on
 the shear stress .tau. developed by the flowing water at the soil-water
 interface. Indeed, at that interface the flow is tangential to the soil
 surface regardless of the flow condition above it because very little
 water, if any, flows perpendicular to the soil-water interface. If the
 water velocity v in the water 12 is in the range of 0.1 m/s to 3 m/s, the
 bed shear stress .tau. is in the range of 1 to 50 N/m.sup.2. The shear
 stress increases with the square of the water velocity v.
 Shear Stress in the Erosion Function Apparatus 100
 The pressure sensors 120, 122 upstream and downstream of the sample
 location provide the differential pressure .DELTA.p necessary to calculate
 the shear stress .tau. applied by the water. The following equation is
 used:
EQU .tau.=R/2.times..DELTA.p/l
 where R is the radius of the pipe and .DELTA.p/l is the pressure drop
 (.DELTA.p) per length (l) of pipe. Alternatively, the pressure drop can be
 calculated by using the Moody Chart (Moody, L. F., "Friction Factors for
 Pipe Flow," Transactions of the ASME, Vol. 66, 1944).
 A z vs. .tau. curve is then developed for different fluid flow rates or
 velocities v using data points obtained from testing the soil sample at
 various fluid flow velocities. Representative curves for coarse sand and
 porcelain clay are shown in FIGS. 3A and 3B, respectively.
 Maximum Shear Stress Around a Pier
 When an object obstructs the flow in an open channel with a flat bottom,
 the maximum shear stress .tau..sub.max is many times larger than the shear
 stress value when there in no obstruction. FIG. 4 shows an exemplary
 distribution of the value of the shear stress .tau. (expressed as a ratio
 of .tau. to .tau..sub.max) at various locations around a pier 10. Contours
 30 are provided which map the locations and provide boundaries for the
 locations of specific shear stress values.
 A cylindrical obstruction, representative of the shape of many bridge
 support structures, is used as an example here. However, it should be
 understood that the inventive methods are easily generalized to structures
 having other cross-sectional shapes.
 The maximum shear stress .tau..sub.max at bridge support 10 can be
 calculated based upon the size of the support 10 that is to be placed in
 the bed 14. For example, if the bridge support 10 is a cylindrical
 structure, and the bed 14 forms a substantially flat surface, the maximum
 shear stress .tau..sub.max is dependent upon the Reynold's number R.sub.e,
 the mean flow velocity V and the mass density p of the water 12. The
 following equation, developed using the Chimera-RANS numerical method, is
 used:
EQU .tau..sub.max =0.094 p V.sup.2 (1/logR.sub.e -1/10)
 where the Reynold's number R.sub.e is defined as VD/v where V is the mean
 flow velocity, D is the diameter of the bridge support 10, and v is the
 kinematic viscosity of the water 12 (10.sup.-6 m.sup.2 /s at 20.degree.
 C.). If this value of .tau..sub.max is larger than the critical shear
 stress .tau..sub.c that the soil can resist, scour is initiated. As the
 scour hole 18 deepens around the support 10, the shear stress .tau. at the
 bottom of the hole 18 decreases.
 Critical Shear Stress
 The critical shear stress .tau..sub.c is considered to be the shear stress
 .tau. that will generate a predetermined minimum scour rate. For example,
 the critical shear stress .tau. for soils tested using the erosion
 function apparatus 100 can be the shear stress which results in an erosion
 of 1 mm/hr (24 mm/day) of the tested soil sample.
 The initial scour rate z.sub.i is then read on the z versus .tau. curve,
 obtained as described earlier from the erosion function apparatus 100, at
 the value of .tau..sub.max. Thus, the initial scour rate z.sub.i is
 obtained that corresponds to .tau..sub.max. The initial scour rate z.sub.i
 is the rate at which portions of the river bed 14 will scour away when the
 bed 14 is essentially unscoured, and the bed 14 does not have any
 substantial scour hole, such as the hole 18 depicted in FIG. 1.
