Welcome to my exciting project, building on 60 years of work in sand dispersity sedimentology. Jiří Březina, Founder of GranoMetry. Info more  



GranoMetry™ — Science with Applications





Welcome to Granometry - my primary web site and summary of my life's work. On the following pages, you will read about:

  1. My pioneering research work in the field of sand texture sedimentology.
  2. My development and production of laboratory instruments for the analysis and separation of sand.
  3. My education and studies, from the earliest years up through my post-doctoral work.
  4. My 40 years of teaching thousands of students at an American university in Germany and planetology students in the Czech Republic.


 Booklet "Jiří Březina — Founder of GranoMetry — Science with Applications": e-book here  and pdf book 


Miracle of Sand 

After a lifetime of study and research in the many aspects of sand sedimentology, I have come to realize that sand has a mysterious, hidden quality that I call the miracle of sand. This phenomenon of nature has been a lodestone for much of my work and research. 

The miracle of sand — it precisely identifies and describes the sand's past and current mobility in water — by its settling rate mass distribution. That property, when correctly measured and characterized on multiple samples in space (a sedimentation basin), can display the past and current streams – trace the sand motion on a beach and other environments. The moving sand may be related to great economic value on locations, where it is either needed (such as in recreational regions) or harmful (e. g. limiting the passage of ships in channels). Tracing the miracle of sand may help in finding petroleum, gas and mineral resources associated with the sand movement (‍ http://www.granometry.com/index.php/en/#applications ). 

Failures of the Former Settling Tubes and of the Higher Moments

During the last 60 years of the 20th century, the low sensitivity of the settling tubes required high particle concentration (too large samples). This caused streaming and particle interaction, which strongly disqualified the sedimentation by intrinsic errors. As distribution characteristics, higher moments had been correlated with the sample known properties and used — an unprofessional solution free of causal relationship. In his Editorial, Robert EHRLICH (1983)  criticized the inefficiency of both the method and the distribution characteristics by higher moments, without indicating the failure reasons. That killer critique stopped most sand distribution studies as wasted time ("tatting"). 

Unhindered Sedimentation by Small Particle Concentration

Knowing that the too high particle concentration caused the failures of the previous settling tubes, I applied all possible efforts to develop instruments sensitive for using the lowest particle concentration  given by my equation for the sample size (satisfying also the statistical sample representativity). This resulted into the incredible accuracy of my instruments. The sample size must be reduced by using a good rotational sample splitter. Non-rotational sample dividers (riflers) are inaccurate.

Samples consisting of laminae should be sampled mixed in original proportion —  our SHAPE™ program will decompose the mixed distributions and thus preserve the Gaussian components of the laminae. 

Both my instruments, Analyzer™ and  Separator™, arrange the  sand particles according to their settling rate without measurable influence of streaming and particle interaction with highest accuracy so, as each of the multiple particles would sediment individually in clean water. 

Measuring Sedimentation 

The settling rate of individual particles in clean water is the most accurate particle feature. In my Analyzer™, the particles are introduced to sedimentation well dispersed into a large volume without streaming and mutual particle interaction. The particle sediment is weighed with accuracy of ±0.01 percent of the total sample mass in settling time to milliseconds along 185 cm settling distance. The underwater weighing is performed with highest possible speed and free of environmental signal noise. This provides the ultimate effective accuracy, much higher than that of optical microscope, sieving, etc. and — of course — of previous settling tubes. My SedVar™ program can convert the Analyzer™ settling rate mass distributions into distributions of any independent particle variable, such as PHI particle size, PSI particle settling rate, particle density, particle shape, particle Reynolds' number. My SHAPE™ program can decompose the mixed distributions into Gaussian distribution components (we recommend a limit of maximum 5 components). 

Separation of Sedimenting Particles 

In my  Separator™, after 185 cm settling distance, the separation is controlled in milliseconds. The Separator™ is isolating particles into 25 (or more) log settling rate fractions defined by the user without losing any particle. If the sample particles have the same particle density, the settling rate fractions correspond to particle size fractions. If the sample particles have the same size (the sample is one narrow sieving fraction), my Separator™ will isolate them into density (mineral) fractions, including the bulk density of particles of porous minerals, such as porous calcite of microfossils e. g. Foraminifera (see Entrainment of planctonic foraminifera: effects of bulk density ). 

