16TH INTERNATIONAL CONGRESS FOR MINE SURVEYING, BRISBANE, AUSTRALIA, 12-16 SEPT 2016
Influence of Temperature and Humidity on
Equivalent Material and Its Control Measures
Zha Jian-feng1,2,*, Li Huai-zhan1,2, Guo Guang-li1,2
1
Key Laboratory for Land Environment and Disaster Monitoring of SBSM, China University of Mining &
Technology Xuzhou, China
2
The Main Laboratory of Resource Environment Information of Jiangsu
*
Xuzhou
China
Contact: [email protected]
Abstract: A simulation using equivalent (similar) materials is
one of the most common research methods in the field of
geotechnical engineering. The properties of equivalent material
will vary over time in certain environment, and the timevarying characteristics of material strength lead to the
dissimilarity between dynamics and kinematics of model and
prototype. This may affect the reliability of simulation results.
The time-varying strength characteristics of equivalent
material were studied through a block experiment. On this
basis, the measures reducing the influence of time-varying
material strength characteristics on simulation results were
developed to extend the effective monitoring time of an
equivalent material model in the natural environment of
constant temperature and humidity. Research results show
that: 1) The strength of equivalent material has the exponential
relationship with its moisture content. This relationship can be
divided into three phases. With reduction of moisture the
strength is slowly increasing in the initial relatively small
phase, then it is steadily increasing and in the next moderate
phase, and then is significantly increasing in the ultrahigh
phase. The material strength from the steadily increasing and
moderate phases should be selected as the representative
strength, and model experiment should also be performed in
these phases. 2) When the equivalent material model is build,
sampling method and homemade equipment monitoring
method can be adopted to control the experiment. The
temperature monitoring equipment can monitor the critical
change of moisture content. 3) The constant temperature and
humidity can extend the effective monitoring time of the model.
During the experiment, the temperature and humidity should
be set at reasonable levels, and the model monitoring time
should also be arranged reasonably, based on the experiment
requirements. Experiment results can provide evidence for
model monitoring period and the reliability of simulation.
I. INTRODUCTION
The equivalent material simulation method is used to
imitate and analyse the situations in field strata according to
the observations derived from an equivalent material model.
The model is made of equivalent materials based on
similarity theory and the prototype. In 1937, for the first
time, the researchers from the Soviet Union Mine Surveying
Science Research Institute used the equivalent material
model method to study the strata and surface movement.
Because the similar material model has advantages of low
cost, short cycle, visual image and repeatability, it has been
widely applied to study strata and surface movement [1-14].
Researchers in China and abroad significantly contributed to
the research regarding building of equivalent material
model, model monitoring methods, and model error
analysis.
When building an equivalent material model of deep
mining, uniformly distributed load is used to replace the real
strata in order to reduce the model height. Xu has studied
influence of load on the model simulation results. Research
results show that if there is a key stratum, in the omitted
strata, it would lead to the distortion of the load distribution
and the simulation result of key strata fracture interval. In
such case, only the strata above the main key stratum can be
simplified as an uniform load. The equivalent load for the
omitted strata can be calculated on the basis of the key strata
location in the omitted portion of strata and its fracture
characteristics [15].
Lens method is the original monitoring method of similar
material model [16]. With the continuous development of
digital cameras and photographic measurement technology,
these new monitoring technologies are applied to monitor
model by some scholars. Yang used a digital close-range
photogrammetric method to monitor model [17]. Chai
adopted optical fiber as sensors to monitor similar material
model [18]. Yao proposed a new monitor method of similar
material model based on ordinary digital camera [19].
In term of error analysis of similar material model, Cui
analyzed the sources of experiment errors from the point of
equivalent theorem, equivalent material, boundary
condition, temperature and humidity. In his view, these
experimental errors can be divided into three types:
controllable, amendable and unavoidable. The similar errors
of dynamics, kinematics and boundary condition errors are
unavoidable errors. The errors caused by compression
settlement and splitting on the model boundary are
amendable errors [20].
The major errors of similar materials model are model
errors, quality control errors in model design, dynamic
changes of similar material properties as well as model
monitoring errors. Model errors depend on whether the real
problems have been simplified reasonably and the major
contradictions of practical problems have been grasped.
