Devices and methods for determining particle size distribution by water pressure during sedimentation

Abstract

Methods and devices for determining particle size distribution (PSD) include introducing solid particles into a first end of a liquid-filled column. Fluid pressure is measured above a pressure port as the solid particles pass through the column to determine respective amounts of solid particles at the distinct times. A PSD is determined based in part on the respective amounts of solid particles above a pressure port at the distinct times and in part on a plurality of particle sizes based on respective settling velocities of the solid particles at the distinct times. The column has a height ≥ about 1 meter, a pressure port disposed in a wall of the column at a height above where the particles collect, a conduit in fluid communication with the pressure port that receives a portion of the liquid free of solid particles, and a pressure measuring component associated with the conduit.

Description

Attorney Docket No. 2115-008418-WO-POADEVICES AND METHODS FOR DETERMINING PARTICLE SIZE DISTRIBUTION BY WATER PRESSURE DURING SEDIMENTATIONGOVERNMENT SUPPORT

[0001] This invention was made with government support under 1825189 awarded by the National Science Foundation. The government has certain rights in the invention.CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of U.S. Provisional Application No. 63 / 683,293, filed on August 15, 2024. The entire disclosure of the above application is incorporated herein by reference.FIELD

[0003] The present disclosure relates methods and devices for determining a particle size distribution of a mixture of solid particles by pressure measurements of liquid in a column as the solid particles pass through.BACKGROUND

[0004] This section provides background information related to the present disclosure which is not necessarily prior art.

[0005] Determining particle sizes of solid particles is important in many industries. Mixtures of solid particles are typically poly disperse and have different sizes. A particle size distribution (PSD) is a common technique to characterize and compare such solid particle mixtures. Particle size distribution (PSD) serves as a fundamental soil index property in engineering, earth science and agriculture, among others. Every Civil Engineering construction project begins with a site characterization, which includes soil borings and soil sampling from various locations and depths below the surface. The collected specimens are taken to a laboratory for testing.

[0006] Thus, the first and most common test is one that determines the soil specimens’ particle size distributions (PSD). For example, the PSD is essential for soil classification which in turn is the starting point for all geotechnical engineering design. For sands, it is determined in thousands of soil testing laboratories throughout the world using a standard sieve test. By way of example, ASTM International Standard C136-C136M-19 “ Standard Test Method for Sieve Analysis of Fine and Coarse Aggregates” may be conducted to determine particle size distribution.Attorney Docket No. 2115-008418-WO-POAMore specifically, a series of sieves with different sized openings are stacked on one another onto which a sample is placed, followed by inserting it into a sieve shaker to determine particle size distribution of gravel and sand samples as they fall through the series of sieves. Each sieve with a distinct opening size provides a data point for grain size, for example, percent passing (or percent finer) versus percent retained (or percent coarser). The particle size distribution by ASTM Cl 36- C136M-19 test typically provides six to eight standard sieve sizes or data points, which are then fitted into a curve. The determination of particle size distribution (PSD) of sands has remained staunchly reliant on sieve analysis.

[0007] Other tests include hydrometer testing used for solid particles of fine sizes, like silt and clay, by employing a tool to measure the density or specific gravity of a liquid when compared to water by using a calibrated glass tube with a scale, and employing Stokes’ Law. However, hydrometer testing only works for very small solid particles and further is based on the assumption that the particles are spherical. However, this assumption does not work for sand particles. Besides, the falling velocity of sand particles can be orders of magnitude higher than that of silt and clay. It would be desirable to provide new techniques and devices that rapidly characterize particle size distribution of complex mixtures with larger particles, like sand, without requiring the need for cumbersome and costly sieve shaking tests in a laboratory.SUMMARY

[0008] This section provides a general summary of the disclosure, and is not a comprehensive disclosure of its full scope or all of its features.

[0009] In certain aspects the present disclosure relates to a device for determining a particle size distribution of a mixture of solid particles. The device may comprise a column for containing a liquid having a height of greater than or equal to about 1 meter. The column has a first end that is open for receiving the liquid and a sample of solid particles and a second end that is sealed. The device further comprises a pressure port disposed in a wall of the column disposed at a height above where the particles collect at the second end of the column. A conduit is in fluid communication with the pressure port that receives a portion of the liquid in the column free of the solid particles. The device further comprises a pressure measuring component associated with the conduit that provides a plurality of pressure measurements of the liquid at the pressure port for a duration that solid particles pass through the column from the first end to the second end to determine respective amounts of solid particles above the pressure port at distinct times. A particle size distribution of the solid particles may be determined in part by the respective amounts of solidAttorney Docket No. 2115-008418-WO-POA particles in the column above the pressure port at the distinct times and in part by a plurality of respective calculated settling velocities of the solid particles at the distinct times.

[0010] In one aspect, the column is a cylindrical column that is transmissive to light having wavelengths in the visible region.

[0011] In one aspect, the column has a diameter of greater than or equal to about 25 mm and the height is greater than or equal to about 1.5 meters to less than or equal to about 2 meters. Further a particle size of the solid particles is greater than or equal to about 0.075 mm to less than or equal to about 4.75 mm.

[0012] In one aspect, the conduit comprises a first region that defines an angle with respect to the column so that the first region of the conduit connects to the pressure port and is graded to a first elevation above the pressure port.

[0013] In one further aspect, the angle is less than or equal to about 30° from vertical corresponding to the column.

[0014] In one aspect, the pressure port is disposed greater than or equal to about 16 cm above the second end of the column.

[0015] In one aspect, the pressure measuring component is a pressure transducer configured to take continuous pressure measurements of the liquid.

[0016] In one further aspect, the pressure transducer is configured to measure a pressure of the liquid at greater than 0 kPa to less than or equal to about 30 kPa.

[0017] In one aspect, the device further comprises a processor in electrical communication with the pressure measuring component. The processor is configured to receive and record the plurality of pressure measurements from the pressure measuring component.

[0018] In one further aspect, the processor is configured to calculate the plurality of respective calculated settling velocities (v) of the solid particles passing the pressure port on the column at any given time during the settling process by using a settling distance divided by a settling time.

[0019] In one further aspect, the processor is programmed to determine a plurality of particle sizes from previously determined settling velocities (v) by using settling velocity models, such as, but not limited to, the model provided by Jimenez, J. A., and Madsen, O. S. “A simple formula to estimate settling velocity of natural sediments J. Waterw. Port Coastal Ocean Eng. 129 (2): pp. 70-78 (2003), https: / / doi.org / 10.1061 / (ASCE) 0733-950X (2003) 129:2(70)):Attorney Docket No. 2115-008418-WO-POA where Gsis specific gravity of the solid particles, g is an acceleration constant due to gravity, (IN is a nominal particle diameter of a respective solid particles, fl is kinematic viscosity of the liquid, AJM is a first dimensionless coefficient based on a shape and roundness of the solid particles, BJM is a second dimensionless coefficient based on a shape and roundness of the solid particles.

[0020] In one further aspect, the plurality of pressure measurements of the liquid include a first pressure ( / / ’’) measurement taken where the liquid is at a first height ( / zi) between the pressure port and an upper boundary of the liquid in the column; a second pressuremeasurement taken where the liquid is at a second height (fe) between the pressure port and the upper boundary of the fluid (e.g., liquid) in the column; and the processor is programmed to determine a unit weight (yy) of the liquid in the column by

[0021] In one aspect, the plurality of pressure measurements of the liquid include a third pressure (uF) measurement taken before the solid particles pass the pressure port and a fifth pressure measurementafter all the solid particles have passed the pressure port and are collected at the second end, wherein the processor further determines specific gravity (Gs) of the unit weight of water at 4 °C.

[0022] In one further aspect, the processor further determines a total weight of solid particles whereAcis an inside cross-sectional area of the column and ywis a unit weight of water at 4 °C.

[0023] In one aspect, the column comprises an assembly of multiple segments reversibly coupled together.

[0024] In one aspect, the conduit comprises at least one quick connector to reversibly couple with the pressure measuring component.