Distributions Characterized by Gaussian Components Instead of by Moments 

The Gaussian components are the best distribution characteristics and distribution identification. They perfectly define each distribution: one may use them to re-create the original distribution. The moments, even the higher ones, can not re-create the original distributions and do not identify them. This is why the Gaussian components must replace the inefficient higher moment characteristics. The log settling rate of sand particles reflects their mobility: this is why the log settling rate replacing the log particle size in the dispersity mass distributions of sand deposits can reconstruct the sand transportation (motion). 

Goodness of Fit — Evidence of Quality of All Procedures Involved 

Though it is impossible to calibrate the best, one may evaluate the best indirectly. I carefully prepared and analyzed a one-sized polymineral sample. I needed about 8 hours to wet-sieve 0.6916 gram of a monosized fraction on two vibrating precision sieves with circular holes, split it into 8 subsamples, analyzed each by my Analyzer™, summed them into mean analysis and decomposed the result by our SHAPE™ program: the chi-square goodness of fit was smaller than 0.01 — incredible quality resulting from the whole chain of all involved analytical processes. My SedVar™ program converted the settling rate distributions of each component into the log-density distributions providing the means, standard deviations and percentages of the four Gaussian components identified as four minerals (checked by polarizing microscope and x-ray diffraction). No other method can provide these precise results.

Teaching that the Unknown New is Needed 

My ideas and products are completely new: theoretically, there is a worldwide need for them. But practically, the potential users do not yet know that they need them, similarly to Henry Ford's potential car users did not know that they need a car — they only wanted a better horse. Another example was the Czech shoe manufacturer Tomas Baťa https://en.wikipedia.org/wiki/Bata_Shoes ,  who asked his manager to expand the market for shoes in Africa. However, the manager returned with a message that Africans are running barefoot, they did not need shoes. Mr. Baťa used this shoe ignorance for his success — he taught Africans to wear shoes. I am going to teach sedimentologists, oceanographers, geologists, civil engineers etc. to need my sand texture sedimentology ideas and instruments, because they will obtain unique results. That will include also Baťa's idea "using quality as a way to lower cost at the same time as creating customer delight"  https://en.wikipedia.org/wiki/Tom%C3%A1%C5%A1_Ba%C5%A5a .


My Three Principles of Sand Dispersity Sedimentology


The main goal of sedimentology — finding the sediment origin — can be disclosed in the following sediment features:

 in sandy sediments only, because they formed by the transitional hydrodynamic regime: between the laminar/viscous flow (Stokes‘ law) and the turbulent/impact flow (Newton’s law);

 in distributions of particle settling rate (velocity) — not particle (sieve) size — because the velocity is length per time, and length is included in the particle space location caused by transportation (a sieving process does not form a sediment, but the settling rate does — by the particle motion distance); 

 in the Gaussian distribution components — not the higher distribution moments. A mixture of maximum five Gaussian components can perfectly define the measured distribution. It is suitable for trend surface plots in basin and natural tracers analysis.

Success through the Best Technology 

Since the inception of my instruments, I have always incorporated the best technology, I have never been guided by economy. My ultimate goal has been the quality — never "inexpensive" settling tubes. 
This uncompromising approach has resulted in success for users of my products. 


Science with Applications


Sand origin from its distinctive features: 

 Sand dispersity (granularity); 

 Logarithmic settling velocity as the dispersity unit;

 Measuring directly by sedimentation technique under lowest suspension concentration in order to eliminate measurable suspension streaming and particle interaction; 

 Frequency (amount) recorded directly as weight by underwater balance instead of as suspension pressure difference (such as Woods Hole Rapid Sediment Analyzer, and similar "inexpensive" settling tubes)Only an Advanced Sand Sedimentation Analyzer™, such as my MacroGranometer™, can analyze enough small samples to minimize the suspension concentration and thus serious errors from suspension density streaming and particle interaction. It enables analyzing samples as small as to avoid these errors and keep the statistical representativity of the samples. 

The Analyzer's™ Venetian blind with eccentrically vibrating concave lamellae disperses the most concentrated suspension during sample introduction

The Analyzer's electronic underwater balance provides:

1) High sensitivity with ultimate load-signal linearity and excellent S/N (signal-to-noise) ratio (good isolation from environmental vibration and mathematicalfiltering of the perfectly tuned signal from the frequency measuring amplifier). 

2) The negligible balance pan displacement enables high speed measurement even with the 26-cm-diameter balance pan and makes the balance very sturdy. 

