Fracture mechanics testing of intact rocks and impact testing of steel rods with cushion materials or slip mechanism for scientific applications in all walks of life

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Fracture mechanics testing of intact rocks and impact testing of steel
rods with cushion materials or slip mechanism for scientific
applications in all walks of life

Submitted to International Conference on Rock Joints and Jointed Rock Masses 2009, Tucson,

Arizona, USA
-
January 4
-
11, 2009, abstracts deadline April 30th. By

Yi XiaoPing, Nationality, citizen and P.resident of P.R. China; Former resident of R.K. Sweden; Naturalized
citizen and P.resident of D. Canada; P.resident of U.S.A.. April
-
May 2 2008. Ple
ase email comments to:
Yi_Xiaoping@yahoo.com. (* footnote)

1. The propagation of microcracks and cracks in intact rocks

(1.1) Laboratory fracture toughness testing on the short rod specimen of Kallax gabbro and Bjorka marble of
diameter D = 31.5 to 98 mm
and 1.45D length was performed in Lulea, Sweden. Servo
-
controlled loading was
employed to achieve constant crack mouth opening displacement rate to obtain the complete load versus
displacement curve. The loading simulated localized tensile and compressive
stresses found in many situation
(Fig.1). A fluorescent penetrant dye was used to trace crack propagation and the microcracks. Acoustic
emission and visual or microscopic measurements were taken from the 71 mm diameter specimens. The grain
size is less tha
n 1 mm for the gabbro but 0.2 to 3.8 mm (1.1 mm average) for the marble. It was found that in
the hard Kallax gabbro, the main crack was formed by micro
-
cracking, coalescence of microcracks, crack
bifurcation and looping. Only the microcracks absorbed the
fluorescent penetrant but not the grains and their
boundaries, and over 90% of the microcracks ran across grains (Fig. 2). This means that the intact gabbro is air
-
tight and impermeable. Although one main crack may break a specimen into two halves, the roc
k material in the
vicinity of the crack sustained microscopic damage, and a bifurcated crack may remain hidden from the naked
eyes in the rock. While microcracks were created during crack propagation in the hard linear elastic Kallax
gabbro, the damage in
the intermediate Bjorka marble appeared more concentrated on the fracture plane. Non
-
elastic or elastic deformation elsewhere could not be detected because the rock grains and boundaries all
absorbed the fluorescent dye. This meant that the pores and grain

boundaries were interconnected in the marble.
Maximum acoustic emission occurred after the specimen strength was passed, more so in the hard Kallax
gabbro which had 10 times more acoustic emission count rate than the intermediate Bjorka marble which
manif
ested more flexibility or yielding displacement on the complete load versus displacement curve. Existing
data on material properties have also indicated that the higher the strength or fracture toughness, the less
deformation at the strength point. The exp
eriment clearly indicated that an interconnected microcrack zone of
about 10 mm was created in the hard Kallax gabbro. Other researchers have found longer fracture process zones
in granites with ultrasound probing method, or in concrete. The tough rocks an
d rich iron ores in Sweden would
suggest that water content, ice and snow have kept the rocks intact and hard. The different colors of rocks
would suggest that the weather and nature in Sweden was different at the time of the rock formation. The iron
ore m
ay have to do the strong electromagnetic field near the north and south poles. Tidal waves cause stress
increases in the continent and seismic waves cause vibrations or damage in rocks particularly at underground
holes or openings (ref. Ph.D. Thesis). Incr
easing in
-
situ stresses in the continents of the northern hemisphere
may continue to make intermediate rocks into hard ones, or cause earthquakes or volcanoes.

2. The elastic and plastic response of steel rods to impact loading

(2.1) Structural steel rods

of 6.35 to 16 mm diameter and 2.44 or 1.22 m length were tested in the laboratory in
Sudbury, Canada with drop weights from 0.5 to 17.723 kg at heights of 0.1 to 1.4 m (Fig. 3).