[0025] In certain aspects, the present disclosure further relates to a method of determining a particle size distribution of a mixture of solid particles. The method optionally comprises introducing a sample of solid particles into a first end of a column containing a liquid to sort the solid particles by particle size. The method also comprises measuring pressure of the liquid at distinct times as the solid particles pass through the column from the first end to a second end to determine respective amounts of solid particles above the pressure port at the distinct times. The method further comprises determining a particle size distribution of the solid particles based on the respective amounts of solid particles above the pressure port at the distinct times and further based on calculating a plurality of settling velocities of the solid particles corresponding to the distinct times.Attorney Docket No. 2115-008418-WO-POA

[0026] In one aspect, the method further comprises measuring pressure of the liquid prior to the introducing of the sample.

[0027] In one aspect, the measuring the pressure of the liquid includes measuring a pressure after the solid particles collect at the second end of the column.

[0028] In one aspect, the measuring pressure of the liquid occurs by using a pressure transducer continuously taking measurements.

[0029] In one aspect, the column further comprises a pressure port disposed in a wall of the column disposed at a height above where the solid particles collect at the second end of the column. A conduit is provided in fluid communication with the pressure port that receives a portion of the liquid in the column free of the solid particles. Further, a pressure measuring component is associated with the conduit that conducts the measuring pressure of the liquid at distinct times as the solid particles pass through the column from the first end to a second end.

[0030] In one aspect, prior to the introducing the sample of solid particles, the method further comprises introducing a first portion of the liquid into the column as a first height ( / zi) where the liquid fills the column to above the pressure port, measuring a first pressure ( / / ’’) of the liquid at the first height ( / zi). The method further comprises introducing a second portion of the liquid into the column at a second height (fe) above the first height ( / zi) and measuring a second pressure of the liquid at the second height (fe). Further, the method includes determining aunit weight (yy) of the liquid in the column by .

[0031] In one aspect, the measuring pressure of the liquid at distinct times includes measuring a third pressure ( / / ) before the solid particles pass the pressure port.

[0032] In one aspect, the measuring pressure of the liquid at distinct times includes measuring a fifth pressureafter all the solid particles have passed the pressure port and are collected at the second end.

[0033] In one aspect, the method further comprises determining specific gravity (Gs) of unit weight of water at 4 °C.

[0034] In one aspect, the method further comprises determining a total weight of solid particles (Ws) of the solid particles by Wswhere Acis an inside cross-sectional area of the column and ywis a unit weight of water at 4 °C.

[0035] In one aspect, the determining the particle size distribution includes calculating a plurality of particle sizes by using settling velocity models. The method optionally further comprises determining particle sizes of the solid particles from the plurality of settling velocitiesAttorney Docket No. 2115-008418-WO-POA(v) by using settling velocity models, such as, but not limited to, the Jimenez and Madsen model (2003):where Gsis specific gravity of the solid particles, g is an acceleration constant due to gravity, dN is a nominal particle diameter of a respective solid particles, fl is kinematic viscosity of the liquid, AJM is a first dimensionless coefficient based on a shape and roundness of the solid particles, BJM is a second dimensionless coefficient based on a shape and roundness of the solid particles.

[0036] In one aspect, the measuring pressure of the liquid at distinct times includes measuring the pressure as the solid particles pass the pressure port to provide a plurality of fourth pressures (MG).

[0037] In one aspect, the pressure measuring component associated with the conduit is a pressure transducer that measures the pressure of the liquid in the column at distinct times.

[0038] Further areas of applicability will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.DRAWINGS

[0039] The drawings described herein are for illustrative purposes only of selected embodiments and not all possible implementations, and are not intended to limit the scope of the present disclosure.

[0040] FIG. 1 shows a side view of a system / device for determining a particle size distribution of a mixture of solid particles according to certain aspects of the present disclosure, including a sedimentation column and a pressure measuring component in the form of a pressure transducer.

[0041] FIGS. 2A-2C show a specific embodiment of system / device for determining a particle size distribution of a mixture of solid particles (“u-Sed” system) according to certain aspects of the present disclosure, including a sedimentation column and a pressure measuring component in the form of a pressure transducer. FIG. 2A shows a lower region of a sedimentation column and a pressure transducer during a test. FIG. 2B shows a close-up view of a pressure port and a push-to-connect fitting. FIG. 2C shows a close-up view of a base and pedestal for supporting the column.

[0042] FIG. 3 shows pressure stages A-H during tests to determine a particle size distribution of a mixture of solid particles (“u-Sed” system) according to certain aspects of theAttorney Docket No. 2115-008418-WO-POA present disclosure. The upper portion of FIG. 3 illustrates ten moments in time of a water column, before, during and after sedimentation of the soil particles through a water column. The lower portion of FIG. 3 shows a pressure time history (pressure “w” versus time (“t”)) corresponding to the time sequence in the upper portion.

[0043] FIG. 4 shows typical pressure time histories for fine (FS), medium (MS), coarse (C), and gap-graded sands (G) during Stages F-H in FIG. 3.

[0044] FIG. 5 shows turbulent and laminar flow coefficients for Ahrens’ model (based on Ahrens, 2000), as will be further described below.

[0045] FIGS. 6A-6B show how to determine AJM (FIG. 6A) and BJM (FIG. 6B) coefficients based on the Jimenez and Madsen 2003 model.

[0046] FIG. 7 shows images of sixteen (16) soil specimens with their percentages of coarse, medium and fine sand tested in accordance with certain aspects of the present disclosure.

[0047] FIGS. 8A-8C show comparisons of particle size distributions for particle mixtures including coarse, medium, and fine sands determined by a sieve test and as determined by using systems according to the present disclosure calculated by either Ahren’s model or Jimenez and Madsen’s model. FIG. 8A shows samples 1 to 3, FIG. 8B shows samples 4 to 6, and FIG. 8C shows samples 7 and 8.

[0048] FIGS. 9A-9C show comparisons of particle size distributions for particle mixtures including uniform coarse, uniform medium, and uniform fine sands determined by a sieve test and as determined by using systems according to the present disclosure calculated by either Ahren’s model or Jimenez and Madsen’s model. FIG. 9A shows samples 9 to 11, FIG. 9B shows samples 12 to 14, and FIG. 9C shows samples 15 and 16.

[0049] Corresponding reference numerals indicate corresponding parts throughout the several views of the drawings.DETAILED DESCRIPTION

[0050] Example embodiments are provided so that this disclosure will be thorough, and will fully convey the scope to those who are skilled in the art. Numerous specific details are set forth such as examples of specific compositions, components, devices, and methods, to provide a thorough understanding of embodiments of the present disclosure. It will be apparent to those skilled in the art that specific details need not be employed, that example embodiments may be embodied in many different forms and that neither should be construed to limit the scope of the disclosure. In some example embodiments, well-known processes, well-known device structures, and well-known technologies are not described in detail.Attorney Docket No. 2115-008418-WO-POA

[0051] The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting. As used herein, the singular forms “a,” “an,” and “the” may be intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms “comprises,” “comprising,” “including,” and “having,” are inclusive and therefore specify the presence of stated features, elements, compositions, steps, integers, operations, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. Although the open-ended term “comprising,” is to be understood as a non-restrictive term used to describe and claim various embodiments set forth herein, in certain aspects, the term may alternatively be understood to instead be a more limiting and restrictive term, such as “consisting of’ or “consisting essentially of.” Thus, for any given embodiment reciting compositions, materials, components, elements, features, integers, operations, and / or process steps, the present disclosure also specifically includes embodiments consisting of, or consisting essentially of, such recited compositions, materials, components, elements, features, integers, operations, and / or process steps. In the case of “consisting of,” the alternative embodiment excludes any additional compositions, materials, components, elements, features, integers, operations, and / or process steps, while in the case of “consisting essentially of,” any additional compositions, materials, components, elements, features, integers, operations, and / or process steps that materially affect the basic and novel characteristics are excluded from such an embodiment, but any compositions, materials, components, elements, features, integers, operations, and / or process steps that do not materially affect the basic and novel characteristics can be included in the embodiment.

[0052] Any method steps, processes, and operations described herein are not to be construed as necessarily requiring their performance in the particular order discussed or illustrated, unless specifically identified as an order of performance. It is also to be understood that additional or alternative steps may be employed, unless otherwise indicated.