They belong to design issues and will be reduced with deep
knowledge of real problems. Quality control of model
design is mainly to ensure the consistency of the model and
the prototype. The errors caused by model design can be
reduced by enhancing the process management. Model
monitoring errors refer to the stress and displacement during
monitoring. Current monitoring methods can satisfy the
experiment requirements. While time-varying characteristics
of material strength have been seldom studied. In
geotechnical engineering field, the similar materials are
generally river sand, lime and gypsum. Their properties will
change over time, leading to the dissimilarity of dynamics
and kinematics of model and prototype and even affecting
the reliability of simulation results. Based on this, material
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16TH INTERNATIONAL CONGRESS FOR MINE SURVEYING, BRISBANE, AUSTRALIA, 12-16 SEPT 2016
strength time-varying characteristics are studied through
block experiment and measures of reducing the influence of
material strength time-varying characteristics on simulation
results are also further studied.
II. BASIC PRINCIPLES OF SIMILAR MATERIAL SIMULATION
METHOD AND EXISTING PROBLEMS
The nature of similar material simulation is to construct
the similar material model of the proportional reduced strata
in accordance with similarity theory, then to simulate coal
seam mining and observe the strata movement and failure in
the similar model. Finally the conditions of real strata can be
analyzed and predicted by using the similarity criteria. The
similarities of model and prototype are divided into three
categories, that is geometrical similarity, kinematics
similarity and dynamics similarity. Geometrical similarity
refers to that geometry of model and prototype is similar.
Kinematic similarity requires that movement similar of all
corresponding points in model and prototype and movement
time maintain a certain proportion. Dynamic similarity
requires that all forces between the model and the prototype
are similar. In general, it is easy to assure the geometrical
similarity, but kinematic similarity and dynamic similarity
are closely related to the proportion of similar material.
Similar material proportion is determined by the
properties of dry similar material blocks. At present, dry
time of blocks is fixed by habits and it may keep for three
days, seven days, ten days and so on. However, test time of
similar material block will affect the strength. Strength of
similar material changes with its moisture content and may
lead to dissimilarity between dynamics and kinematics of
model and prototype. Finally the reliability of simulation
results will reduce. In general, test time of similar material
block is lack of evidence.
In addition, the maintainable time of model’s similar
strength is the key to keep kinematic similarity and dynamic
similarity, as well as the important basis of model effective
monitoring time. Model effective monitoring time is the
time in which model strength is consistent with design
strength. Similar material experiment should be conducted
in the effective monitoring time. When similar material
strength meets the design strength and changes rapidly, it
will cause the decrease of model effective monitoring time.
Therefore, the maintaining time of similar model is directly
related to model effective monitoring time. However, the
model monitoring periods have not been studied yet.
III. VARIATION CHARACTERISTICS OF SIMILAR MATERIAL
STRENGTH
A. Similar Material Test Scheme
Similar material models used for simulation prototype
need to meet geometric similarity, kinematic similarity and
dynamic similarity. Dynamic similarity is the similarity
between the model and the prototype, but strata types and
structure are various and complicated in the real application.
Therefore, the relationship between strata with different
lithological characters and moisture content should be
studied. Given that the real strata have the characteristics of
wide range and complicated structure, it is necessary to
classify and study similar material test blocks’ relationship
between moisture content and strength. There are hard
strata, medium-hard strata and soft strata in mining
subsidence area. This paper selects soft, medium-hard and
hard strata as study objects. Based on the similar material
ratio table in table 1, the ratio of the three strata and specific
materials are shown in table 1.