 Universal sedimentation equation — drag coefficient CD  as a function of Reynolds' number Re and shape factor SF,
2D diagram  
  Universal sedimentation equation — drag coefficient CD, as a function of Reynolds' number Re and shape factor SF,
3D diagram 

My Universal Sedimentation Equation (BREZINA 1979, PARTEC) is valid for fine particles (Stokes' law), coarse particles (Newton's law), the intermediate range and not only for spheres but also for non-spherical particles with shape specified by Corey's Shape Factor, SF (A. T. COREY 1949, independently J. S. McNOWN and J. MALAIKA, 1950). The particle shape of sand particles strongly reduces their sedimentation velocity and therefore the grain size calculated from it (the diagram on the right). This is why the particle shape must be never taken as that for spheres but as an approximate real SF, such as SF' = 0.6.  
   The non-spherical shape (SF'<1,18) of particles reduces their sphere (equivalent) size, strongest with the coarse ones 

Below are diagrams displaying  PSI settling rate as function of PHI particle size in groups of four log-equidistant particle densities (2.5, 5, 10, 20) and groups of four log-equidistant SF (0.15, 0.3, 0.6 and 1.2). Please note that the PSI-curves of the SF-specified PHI parricle size (the group of the four particle densities on the left) converge to slow fine particles, whereas the PSI-curves of the four equidistant densities are parallel. That comparison shows that the settling rate is influenced by particle density at any particle size, whereas the particle shape influence increases with the settling rate and particle size.  

Settling rate PSI, function of particle size PHI and shape factor SF for four log-equidistant densities Rs

 Settling rate PSI, function of particle size  PHI and four log-equiditant densities for four log-equidistant shape factors SF

Taking log particle size instead of log settling rate in distributions creates most negative log particle size skewness/asymmetry (3rd moment) — the negative log particle size (PHI) skewness observed by many authors as I showed in my 1963 paper .

Taking log settling rate instead of log particle size in distributions reduces/removes most negative log particle size skewness/asymmetry (3rd moment) In my 1963 paper, Kapteyn's Transformation of Grain Size Distributions , I showed that most of the often observed negative PHI-skewness can be reduced or eliminated by taking log settling rate instead of log particle size as independent distribution variable.

Unfortunately, the settling rate values of natural irregular particles I used (paper by A. A. Sarkisian, 1958) were incorrect as I found in my later thorough studies, which resulted into my Universal Sedimentation Equation (PARTEC-paper, 1979). The two diagrams below (you may click on each to see it in full size) are based on my universal equation — they update the Fig. 4 of my 1963 paper. The left-hand diagram shows the SDPHI (PHI-standard deviation), the right-hand diagram shows the SKPHI (PHI-skewness), all values are negative. The title of this paragraph is reversible:


 SDPHI (PHI-standard deviation) 
as function of the PHI-mean
 SKPHI (PHI-skewness)  as function of the PHI-mean

Distributions characterized and defined as mixtures of Gaussian distribution components 

I revised the distribution characteristics. In recent marine environment, Dr. Joseph R. CURRAY (1960) had usedt the Gaussian distribution components of sieve size distributions as natural tracers of sand moved by water. I found that especially the Gaussian distribution of log (PSI) settling rate distributions are tracing the sand movement best. Moreover, the first two moments have physical meaning, whereas the higher (3rd and 4th) distribution moments do not. I am decomposing the measured log (PSI) distributions into a few (up to 5) Gaussian components using the program with the unique algorithm by Isobel CLARK (1977, her program ROKE), such as in this example (click). The first two moments and percentages of each of the Gaussian component define and sufficiently specify the measured distribution. 

Tools for reconstruction of sedimentation basins are available

I completed a system of both hardware and software for the efficient study of sand dispersity. The distribution components of log (PSI) settling rate characterize also those of the horizontal streams and thus they are not only natural tracers, but enable also a reconstruction of the sedimentation basins. In contrast to artificial tracers, which are material admixtures (e.g. radioactive ones and color [such as fluorescein] tracers), disperse and disappear in time and space, these natural tracers are intrinsic properties of the sand sediment, therefore do not disperse and disappear: they only continuously adjust to the changing environment. 

Separator of the Settling Rate Sand Fractions

To isolate the settling rate sand fractions, I developed a Sand Sedimentation Separator™, 3S™.

This instrument, when used for separation of equal-sized grains, such as sieve fractions, separates the grains into fractions of the same density, isolating e.g. heavy minerals and even porous microfossils, such as Foraminifera. This use is unique: heavy minerals have not yet been separatable without (mostly toxic) heavy liquids, which do not separate porous microfossils (they have to be isolated manually). 



I am Looking for Supporters

On April 6, 2017, my 84th birthday, I started emailing the following message to my friends, colleagues etc.. Please download the pdf-document here: Project . Thank you for supporting my Life Project. 