[0053] When a component, element, or layer is referred to as being “on,” “engaged to,” “connected to,” or “coupled to” another element or layer, it may be directly on, engaged, connected or coupled to the other component, element, or layer, or intervening elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly engaged to,” “directly connected to,” or “directly coupled to” another element or layer, there may be no intervening elements or layers present. Other words used to describe the relationship between elements should be interpreted in a like fashion (e.g., “between” versus “directly between,” “adjacent” versus “directly adjacent,” etc.). As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items.Attorney Docket No. 2115-008418-WO-POA

[0054] Although the terms first, second, third, etc. may be used herein to describe various steps, elements, components, regions, layers and / or sections, these steps, elements, components, regions, layers and / or sections should not be limited by these terms, unless otherwise indicated. These terms may be only used to distinguish one step, element, component, region, layer or section from another step, element, component, region, layer or section. Terms such as “first,” “second,” and other numerical terms when used herein do not imply a sequence or order unless clearly indicated by the context. Thus, a first step, element, component, region, layer or section discussed below could be termed a second step, element, component, region, layer or section without departing from the teachings of the example embodiments.

[0055] Spatially or temporally relative terms, such as “before,” “after,” “inner,” “outer,” “beneath,” “below,” “lower,” “above,” “upper,” and the like, may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. Spatially or temporally relative terms may be intended to encompass different orientations of the device or system in use or operation in addition to the orientation depicted in the figures.

[0056] In this application, the term “processor,” “module” or the term “controller” may be replaced with the term “circuit.” The term “module” may refer to, be part of, or include: an Application Specific Integrated Circuit (ASIC); a digital, analog, or mixed analog / digital discrete circuit; a digital, analog, or mixed analog / digital integrated circuit; a combinational logic circuit; a field programmable gate array (FPGA); a processor circuit (shared, dedicated, or group) that executes code; a memory circuit (shared, dedicated, or group) that stores code executed by the processor circuit; other suitable hardware components that provide the described functionality; or a combination of some or all of the above, such as in a system-on-chip.

[0057] The module may include one or more interface circuits. In some examples, the interface circuits may include wired or wireless interfaces that are connected to a local area network (LAN), the Internet, a wide area network (WAN), or combinations thereof. The functionality of any given module of the present disclosure may be distributed among multiple modules that are connected via interface circuits. For example, multiple modules may allow load balancing. In a further example, a server (also known as remote, or cloud) module may accomplish some functionality on behalf of a client module.

[0058] The term code, as used above, may include software, firmware, and / or microcode, and may refer to programs, routines, functions, classes, data structures, and / or objects. The term shared processor circuit encompasses a single processor circuit that executes some or all code from multiple modules. The term group processor circuit encompasses a processor circuit that, inAttorney Docket No. 2115-008418-WO-POA combination with additional processor circuits, executes some or all code from one or more modules. References to multiple processor circuits encompass multiple processor circuits on discrete dies, multiple processor circuits on a single die, multiple cores of a single processor circuit, multiple threads of a single processor circuit, or a combination of the above. The term shared memory circuit encompasses a single memory circuit that stores some or all code from multiple modules. The term group memory circuit encompasses a memory circuit that, in combination with additional memories, stores some or all code from one or more modules.

[0059] The term memory circuit is a subset of the term computer-readable medium. The term computer-readable medium, as used herein, does not encompass transitory electrical or electromagnetic signals propagating through a medium (such as on a carrier wave); the term computer-readable medium may therefore be considered tangible and non-transitory. Nonlimiting examples of a non-transitory, tangible computer-readable medium are nonvolatile memory circuits (such as a flash memory circuit, an erasable programmable read-only memory circuit, or a mask read-only memory circuit), volatile memory circuits (such as a static random access memory circuit or a dynamic random access memory circuit), magnetic storage media (such as an analog or digital magnetic tape or a hard disk drive), and optical storage media (such as a CD, a DVD, or a Blu-ray Disc).

[0060] The apparatuses and methods described in this application may be partially or fully implemented by a special purpose computer created by configuring a general purpose computer to execute one or more particular functions embodied in computer programs. Any functional blocks, flowchart components, and other elements described above serve as software specifications, which can be translated into the computer programs by the routine work of a skilled technician or programmer.

[0061] The computer programs include processor-executable instructions that are stored on at least one non-transitory, tangible computer-readable medium. The computer programs may also include or rely on stored data. The computer programs may encompass a basic input / output system (BIOS) that interacts with hardware of the special purpose computer, device drivers that interact with particular devices of the special purpose computer, one or more operating systems, user applications, background services, background applications, etc.

[0062] The computer programs may include: (i) descriptive text to be parsed, such as HTML (hypertext markup language), XML (extensible markup language), or JSON (JavaScript Object Notation) (ii) assembly code, (iii) object code generated from source code by a compiler, (iv) source code for execution by an interpreter, (v) source code for compilation and execution by a just-in-time compiler, etc. As examples only, source code may be written using syntax fromAttorney Docket No. 2115-008418-WO-POA languages including C, C++, C#, Objective-C, Swift, Haskell, Go, SQL, R, Lisp, Java®, Fortran, Perl, Pascal, Curl, OCaml, Javascript®, HTML5 (Hypertext Markup Language 5th revision), Ada, ASP (Active Server Pages), PHP (PHP: Hypertext Preprocessor), Scala, Eiffel, Smalltalk, Erlang, Ruby, Flash®, Visual Basic®, Lua, MATLAB, SIMULINK, and Python®.

[0063] None of the elements recited in the claims are intended to be a means-plus-function element within the meaning of 35 U.S.C. § 112(f) unless an element is expressly recited using the phrase “means for,” or in the case of a method claim using the phrases “operation for” or “step for.”

[0064] Throughout this disclosure, the numerical values represent approximate measures or limits to ranges to encompass minor deviations from the given values and embodiments having about the value mentioned as well as those having exactly the value mentioned. Other than in the working examples provided at the end of the detailed description, all numerical values of parameters (e.g., of quantities or conditions) in this specification, including the appended claims, are to be understood as being modified in all instances by the term “about” whether or not “about” actually appears before the numerical value. “About” indicates that the stated numerical value allows some slight imprecision (with some approach to exactness in the value; approximately or reasonably close to the value; nearly). If the imprecision provided by “about” is not otherwise understood in the art with this ordinary meaning, then “about” as used herein indicates at least variations that may arise from ordinary methods of measuring and using such parameters. For example, “about” may comprise a variation of less than or equal to 5%, optionally less than or equal to 4%, optionally less than or equal to 3%, optionally less than or equal to 2%, optionally less than or equal to 1%, optionally less than or equal to 0.5%, and in certain aspects, optionally less than or equal to 0.1%.

[0065] In addition, disclosure of ranges includes disclosure of all values and further divided ranges within the entire range, including endpoints and sub-ranges given for the ranges.

[0066] The disclosure of all patents, patent applications, articles, and literature referenced or cited in this disclosure are hereby incorporated by reference herein.

[0067] Example embodiments will now be described more fully with reference to the accompanying drawings.

[0068] The present disclosure contemplates methods and devices for determining a particle size distribution of a mixture of solid particles where multiple pressure measurements of liquid in a column are taken as the solid particles pass through. In this manner, the pressure measurements from the devices of the present teachings can be used to create highly accurate particle size distributions for mixtures comprising solid particles without any need for traditionalAttorney Docket No. 2115-008418-WO-POA sieving tests. The devices provided by certain aspects of the present disclosure will also be referred to interchangeably herein as “u-Sed,” where u is a traditional notation for water pressure and Sed refers to sedimentation (or settling rates). The u-Scd test and device can thus eliminate the need to do any sieving of samples of solid particles, especially those considered sands. In various aspects, the present disclosure contemplates analyzing mixtures of solid particles, which includes a plurality of particles that may have a range of distinct particle sizes (e.g., average particle diameters), including those having a minimum particle size of greater than or equal to about 0.075 mm and a maximum average particle size of less than or equal to about 4.75 mm, which are typically classified as sands. For example, ASTM-defined sands may have a particle size of greater than or equal to about 0.075 mm to less than or equal to about 4.75 mm. Thus, the methods and devices described herein pertain to determining a particle size distribution of a mixture of solid particles classified as sand and having a minimum particle size of greater than or equal to about 0.075 mm and a maximum particle size less than or equal to about 4.75 mm, in certain aspects.

[0069] The methods of the present disclosure take considerably less time to perform than a traditional sieve test. Further, the devices of the present disclosure require less and smaller equipment, which advantageously occupies a small footprint. Unlike the sieve test which typically provides only 6 to 8 data points, in certain variations, the methods of the present disclosure can generate a continuous or near-continuous PSD curve. Unlike sieves, there is nothing to clean, store or maintain. Further, the systems provided by the present disclosure are portable and can be taken on-site. The devices have no moving parts, make no noise or dust, and consume considerably less energy than sieving.

