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Warping and porosity effects on the mechanical response of FG-Beams on non-homogeneous foundations via a Quasi-3D HSDT

  • Mokhtar Nebab;Hassen Ait Atmane;Riadh Bennai;Mouloud Dahmane
    • Structural Engineering and Mechanics
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    • v.90 no.1
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    • pp.83-96
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    • 2024
  • This paper suggests an analytical approach to investigate the free vibration and stability of functionally graded (FG) beams with both perfect and imperfect characteristics using a quasi-3D higher-order shear deformation theory (HSDT) with stretching effect. The study specifically focuses on FG beams resting on variable elastic foundations. In contrast to other shear deformation theories, this particular theory employs only four unknown functions instead of five. Moreover, this theory satisfies the boundary conditions of zero tension on the beam surfaces and facilitates hyperbolic distributions of transverse shear stresses without the necessity of shear correction factors. The elastic medium in consideration assumes the presence of two parameters, specifically Winkler-Pasternak foundations. The Winkler parameter exhibits variable variations in the longitudinal direction, including linear, parabolic, sinusoidal, cosine, exponential, and uniform, while the Pasternak parameter remains constant. The effective material characteristics of the functionally graded (FG) beam are assumed to follow a straightforward power-law distribution along the thickness direction. Additionally, the investigation of porosity includes the consideration of four different types of porosity distribution patterns, allowing for a comprehensive examination of its influence on the behavior of the beam. Using the virtual work principle, equations of motion are derived and solved analytically using Navier's method for simply supported FG beams. The accuracy is verified through comparisons with literature results. Parametric studies explore the impact of different parameters on free vibration and buckling behavior, demonstrating the theory's correctness and simplicity.

Static bending response of axially randomly oriented functionally graded carbon nanotubes reinforced composite nanobeams

  • Ahmed Amine Daikh;Ahmed Drai;Mohamed Ouejdi Belarbi;Mohammed Sid Ahmed Houari;Benoumer Aour;Mohamed A. Eltaher;Norhan A. Mohamed
    • Advances in nano research
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    • v.16 no.3
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    • pp.289-301
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    • 2024
  • In this work, an analytical model employing a new higher-order shear deformation beam theory is utilized to investigate the bending behavior of axially randomly oriented functionally graded carbon nanotubes reinforced composite nanobeams. A modified continuum nonlocal strain gradient theory is employed to incorporate both microstructural effects and geometric nano-scale length scales. The extended rule of mixture, along with molecular dynamics simulations, is used to assess the equivalent mechanical properties of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beams. Carbon nanotube reinforcements are randomly distributed axially along the length of the beam. The equilibrium equations, accompanied by nonclassical boundary conditions, are formulated, and Navier's procedure is used to solve the resulting differential equation, yielding the response of the nanobeam under various mechanical loadings, including uniform, linear, and sinusoidal loads. Numerical analysis is conducted to examine the influence of inhomogeneity parameters, geometric parameters, types of loading, as well as nonlocal and length scale parameters on the deflections and stresses of axially functionally graded carbon nanotubes reinforced composite (AFG CNTRC) nanobeams. The results indicate that, in contrast to the nonlocal parameter, the beam stiffness is increased by both the CNTs volume fraction and the length-scale parameter. The presented model is applicable for designing and analyzing microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) constructed from carbon nanotubes reinforced composite nanobeams.

Optimization of Growth Environments Based on Meteorological and Environmental Sensor Data (기상 및 환경 센서 데이터 기반 생육 환경 최적화 연구)

  • Sook Lye Jeon;Jinheung Lee;Sung Eok Kim;Jeonghwan Park
    • Journal of Sensor Science and Technology
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    • v.33 no.4
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    • pp.230-236
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    • 2024
  • This study aimed to analyze the environmental factors affecting tomato growth by examining the correlation between weather and growth environment sensor data from P Smart Farm located in Gwangseok-myeon, Nonsan-si, Chungcheongnam-do. Key environmental variables such as the temperature, humidity, sunlight hours, solar radiation, and daily light integral (DLI) significantly affect tomato growth. The optimal temperature and DLI conditions play crucial roles in enhancing tomato growth and the photosynthetic efficiency. In this study, we developed a model to correct and predict the time-series variations in internal environmental sensor data using external weather sensor data. A linear regression analysis model was employed to estimate the external temperature variations and internal DLI values of P Smart Farm. Then, regression equations were derived based on these data. The analysis verified that the estimated variations in external temperature and internal DLI are explained effectively by the regression models. In this research, we analyzed and monitored smart-farm growth environment data based on weather sensor data. Thereby, we obtained an optimized model for the temperature and light conditions crucial for tomato growth. Additionally, the study emphasizes the importance of sensor-based data analysis in dynamically adjusting the tomato growth environment according to the variations in weather and growth conditions. The observations of this study indicate that analytical solutions using public weather data can provide data-driven operational experiences and productivity improvements for small- and medium-sized facility farms that cannot afford expensive sensors.