Strain gauges and
a computer data acquisition instrument were used to record

the strain waves. Conveyor belt rubber layers of
13.5 to 108 mm thickness, a manufactured wood wool plate of 11 to 13 mm thickness and a soft wood block of
39 mm thickness were tested as cushions. A steel clamp was tested as a frictional slip device. It w
as found that
the strain and stress wave in the steel rod exhibited a unified law of mass impact, stress wave and vibration. The
rider stress wave was due to the instantaneous impact and it was reflected at the rigid top and the plated but
otherwise free b
ottom connection points. The superposition of this stress wave going up and down the steel rod
constitutes the unified wave which includes the lower frequency vibration wave (Fig. 4). Computer simulations
demonstrated the importance of wave reflection or t
ransmission at the top and bottom interfaces. The vibration
can also be explained as the loading of the steel rod by the gravitational energy of the dropped steel weight. As
the drop weight to steel rod mass ratio was decreased, the rider stress wave becam
e more significant or
dominant. Conversely, as the ratio increased, the vibration wave became more significant or dominant. It was
found that when the steel rod was dynamically loaded into yielding deformation, the rider wave that was present
in the elasti
c range disappeared, i.e., the yielding steel did not transmit the rider wave. The test demonstrated the
energy transfer of the drop weight to the strain energy of the steel rod in the mechanical system. The above
proof of the "three part unity of mass imp
act, stress wave and vibration" would lead to broad applications of the
stress wave and the resonance or perturbation vibration theories.

(2.2) It was also found that the simple impact test in the laboratory that was designed to exert uniaxial tension
als
o caused minor bending and torsion stresses due to clamped constraint at the top and threaded plate at the
bottom points. Bending or certain torsion conditions create local tension and compression. The cushions in the
tests all had the effect of eliminatin
g the rider stress wave. Thick cushions reduced the stress amplitude but
increased the time duration or period of the vibration wave. The thick conveyor belt rubber cushions behaved
elastically but the soft wood cushion underwent yielding damage visible wi
th naked eyes. The number of
impacts required to break the steel rods varied from 12.8 without cushion to 19.5 with 108 mm rubber cushions.
The number was 12 for a test on a soft wood cushion. In geomechanics studies, these cushions may be
compared to soil
, biomass, fossil or soft rocks in the earth. The frictional sliding clamp sometimes demonstrated
the classical stick
-
slip frictional behavior when the clamping stress was not too low and not too high. It reduced
steel plastic deformation caused by the imp
act loading while creating higher frequency elastic waves. The tests
indicated that about 8.8% of the plastic strain for the steel rod was uniformly distributed on the entire length.
The remaining 3.2% was localized in steel necking at the final rupture po
int. The accumulation of plastic strains
over the number of impacts that have exceeded the yield point during the elapse of time would require special
attention in rock mechanics, earthquake, rockburst, volcano or blasting conditions. So does the case wher
e the
existing static load is just below strength such that additional dynamic load would exceed the yield point. For
jointed rockmass, non
-
elastic displacement is often measured at relatively low stresses. It is clear that three
types of criteria for stre
sses, strains and energy should be used for damage and failure assessment and support
design.

3. Applications of the experimental and analytical results

(3.1) The above discoveries may be applied to sciences, technologies, arts, health, engineering, law,
politics and
economics, especially to the study and analysis of systems. Biomass and fossils on the ocean shelf and floor
could help form inverted flexible arches under favorable conditions to dissipate the dynamic energy of the
ocean salt water at islands

or continents, and of the movement of rock blocks. So could live creatures. Dynamic
energy could be dissipated in rockmass that is rich in moisture, biomass, roots, fossils, oils or binding minerals.
Such dynamic energy could even help make soil into rock
s, soft rocks into hard ones or even into mineral
deposits under ideal conditions in the earth. Otherwise, the extra dynamic energy at the oceans or high
mountains causes rock fracturing or earthquakes to dissipate the energy (ref. San Francisco Bay, Himal
ayas and
Kunlun mountains of Asia). On the west coast of America, such as central America, besides soft rock failure in
bay areas, the undercutting of vertical mountains due to vertical gravity stress and horizontal ocean wave
loading may occur. On one han
d, the rockmass in water or with bio
-
material filling and sealing in moisture
environment is kept strong. On the other hand, in dry open joints or fractured rockmass, occasional water pore
pressure could reduce the clamping rock stress on joints or faults
to cause seismic slip. Rockmass fracturing and
the rupturing of cablebolt or rebar can be heard with naked ears in large scale deep underground mining (ref.
Golden Giant, Williams and David Bell mines in Marathon, Province of Ontario, Canada). The test res
ult that
the yielding steel did not transmit the rider wave would suggest that a massive rupturing earthquake may not be
detected or fully measured by the earthquake monitoring system, particularly in jointed, damaged or soft rocks
(ref. the 1906 San Franc
isco Earthquake of estimated 8.25 magnitude on the Richter scale). The test result that
boundary interfaces play a critical role in stress wave and vibration energy dissipation would suggest that joints
and faults require proper treatment. The geotechnical

practice of draining engineering foundation to prevent
ground water pressure buildup may cause gradual cracking and fracturing of the rockmass. Comprehensive
elastic and biological methods should be used for long term stability and safety of foundations,
structures and
buildings.