TABLE 1 SIMILAR MATERIAL RATIO OF THREE DIFFERENT LITHOLOGICAL CHARACTERISTICS
Soft strata ratio
Ratio
97:3
5:5
Ratio
92:8
5:5
Sand/kg
Gypsum/kg
2.91
0.045
Medium-hard strata ratio
Sand/kg
Gypsum/kg
2.76
0.12
Calcium
Carbonate/kg
0.045
Water/ml
Calcium
Carbonate/kg
0.12
Water/ml
Calcium
Carbonate/kg
0.27
Water/ml
300
300
Hard strata ratio
Ratio
82:18
5:5
Sand/kg
Gypsum/kg
2.46
0.27
Firstly, similar material blocks are designed in
accordance with the ratio. The blocks for compressive
strength test are cylindrical with height of 100mm and
diameter of 50mm. The blocks for tensile strength test are
300
standard blocks with height of 50mm and diameter of
25mm. In each ratio, there are 60 blocks for tensile strength
test, and 45 blocks for compressive strength test. A total of
315 test blocks are made, as shown in Figure 1.
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16TH INTERNATIONAL CONGRESS FOR MINE SURVEYING, BRISBANE, AUSTRALIA, 12-16 SEPT 2016
(a) Blocks for compressive strength test
(b) Blocks for tensile strength test
Fig.1 Some Similar Material Test Blocks
B. Relational Model for Similar Material Blocks’ Moisture
Content and Strength
Test data indicate that similar material blocks’ strength
tends to increase with the decrease of moisture content. The
increase amplitude grows as the moisture content decreases.
Assuming that variation of similar material blocks with
moisture content is proportional to the difference between
one block strength with certain moisture content and the
block’s final strength, then
!"
!!
= !(p-b)
the material strength is relatively small which is easy to
collapse in experiment. Therefore, the experiment should
not be conducted in slowly increasing and relatively small
phase. During the steadily increasing and moderate phase,
model strength can guarantee model stability and it changes
relatively slower. Therefore, the experiment should be
conducted in steadily increasing and moderate phase.
During the significantly increasing and ultrahigh phase,
material strength is extremely unstable, and the phase is not
suitable for the experiment.
0.07
1
By calculating the differential equation, the following
formula can be obtained.
0.05
steady increase and moderate phase
0.04
0.03
slowly increase and
relatively small phase
0.02
0.01
2
6
C. Test Results Analysis
By formula (2), the relationship between compressive
strength and tensile strength of three materials specimen
with different lithology and moisture content can be
obtained by fitting method, as shown in figure 2. The fitting
degree is over 0.8.
From the analysis of figure 2 (a), the compressive
strength of similar material blocks shows an exponential
relation with moisture content. As moisture content
increases, the material’s compressive strength will increase.
The relationship curve between compressive strength and
moisture content is different for similar material blocks with
different lithology. For instance, the compressive strength of
hard lithological blocks is the largest, and the medium-hard
lithological blocks’ compressive strength is bigger than that
of soft lithological blocks. The variation trend of material
strength with moisture content is similar, that is, as the
moisture content decreases, the material strength will
increase. Meanwhile, the compressive strength variation
with moisture content can be divided into three phases:
slowly increasing and relatively small phase, steadily
increasing and moderate phase, significantly increasing and
ultrahigh phase. During the slowly increasing and relatively
small phase, the change of material strength with the
moisture content is slow and material strength is stable, but
5
4
3
2
1
0
Moisture content/%
(a) compressive strength
soft strata
medium-hard strata
0.020
Tensile strength/Mpa
! = ! !!!! + !
significant increase
and ultrahigh phase
soft strata
medium-hard strata
hard strata
0.06
Compressive strength/Mpa
Similar material test blocks’ tensile strength and
compressive strength are conducted by electronic universal
testing machine with ultimate load of 30KN, as shown in
figure 3. The tensile strength is measured by splitting test.
significant increase and
ultrahigh phase
0.015
steady increase and moderate phase
0.010
slowly increase and
relatively small phase
0.005
0.000
6
5
4
3
2
1
0
Moisture content/%
(b) tensile strength
Fig.2 Relationship between the strength of similar material blocks with
different lithology and moisture content
From the analysis of figure 2 (b), similar material blocks’
tensile strength also shows an exponential relation with
moisture content. The relationship between the compressive
strength of similar material blocks with different lithological
characteristics and moisture content is different. Meanwhile,
the tensile strength variation with moisture content also can
be divided into three phases: slowly increasing and
relatively small phase, steadily increasing and moderate
phase, significantly increasing and ultrahigh phase.