Effects of hygro-thermal environment on dynamic responses of variable thickness functionally graded porous microplates

  • Quoc-Hoa Pham;Phu-Cuong Nguyen;Van-Ke Tran
    • Steel and Composite Structures
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    • v.50 no.5
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    • pp.563-581
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    • 2024
  • This paper presents a novel finite element model for the free vibration analysis of variable-thickness functionally graded porous (FGP) microplates resting on Pasternak's medium in the hygro-thermal environment. The governing equations are established according to refined higher-order shear deformation plate theory (RPT) in construction with the modified couple stress theory. For the first time, three-node triangular elements with twelve degrees of freedom for each node are developed based on Hermitian interpolation functions to describe the in-plane displacements and transverse displacements of microplates. Two laws of variable thickness of FGP microplates, including the linear law and the nonlinear law in the x-direction are investigated. Effects of thermal and moisture changes on microplates are assumed to vary continuously from the bottom surface to the top surface and only cause tension loads in the plane, which does not change the material's mechanical properties. The numerical results of this work are compared with those of published data to verify the accuracy and reliability of the proposed method. In addition, the parameter study is conducted to explore the effects of geometrical and material properties such as the changing law of the thickness, length-scale parameter, and the parameters of the porosity, temperature, and humidity on the free vibration response of variable thickness FGP microplates. These results can be applied to design of microelectromechanical structures in practice.

Estimation of surface nitrogen dioxide mixing ratio in Seoul using the OMI satellite data (OMI 위성자료를 활용한 서울 지표 이산화질소 혼합비 추정 연구)

  • Kim, Daewon;Hong, Hyunkee;Choi, Wonei;Park, Junsung;Yang, Jiwon;Ryu, Jaeyong;Lee, Hanlim
    • Korean Journal of Remote Sensing
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    • v.33 no.2
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    • pp.135-147
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    • 2017
  • We, for the first time, estimated daily and monthly surface nitrogen dioxide ($NO_2$) volume mixing ratio (VMR) using three regression models with $NO_2$ tropospheric vertical column density (OMIT-rop $NO_2$ VCD) data obtained from Ozone Monitoring Instrument (OMI) in Seoul in South Korea at OMI overpass time (13:45 local time). First linear regression model (M1) is a linear regression equation between OMI-Trop $NO_2$ VCD and in situ $NO_2$ VMR, whereas second linear regression model (M2) incorporates boundary layer height (BLH), temperature, and pressure obtained from Atmospheric Infrared Sounder (AIRS) and OMI-Trop $NO_2$ VCD. Last models (M3M & M3D) are a multiple linear regression equations which include OMI-Trop $NO_2$ VCD, BLH and various meteorological data. In this study, we determined three types of regression models for the training period between 2009 and 2011, and the performance of those regression models was evaluated via comparison with the surface $NO_2$ VMR data obtained from in situ measurements (in situ $NO_2$ VMR) in 2012. The monthly mean surface $NO_2$ VMRs estimated by M3M showed good agreements with those of in situ measurements(avg. R = 0.77). In terms of the daily (13:45LT) $NO_2$ estimation, the highest correlations were found between the daily surface $NO_2$ VMRs estimated by M3D and in-situ $NO_2$ VMRs (avg. R = 0.55). The estimated surface $NO_2$ VMRs by three modelstend to be underestimated. We also discussed the performance of these empirical modelsfor surface $NO_2$ VMR estimation with respect to otherstatistical data such asroot mean square error (RMSE), mean bias, mean absolute error (MAE), and percent difference. This present study shows a possibility of estimating surface $NO_2$ VMR using the satellite measurement.

