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These two books are a significant advance in physical science that now includes the mechanics
inside of our earth.


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Deterministic Earth
Mechanical Science

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Pore Pressure through Earth Mechanical Systems
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the unique ISBN's found below.

Deterministic Earth
Mechanical Science
ISBN: 0-9708083-3X

Pore Pressure through Earth Mechanical Systems
ISBN: 0-9708083-2-1



Textbooks on Deterministic Earth Mechanical Science


Earth Mechanical Systems Science applies directly to Drilling Reservoirs and Geomechanics
The Forces that govern Earth Mechanics are a small subset of Universal physical laws!

( Note: There are special conventions used in this file. Square brackets [ ] encompass physically meaningful terms that are conserved; for instance [ mass-energy] ; [stress/ strain]; and [ mass-energy-space-time]. Words that have rigorous physical meanings have color codes. The color codes highlight rigorous mechanical and conservation law terms that overlap with much looser language terms. Wherever not specified, assume that the more rigorous physical definition is intended.

When deterministic physical laws and related definitions are used, conclusions are much stronger. Mass and energy are conserved as such in the laboratory, the earth, and the Universe. A specific cross-referencing of [mechanical terms] between the laboratory and the earth is shown in Comparison of Laboratory and in situ Rock Mechanics systems.

Synthesis of accepted physical laws explains Earth
Mechanics and Pore Pressure

[Mass-energyy] synthesis inside the earth's crust is a significant advance in physical science. Great scientists applied conservation laws and discovered new physical laws. Newton and Einstein discovered closed-form [ mass-energy] conserved laws that apply on and above the earth. There is a compatible mathematical solution that seems to apply within the earth.

Pore pressure and effective stress are potential energies in the earth's sedimentary crust. The sum of two-phase energy is generated and regulated by overburden mass. Overburden mass is fluid and mineral mass that is integrated over depth. Grain-matrix strain coincides with solid mass conservation. Grain-matrix strain is also the mathematical complement of measurable porosity. It denotes fluid and solid mineral partitioning. There are three closed-form solutions for these physical, geologic, and mechanical terms that conserves [ mass-energy]!

The physical explanation of earth forces is a summation of physical and conservation laws in the earth. These laws act in conjunction with the earth's own gravity. [Mass-energy] is thereby explicitly conserved within our three-dimensional, solid-liquid phase planet!!

These two books are a significant advance in physical science that now includes the mechanics inside of our earth.   RETURN TO TOP


About the book covers: The laws of Newton, Hooke, and Coulomb were discovered before 1800. Their laws were combined using a few applicable conservation laws to define Pore Pressure through Earth Mechanical Systems; The Force Balanced Physics of the Earth's Sedimentary Crust . The fluid in a borehole (Pb) presses against the natural Pore pressure (PP) and fracture pressure (Pf) forces in the earth at the borehole wall. Unbalanced forces can cause loss of circulation and/or well blowout disasters.

More recently, "Deterministic Earth Mechanical Science" was written to explain the macro-mechanics revealed in the first book. "Molecular mechanics" bridges and explains the conceptual gap between Newtonian macro-mechanics and quantum mechanics. It also provides a much broader deterministic explanations of the great questions of earth science.

The newer book's cover is shown on the left above. The first two essays in News give the most up to date physical explanations on the whole of Deterministic Earth Mechanical Science. A Physical Law Synthesis that Explains Earth Mechanics covers the highlights. Each of the aforementioned book's list of chapters can be seen by clicking on the book's titles above. Each book also has a short list of keywords and a glossary of important mechanical terms.   RETURN TO TOP

Hyperlinks within the website related Earth Mechanical Systems Subjects

Earth mechanical systems rigorously explain a great deal about geology. They explain earth physiography and quantify the forces involved in continental drift. The earth's [ mass-energy ] conservation laws are given and explained. The earth's mechanical limits triangle describes the earth's mechanical [stress/strain] limits using equivalent [mass-energy] conservation laws. The question, "Why learn about the earth's [two-phase] mechanics? " is asked and answered. A very short abstract touches the highest points. A longer synopsis covers the most important scientific points. Feel free to contact phil@force-balanced.net with short questions and/or book orders.