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16TH INTERNATIONAL CONGRESS FOR MINE SURVEYING, BRISBANE, AUSTRALIA, 12-16 SEPT 2016
From the above analysis, the change process of similar
materials strength with its moisture content can be divided
into three phases: slowly increasing and relatively small
phase, steadily increasing and moderate phase, significantly
increasing and ultrahigh phase. The material strength in the
steadily increasing and moderate phase should be chosen as
the calculated strength of material ratio, and model
experiment also should be performed in this phase. This
paper takes the durations of steadily increasing and
moderate phase as the basis of judging model effective
monitoring time. When the moisture content of similar
model is 4%, the model effective monitoring time will begin
and when the model moisture content reaches 1%, the model
effective monitoring time will finish.
Fig.3 Circuit diagram of this monitoring equipment
IV. CONTROL MEASURES IN NATURAL ENVIRONMENT
Currently, similar material models are often laid in
natural environment. In order to control the effect of timevarying characteristics of similar material on the simulation
results, two regulation measures are proposed in the natural
environment.
B. Homemade Monitoring Equipment
Strength time-varying characteristics of similar
material model are closely related to material moisture
content, and the material moisture content and its humidity
is relevant. Therefore, the moisture content of similar
material can be monitored by monitoring the similar
material humidity, so as to realize the goal of controlling
similar material model strength.
In order to monitor the model humidity in real time, a
kind of relative humidity measurement equipment of similar
model is designed based on AT89S52 microcontroller. Due
to the long monitoring cycle of model, the sensor which can
measure temperature and humidity simultaneously was
chosen to provide temperature compensation for relative
humidity monitoring value. The equipment adopted the
AT89S52 microcontroller as the controller, and used
multiple SHT15 digital temperature and humidity sensors to
acquire model temperature and humidity. The monitoring
data were displayed through the LCD screen. This
equipment can also give an alarm when the humidity
monitoring value is over the humidity threshold.
Main hardware circuits of this equipment are processor,
crystal circuit, sensor circuit, LCD display circuit, button
circuit and alarm circuit. Hardware structure configuration
diagram is shown in figure 3. Figure 4 shows a photo of this
relative humidity measurement equipment of similar model.
Fig.4 Photo of this relative humidity measurement equipment of similar
model
In order to verify the feasibility of humidity monitoring
equipment of similar material model, three blocks are
monitored by this equipment in environment with
temperature of 200C and humidity of 60%, temperature of
100C and humidity of 70% and natural circumstances.
Figure 5 are the specific monitoring data. Figure 6 shows the
change process of temperature and humidity in natural
environment.
100%
The monitoring humidity /%
A. Sampling Method
From the above conclusion, we can know that similar
material strength is related to its moisture content.
Therefore, we can monitor the strength of similar material
model through monitoring its moisture content. After the
similar material models were laid, moisture content of
similar material can be measured by irregular sampling, and
the corresponding strength change of similar material can be
obtained according to the relationship. Similar material
experiment can be conducted under the condition of
controllable strength.
90%
80%
70%
60%
50%
10%
temperature 200C humidity 60%
temperature 100C humidity 70%
natural environment
9%
8%
7%
6%
5%
4%
3%
2%
1%
0%
Material moisture content/%
Fig. 5 Relationship between the monitoring humidity and moisture content
From the analysis of figure 5, the relationship between
monitoring humidity and moisture content is not linear
correlation, while they have some connections. When the
temperature is 10 and humidity is 70%, as the moisture
content diminishes to 2.2%, the monitoring humidity begin
to decline from 100%. When the temperature is 20 and
humidity is 60%, as the moisture content diminishes to
1.8%, the monitoring humidity will begin to decline from
100%. When the model experiment is in natural
environment, as the moisture content diminishes to 1.7%,
the monitoring humidity will begin to decline from 100%.
From the above analysis, when the moisture content of
similar material model is close to 2%, the monitoring
humidity begins to decline from 100% and the material
strength is in steadily increasing and moderate phase. While
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16TH INTERNATIONAL CONGRESS FOR MINE SURVEYING, BRISBANE, AUSTRALIA, 12-16 SEPT 2016
the moisture content of similar material model reaches 1%,
model effective monitoring time is over. Therefore,
homemade monitoring equipment can remind experimenter
that model moisture content is close to 2% and the model
monitoring effective monitoring time is coming to an end.