Development of a Method to Measure the Radiation Isocenter Size of Linear Accelerators and Quantitative Analysis of the Radiation Isocenter Size for Clinac 21EX Linear Accelerator (선형가속기 방사선 중심점의 크기 측정 방법 개발과 Clinac 21EX 선형가속기의 방사선 중심점 크기 분석)

  • Jeon, Ho-Sang;Nam, Ji-Ho;Park, Dahl;Kim, Yong-Ho;Kim, Won-Taek;Kim, Dong-Won;Ki, Yong-Kan;Kim, Dong-Hyun
    • Progress in Medical Physics
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    • v.22 no.3
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    • pp.131-139
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    • 2011
  • A method to get a size of the radiation isocenter of linear accelerators using star-shot images was presented and a computer program was developed to automate the method. Accuracy of the method was verified. The developed program was used to measure sizes of the radiation isocenters for a Clinac 21EX (Varian, USA) using data of quality assurance (QA) performed from June 2008 to December 2010. To calculated the size of radiation isocenter, positions of two points on each central ray of the star-shot image were found and the equation of the central ray was determined using the positions of two points. Using the equations of central rays the radius of the minimum circle intersecting all the central rays, which is one half of the size of radiation isocenter, was calculated. The program measured x-intercepts and y-intercepts of the central rays within errors of 0.084 mm and sizes of radiation isocenters within 0.053 mm. All the errors were less than the spatial resolution of star-shot images 0.085 mm. The radiation isocenter sizes of Clinac 21EX were $0.33{\pm}0.27mm$, $0.71{\pm}0.36mm$, $0.50{\pm}0.16mm$ for collimator, gantry and couch respectively. During the measurement period all the measured sizes were less than 2.0 mm and within tolerance. The developed program could calculate the size of radiation isocenters and it would be helpful to routine QA.

Estimation of Glomerular Filtration Rate from Plasma Creatinine and Height in Children (소아에서 신장과 혈장 Creatinine 농도를 이용한 사구체여관율 측정)

  • Kim, Jeong-Lan;Park, Yong-Hoon;Hah, Jeong-Ok
    • Journal of Yeungnam Medical Science
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    • v.5 no.1
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    • pp.93-100
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    • 1988
  • In clinical practice, creatinine clearance(Ccr) remains the most commonly used laboratory assessment of glomerular function despite methodological and technical problems of urine collection. Schwartz et al. in 1976, reported that an accurate estimate of glomerular filtration rate(GFR) could be obtained from the simple determinations of plasma creatinine(Pcr) and body length(L) : GFR($m{\ell}/min/1.73m^2$=k L(cm)/Pcr(mg/$100m{\ell}$), (k=constant). The subject of this study were ill children admitted to our pediatric department from July, 1985 to June, 1987 and they were divided into three groups; group I, from 1 to 5 years old, group II, from 6 to 10 years old, group III. from 11 to 15 years old. The results were as following ; 1) Measured creatinine clearance($Ccr_M$, $m{\ell}/min/1.73m^2$) were $109.73{\pm}9.97$ in group I, $108.26{\pm}9.02$ in group II, $96.20{\pm}4.72$ in group III and $105.48{\pm}5.23$ in all age group. 2) Measured k($k_M$) obtained from $Ccr_M=k$ Ht/Pcr were $0.49{\pm}0.03$ in group I, $0.48{\pm}0.02$ in group II, $0.43{\pm}0.02$ in group III, and $0.47{\pm}0.02$ in all age group.(Ht ; height) 3) Linear equations and correlation coefficients between Ht/Pcr(x) and Ccr(y) were y=0.822x-65.63(r=0.99) in group I, y=0.61x-23.46(r=0.72) in group II, y=0.18x+54.44(r=0.54) in group III and y=0.58x-22.13(r=0.81) in all age group. 4) $Ccr_E$ was again estiamted from linear equations between Ht/Pcr and $Ccr_M$ and $k_E$ was calculated with Ht/Pcr and $Ccr_E$ were $0.48{\pm}0.01$ in group I, $0.49{\pm}0.01$in group II, $0.43{\pm}0.01$ in group III and $0.47{\pm}0.00$ in all age group. 5) Consistant values of $k_E$ and $k_M$ were highly significant as 95~97.5% in group I and II, 90~95% in group III and 97.5~99% in all age group. In summary, we could estimate GFR with height, plasma creatinine and measured k($k_M$) according to the age in easy and rapid way.

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A Study on the Equations of Estimating the Leaf Area of Broad-Leaf Species in Mt. Jiri (지리산(智異山) 주요(主要) 활엽수종(闊葉樹種)의 엽면적(葉面積) 추정식(推定式)에 대(對)한 연구(硏究))

  • Kim, Si Kyung;Lee, Kyeong Hack
    • Journal of Korean Society of Forest Science
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    • v.70 no.1
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    • pp.103-108
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    • 1985
  • This paper is concerned with estimating equations of leaf area(A) obtained from linear measurements - leaf length(L) and leaf width(W) - on the leaves of 13 species composing a natural mixed stand in Mt. Jiri. This method is known to be rapid and non-destructive in estimating leaf area. The equation of A=bLW is frequently used in rough and rapid estimation. Each species in this study has its own coefficient b according to its geometrical leaf shape. The range of coefficients of 13 species was 0.579 to 0.717. This means that the relationship A=2/3LW is suitable to most broad leaf species in a natural mixed stand in Mt. Jiri. When more precise estimation of leaf area is needed, full regression equation is used. In this study, the form of ${\log}A=b_0+b_1{\log}LW$ was the most precise estimation equation in 8 species. In addition to this, the form of $A=b_0+b_1LW$ and $A=b_0+b_1L^2+b_2W^2$ were founded to be suitable for estimation of leaf area. In comparision of these two forms, the determination coefficient were about the same, but the F-value of the former was greater than that of the latter. Therefore, the use of the former seems to be more reliable and practical.