(3.2) As seen from the general vibration theory, if a steel rod that is used to reinforce a blocky material and it is
prestressed statically, it will behave like the above impact test when the prestress or a block weight is someh
ow
released suddenly, such as in explosion, blasting or sudden element failure. The unified law of mass impact,
stress wave and vibration has important applications for earth sciences, earthquake and rockburst monitoring,
and structural or machine design i
n and on rock blocks, islands or in water. The existing technologies of
geophones or accelerometers may not detect the rider stress wave or the base vibration wave in certain
situations, or the vibration wave may be mistaken as the seismic wave in some oth
er situations. The small and
intermediate earthquakes are valuable for research purposes. The author experienced the Gilroy earthquake of
5.2 magnitude located in the south of San Francisco on May 13, 2003 in San Rafael, Marin County, to the north
of the G
olden Gate Bridge, California (ref. www.usgs.gov). The earthquake occurred during strong southern
wind and caused horizontal vibration in the three storey apartment building.

A retired school teacher said that
the past earthquakes showed up as more vertica
l vibrations. Such earthquakes or the existence of fresh faults or
joints are indications that the surrounding rockmass is subject to high stresses. Conversely, high stresses are one
of the conditions for earthquakes or rockbursts. The existing seismic mon
itoring system can normally detect slip
type of earthquakes due to compressive and shear stresses.

(3.3) The three part unified law of mass impact, stress wave and vibration can help explain and extend the
unified theory of light as particles and waves to

include stress and vibration (cf. Chinese characters "Xing
Guang" in the sentence "Zu You Xing Guang Yuan" (
) from the Yi Shi Zu Pu Zong Ci of
MaiYuan, WuJiaQiao township, DongAn county, Hunan Province, P.R.China at 1400 AD, which meant
seasonal sound, food plant fragrance and light; Newton 1643
-
1727; Maxwell 1831
-
1879; Hertz 1857
-
1894;
Einstein 1879
-
1955). The Newton equation of kinetic energy,
E = (1/2)mvv with "m" for mass and "v" for
velocity, and the Einstein (1879
-
1955) energy equation, E = mcc with "c" for the speed of light, indicates that
the earth's atmosphere and gravity affects at least half of the light's energy arriving on the surfac
e of earth, the
other half being the internal energy of the intact light photons. Such internal energy may go into food and wood
growth in photosynthesis or be released as heat in adverse conditions such as on desert or beach sand. Sir Issac
Newton's name
means "think of the earth, mountain pines rely on water buffalo and river pool village" in
Chinese. He was interested in the fruit trees and how the earth could have the intellectual and physical ability to
maintain normal voyage around the sun. Powered st
eel
-
concrete buildings, urbanization, water
-
sewage,
transportation, machines, weaponry, or other industrialization based on the three Newton's laws are contrary to
the philosophy of Newton. Catalyst spray with airplane or cannons to force down cloud, rain
or snow is against
the earth and the human kind. So are pollution of dew, water and snow on the ground, or the waste of electro
-
magnetic resources contrary to the seasonal weather change. "Einstein" sounds like the Chinese "Ai Yin Si Tun"
(love cloud and t
ree shade and think of flowing water pool village). With gas, particle and electromagnetic
wave air pollution, the earth's surface may receive the impact of particles, molecules and atoms much heavier
than the photons. Invisible microwaves of 1 to 300 mm w
ave length (300 megaHertz to 300 gigaHertz) likely
create resonance in oil and water or other molecules to heat up quickly. Einstein energy equation also shows the
importance of burning renewable firewood for cooking and plant oil for light. Nuclear energy

or solar electricity
in Einstein's name is contrary to the purposes of science and technology. The things on earth either act as
medium to absorb the light energy in photosynthesis, as sunshine impact cushions for the earth, or reflect the
sunshine on the

white snow or clean ocean water. The above impact tests on cushions provided a simple
explanation of the Einstein's theory of relativity to consider the three dimensional space and matter on the earth
surface or under water as cushions, and life span as t
ime. Prudence, indeed, dictates that every person must use
less resources and energy, reduce waste and pollution, and cultivate earth resources for everlasting eternity and
to prevent the occurrence of human or natural disasters.