25
april
april
april
april
april
Temperature/0C
20
14
15
16
17
18
15
10
5
0
0
5
10
15
20
25
Time/h
(a) temperature
Therefore, the change rules of material moisture content
with curing time with different lithological strata under the
same environment are basically consistent.
When the temperature is 10
and humidity is 70%,
similar material moisture content decreases with the increase
of curing time, yet its change trend is relatively slower than
the change trend of material moisture content vary with
curing time in natural environment. Compared with model
effective monitoring time in natural environment, model
effective time extends 15 hours under the environment with
temperature of 10 and humidity of 70%. But the constant
temperature and humidity environment does not necessarily
extend the model effective monitoring time, as shown in
figure 8. Figure 8 shows the relationship between similar
material moisture content and curing time under natural
environment and the environment with temperature of 20
and humidity of 60%
100%
10%
hard strata under environment of temperature 200C and humidity 60%
hard strata under natural environment
8%
Moisture content/%
Humidity/%
80%
60%
40%
april 14
april 15
april 16
april 17
april 18
20%
0%
0
5
10
15
20
V. INFLUENCE MECHANISM ANALYSIS IN CONSTANT
TEMPERATURE AND HUMIDITY ENVIRONMENT
In order to make clear the influence mechanism of
constant temperature and humidity environment on timevarying characteristics of similar material strength, the
experiment under natural environment and the environment
of temperature of 10 and humidity of 70% is conducted to
study the relationship between moisture content and curing
time. Figure 7 shows the experiment results and the change
curve of temperature and humidity in natural environment as
shown is figure 6.
10%
hard strata under natural environment
medium-hard strata under natural environment
soft strata under natural environment
hard strata under environment of temperature 100C and humidity 70%
medium-hard strata under environment of temperature 100C and humidity 70%
soft strata under environment of temperature 100C and humidity 70%
Moisture content/%
4%
2%
0%
20
40
60
80
0
20
40
60
80
100
120
Fig.8 Relationship between similar material moisture content and curing
time under natural environment and the environment of temperature 20
and humidity 60%
Fig.6 change process of temperature and humidity of natural environment.
0
2%
Time/h
(b) humidity
6%
4%
0%
25
Time/h
8%
6%
100
120
140
160
Time/h
Fig.7 Relationship between similar material moisture content and curing
time under natural environment and the environment of temperature of 10
and humidity of 70%
From the analysis of figure 7, with the temperature of 10
and humidity of 70%, the change rules of material
moisture content with curing time with different lithological
strata are basically consistent. Different lithological strata
include hard strata, medium-hard strata and soft strata.
From the analysis of figure 8, the change trend of
material moisture content vary with curing time in the
environment of temperature of 20 and humidity of 60% is
not slower than the change trend of material moisture
content with curing time in natural environment, instead, the
model effective monitoring time in natural environment is
longer than that with temperature of 20 and humidity of
60%. Hence, constant temperature and humidity
environment does not necessarily extend the model effective
monitoring time.
VI. CONCLUSIONS
1) The model about the relationship between moisture
content of similar material and the strength is in accordance
with the variation of similar material strength with its
moisture content. The change process of similar materials
strength with its moisture content can be divided into three
phases, that is slowly increasing and relatively small phase,
steadily increasing and moderate phase, significantly
increasing and ultrahigh phase. The material strength at the
steadily increasing and moderate stage should be chosen as
the calculated strength of material ratio and model
experiment also should be performed in this phase.
2) When the similar material model is laid in natural
environment, sampling method and homemade equipment
monitoring method can be adopted to achieve the goal of
controlling the similar material model experiment.
Homemade similar material relative temperature monitoring
equipment can monitor the critical change value of moisture
content and remind experimenter that model monitoring
effective monitoring time will come to an end.
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16TH INTERNATIONAL CONGRESS FOR MINE SURVEYING, BRISBANE, AUSTRALIA, 12-16 SEPT 2016
3) Constant temperature and humidity environment could
extend the effective monitoring time of similar material
model.
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