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A Case Study on Students' Mathematical Concepts of Algebra, Connections and Attitudes toward Mathematics in a CAS Environment (CAS 그래핑 계산기를 활용한 수학 수업에 관한 사례 연구)

  • Park, Hui-Jeong;Kim, Kyung-Mi;Whang, Woo-Hyung
    • Communications of Mathematical Education
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    • v.25 no.2
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    • pp.403-430
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    • 2011
  • The purpose of the study was to investigate how the use of graphing calculators influence on forming students' mathematical concept of algebra, students' mathematical connection, and attitude toward mathematics. First, graphing calculators give instant feedback to students as they make students compare their written answers with the results, which helps students learn equations and linear inequalities for themselves. In respect of quadratic inequalities they help students to correct wrong concepts and understand fundamental concepts, and with regard to functions students can draw graphs more easily using graphing calculators, which means that the difficulty of drawing graphs can not be hindrance to student's learning functions. Moreover students could understand functions intuitively by using graphing calculators and explored math problems volunteerly. As a result, students were able to perceive faster the concepts of functions that they considered difficult and remain the concepts in their mind for a long time. Second, most of students could not think of connection among equations, equalities and functions. However, they could understand the connection among equations, equalities and functions more easily. Additionally students could focus on changing the real life into the algebraic expression by modeling without the fear of calculating, which made students relieve the burden of calculating and realize the usefulness of mathematics through the experience of solving the real-life problems. Third, we identified the change of six students' attitude through preliminary and an ex post facto attitude test. Five of six students came to have positive attitude toward mathematics, but only one student came to have negative attitude. However, all of the students showed positive attitude toward using graphing calculators in math class. That's because they could have more interest in mathematics by the strengthened and visualization of graphing calculators which helped them understand difficult algebraic concepts, which gave them a sense of achievement. Also, students could relieve the burden of calculating and have confidence. In a conclusion, using graphing calculators in algebra and function class has many advantages : formulating mathematics concepts, mathematical connection, and enhancing positive attitude toward mathematics. Therefore we need more research of the effect of using calculators, practical classroom materials, instruction models and assessment tools for graphing calculators. Lastly We need to make the classroom environment more adequate for using graphing calculators in math classes.

Studies on the Mechanical Properties of Weathered Granitic Soil -On the Elements of Shear Strength and Hardness- (화강암질풍화토(花崗岩質風化土)의 역학적(力學的) 성질(性質)에 관(關)한 연구(硏究) -전단강도(剪斷强度)의 영향요소(影響要素)와 견밀도(堅密度)에 대(對)하여-)