(3.4) The stop and revers
al of global warming and drying, no risk construction on land surface, and the
agricultural use of wood and bamboo materials, simple wood based machines and small metal tools are most
appropriate for the human kind and the earth. Trees, wood, mud and rocks

are clearly better than manufactured
materials for protecting the rockmass and the earth, and to use as construction materials. For people who do not
know about the costs and waste of human resources, energy, materials, long term pollution and damage of
e
cosystems in the design, making, employment and waste disposal of machines and vehicles. These luxuries
have caused lots of misunderstanding about the distinction between useful and useless work or job. Mechanized
production in agriculture demanded large d
ry and even land field, but with much less yield per unit land surface,
less food variety, much more pollution and damage of the land and ecosystem. Failing to understand the cost or
waste of money administration, mining, manufacturing, distribution, banki
ng, protection, spending, devaluation,
commodity depreciation, property redistribution, garbage disposal and investment services for retirement and
higher education would fall into the same pitfall. The plastic or brittle damage of some used materials like

steel
can not be seen by the naked eyes and are difficult to detect. Similarly, used power machines may have
undergone accumulated damage that can not be found with naked eyes and is nearly impossible to detect. In
order to avoid and prevent dynamic mater
ial damage and waste, it is preferable to apply renovation, repair or
spare part replacement of existing buildings, structures or machines than to blast or mechanically excavate them
down. Due to the added cost and environmental impact of import
-
export adm
inistration, dismantling, cleaning,
packaging, transportation, storage of goods and their final waste disposal, international trade of used materials
and machines, or even some new goods, for the purposes of creating jobs may not be worth the effort. The
w
isdom expressed by Francis Bacon (1561

1626): "knowledge is power" is more relevant than ever.

4. The meanings of the word "science" and the characters "Ke Xue" (
)

(4.1) The English word "Science" came from the words "Yi Scenery" from the ancient Chinese book entitled
"Yi Jing" (I Ching) which consisted of 81 Chinese characters and 64 hexagrams. It includes the first "Yi Jing
Ten Sceneries" of nature and agricu
lture, that is, "Yi Jing Qian Kun Tun Meng Xu Song Shi Bi"
(
). In fact, the 26 letters of Chinese PinYin and English language came from the first
Chinese ch
aracter "Yi" here. Since it sounds the same as the Chinese number "1", this "Yi" is probably the first
Chinese character. The Chinese characters for science "Ke Xue" represented more or less the same meanings as
"Science". The Chinese character "Xue" shows

"Mountain, Flowing Water, Small, Eight, Characters
-
Words,
Shelter and Rain Cloud, Protect Children", and "Ke" shows "He Dou" (Wood, Work, Rice Plants, Food Plants,
Beans, Roots, Head, etc.). The ancient book "Yi Jing" (I Ching) was passed down mainly for
the purposes of
remembering the ancient life environment and a way of life, the origin and importance of written languages, and
signs or sound signals. It ought to be mentioned that there are many mistakes in the popular English translation
of "I Ching" (B
ook of Change). The English word "Technology" means "take in knowledge". The
corresponding Chinese character "Ji Shu" means "to aid the chicken and trees and the Garden of Eden". During
the change of weather around the earth in yearly cycles, fresh water (
H
2
O), moisture air, rain, ice and snow are
the most important mobile matters for the earth to function normally and sustain living things and the human
kind. Together with the connected continents, fresh water matters can help quickly redistribute and equa
lize
sunshine and fresh air energy throughout the earth. Insufficient fresh water and trees would lead to overheating
and overcooling of land areas to cause the loss of soil, fracturing of rockmass, the spread of deserts and
atmospheric temperature increas
e. "Fresh Water" in Chinese is "Dan Shui", which means "should shoulder
water or have sufficient sleep". "Fresh Water" sounds like "free fishy water" in English, and "free rich happy
person; frogs, hoeing, talking, plant leaves and sprout, etc." in Chinese
. The molecular formulas "HHO" coded
concise and practical information. "Hh" look like "a person walks and shoulders firewood branches on a pole,
high mountain, river tributary". "H" is a 90 degree rotation of the Chinese character "Gong" for "work", that
is,
work of the sun, moon, earth and humans. "Hh" sound like the Chinese "He" that sounds like the Chinese
"River, Drink, Clam, Rice Plant, Water Lotus, Tree Nuts, Crane Bird, Jackal, Brown
-
Black, Peace, Harmony,
Cooperation, Why, Congratulate, Expose, Fri
ghten, Unity" etc.. "Oo" look like "Oceans, Seas, Lakes, River or
Canal Pools, Marsh Mire, Rice Paddies, Ponds, Trees, Earth, Moon, Sun" etc.. They sound like "Water" and the
Chinese "Wo" meaning "Me, Keep
-
Hold, Nest, Shelter
-
Shed
-
Shack, Excrete, Lie Down
or Sleep, etc" . These
things and activities help reduce the consumption and waste of water or help conserve fresh water and make
hydrogen (H), oxygen (O) and water (HHO) bit by bit. Light hydrogen and carbon gases are released from cut
off grass, leaves,
flowers and tree stems in water or on land, but the heavier oxygen gas together with nitrogen
is probably released from the intestine gas and excrement of creatures and plants in water or on land, firewood
burning and food cooking. Hydrogen, carbon, nitrog
en and oxygen, whose atomic weights are 1, 12, 14 and 16
respectively, may combine into fresh rain in lightening and thunder. "H
2
O" may also represent the effective
world population policy of "two children per couple or less".