Earth mechanical systems are a unifying concept that has eluded earth scientists for over 200 years. The minerals and fluid that compose the earth are the medium. Physical laws are the mechanisms. The medium and mechanisms are a continuous [mass-energy] conserved field. Einstein and Newton's syntheses describes a [mass-energy-space-time] continuum of which the earth's interior is now a part.   RETURN TO TOP

"Pore pressure through Earth Mechanical Systems", describes a very important special case of mass-energyconservation law physics. The force of its own gravity operates in concert with other conservation laws in our 3-dimensional earth. Electrostatic repulsion of adjacent molecular electron clouds keep the earth from collapsing to the size of a marble.

The mineral and fluid molecular phases of the earth generate, bear, and transmit all the loads. Stress and strain have solid mass conservation and porosity in common. The correlations of stress, fluid pressure and physical properties through conservation laws are shown and explained in the first book.

The Chapters in the first book; 1) - Explain the above mentioned globally applicable controlling physics with respect to rock, mineral, and fluid physical properties. 2) - Details mineralogic inter- and intra-particle controls of sediment compaction. 3) - Mineral specific compaction curves are demonstrated to be [stress/strain] causal relationships. 4) - Presents data that demonstrates differential stress minimization in normal-fault and strike-slip tectonic regimes. 5) - Describes the interactions of petrophysical instruments with minerals, fluid and porosity. 6)- Explains earth mechanics as a continuous [stress, fluid pressure ] / [mass-mineralogic strain] field. 7) - Demonstrates that fracture pressure regulates pore pressure profiles. 8) - Explains the calibration of unloading limb stress/strain and demonstrates that Hooke's law and fracture pressure are limits. 9) - Organizes and categorizes published empirical pore pressure methods.10) - Points out some of the important ensuing applications that are possible through synthesizing physical laws. The Glossary – explains and relates over 100 technical terms in earth mechanics.

Speaking broadly, chapter 1, 3 and 6 are [stress/strain] conservation. Chapters 2 and 4 are [stress] conservation. Chapter 7 demonstrates inter-dependant [load] conservation. Chapter 8 explains how elastic and plastic mechanical terms connect, both of which are conservation laws in the earth.   RETURN TO TOP

Physical laws combine in the earth's sedimentary crust to explain all the above!

This synthesis is a quantum step in the evolution of geologic science, physical science, and civil engineering. The synthesis applies to the common sedimentary minerals from the surface to total consolidation. It applies from 0 to 100% porosity with mineralogically defined effective stress limits.

text books

These four panels shown above are central points of the earth's mechanical system. They represent (UL) the effective stress law in Normal Fault regime basins (chapter 4). (UR) Compactional and Hooke's law [stress/strain] limits (Chapter 8). This [stress/strain] plane corresponds to two sides of the [mass-energy] limits triangle. (LL) Fracture pressure and hydrostatic limits to pore pressure profiles (chapter 7). (LR) Loading limb relationships for natural mixed-mineral sedimentary rocks (chapter 3). All the above are physically linked to each other in the earth's sedimentary crust. The two right panels also appear on the cover of "Deterministic Earth Mechanical Science".

The earth's mechanical limits triangle describes the earth's [stress/strain] limits using equivalent conservation laws. (Keep the upper right [stress/strain] diagram in mind if you jump to the limits triangle now. The two triangles are mechanical and conservation law equivalents.)

Minerals and fluids are the matter of our earth's mechanical system. Sediment or rock composition reflects the sum of energy [effective stress + fluid pressure]. Loading and unloading [stress/strain] relationships are tangent to time sensitive [mass-energy] conservation laws. Observations in the earth can add new data points to the existing [mass-energy-space-time] continuum.