[0070] In certain aspects, the present disclosure provides a device 50 for conducting such methods and thus for determining a particle size distribution of a mixture of solid particles or (“w- Sed” device), for example, as shown in FIG. 1. The device 50 includes a vessel for holding liquid 52, such as a column 54. The column 54 may have a major axis (longitudinal axis) that is vertically oriented with a circular cross-section and thus cylindrical shape. The wall 56 of the column 54 thus defines an open volume. The column 54 has a first end 60 with an opening 62 that serves as an inlet to the column 54. The opening 62 may receive a liquid 52 within the open volume defined by the column 54, as well as a sample of the solid particles (not shown) to be analyzed for determining a particle size distribution. In this manner, the column 54 serves as a sedimentation column through which the particles may fall at different settling velocities, as described further herein. Notably, an optional funnel 58 or other similar device may be used to feed a sample of solid particles into the opening 62 at the first end 60 of the column 54. The column 54 includes a second end 70 opposite to the first end that is sealed and fluid-tight. By way of example, one orAttorney Docket No. 2115-008418-WO-POA more gaskets or O-ring seals 72 may be used within a pedestal 74 that seats on a base 76. The column 54 may be a single unitary component (as shown) or may comprise an assembly of multiple segments reversibly coupled together, which may facilitate portability.

[0071] The column includes an aperture that serves as a pressure port 78 disposed in the wall 56 of the column 54 disposed at a port height (designated “ / ?o”) above pedestal 74 above which a lower region 80 of the column 54 is defined where the particles will collect to a maximum collection height (designated “ / ?c”) at the second end 70 of the column 54. In certain aspects, the pressure port 78 is disposed so that the port height (ho) is greater than or equal to about 16 cm above the terminal / second end 70 of the column 54. A conduit 82 in fluid communication with the pressure port 78 is configured to receive a portion of the liquid 52 in the column 54. The liquid 52 that enters the conduit 82 is free of any solid particles. The conduit 82 comprises an angled first region 84 that defines an angle (ff) with respect to the major longitudinal axis (corresponding to wall 56) of column 54, so that the first region 84 of the conduit 82 connects to the pressure port 78 and is graded so that it rises on an incline to a second elevation (designated “ha that is greater than a first elevation (designated “ / zci”) of the pressure port 78. For example, the angle (ff) may be less than or equal to about 30° from vertical (corresponding to the wall 56 / major longitudinal axis) of column 54. Such an angle (ff) serves to prevent the solid particles from flowing into the angled first region 84 of the conduit and thus only liquid flows therein. Other alternative components, such as filters, may instead be used to prevent the solid particles from entering the conduit 82 with liquid 52.

[0072] A lateral second region 86 of the conduit 82 may terminate in a quick connector 88, for example, push-to-connect fitting. Another conduit, such as flexible tubing 90, may connect to the quick connector 88 and a pressure measuring component. As shown in FIG. 1, the pressure measuring component is a pressure transducer 92 that can intermittently or continuously monitor a pressure of the liquid in conduit 82. The pressure of the liquid 52 in the conduit 82 reflects corresponding pressure of the liquid 52 at the pressure port 78. As will be described further herein, the pressure measuring component associated with the conduit 82 provides a plurality of pressure measurements of the liquid 52, including providing pressure measurements for at least a portion of the duration that solid particles pass through the column 54 from the first end 60 to the second end 70 to determine a particle size distribution of the solid particles based on diameters of the particles passing the pressure port and the percentage of particles above the pressure port (finer than the particles passing through the pressure port). In certain variations, the pressure transducer 92 is configured to take continuous pressure measurements of the liquid 52, for example, as the solid particles are passing by the pressure port 78. In certain aspects, the pressure transducer 92 isAttorney Docket No. 2115-008418-WO-POA configured to measure a pressure of the liquid at greater than 0 kPa to less than or equal to about 30 kPa. Notably, in this embodiment, the fluid transmits pressure through the pressure port 78 and into the conduit 82, which is measured, but negligible flow occurs into or from the pressure port 78 or conduit 82.

[0073] During the entire process in which solid particles travel from the first end of the column to the second end, the particles are sorted by size, with larger ones settling faster, followed by finer ones. These pressure measurements are collected to determine the weight of solid particles still above the pressure port, and, combined with settling velocity models described further below, determine the sizes of particles passing the pressure port according to their settling velocities, thereby obtaining a particle size distribution of the solid particles.

[0074] The pressure measurements taken by the pressure transducer 92 can thus provide information about a first portion or percentage by weight of the sample of the solid particles above the pressure port 78 and a second portion or percentage by weight of the sample that is below the pressure port 78. As distance is known as to how far the solid particles travel in the column 54, the settling velocity of whatever particles are at the pressure port 78 at any given time can be determined. As described further below, certain equations can be used to determine a particle size at the pressure port 78 at a given point in time that corresponds to a particle settling velocity.

[0075] In certain aspects, the column 54 is formed of a clear or translucent material, for example having a high level of transmissivity (e.g., greater than or equal to about 75%) to light having wavelengths in the visible region. By way of non-limiting example, the column 54 may be formed of a clear plastic, such as an acrylic, glass, or the like. In this manner, after the particles have collected in the lower region 80 following processing in the column 54 to determine a particle size distribution, the solid particles can be further observed, characterized, and / or analyzed, for example, by image analysis systems.

[0076] A major longitudinal axis or height of the column 54 may be greater than or equal to about 1 meter (about 3.3 feet), optionally greater than or equal to about 1.5 meters (about 5 feet), and in certain aspects, optionally greater than or equal to about 1.8 meters (about 6 feet). As discussed above, the sample of solid particles is introduced into the opening 62 at the first end 70 of the column and thus fall through the liquid 52 at different rates or velocities depending on particle size and density. Thus, a height of the column 54 is advantageously high enough so that the particles can establish respective terminal settling velocities and / or sort by size before passing the pressure port 78 at different points in time. Thus, depending on a maximum particle size of the particles in the sample, the height of column 54 may be greater than about 1.8 meters to 2 meters, if the maximum particle size is greater than a sand classification that has a maximumAttorney Docket No. 2115-008418-WO-POA diameter of about 4.75 mm, to permit an adequate distance for the particles to fall. Stated in another way, the height of the sedimentation column 54 is sized to ensure that the particles in the solid sample have sorted themselves by size by the time they pass an elevation corresponding to the pressure port 78.

[0077] In certain aspects, the column 54 may have a height of greater than or equal to about 1.5 meters to less than or equal to about 2 meters, wherein a maximum particle size of the solid particles is less than or equal to about 4.75 mm and a minimum particle size of the solid particles is greater than or equal to about 0.075 mm. Further, in certain aspects, the column 54 has a diameter greater than or equal to about 25 mm when the mixture of particles introduced to the first end / top of the column has a mass in excess of 50 grams. Again, a diameter of the column 54 may be enlarged to accommodate a larger sample size of solid particles, as necessary.

[0078] In various aspects, while not shown, the device 50 may be part of a system that furthers include a processor in electrical communication with the pressure measuring component 92. For example, the processor may be a computer processing unit (CPU) that may be operated or programmed with various modules, as appreciated by those of skill in the art. The processor is configured to receive and record a plurality of pressure measurements taken by the pressure measurement component 92 and may include continuous pressure measurements. For example, the pressure measurements are collected or recorded by the processor and can be used to determine a weight or mass of solid particles still above the pressure port elevation where the pressure readings are taken, for example, at a plurality of distinct times. The processor is optionally further configured to calculate the plurality of respective settling velocities of the solid particles based on the settling distance at the same respective distinct times. Thus, the processor may determine a particle size distribution of the solid particles by determining the respective amounts of solid particles above the pressure port at the distinct times based on the plurality of pressure measurements and further by the plurality of respective calculated settling velocities of the solid particles at the distinct times, as will be described further herein. Thus, an overall system for determining a particle size distribution including device 50 may be an automated system.