5. Perspective remarks

(5.1)

The earth is likely not a solid globe but like a floating balloon, that is, a globe of mixed solid, frozen
materials, gas and liquid materials sealed in a rocky or frozen crust, which is maintained by internal air and
external water and air pressures. The

rocks were likely formed of a mixture of fossils, heat treated rocks and
early meteorites. Like the needle injections on the human body, hole drilling in the earth's crust will reduce the
life span on the long run. The earth's self rotation axis is tilted

at about 23.4 degree (ref. www.wikipedia.org)
and points approximately to the north of the solar system. The axial angle from the solar system plane is
unknown. This is the reason for the yearly seasonal changes. Geological evidences such as the limestone

rock
on the plateau of Yunnan province of China and the dried out sandy river bed in the Chino State Park in the east
of Orange County, Southern California indicate that the land has dried up and ocean water level lowered
continuously in history. The decr
eased weight of the rockmass, water and trees, together with reduced
permanent ice and snow area in the pole regions and the weakening of electro
-
magnetic fields has probably
made the earth's axis more vertical (Fig.5), that is, from a more horizontal recl
ining position to a more vertical
position where the sunshine is more concentrated around the equator. In other words, the yearly seasonal
weather change was more widespread from the Antarctic to the Arctic regions, and the equator region also had
seasonal

weather changes. The name "Dominion of Canada" and the "Dominic Republic" may suggest that
"Dao Mi" (rice) was planted by the native Americans at early times. Books have recorded that native tribes
planted wild rice and migrated to live by the seasonal ch
ange. This may be cultural evidence for different
weather conditions in the past. The American Indians and many other people all around the world did not
establish permanent residences like the Chinese comprehensive farmers. That was in a way unfortunate f
or them
and the earth. They keys for happy permanent residence is to perform different works according to seasonal
weather change, such as comprehensive agriculture, sufficient rest and sleep, literary, intellectual and handicraft
works during the winter.
It is probable that the gradual earth's axial change has been caused by factors such as
global warming, drying up of the crust in the northern hemisphere, reduction of permanent ice and snow at the
pole regions, deforestation and food production on hills a
nd mountains, mineral and oil mining and heavy
material transportation from the north to the south.

(5.2) The author's observational study of weather and solar system in the United States of America from 2004 to
2008 (cf. Planet Finder on www.lightandmatt
er.com) has indicated that there are distinct weather changes at the
four critical phases of the moon: full moon or moon eclipse on the 15th, half moon in early morning of the 3rd
week, invisible moon at solar eclipse on the 1st, and half moon in the eveni
ng at the 1st week of the lunar
calendar. The dew on the grass may become the cloud in the sky, and vice versa, in the monthly cycles. The
earth and the moon have three possible relations: (i) the moon orbits around the bigger earth; (ii) the earth orbits
around the bigger moon; and (iii) the earth and the moon follow the same circular orbit at 180 degrees apart.
The Chinese meanings of the English words "Earth" (moving ears and child) and "Moon" (mother person, forest
shade, not the hard way) would suggest