Geologic and geophysical observables are consistent with the conservation of [mass-energy]. We can use these observables interchangeably if we keep in mind how they represent minerals and fluids. Reservoir fluid and ground water production should trend along a [mass-energy-space-time] continuum.

The energy that drives continental plates and reduces porosity is effective stress. The sum of the three vectorial principal stresses is conserved. For plastic granular solids the compactional effect of each vectorial stress is equal. There are three easily recognized tectonic regimes in the earth's sedimentary crust. Integer stress ratios that indicate vectorial-volumetric stress equilibration dominate the observed data. These are explained in chapter 4.

Effective stress minimization explains how conserved vector and scalar energies interacts in the earth. Porous grain matrices respond by approaching a local minimum effective stress state. Stress equilibration can be through fault movement, microscopic pressure solution, or both. Earth mechanics explain earth physiography and quantify the forces involved in continental drift.    RETURN TO TOP

The earth is a self-contained gravitational-mechanical system.

text books

All of the features on the map above are geometric. Tectonic regimes and continental drift have previously been explained only through relative stress relationships. Tectonic regimes on all continents have been classified by observed shear fault geometry. The three Andersonian fault regimes have three corresponding shear fault orientations. Anderson explained the relative but not absolute magnitudes of the three principal stresses. The additional concept of discrete energy minima provides more closely quantitative results and truly causal explanations.

Shear faults and continental drift result from unequal stresses. Gravity is necessarily a principal stress in all three earth tectonic regimes. Gravity is either the maximum, intermediate or minimum principal stress. Synthesis of physical laws provides quantitative and balanced force predictions of the three principal stresses.

There are three local minima in the effective stress conservation. The minima are integer relationships between the three [v:H:h] vectors within the average effective stress scalar. The earth's vectorial stresses are symmetrical about the integer <2>. Newton's gravitational law, Coulomb's electrostatic law, and Einstein's theory of relativity also have physical <2> symmetry.

Data clustering about the positive integer ratio minima is confirmed in normal and strike-slip tectonic regimes.   

text books

The equations that limit earth mechanics are the extended elastic equations of Hooke’s law and Newton’s law. These operate in conjunction with other conservation laws. Synthesis of these physical laws relates geologic forces, grain-matrix-strain, pore pressure and elastic wave propagation directly to earth physical properties. These relationships are co-dependant at the minimum [mass-energy] equilibrium state.    RETURN TO TOP

Mass-Energy conservation within the earth

[mass-energy] conservation within the earth is more complex than that above the earth. But the earth's mechanical behavior is readily understood through companion conservation laws. Gravitational force varies in very close proportion to overburden mass. It is directed toward the earth's center.

The earth's reaction to gravitational force pushes out against horizontal containment. The coupled minimum horizontal load is exactly fracture propagation pressure! It is a co-dependant conservation law in accordance with [mass-energy] conservation. Fracture propagation pressure is a plastic, not an elastic relationship (as explained in the earth's mechanical limits triangle just below).

Newton's law and Hooke's law are linear parent [mass-energy] conservation laws. These two physical laws are vertices of a new three-dimensional earth mechanics [stress/strain] physical limits triangle. It is shown below.

Newton and Hooke's law [mass-energy] conservation commonality was established well after Hooke's death. The third vertex is the previously described synthesis of physical laws that applies to the earth's sedimentary crust. He's alive today and you can talk to him. You can contact him by e-mail at phil@force-balanced.net to place a book order or for more information. If you're interested in the earth as a mechanical system, read on.   RETURN TO TOP

The earth's mechanical limits triangle


The details of [mass-energy] conservation are explained in chapter 6 of Pore pressure through Earth Mechanical Systems "The article, Holbrook, P W, 2000, "How do Poisson’s Ratio and Plasticity relate to Fracture Pressure?",  World Oil , March, pp. 91-96. briefly explains the [stress/strain] triangle shown above. The left side of the mechanical limits triangle is the lower half of figure 3 in the article. Fracture Pressure in the article is related to the left side plastic limit of the mechanical limits triangle, not the right side elastic limit. Hooke's law coefficients (i.e. Poisson's ratio) have meaning only within the elastic domain. Both limits are explained and related in the article. This is a .pdf file that will open automatically if an Adobe Acrobat browser is on your computer system.)