  • Cho, Hi Doo
    • Journal of Korean Society of Forest Science
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    • v.66 no.1
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    • pp.16-36
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    • 1984
  • It is very important in forestry to study the shear strength of weathered granitic soil, because the soil covers 66% of our country, and because the majority of land slides have been occured in the soil. In general, the causes of land slide can be classified both the external and internal factors. The external factors are known as vegetations, geography and climate, but internal factors are known as engineering properties originated from parent rocks and weathering. Soil engineering properties are controlled by the skeleton structure, texture, consistency, cohesion, permeability, water content, mineral components, porosity and density etc. of soils. And the effects of these internal factors on sliding down summarize as resistance, shear strength, against silding of soil mass. Shear strength basically depends upon effective stress, kinds of soils, density (void ratio), water content, the structure and arrangement of soil particles, among the properties. But these elements of shear strength work not all alone, but together. The purpose of this thesis is to clarify the characteristics of shear strength and the related elements, such as water content ($w_o$), void ratio($e_o$), dry density (${\gamma}_d$) and specific gravity ($G_s$), and the interrelationship among related elements in order to decide the dominant element chiefly influencing on shear strength in natural/undisturbed state of weathered granitic soil, in addition to the characteristics of soil hardness of weathered granitic soil and root distribution of Pinus rigida Mill and Pinus rigida ${\times}$ taeda planted in erosion-controlled lands. For the characteristics of shear strength of weathered granitic soil and the related elements of shear strength, three sites were selected from Kwangju district. The outlines of sampling sites in the district were: average specific gravity, 2.63 ~ 2.79; average natural water content, 24.3 ~ 28.3%; average dry density, $1.31{\sim}1.43g/cm^3$, average void ratio, 0.93 ~ 1.001 ; cohesion, $ 0.2{\sim}0.75kg/cm^2$ ; angle of internal friction, $29^{\circ}{\sim}45^{\circ}$ ; soil texture, SL. The shear strength of the soil in different sites was measured by a direct shear apparatus (type B; shear box size, $62.5{\times}20mm$; ${\sigma}$, $1.434kg/cm^2$; speed, 1/100mm/min.). For the related element analyses, water content was moderated through a series of drainage experiments with 4 levels of drainage period, specific gravity was measured by KS F 308, analysis of particle size distribution, by KS F 2302 and soil samples were dried at $110{\pm}5^{\circ}C$ for more than 12 hours in dry oven. Soil hardness represents physical properties, such as particle size distribution, porosity, bulk density and water content of soil, and test of the hardness by soil hardness tester is the simplest approach and totally indicative method to grasp the mechanical properties of soil. It is important to understand the mechanical properties of soil as well as the chemical in order to realize the fundamental phenomena in the growth and the distribution of tree roots. The writer intended to study the correlation between the soil hardness and the distribution of tree roots of Pinus rigida Mill. planted in 1966 and Pinus rigida ${\times}$ taeda in 199 to 1960 in the denuded forest lands with and after several erosion control works. The soil texture of the sites investigated was SL originated from weathered granitic soil. The former is situated at Py$\ddot{o}$ngchangri, Ky$\ddot{o}$m-my$\ddot{o}$n, Kogs$\ddot{o}$ng-gun, Ch$\ddot{o}$llanam-do (3.63 ha; slope, $17^{\circ}{\sim}41^{\circ}$ soil depth, thin or medium; humidity, dry or optimum; height, 5.66/3.73 ~ 7.63 m; D.B.H., 9.7/8.00 ~ 12.00 cm) and the Latter at changun-long Kwangju-shi (3.50 ha; slope, $12^{\circ}{\sim}23^{\circ}$; soil depth, thin; humidity, dry; height, 10.47/7.3 ~ 12.79 m; D.B.H., 16.94/14.3 ~ 19.4 cm).The sampling areas were 24quadrats ($10m{\times}10m$) in the former area and 12 in the latter expanding from summit to foot. Each sampling trees for hardness test and investigation of root distribution were selected by purposive selection and soil profiles of these trees were made at the downward distance of 50 cm from the trees, at each quadrat. Soil layers of the profile were separated by the distance of 10 cm from the surface (layer I, II, ... ...). Soil hardness was measured with Yamanaka soil hardness tester and indicated as indicated soil hardness at the different soil layers. The distribution of tree root number per unit area in different soil depth was investigated, and the relationship between the soil hardness and the number of tree roots was discussed. The results obtained from the experiments are summarized as follows. 1. Analyses of simple relationship between shear strength and elements of shear strength, water content ($w_o$), void ratio ($e_o$), dry density (${\gamma}_d$) and specific gravity ($G_s$). 1) Negative correlation coefficients were recognized between shear strength and water content. and shear strength and void ratio. 2) Positive correlation coefficients were recognized between shear strength and dry density. 3) The correlation coefficients between shear strength and specific gravity were not significant. 2. Analyses of partial and multiple correlation coefficients between shear strength and the related elements: 1) From the analyses of the partial correlation coefficients among water content ($x_1$), void ratio ($x_2$), and dry density ($x_3$), the direct effect of the water content on shear strength was the highest, and effect on shear strength was in order of void ratio and dry density. Similar trend was recognized from the results of multiple correlation coefficient analyses. 2) Multiple linear regression equations derived from two independent variables, water content ($x_1$ and dry density ($x_2$) were found to be ineffective in estimating shear strength ($\hat{Y}$). However, the simple linear regression equations with an independent variable, water content (x) were highly efficient to estimate shear strength ($\hat{Y}$) with relatively high fitness. 3. A relationship between soil hardness and the distribution of root number: 1) The soil hardness increased proportionally to the soil depth. Negative correlation coefficients were recognized between indicated soil hardness and the number of tree roots in both plantations. 2) The majority of tree roots of Pinus rigida Mill and Pinus rigida ${\times}$ taeda planted in erosion-controlled lands distributed at 20 cm deep from the surface. 3) Simple linear regression equations were derived from indicated hardness (x) and the number of tree roots (Y) to estimate root numbers in both plantations.

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