 A maximum depth of scour z.sub.max is then calculated. Using the results of
 flume tests, the inventors have developed the following equation:
EQU z.sub.max (in mm)=0.18 R.sub.e.sup.0.635
 where Re is the Reynold's number previously identified. The same flume
 experiments conducted by the inventors have determined that scour depth
 versus time for a particular soil type can be modeled as a hyperbola with
 the following equation:
 ##EQU1##
 where z.sub.i is the initial slope of the z versus t curve and z.sub.max is
 the ordinate of the asymptote. The parameter z.sub.max represents the
 final depth of scour at t=.infin.. Knowing z.sub.i from the erosion
 function apparatus curve and z.sub.max from the previous equation, the
 complete curve is given by the hyperbolic equation for the design problem
 considered. A similar approach can be taken for other types of scour.
 An exemplary curve-fitted hyperbola is depicted in FIG. 5, and provides an
 example. z.sub.max is used as the asymptotic value of the hyperbola. In
 this instance, z.sub.max is 179 mm. z.sub.i, which is the initial scour
 rate, determined previously, provides the value (here 2.5 mm/hr) for the
 initial slope of the hyperbola.
 The methods of the present invention permit the prediction and
 extrapolation of scour-related information for successive "flood events"
 wherein an expected water flow velocity is expected to occur for an
 expected period of time. Referring now to FIGS. 6A, 6B, 6C and 6D, such
 methods are illustrated. As FIG. 6A shows, flood event 1 has a velocity
 v.sub.1 and lasts for a defined length of time t.sub.1. Flood event 2 has
 a velocity v.sub.2 and lasts for a period of time t.sub.2.
 FIG. 6B shows the relationship of scour depth versus time for the velocity
 v.sub.1 caused by flood 1; while FIG. 6C shows the relationship of scour
 depth versus time for the velocity v.sub.2 caused by flood 2. FIG. 6B
 shows that after t.sub.1, a scour depth z.sub.1 is reached. This depth
 z.sub.1 would have been reached in an equivalent period of time t.sub.e
 (shown in FIG. 6C) if the bed 14 had been subjected to the velocity
 v.sub.2 instead of v.sub.1. Therefore, when flood event 2 begins, it is
 considered to be as if flood event 1 had not taken place and, instead,
 flood event 2 had been occurring for a time t.sub.e. The time t2 of flood
 event 2 is added to t.sub.e and the scour depth after both flood events is
 z.sub.2 corresponding to point C on FIG. 6C. The combined z versus t curve
 for the two flood events can be assembled as shown in FIG. 6D. More than
 two flood event curves may be combined in this manner. A large number of
 curves are best combined using a computer.
 There are often layers of different material found in the bed 14. For
 example, a bed of sand may overlie a layer of clay. A composite z versus
 .tau. curve can be developed by averaging the z versus .tau. curves from
 all the different materials found in the bed 14 within the scour depth Z.
 If the strength of the layers of material varies significantly, however, it
 may be necessary to perform a multilayer analysis. An example is explained
 with the aid of FIGS. 7A-7D. If the soil in the bed 14 is made up of a
 first layer 150, which is depicted graphically in FIG. 7C, and a second
 layer 152, that underlays the first layer 150. The first layer 150 is
 .DELTA.z.sub.1 thick, and the second layer 152 is .DELTA.z.sub.2 thick.
 Two separate scour depth (Z) versus time (t) curves, shown in FIGS. 7A and
 7B, are developed. The time t.sub.1 required to scour .DELTA.z.sub.1 is
 found from the chart for layer 150 (FIG. 7A). After the time t.sub.1, the
 scour depth versus time curve switched to the curve for layer 2. In FIG.
 7D, this occurs at point "A" on the combined curve shown.
 The calculations described herein may be performed by computer software, if
 desired, in order to eliminate the need for manual calculations.
 It should be understood that while the invention has been herein shown and
 described in what is presently believed to be the most practical and
 preferred embodiments thereof, it will be apparent to those skilled in the
 art that many modifications may be made to the invention described while
 remaining within the scope of the claims.