The left side of the physical law limits triangle corresponds to the lower half of figure 6.1 in the textbook and figure 3 in the article. The light blue and tan background areas translate governing conservation laws into conventional mechanical terms. Tan background is [load-pressure-stress] energy. The blue background area is [mass-mineralogic strain]. Quite naturally, [mass-energy] conservation is three dimensional in our three dimensional earth!

The [mass-energy] plane is a matrix of conservation law equalities. The [mass-energy] equal (=) signs are along the diagonal of the matrix. The solution is a simultaneous summation of physical laws with connecting conservation equations.

Even non-mathematicians appreciate the basic concept. The whole is equal to the sum of its parts. In this specific case, we are conserving [mass-energy], which is the foundation of the physical science! This summation raises [mass-energy] conservation from one dimensional to three-dimensional in our earth!!

Each of the equations on the plane is a physical or conservation law. The vectors and scalars are conserved. They are subscripted and color coded on the figure. [Mass-energy] are conserved from left to right and from top to bottom. This is mathematically simple as are the final forms of Newton's and Einstein's laws.

The right elastic limb of the mechanical limits triangle is the upper half of figure 3. This is the extended elastic equations domain of Hooke's law. The Vp2 vs. Vs2 planes shown on figures 1, and 2 are the elastic mechanical systems plane. Figure 2 in the article demonstrates that the dry and wet sedimentary clay minerals have Poisson's ratio values of about 0.29. Water-wet clay mineral have very low elastic moduli. Their associated electrostatically bound water acts as a surrounding cushion until almost all water is forced out due to compaction.

Poisson's ratio is a constant for individual minerals a virtual constant for SiAlic sedimentary clay minerals at 0.29. Poisson's ratio as a mineralogic property does not change with depth. Fracture pressure changes in complete accordance with [mass-energy] conservation. This applies to clay, quartz, and calcite minerals as well as mixtures thereof.

Minerals respond differently due to differing elastic and plastic properties. Each mineral conserves [mass-energy] with the means at it's disposal. Fracture pressures in claystones, sandstones, and limestones are different. But, they all respond in the same way. This is an end-member plastic relationship for all minerals.

The elastic mineral and fluid coefficients map directly from figure 1 to figure 3 in the article. Mass conservation is identical in both domains. Thus we have both elastic and plastic [mass-energy] mapped on the same figure! Their representation as related conservation laws was shown on mechanical limits triangle. Earth mechanical limits are a direct response to [mass-energy] conservation in the earth.

[Mass-energy] is also conserved at the Newton and Hooke vertices of mechanical limits triangle. These two men are the founders of today's mechanics. Pascal is the founder of fluid mechanics. Isaac Newton, Coulomb and Hooke are honored by their placement on the cover of "Pore pressure through Earth Mechanical Systems". I'm happy to have brought their physics together in our host planet earth.    RETURN TO TOP

Interior of the Earth's mechanical systems triangle

Solid matter response is asymmetrical within [mass-energy] boundary conditions. The asymmetries are positive integer ratios constant <2> .Deep and strong rocks can store more potential energy and "stick" longer. This stored potential energy is released suddenly causing earthquakes. The total energy released can be measured with seismometers.

The lowest earth [mass-energy] occurs in recently deposited sediments that are just below the earth's surface. These sediments have the lowest strength and provide the truest direct measure of [mass-energy] in the earth. The even number tendencies prescribed by the effective stress conservation law are most closely met in these sediments. Physically explicable deviations increase with increasing [mass-energy].