that the earth or the moon may travel out of the solar system plane in
monthly cycles. The characteristics of the moon could range from a globe like the earth to a planet like a
burned
-
out sun. The size of the sun could be of the same order of magnitude a
s the moon or the earth. Beside
the meaning given in Section (3.3), the sentence "Zu You Xing Guang Yuan" might also suggest that the earth
came to the solar system or that the human kind came to the earth. The human kind may not damage the earth to
find t
he unique truth because the truth would have changed by the time the truth is discovered. Careful passive
observations and listening over longer periods of time can lead to great discoveries without causing damage. In
the year 2008 in Dublin, Ohio, the aut
hor found that the popular belief that the North Star in the 7
-
Star Little
Dipper ("?" shaped formation) pointed to the north direction is untrue in the winter and spring seasons. The
hitherto claims of moon landing and safe return were mere movie footages

(ref. airplane pilot and Apollo
astronaut Neil Armstrong).

(5.3) The name "Canada" came from the Indian First Nations St. Lawrence Iroquoian language for "village" or
"settlement". According to the Chinese
-
English dictionary, "Iroquoian" was related to t
he Chinese character
"Yi". "Canada" was likely related to "China Da" or "Kina Da" which would mean "China Is Great" or "Great
China". Christopher Columbus (1451

1506) made three ship voyages from Spain to Central America. His time
was in the Chinese Ming d
ynasty (1368

1644) immediately after the Yuan dynasty (1271

1368) that created
international markets from Asia to Europe. Rapid expansion from Asia, Europe and Africa to the new continent
of America likely occurred in the Yuan and Ming dynasties. During th
ese periods, the Chinese comprehensive
agriculture was prosperous in southern China. Today, the human kind has realized that population and industrial
expansion have resulted in the rapid global warming and worsening of the earth's ecosystems and the livin
g
environment. It is likely that the earth moves with a combination of internal biological and electro
-
magnetic
energy, sunshine energy and occasional external input or output in connection with the moon. The principles of
photon impact, stress wave and vi
bration are at work. Occasional high energy exploration and military rockets
or explosions, volcano eruption or the accumulated jet propulsions, stress waves and vibrations could damage
the earth or alter its movement. In the recent century of industrializ
ation, air pollution became a major problem.
Photons, electromagnetic waves and man
-
made particles, molecules and atoms may have collided with each
other to create heat and secondary pollutions.

(5.4) The fear of flood water and wild animals as expressed
in the first book of “Genesis” and the last book of
“Revelation” of the "Holy Bible" was a thing of the past or predictions without science. The Genesis was
adapted from the first 60 hexagrams of "Yi Jing" (I Ching) and the Chinese "Surname Tribal Genealog
y and
Naming Poem" tradition. It was a mistake to expand the tradition into big religious congregations that do not
even have a family name. The 930 years of longevity for Adam Eve was most likely mistaken for 930 months
(with the Chinese "Yue" mistaken as

"Year"), that is, 77.5 years. The 110 years of longevity for Joseph, who
was the 11th son of Jacob Israel and a minister in Egypt, was probably true based on the current longevity of
women in the countryside or in the city. The word "Eve" referred to evol
ution and progress. The title "BIBlE"
was likely meant to refer to the "81" Chinese characters of "Yi Jing" (I Ching) and another "81" Chinese
characters of the "Yi Shi Zu Pu" (Zong Ci) of the Chinese "Surname Tribal Genealogy and Naming Poem"
tradition. "
Yi Jing" was likely used as a reminder of the much better and much less ambiguous "Yi Shi Zu Pu
Zong Ci". This was likely meant to prevent intentional or unintentional damage. But with population expansion,
internal and external struggles and wars, this wa
s unfortunately forgotten. Even the correlation between "Jesus
Christ" and the 60th hexagram "Jie" of "Yi Jing" has been mis
-
interpreted. The Chinese "Jie" means mainly
"connection, thrift, festival, save, moderation, abstinence".