[0079] FIGS. 2A-2C show a specific design of a particle size distribution system / device (“u-Sed”) according to certain aspects of the present disclosure. The u-Sed system / device includes a sedimentation column and a pressure transducer, as shown in FIG. 2A. The sedimentation column is formed of clear acrylic and measures 1.8 m (6 ft) in height, with an opening diameter of 25.4 mm (1 inch) and having a wall thickness of 3.2 mm (1 / 8 inch). The base of the column sits on a detachable acrylic base and pedestal with two O-rings to ensure water / fluid tightness.Attorney Docket No. 2115-008418-WO-POA

[0080] A pressure port is located 16 cm above the pedestal that connects to the pressure transducer. The pressure port inlet is angled at 30° from vertical to prevent the falling particles from entering a tube that connects to the pressure transducer. The elevation of the pressure port ensures that it remains above the top of the fully settled soil specimen. Typically, a 50 g soil specimen would settle to approximately an 8 cm height, but to provide an extra margin, the port may be located 16 cm above the top of the pedestal.

[0081] The pressure transducer’s measurement range is 0 to 30 kPa with an accuracy of ±0.005 kPa. Its housing has a small vent hole to expel trapped air from the tubing and transducer chamber. Connection to the pressure port is via a 9.53 mm (3 / 8 inch) diameter plastic tube and a push-to-connect fitting affixed to the pressure port.

[0082] Thus, in this embodiment, a pressure transducer records liquid / water pressure, u, during sedimentation in a sedimentation column, where the pressure transducer essentially acts as a scale to measure the mass or weight of soil particles (solids) above the pressure port elevation with time while the particles, having been sorted by size while settling, travel past the pressure port. Thus, the device that includes the pressure transducer may provide information on what percentage (%) of the solid sample / specimen is above the pressure port at any instant in time. In this manner, the amounts of solid particles above the pressure port may be determined for various distinct times. As described above, the determination of the size of particles at the port elevation occurs by utilizing the relationships between individual particle sizes and their settling velocities in fluids. This u-Scd variation has many advantages over the traditional particle size distribution technique of sieving, including simple low-cost portable hardware that has a relatively small laboratory footprint and requires minimal maintenance; much shorter test durations than by sieving, data collection at high sampling rates that yield continuous PSD curves, and a noiseless, dust-free testing environment. Most importantly, tests on sands of various geologic origins and gradations demonstrated that the PSDs by the u-Scd test are virtually the same as obtained by sieving.

[0083] Various embodiments of the inventive technology can be further understood by the specific examples contained herein. Specific Examples are provided for illustrative purposes of how to make and use the compositions, devices, and methods according to the present teachings.

[0084] ExampleSixteen tests on a wide range of sands were performed to evaluate the u-Scd test. The soils came from various geologic or artificial origins, some were highly uniform in size, others were well-graded, and a couple were gap-graded (having discrete particle sizes). Most of the specimens were natural sands, one was a crushed material and three were coarse-grained sands usedAttorney Docket No. 2115-008418-WO-POA commercially for aquariums. As will be described further herein, the test results provided by the systems and methods of certain aspects of the present disclosure match results by sieve tests exceptionally well for all sixteen specimens.

[0085] First, pressure time histories are conducted as shown in FIG. 3. The upper portion of FIG. 3 illustrates ten moments in time of a water column, before, during and after sedimentation of the soil particles through a water column. The lower portion of FIG. 3 shows a pressure time history corresponding to the time sequence in the upper portion, including Stages A-H. During Stage A, water is being introduced into the column and the pressure rises accordingly. The water level is brought to water level #1 at a height hi above the pressure port. It is held there for a few seconds in Stage B to record the pressure, uB. During Stage C, water is raised to water level #2 at a height of hi above the port and held there during Stage D for a second pressure reading, uD. The unit weight of the fluid in the sedimentation column, yf is computed by:

[0086] In Stage E, the sample of soil particles are introduced into the column as quickly as possible, so that they all have about the same starting sedimentation time. The rapid introduction of the soil into the column causes a steep rise in pressure to the level shown by Stage F. During Stage F, the particles are sorting while settling through the liquid in the column, but none have yet arrived at the pressure port elevation so the pressure remains constant at uF. In Stage G, the particles are passing the port so the pressure diminishes accordingly with time. Finally, at Stage H, all the particles have travelled past the pressure port and settled at the bottom of the column, thus the pressure is once again constant, this time at uH. The final pressure during Stage H is slightly higher than during Stage D, because the water level has risen due to upward displacement of the fluid by the solid particles.

[0087] Thus, the specific gravity of the solids, Gs, can be calculated as follows by the derived equation:where ywis 9.807 kN / m3, which is the unit weight of water at 4 °C.

[0088] The difference in pressure between Stages F and H reflects the total weight of solids which is computed by derived Equation (3):where Acis the inside cross-sectional area of the sedimentation column. It follows from Eq. (3) that the weight of solids still above the pressure port at any time during Stage G is:Attorney Docket No. 2115-008418-WO-POA

[0089] The ratio of Eq. (4) to Eq. (3) is the fraction of specimen solids still above the pressure port at any time during Stage G:

[0090] Because of particle sorting over the settling distance, at any pressure uGthe percent by weight of particles that are finer than the particle at the port elevation at that moment is given by Eq. (5) x 100%. Equation (5) reveals that Wsis not needed to develop the PSD. However, if the specimen weight is obtained using a laboratory scale prior to sedimentation, a comparison to the computed value of Wsby Eq. (3) serves as a check on the quality of the pressure recording. While knowledge of Wsis optional, in certain variations, the values of y and Gsas computed by Eqs. (1) and (2) respectively will be used by the particle settling velocity models employed to calculate particle size distribution.

[0091] As shown in FIG. 2A, the pressure transducer sits at a lower elevation than the pressure port. Therefore, it will record a pressure higher than at the port. However, Eqs. (1) to (5) utilize only differences in pressures during the various test stages. Therefore, the difference in elevations between the pressure transducer and the port is arbitrary and has no effect on the results; however, the elevation should remain fixed during the period of any single test.

[0092] FIG. 4 contains actual recorded pressure time histories for fine, medium, coarse and gap-graded sands. Only Stages F, G and H are shown in FIG. 4. It is no coincidence that the pressure time histories resemble traditional particle size distribution curves. The remaining task is to convert the time axis to particle sizes, by using the models described further below.

[0093] In accordance with the present disclosure, various models for calculating sedimentation rates and / or settling velocities may be used, as appreciated by those of skill in the art. The models of Ahrens (2000), Jimenez and Madsen (2003), or both models are adopted for the u-Scd test according to certain aspects of the present disclosure. It should be noted that these models had previously been confined to characterizing sedimentation rates, but none had been considered for the current application as a model to develop particle size distribution (PSDs) of soils.

[0094] Although earlier researchers, including Hallermeier (1981), recognized that fine sands settle in a laminar regime while coarser sands settle turbulently, Ahrens, J. P., “A fallvelocity equation,” J. Waterw. Port Coastal Ocean Eng. 126 (2): pp. 99-102 (2000), https: / / doi.org / 10.1061 / (ASCE) 0733-950X(2000) 126:2(99) (“Ahrens (2000)”), the relevant portions of which are incorporated herein by reference), reevaluated earlier laboratory data andAttorney Docket No. 2115-008418-WO-POA proposed a single continuous equation (across the turbulent to laminar regimes for coarse to fine sand) to predict sediment fall velocity. Using traditional geotechnical notation, the Ahrens equation is:where v = particle fall velocity d = characteristic (sieve) diameter of the particle i9 = kinematic viscosity of the fluid, and g = acceleration constant due to gravity.Ci and Ct= coefficients for the laminar and turbulent flow regimes respectively.

[0095] As shown in FIG. 5, q dominates in the laminar regime (very fine sand and silt), Ctdominates in the turbulent regime (medium and coarse sand) and both contribute in larger fine sands. Ahrens’ equations corresponding to FIG. 5 are: q = 0.055 tanh [12A0 59exp(-0.0004A)] (7)Ct= 1.06 tanh [O.O16A0 50exp(-120 / A)] (8) in which A is the Archimedes buoyancy index:

[0096] In the example here, FIG. 5 includes the addition of coarse, medium and fine sand size ranges. This required assuming typical values of Gs= 2.65, i9 = 0.8927 mm2 / s and y = yw. The Ahrens model does not account for particle shape and was intended only for “typical natural sand,” which Ahrens described as being “somewhat angular” to distinguish them from perfect spheres. Thus, Ahrens can be used where the particle shapes are known and have a typical natural sand morphology.