Data from the Long Beach Field is within the sheared zone between the North American and Pacific plates (chapter 4). It shows strong [1:2:3] ratio predominance above 5000 feet. Data from the passive margin Gulf of Mexico shows a strong [2:-1:-1] predominance. That even number is also strongest in the shallow sediments. Stress ratios in both sheared and passive margins, and in all lithologies present seem to obey the effective stress conservation law!

The mechanical systems triangle may be a curved surface. The rates of relative particle motion increase from the plastic to the elastic limits. Both limits are finite and the shape of the triangle's surface can be mapped. The triangle's surface is probably smooth and continuous with respect to time, rate, mass and energy. A contoured surface might provide a non-linear boundary to Newton's law as Einstein's law did. Time and measurements will tell.

The earth's interior is the only place where humans can make such measurements. Geologists can examine this unusually [high mass low velocity] data. Whether near end-member data is planar or curved bears on the overall [mass-energy-space-time] continuum. Prediction of transitional time-dependent [stress/strain] relationships will be more reliable in either case.   RETURN TO TOP

Why learn about the earth's two-phase mechanics?

The earth is a two-phase planet. This earth specific [mass-energy] synthesis explains the forces and fluid pressure therein. There is no way of escaping the fact or this conclusion. Most geoscientists must face and explain earth mechanical relationships to other scientists and engineers sometime in their career. Whether that explanation makes mechanical sense or not reflects directly on us. Other scientists can quickly detect mechanical nonsense when they hear it. Anybody can tell when the dimensional units don't correspond. If we are vague or speak mechanical nonsense, our overall credibility goes down.

One possible short answer could be "Newton's law applied under the earth's horizontal effective stress boundary conditions." That definition when carried out further goes on to explain force magnitudes in the three earth tectonic regimes, continental drift and compaction. These have been fundamental questions in geologic sciences that have dozens of proposed answers.

All physically reasonable answers should be consistent with the conservation of [mass-energy] in the earth. This is an easy test to define that few of the competing hypotheses can pass. Both the limiting mechanical systems just mentioned conserve and relate [mass-energy]. The transitional mechanical systems within the area of the mechanical limits triangle do as well. Stick along faults may be outside the triangle for a geologic moment. But inevitably slip or pressure solution will restore force balance.

Newton's [mass-energy] answer applies above the earth. If you algebraically add appropriate conservation laws, [mass-energy] conservation works in the earth. It also explains a whole lot about earth mechanics. [Mass-energy] conservation in the earth represents significant forward progress in the history of science and earth science.

Working professional geoscientists and earth science students have a more pressing need to understand earth mechanics. The pressures that we drill into can kill. If you missed it, you can go back to the mass-energy passage. Less dramatic but also very important is the economic production of hydrocarbons from the earth. Accurate continuous information about loads and fluid pressures can be used to optimize hydrocarbon recovery. See the paragraph immediately preceding the "why learn" question.

[Mass-energy] conservation is accomplished by the earth throughout production of a reservoir. [Mass-energy] is neither gained nor lost. Most of our attempted force fits to data are now done without using any boundary conditions. Today's engineers and geoscientists are generally unaware of the physically real constraints that are expressed by the mechanical systems limit triangle.

By not using real mechanical constraints, they probably miss their fluid recovery objectives quite often. Using mechanical constraints would give results like a bowling lane with walls instead of gutters. Through education we can first understand and then erect those physically real mechanical systems limit walls.


The Menu bar below facilitates access to other areas of this website. The primary mission is to educate geoscientists to the forces in the earth. Other people with a general interest in physical science are also welcomed. News contains latest press releases. Related free_ publications and books are listed. Consultative services including force balanced logs are available. In house training in the form of short courses and mentoring is also available.   RETURN TO TOP