(5.5) Statistical studie
s indicate that the reliability probability of a feasible system of A, B and C elements in
series decreases as the product of "A x B x C" for imperfect neutral elements. For example, three 80% reliability
elements in serial connection would make a 51.2% re
liability system. The connection joints are assumed to be
perfect here. The long term reliability probability of a feasible system of A, B and C elements in parallel
connection is the average of the elements "(A + B + C)/3" for imperfect neutral elements.
For example, three
elements of 70%, 80% and 90% reliability respectively in parallel would make an 80% reliability system. The
long term system reliability should increase for learning and supportive elements, especially for interconnected
elements found i
n many bio
-
systems. It should decrease for non
-
learning and damaging elements. For all cases,
the addition or perfection of elements in a system is limited to the available space, resources and time. The
Chinese proverb of "one monk shoulders water, two mo
nks together shoulder water, three monks have no water
to drink" is wise for independence, cooperation and association. It looks like a law of the planets and stars in the
universe. The Chinese "Xing Shi Zu Pu he Zong Ci" (Surname Tribal Genealogy and Nami
ng Poem) tradition
together with a unified peaceful association or government that is free of charge in principle would provide
great opportunities for the free development and perfection of each and all (ref. the manifesto by Marx and
Engels). Unfortunate
ly, the practice of the "chain command" management in some government agencies,
military or police establishments, or corporations is like the above serial system. It is no wonder that there is no
fresh water to drink. The Chinese language or other mature
languages are interconnected systems of literacy,
wisdom, science and technology that took thousands of years to form, improve and perfect. Its learning,
maintenance, accurate use and application is of the most importance to the earth and the human kind.

(5.6) The beginning of the new millennium is the right time to spread the sustainable ways of production and
life that has been established in China or elsewhere to enable each and every person to live happy and healthy
longevity on the eternal and everlas
ting earth. The mining engineering specialty is the earliest industry that
helped the human kind to stand up and engage in food production, clothes making and dwelling construction,
etc.. It is still the most widespread and important industry all around th
e world. The spread of knowledge,
education, research, training in mining engineering and industry have been on the decline and should be
improved. Comprehensive popular earth science and agriculture education and practice need to be increased.
The Chinese

education policy should be a guide for countries all over the world, that is, "Our education policy
should be to enable the educated people to develop in ethical, intellectual, physical educations and several other
aspects to become manual workers with so
cialist conscience and literary cultures.". Bureaucracy, militarization,
urbanization and industrialization should stop. Industrial plants should not forget one of the meanings of
"industry" ("Gong Ye" in Chinese), that is, "to work for leaves and tree sha
de". Research results should be open
to the public and existing technologies should be fully used and perfected to realize the profit and benefit of past
investment and to reduce new cost of research and development.

(5.7) The normal voyage of the earth r
equires hills and mountains. The 7 km high Himalayas would not show
up on the circular earth of 12,742 km in diameter if viewed from the moon. Like a pearl from the clams, a
mountain view of the distant sceneries or a bird eyes view of the earth, the prese
nt 10 page short article is
condensed from the author's 150 page pre
-
doctoral Licentiate of Engineering thesis from Sweden and 270 page
Doctor of Philosophy thesis from Canada as well as articles from additional research. The readers are
encouraged to read

the two thesis book and other published articles posted on the internet as shown in the
references.



Figure 1. Fracture toughness test set
-
up.


Figure 2. Grains, cracks and microcracks on a slice of tested Kallax gabbro specimen. The grain size was less
than 1 mm and the photograph was taken at 10 magnification.


Figure 3. Experimental set
-
up for weight drop tests of steel rods.


Figure 4. Rider strain wave and vibration base wave from a weight drop test No. 4
-
2
-
1.


Figure 5. Sketch of the earth, moon and sun relations. There are three
possible relations between the earth and
the moon.

References (**)

(1) Yi Xiaoping 1987. Crack Propagation and Fracture Toughness in Short Rod Specimens of Hard Rocks. Pre
-
Doctoral Licentiate of Engineering Thesis, Division of Rock Mechanics, Lulea Univer
sity, Lulea, Sweden.
In
English
.

(2) Yi Xiaoping 1993 "DYNAMIC RESPONSE AND DESIGN OF SUPPORT ELEMENTS IN ROCKBURST
CONDITIONS ". Doctoral Thesis, Queen's University,
Laurentian University and University of Toronto
In
English

(3) Yi Xiaoping 2005 "The Meaning of Mining". Internet Publication.
In English


(4) Yi Xiaoping et al.. Journal or conference publications from the theses and more are posted on the internet at
w
ww.Geocities.com/Yi_XiaoPing
.

(5) www.wikipedia.org the internet encyclopaedia. www.lightandmatter.com the Java applet Plant Finder.