[0097] Jimenez, J. A., and Madsen, O. S. “A simple formula to estimate settling velocity of natural sediments.” J. Waterw. Port Coastal Ocean Eng. 129 (2): pp. 70-78 (2003), https: / / doi.org / 10.1061 / (ASCE) 0733-950X (2003) 129:2(70), (herein “Jimenez and Madsen (2003)”, the relevant portions of which are incorporated herein by reference) proposed a model for settling velocity that accounted for particle shape and roundness:where c v = a nominal particle diameter. AJM and BJM are Jimenez & Madsen’s dimensionless coefficients based on particle shape and roundness found from FIGS. 6A-6B.Attorney Docket No. 2115-008418-WO-POA

[0098] Jimenez and Madsen used Raudkivi’s (Raudkivi, A J. 1990. Loose boundary hydraulics. 3rd ed. Oxford, UK: Pergamon Press) approximation of the nominal diameter being ds / Q.9 where dsis the sieve diameter. The same “rule of thumb” is used herein. Jimenez and Madsen point out that in many practical applications the sand will be a “naturally worn quartz” with a Corey Shape Factor, csf= cKab'f15of approximately 0.7. The particle dimensions a, b and c are defined in FIGS. 6A-6B. For csf= 0.7, AJM = 0.954 and BJM = 5.121. Unlike Ahren’ s model (Eq. 6), Eq. (10) assumes = yw. It has been observed that this simplification has almost no effect on PSDs even when plain tap water is used.

[0099] A procedure for performing the u-Scd test method according to certain aspects of the present disclosure is described herein. A u-Scd test begins with filling the sedimentation column with water to approximately mid-height. Opening the vent valve on the pressure transducer allows water to drain from the column until the level drops slightly below water level #1 in FIG. 3. This drainage purges air bubbles from the lines and the pressure transducer chamber.

[0100] Using a squeeze bottle, water is then gently added to the column until the meniscus rises back to water level #1. The corresponding pressure reading, uBis recorded. Water is then added to the column until the meniscus reaches water level #2 at which the new pressure, uDis obtained. The unit weight of the column fluid is then computed by Eq. (1). In this variation of the u-Sed system,is fixed at 1.40 m. Notably, the water does not need to be fully de-aired. For that matter, the fluid need not even be water, but may be any liquid. Tap water that has been brought to a steady room temperature or ambient conditions (e.g., 25 °C). It was also observed that there is virtually no change in y during a day of u-Scd testing. Therefore, if the same source of room-temperature water is used, Stages B through E do not need be performed with every u-Scd test.

[0101] Continuous pressure recording begins just before the soil is introduced into the column and continues at regular intervals, for example, at 0.1 second intervals, until test completion. Nominally, a 50-gram specimen or sample of dry soil comprising solid particles is used. However, the weight of the sample may vary. The sample is introduced as instantaneously as possible into the column using a wide-mouth funnel, so that all particles begin settling at about the same time. The soil particles settle through the column and sort themselves by size as they advance towards the pressure transducer port. As described earlier, the passage of particles past the port causes a drop-off in pressure. The readings stabilize once all particles have passed the port. The time required for settlement depends on the smallest particle size in the specimen. Once all the particles pass the pressure port, the recording ends and the pressure time history is converted to a PSD.Attorney Docket No. 2115-008418-WO-POA

[0102] PSD can be determined as follows. The pressure time histories provide the percentage of soil particles by weight that have (and have not) yet passed the pressure port as a function of time. In other words, the percentage by weight of particle in a specimen that are larger (and smaller) than the particles at the pressure port elevation at any instant in time. In sieving terminology, this is equivalent to the “percent coarser” (and “percent finer”) by weight than a given sieve opening size. The settling velocity of a particle at the port elevation at any time is obtained using an average travel distance of (hi + hi)l2 (FIG. 3). Either equations (6) by Ahrens and (10) Jimenez & Madsen (or both) may then be solved for the particle size passing the pressure port at any given time.

[0103] With renewed reference to FIG. 3, Stage E is the point or time at which the sample comprising the particles is introduced into the column. Stage E only lasts a short duration, for example, about 0.1 second. At the instant when Stage E ends and Stage F begins, the last particles of the sample enter the sedimentation column. An average of the start of Stage E and start of Stage F can be used as “zero time.”

[0104] Throughout Stage F, the particles are settling and sorting in the sedimentation column, but all are still at a height above the pressure port. Hence, the pressure reading during Stage F does not change. Stage G begins when the first (largest) particles pass the pressure port.

[0105] At any instant in time during Stage G, pressure readings indicate what percent of the soil specimen by weight is still above the pressure transducer port. For example, this may be designated x%. The percentage of the soil that has passed the port can be represented by (100- x)%.

[0106] If the size (diameter, D) of the particles passing the pressure transducer port at the moment that measurements are taken by the pressure transducer was known, it would provide a data point for developing a particle size distribution (PSD) of the sample. In other words, it could be determined that x% of the sample by weight comprised particles smaller than diameter (D). As there may be hundreds of pressure data points throughout Stage G, this can provide hundreds of data points to create the complete PSD. In accordance with certain aspects of the present disclosure, the size of the particle at the pressure port at any instant during Stage G is determined by employing the Ahrens (2000) and / or Jimenez and Ahrens (2003) equations.

[0107] Particles fall through a known distance of the sedimentation column (an average of hi and hi in FIG. 3) and it is also known the time at which the particles began falling (Stage E), so the settling velocity of a particle which is at the pressure port elevation at any time during Stage G can be computed by using settling distance divided by settling duration. Thus, by using the settling velocity, particle size “D” can be calculated from Ahrens (2000) and / or Jimenez &Attorney Docket No. 2115-008418-WO-POAMadsen (2003) equations for respective times. As such, the pressure transducer measurements indicate the % of solid particle sample that is still above the pressure port at any time, but do not directly provide respective sizes of the particles. By using the Ahrens (2000) and / or Jimenez and Madsen (2003) equations, the size of the particles at the pressure port at any time can be determined. Thus, a vertical axis of the PSD is developed (e.g., % passing by weight obtained from the pressure transducer measurements) and a horizontal axis of the PSD (conversion from time to particle size) is provided by the Ahrens (2000) and / or Jimenez and Madsen (2003) equations. Thus, at any instant in time during Stage G, the pressure transducer gives us the % passing, while the Ahrens (2000) and Jimenez and Madsen (2003) equations indicate a size D of the particles passing the pressure port at that same instant in time.

[0108] To evaluate the viability of the u-Scd test according to certain aspects of the present disclosure and to compare results with sieve-based PSDs, ten soils were chosen for testing. Two of the sands, Michigan 2NS and Griffin, IN are natural glacial quarry materials exhibiting a wide range of particle sizes. As such, these two sands were pre-sieved and reconstituted in various percentages of fine, medium and coarse components. Each of these two sands was used to produce 4 different gradations as listed in Table 1. Three coarse sands: Petco® sand, Stoney® sand, and GloFish® sand are commercially available aquarium sands. One material is an artificial Brown Fused Aluminum Oxide (BFAO) which is crushed and used commercially as an abrasive. It was selected for the study because of its extreme angularity and relatively high specific gravity compared to the other sands. A sand from Treasure Island in San Francisco Bay and a sand from New Madrid, MO were chosen for their historical significance in geotechnical earthquake engineering. A very dark, basalt-rich beach sand from Costa Rica was chosen because of its high specific gravity and fine size uniformity. Finally, a partly volcanic / partly calcareous sand from the Big Island in Hawaii was included for its unusual constituent blend. Images of all 16 specimens are shown in FIG. 7 and the sieve-based compositions of each specimen are listed in Table 1. The images in FIG. 7 have an image resolution of 246.6 pixels per mm and all display the same 8.5 mm x 8.5 mm fields of view.

[0109] Table 1. Tested Soil Specimens, Size Composition and Comparison of Cuand CcAttorney Docket No. 2115-008418-WO-POA

[0110] The first half of the 16 specimens in Table 1 were various mixtures of coarse (c), medium (m) and fine (f) sand. The ASTM D2487-17 “Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System)” definitions of particle size were used. Two of the specimens were only c and m, two were only m and f, two were only c and f (i.e., gap-graded), and two contained all three sizes, c, m, and f. The second half of the specimens in Table 1 were entirely either c, m or f. In all 16 tests, the u-Scd pressure time histories were converted to PSDs using the Ahrens (2000) and Jimenez & Madsen (2003) settling velocity models and Eq. (5).