I am Looking for Followers

During my 60 years of research and work, I have never allowed time and economy to pressure me — my criterion has always been achieving the ultimate quality standards. This approach paid off: though it was often the most difficult, it was straightforward; though it was seemingly expensive, it turned out to be the most economic; though it appeared slow, it became the fastest and made possible the impossible. Now, as I prepare for the transition from my lifetime of personal involvement to those who will succeed me in this field, I am confident that I am passing on perfectly proven results and the promise of reliability in the future. I hope the following facts will encourage those of you who consider joining me now and continuing after me into the future. Branch, which I founded — not just narrowly specialized and theoretical — has economically useful applications, such as:

 searching for oil and gas in fragmental rocks (sand), 
 tracing of sand moved by water currents,
 prospecting heavy minerals in sandy sediments: titanium and tin ores, gold, platinum, rare earth minerals, zircon, garnet, diamond, etc..

Want to devote yourself professionally to the GranoMetry field? It has a bright future. Feel free to contact me personally per e-mail or telephone. Consultation, internship, or help in your application of what I have learned can be your first step in finding a focus for your future career. This is a unique opportunity that I may not be able to offer again. Use it. 


GranoMetry™ has Applications in 

  • geology: 
    • petroleum geology & basin analysis, 
    • facial and stratigraphic correlation;
    • reservoir evaluation;
    • enhanced recovery,
    • heavy oil & tar sand production,
    • micropalaeontology — isolation of porous microfossils, such as foraminifers & conodonts  (see Distribution Decomposition)
    • stratigraphy — correlation by finest textural features, 
    • prospecting and isolation of heavy mineral (placer) deposits  (see Distribution Decomposition) , such as
      • gold,
      • platinum group minerals,
      • rare earth minerals,
      • diamond,
      • titanium & tin ores,
      • zircon & monazite
      • garnets; 
      • corundum;
  • oceanography - coastal processes & protection studies  • tracing sand movement, particularly due to longshore currents (litoral drift) through mixed distribution components (see Distribution Decomposition), 
  • ecology, 
  • mechanical & chemical engineering (in German: mechanische Verfahrenstechnik), 
  • quality control, 
  • forensic research & analysis, 
  • astronomy. 

Teaching more than 7.000 Students in 37 Years

 University of Maryland University College Europe (more ...)
 Charles University, Faculty of Natural Sciences, Geology (more ...) 



My Exciting Project




I am initiating a project “Sand Dispersity Sedimentology“. It will present a new concept of studying texture/granularity or, better to say dispersity, of sand deposits. This concept should replace the current approach, which has been in use half a century after the World War II and failed. 

The project will introduce the following four principles instead of the currently used ones:

  1. PSI settling rate of grains instead of PHI grain size, 
  2. Carefull sampling which enables using the advanced settling tubes by minimum particle concentration
  3. Advanced settling tubes instead of the “inexpensive” ones,
  4. Gaussian distribution components with their first two moments instead of higher distribution moments.

A prominent publisher should release the results of the study of all participants in a special Symposium.

The first study part will include the following chapters:

  1. Sand sedimentation;
  2. Universal sedimentation equation;
  3. Concentration effects on sand suspension sedimentation, especially in settling tubes,
  4. Advanced settling tubes;
  5. Distribution characteristics by Gaussian components;
  6. Mixed laminae from outcrop samples preserve the Gaussian components.  

The second study part will employ the upper three principles in applications of prominent users of my instrument, e.g.:

  1. Sand dispersity study on the example of marine Miocene in Moravia — a continuation of my PhD. 1965 thesis. Because all the 14,000 samples I processed and archived in the years 1955 - 1968 have been discarded, Institute of Geological Sciences at University of Brno, Czech Republic, will coordinate the new study, collect and process new samples and formulate general conclusions;
  2. Alfred-Wegener-Institute, Helmholtz-Zentrum for Polar- and Marine Research, Bremerhaven, Germany;
  3. Geological Department, University Wien, Austria;
  4. Geological Department, University Trieste, Italy;
  5. Oceanographic Department, University Faro, Portugal;
  6. Oceanographic Department, Senckenberg Institute, Wilhelmshaven, Germany.

The finalization of my project will provide a powerful tool to sand sedimentologists in seeking the origin of sandy deposits — Legacy of William C. Krumbein — and the culmination of my sixty years research.

The project "Sand Texture Sedimentology — Field of Futurecan be downloaded as an English pdf-document here  sedimentology6.pdf (click),

the project "Sedimentologie textury písků — obor budoucnosti" can be downloaded as a Czech pdf-document here  sedimentologie.pdf (click).