* footnote: Yi XiaoPing, Ph.D. from Canada and China; Predoctoral Lic.Eng. from Sweden and China;
B.Sc.Eng. from P.R. Ch
ina; Eng.I.T. Cert.Prog. from U.S.A.. Agri. worker, Lecturer(Ass. Prof.) of P.R.China;
Former President
-
chairperson
-
CEO of XY RocCAD Inc., P.Eng., Sr.Eng., Adj. Prof., P.resident of D. Canada;
Incorporator of Pulsehead Corp. of U.S.A.; Current postal addre
ss: P.O.Box 664, Dublin, Columbus, Ohio,
43017, U.S.A. Website: www.YiXiaoPing.com (temporary on www.Geocities.com).

** footnote: Searchable digital copy of the author's doctoral degree thesis with software as well as the scanned
pre
-
doctoral Licentiate t
hesis (errata corrected) is available from the author at a processing fee of $20 plus cost
of mailing. Those who can not afford may apply for partial or full fee waiver. Please recommend to your
library. The unbound 270 page Ph.D. thesis can be ordered at
CND$20 or USD$20 from Thesis Service at
http://www.proquest.com/products_umi/dissertations/. Please keep the following kind requests on your mind:

(i) Please help persuade the Chinese communist party, government branches, embassies and consulates to renew

my Chinese passport and permanent resident card according to the 1980 "Chinese Nationality Law" because the
"Naturalized Citizenship" of Canada is not "Nationality" but a replacement for visa. The Chinese government
branches and media have failed to sprea
d this law. The Toronto consulate failed to inform me about this law in
1995 when I changed my passport from "For Public Affairs" to the standard one. Dr. Sun Yatsen (ZhongShan,
Wen), the Chinese people and international friends have struggled for the "Chi
nese Nationality" since 1911. My
grandfather Yi GuangYun (1907
-
1935) died for it at the age of 28. My father Yi ShiPu (1926
-
2003) died for it
in year 2003. Some Chinese Olympians overseas may not be able to attend the 2008 World Olympiad in Beijing
on beha
lf of China if the current practice of denying Chinese passports to Chinese nationals continues.

(ii) The Chinese Education Ministry and the Central South University in Changsha, Hunan, sent the author
abroad to Sweden and Canada since 1984 for cooperativ
e graduate studies and research between China and
friendly countries, but have failed to accept him back. The author has made many achievements and
contributions to China and the world. Please help this author and family return to China to work.

(iii) Wit
h or withour remuneration, the author is available for employment or cooperation to give presentations,
seminars, teaching, training, research, business consulting, administration or management, report writing,
engineering consulting, software services, su
mmer job, internship, grant application with university faculty,
journal or grant application review, or distribute the theses or any other works.

(iv) The author was offered permanent employment by Autodesk Inc., California, U.S.A. in march 2000 but was
illegally and trivially fired on August 15, 2000. Reinstatement is requested.

(v) The author's software RocCAD 14.5 for AutoCAD 14 (copyright 1997
-
2008 Yi Xiaoping registered with
Canada Government) was put in the temporary care of Flairbase Inc., Provinc
e of Quebec, Dominion of Canada
in year 2000 when the author was under the influence of persecution, coersion and anti
-
depression pills imposed
by Canadian gangs. Its return and compensation for copyright infringement or ammendment of the letter
agreement
is requested (more details at http://www.geocities.com/yixiaoping3/OHIO/RocCAD145.htm).

(vi) In December of 2003, the original pre
-
doctoral Licentiate thesis together with books and photo albums were
moved to the author's residence at ShengLi Building #14
, Apt. 108, Central South University, Changsha, Hunan
Province, P.R.China after 14 years storage in parents
-
in
-
law's apartment from 1989 to 2003. But, they went
missing after my request to work at the university was denied and left in December. Please help

find them.

(vii) The original Ph.D. thesis was kept in the author's sleeping Ford Escort car which could not be repaired
because of high repair cost and no government support in August of 2005. The car was parked at the Kingdom
Hall of Jehovah's Witnesse
s in Santa Venetia, San Rafael, California, U.S.A.. A travel suitcase with documents
was stolen in broad daylight at the Ritter homeless house in San Rafael. Please help to get them back.

(viii) Since Alfred Nobel was interested in world peace and human h
appiness, the Nobel Prize Committee
should establish a "Nobel Peaceful Science and Literacy Award" to replace the existing subject prizes. The
million dollar prize money comes from industrialization that defeats Nobel's purposes. Please recommend this
arti
cle, the theses and other articles for the first place "Nobel Peaceful Science and Literacy Award" with a cash
prize of $2008.00 in the currency of P.R.China. (cf. www.nobelprize.org)