[0111] The Ahrens model does not consider particle shape or angularity, therefore its implementation was simple and straightforward for all 16 specimens. For the Jimenez and Madsen model, csf = 0.7 as recommended for “natural sands” was used for all specimens except No. 9 Stoney River, No. 10 Petco and No. 11 GloFish sands. As seen in FIG. 7, these three sands are plate-like. Therefore, 25 randomly selected particles of each sand were measured by a caliper to obtain their three orthogonal dimensions, a, b and c. The average computed csf values were found to be approximately 0.5 for all three materials. This value was therefore used to produce these coarse sands’ PSDs by the Jimenez and Madsen model. Also, for the Jimenez and Madsen model when using FIGS. 6A-6B the “natural sand” curve was used for all specimens except No. 10 Petco, No. 11 GloFish and No. 12 BFAO. Once again referring to the images in FIG. 7, it can beAttorney Docket No. 2115-008418-WO-POA observed that these three sands are highly angular for which the “crushed sand” curve in FIGS. 6A-6B was used.

[0112] FIGS. 8A-8C compare the PSD curves obtained from the u-Sed test according to the present disclosure (including both the curves generated by the Ahrens equation and also Jimenez and Madsen) and those determined by sieving for the mixed size specimens (No. 1 to No. 8). The PSD curves generated by both the Ahrens and Jimenez and Madsen models showed almost perfect agreement with the PSD points obtained by sieving.

[0113] FIGS. 9A-9C compare the u-Scd PSD curves to sieving results for the uniformsized specimens (No. 9 to No. 16). For Specimens No. 13 to No. 16 (all “natural sands”) both the Ahrens and Jimenez and Madsen models are once again almost perfectly aligned with the sieve data. For the crushed No. 12 BFAO, the Jimenez and Madsen model is slightly better than Ahrens in terms of agreement with the sieving results. The anticipated big difference between the two models occurs for the three commercial plate-like aquarium sands, the Jimenez and Madsen (2003) model fits the sieve data better than Ahrens’ model does. The explanation is obvious, there was no provision in the earlier Ahrens (2000) model for the plate-like shape of these coarse sands.

[0114] For soil classification by the Unified Soil Classification System ASTM (2017), the coefficient of uniformity, Cuand the coefficient of gradation, Ccmust be computed. Therefore, a comparison of Cuand Ccvalues by u-Scd and sieving is provided in Table 1. The Jimenez and Madsen curves were used for the plate-like and, or angular Specimens 9 to 12, for all others the Ahrens curves were used. However, there was very little difference between the two. The results for both Cuand Ccfrom the u-Scd test show strong agreement with those obtained from the traditional sieve PSDs.

[0115] Table 2 compares Gsvalues obtained by the u-Scd test (Eq. 2) and those from conventional ASTM specific gravity tests (ASTM D854-14 “ Standard test methods for specific gravity of soil solids by water pycnometer”'). Table 2 also compares the soil specimen mass determined by the u-Scd test (Eq. 3) to values measured by a laboratory weight scale. The results show that the u-Scd test determines both the specific gravity and the mass of the soil specimens very well.

[0116] Table 2. Comparison of Specific Gravity and Specimen MassAttorney Docket No. 2115-008418-WO-POA

[0117] The u-Sed test according to various aspects of the present disclosure appears to provide a highly reliable PSD that matches sieving results. For natural sands, both the Ahrens (2000) and Jimenez and Madsen (2003) models for particle settling velocity are equally accurate. It is only for the highly unusual coarse, plate-like or crushed materials that Jimenez and Madsen’s model outperforms Ahrens’ . This is expected because the Ahrens model was not intended for such materials.

[0118] The devices provided by the present disclosure can be used to conduct a simple and accurate new test to determine the particle size distribution (PSD) of solid sample, such as sands. As discussed above, the device can record water pressures during sedimentation of specimens through a column of water (u-Scd test). The system hardware can include a primaryAttorney Docket No. 2115-008418-WO-POA column, for example, a clear acrylic 1.8 m tall and 25.4 mm diameter column, and a pressure transducer with a 0 to 30 kPa measurement range. The test takes advantage of two models for settling velocity of sand particles through fluids. Sixteen tests on a wide range of sands were performed. The materials came from various geologic or artificial origins, some are highly uniform in size, others are well-graded, and a couple are gap-graded. Most of the specimens were natural sands, one is a crushed material and three are coarse-grained sands used in home aquariums. The sands’ specific gravities, which are also obtained during a u-Scd test ranged from about 2.5 to almost 4.0. The test results all matched PSDs by sieving very well.

[0119] In certain further aspects, as discussed above, methods for determining a particle size distribution of a mixture of solid particles are provided. The methods may comprise introducing a sample of solid particles into a first end of a column containing a liquid. The method also comprises measuring pressure of the liquid at distinct times as the solid particles pass through the column from the first end to a second end. This determines an amount (e.g., mass) of solid particles still above the pressure port. The method also comprises determining the size of particles passing the pressure port using settling velocity models based on the sizes of these solid particles. Further, the method combines these (the respective amounts of particles in the column above the pressure port at distinct times and the respective particle sizes according to settling velocity models at the same distinct times) to determine a particle size distribution of the solid particles.

[0120] In certain aspects, the method further comprises measuring pressure of the liquid (e.g., measuring pressure at least once) prior to the introducing of the sample. The method may include measuring the pressure of the liquid after the solid particles collect at the second end of the column. Further, in certain aspects, the measuring pressure of the liquid may be continuous, for example, occurring by using a transducer which continuously reads pressure.

[0121] In one aspect, the column further comprises a pressure port disposed in a wall of the column disposed at a height above where the particles collect at the second end of the column. The column further includes a conduit in fluid communication with the pressure port that receives a portion of the liquid in the column free of the solid particles. There is also a pressure measuring component associated with the conduit that conducts the measuring pressure of the liquid at distinct times as the solid particles pass through the column from the first end to a second end.

[0122] In one aspect, prior to the introducing the sample of solid particles, the method further comprises introducing a first portion of the liquid into the column as a first height ( / zi) where the liquid fills the column to above the pressure port, measuring a first pressure ( / / ’’) of the liquid at the first height. Further, a second portion of the liquid is introduced into the column at a second height (fe) above the first height ( / zi) and measuring a second pressure of the liquidAttorney Docket No. 2115-008418-WO-POA at the second height (fe). The method also includes determining a unit weight (yy) of the fluid in the column

[0123] In certain aspects, the measuring pressure of the liquid at distinct times includes measuring a third pressure ( / / ) after the solid particles are introduced to the column, but before the solid particles pass the pressure port. The measuring pressure of the liquid at distinct times optionally includes measuring a fifth pressureafter all the solid particles have passed the pressure port and are collected at the second end of the column. In certain aspects, the method, where ywis a unit weight of water at 4 °C. An additional feature of the u-Scd test is that a reasonably accurate value of Gsis obtained with no additional equipment or testing effort than needed to obtain the PSD.

[0124] The method may further comprise determining a total weight of solid particles (TVs) * 1 >* I • ) | of the solid particles bywhere Acis an inside cross-sectional area of the column and ywis a unit weight of water at 4 °C.

[0125] The method may further comprise determining the settling velocities (v) of the solid particles passing the pressure port by dividing a respective settling distance by a respective settling time.

[0126] In further aspects, determining the particle sizes from previously determined settling velocities (v) by using settling velocity models, such as, but not limited to, the Jimenez and Madsen model (2003):where g is an acceleration constant due to gravity, t / ,v is a nominal particle diameter of a respective solid particle, fl is kinematic viscosity of the liquid, AJM is a first dimensionless coefficient based on a shape and roundness of the solid particle, and BJM is a dimensionless coefficient based on a shape and roundness of the solid particle.

[0127] Further, the measuring pressure of the liquid at distinct times may include measuring the pressure as the solid particles pass the pressure port to provide a plurality of fourth pressures (uG).

[0128] Thus, new methods for determining particle size distribution of solid particles, like sands, are presented. The mixture of solid particles may include sand particles, for example, having a particle size of greater than or equal to about 0.075 mm to less than or equal to aboutAttorney Docket No. 2115-OG8418-WO-POA4.75 mm. The device / system records pressures near a base of a water column during sedimentation of samples, e.g., sand specimens, through the column. The pressure time histories contain eight distinct stages. Based on the differences in pressures during the various stages, the u-Scd test yields the unit weight of the fluid in the column, the weight of solids, the specific gravity of solids and the particle size distribution (PSD). To produce the PSD, the u-Sed test relies on previously developed models for settling velocity of sand-sized particles. Sixteen sand specimens with various geologic (or artificial) origins and different gradations and specific gravities were tested. The u-Scd results compares very favorably to ASTM sieving and ASTM specific gravity test results. In various aspects, the present disclosure contemplates systems / devices and methods for conducting a u-Scd test and demonstrates its capabilities for producing accurate PSDs.

[0129] The foregoing description of the embodiments has been provided for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but, where applicable, are interchangeable and can be used in a selected embodiment, even if not specifically shown or described. The same may also be varied in many ways. Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure.

Claims

Attorney Docket No. 2115-008418-WO-POACLAIMSWhat is claimed is:

1. A device for determining a particle size distribution of a mixture of solid particles, the device comprising: a column for containing a liquid having a height of greater than or equal to about 1 meter, wherein the column has a first end that is open for receiving the liquid and a sample of solid particles and a second end that is sealed; a pressure port disposed in a wall of the column disposed at a height above where the solid particles collect at the second end of the column; a conduit in fluid communication with the pressure port that receives a portion of the liquid in the column free of the solid particles; and a pressure measuring component associated with the conduit that provides a plurality of pressure measurements of the liquid at the pressure port a duration that solid particles pass through the column from the first end to the second end, wherein the plurality of pressure measurements determine respective amounts of solid particles in the column above the pressure port at distinct times, so that a particle size distribution of the solid particles is determined in part by the respective amounts of solid particles in the column above the pressure port at the distinct times and in part by a plurality of respective calculated settling velocities of the solid particles at the distinct times.

2. The device of claim 1, wherein the column is a cylindrical column that is transmissive to light having wavelengths in a visible region.

3. The device of claim 1, wherein the column has a diameter of greater than or equal to about 25 mm and wherein the first height is greater than or equal to about 1.5 meters to less than or equal to about 2 meters, wherein a particle size of the solid particles is greater than or equal to about 0.075 mm to less than or equal to about 4.75 mm.

4. The device of claim 1, wherein the conduit comprises a first region that defines an angle with respect to the column so that the first region of the conduit connects to the pressure port and is graded to a first elevation that above the pressure port.

5. The device of claim 4, wherein the angle is less than or equal to about 30° from vertical corresponding to the column.

6. The device of claim 1, wherein the pressure port is disposed greater than or equal to about 16 cm above the second end of the column.Attorney Docket No. 2115-008418-WO-POA7. The device of claim 1, wherein the pressure measuring component is a pressure transducer configured to take continuous pressure measurements of the liquid.

8. The device of claim 7, wherein the pressure transducer is configured to measure a pressure of the liquid at greater than 0 kPa to less than or equal to about 30 kPa.

9. The device of claim 1, further comprising a processor in electrical communication with the pressure measuring component configured to receive and record the plurality of pressure measurements from the pressure measuring component.

10. The device of claim 9, wherein the processor is configured to calculate the plurality of respective calculated settling velocities of the solid particles passing the pressure port at the distinct times while the solid particles pass through the column from the first end to the second end by using a settling distance divided by a settling time.

11. The device of claim 9, wherein the processor is programmed to determine particle sizes of the solid particles based on the plurality of respective calculated settling velocities given by:where Gsis specific gravity of the solid particles, g is an acceleration constant due to gravity, dN is a nominal particle diameter of a respective solid particles, fl is kinematic viscosity of the liquid, AJM is a first dimensionless coefficient based on a shape and roundness of the solid particles, BJM is a second dimensionless coefficient based on a shape and roundness of the solid particles.

12. The device of claim 9, wherein the plurality of pressure measurements of the liquid include a first pressure ( / / ’’) measurement taken where the liquid is at a first height ( / zi) between the pressure port and an upper boundary of the liquid in the column; a second pressuremeasurement taken where the liquid is at a second height (fe) between the pressure port and the upper boundary of the liquid in the column; and the processor uD-uBis programmed to determine a unit weight (yy) of the liquid in the column by gJr = - . h2—h113. The device of claim 12, wherein the plurality of pressure measurements of the liquid include a third pressuremeasurement taken before the solid particles pass the pressure port and a fifth pressure measurementafter all the solid particles have passed the pressure port and are collected at the second end, wherein the processor further determines specific gravity unit weight of water at 4 °C.Attorney Docket No. 2115-008418-WO-POA14. The device of claim 13, wherein the processor further determines a total weight of solid particles (Ws) bywhere Acis an inside cross-sectional area of the column and ywis a unit weight of water at 4 °C.

15. The device of claim 1, wherein the column comprises an assembly of multiple segments reversibly coupled together.

16. The device of claim 1, wherein the conduit comprises at least one quick connector to reversibly couple with the pressure measuring component.

17. A method of determining a particle size distribution of a mixture of solid particles, the method comprising: introducing a sample of solid particles into a first end of a column containing a liquid to sort the solid particles by particle size, wherein the column further comprises a pressure port disposed in a wall of the column disposed at a height above where the solid particles collect at the second end of the column; measuring pressure of the liquid at distinct times as the solid particles pass through the column from the first end to a second end to determine respective amounts of solid particles above the pressure port at the distinct times; and determining a particle size distribution of the solid particles based on the respective amounts of solid particles above the pressure port in the column at the distinct times and further based on calculating a plurality of settling velocities of the solid particles corresponding to the distinct times.

18. The method of claim 17, further comprising measuring pressure of the liquid prior to the introducing of the sample.

19. The method of claim 17, wherein the measuring the pressure of the liquid includes measuring a pressure after the solid particles collect at the second end of the column.

20. The method of claim 17, wherein the measuring pressure of the liquid occurs by using a pressure transducer to take continuous measurements.

21. The method of claim 17, wherein the column further comprises: a conduit in fluid communication with the pressure port that receives a portion of the liquid in the column free of the solid particles; and a pressure measuring component associated with the conduit that conducts the measuring pressure of the liquid at distinct times as the solid particles pass through the column from the first end to a second end.

22. The method of claim 21, wherein prior to the introducing the sample of solid particles, the method further comprises:Attorney Docket No. 2115-008418-WO-POA introducing a first portion of the liquid into the column as a first height ( / zi) where the liquid fills the column to above the pressure port, measuring a first pressurethe liquid at the first height ( / zi); introducing a second portion of the liquid into the column at a second height (fe) above the first height ( / zi) and measuring a second pressureof the liquid at the second height (fe); and determining a unit weight (yy) of the liquid in the column .

23. The method of claim 21, wherein the measuring pressure of the liquid at distinct times includes measuring a third pressure ( / / ) before the solid particles pass the pressure port.

24. The method of claim 23, wherein the measuring pressure of the liquid at distinct times includes measuring a fifth pressureafter all the solid particles have passed the pressure port and are collected at the second end.

25. The method of claim 24, further comprising determining specific gravity (Gs) of , where ywis a unit weight of is a unit weight of waterat 4 °C.

26. The method of claim 25, further comprising determining a total weight of solid particles (Ws) of the solid particles by Wswhere Acis an inside cross-sectional area of the column and ywis a unit weight of water at 4 °C.

27. The method of claim 25, wherein the determining the particle size distribution further comprises calculating a plurality of particle sizes by using a settling velocity model:where Gsis specific gravity of the solid particles, g is an acceleration constant due to gravity, dN is a nominal particle diameter of a respective solid particles, fl is kinematic viscosity of the liquid, AJM is a first dimensionless coefficient based on a shape and roundness of the solid particles, BJM is a second dimensionless coefficient based on a shape and roundness of the solid particles.

28. The method of claim 25, wherein the measuring pressure of the liquid at distinct times includes measuring the pressure as the solid particles pass the pressure port to provide a plurality of fourth pressures29. The method of claim 21, wherein the pressure measuring component associated with the conduit is a pressure transducer that measures the pressure of the liquid in the column at distinct times.Attorney Docket No. 2115-008418-WO-POA30. The method of claim 21, wherein the calculating the plurality of respective settling velocities of the solid particles passing the pressure port at the distinct times while the solid particles pass through the column from the first end to the second end occurs by using a settling distance divided by a settling time.

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