Static Equilibrium Conditions Research Articles

Experimental-Numerical Study of Indexation of Scenic Road Vertical Alignment in China

The vertical alignment design method of road in scenic spots does not evolve enough along the vehicle’s rapid variation. Values of the maximum longitudinal slope (MLS) and longest slope length (LSL) applicable to scenic roads used by the environmental-friendly vehicle (EFV) are not provided. To compensate for this shortage, a multibody vehicle dynamic model in uphill traving is built, providing the static equilibrium state and dynamic balancing process of a typical vehicle. MLS and LSL values in scenic roads are obtained based on this model through numerical simulation, considering typical EFV, maximum velocity loss (MVL), and ideal velocity loss (IVL). Field experiments for verifying the results are also carried out in Huashan Mountain, Cuihua Mountain National Park, and Taiping Forest Park, using two EFV types. MLS and LSL values in scenic roads applicable to EFV obtained in this research vary from 7.8% to 10.2% and 200 to 955 m, respectively, and both are larger than the corresponding values in current criteria. According to verification results, relative errors of climbing velocity vary from 0.0104 to 0.0205, showing the dynamic model’s accuracy and further proving the practicality of MLS and LSL values obtained. The results obtained in this research lay a foundation for establishing the scenic-road vertical alignment design method.

Nonlinear formulation and free vibration of a large-sag extensible catenary riser

The nonlinear formulation using the principle of virtual work-energy for free vibration of a large-sag extensible catenary riser in two dimensions is presented in this paper. A support at one end is hinged and the other is a free-sliding roller in the horizontal direction. The catenary riser has a large-sag configuration in the static equilibrium state and is assumed to displace with large amplitude to the motion state. The total virtual work of the catenary riser system involves the virtual strain energy due to bending, the virtual strain energy due to axial deformation, the virtual work done by the effective weight, and the inertia forces. The nonlinear equations of motion for two-dimensional free vibration in the Cartesian coordinate system is developed based on the difference between the Euler's equations in the static state and the displaced state. The linear and nonlinear stiffness matrices of the catenary riser are obtained and the eigenvalue problem is solved using the Galerkin finite element procedure. The natural frequencies and mode shapes are obtained. The results are validated with regard to the reference research addressing the accuracy and efficiency of the proposed nonlinear formulation. The numerical results for free vibration and the effect of the nonlinear behavior for catenary riser are presented.

Dynamic effect of constant inertial acceleration on vibration isolation system with high-order stiffness and Bouc–Wen hysteresis

Nonlinear vibration isolation provides with an effective way for vibration reduction with broad band and high efficiency. This investigation focuses on the dynamic effects of a constant inertial acceleration on a nonlinear vibration isolation system with high-order stiffness and Bouc–Wen hysteresis. A wire rope-based isolator subject to the inertial acceleration is analyzed to illustrate the uncertainty of the static equilibrium state and the diverse dynamic effects of the acceleration. The frequency responses are obtained through a semianalytical method based on the harmonic balance method. A recursive method is proposed to deal with the polynomial function derived from the nonlinear stiffness. An alternating frequency/time domain technique is adopted to treat the implicit function of the Bouc–Wen hysteresis. The calculation results are verified by a numerical simulation with the Runge–Kutta method. The analysis and the simulations reveal that the inertial acceleration leads to different static equilibrium states according to the paths to the equilibriums. The inertial acceleration, respectively, affects the static equilibrium displacement and the residual hysteretic force, and they change the dynamic responses differently. The acceleration effect on the static equilibrium displacement leads to additional coupling stiffness making the system harder/softener with positive/negative high-order stiffness. Furthermore, the acceleration has a significant effect on the dynamic equilibrium location, and the equilibrium reaches the minimum around the resonance and increases gradually at higher frequencies. The acceleration effect on the residual hysteretic force changes the amplitude–frequency responses indirectly through additional coupling stiffness. A positive residual hysteretic force leads to a positive overall deviation of the dynamic equilibrium location regardless of the positive or negative high-order stiffness.

Notes about the macroscopic fluctuating theory

The macroscopic fluctuating theory developed during the last 30 years is applied to generic systems described by continuum fields ϕ(x, t) that evolve by a Langevin equation that locally either conserves or does not conserve the field. This paper aims to review well-known basic concepts and results from a pedagogical point of view by following a general framework in a practical and self-consistent way. From the probability of a path, we study the general properties of the system’s stationary state. In particular, we focus on the study of the quasipotential that defines the stationary distribution at the small noise limit. To discriminate between equilibrium and non-equilibrium stationary states, the system’s adjoint dynamics are defined as the system’s time-reversal Markov process. The equilibrium is then defined as the unique stationary state that is dynamically time-reversible, and therefore its adjoint dynamics are equal to those of the original one. This property is confronted with the macroscopic reversibility that occurs when the most probable path to create a fluctuation from the stationary state is equal to the time-reversed path that relaxes it. The lack of this symmetry implies a nonequilibrium stationary state; however, the converse is not true. Finally, we extensively study the two-body correlations at the stationary state. We derive some generic properties at various situations, including a discussion about the equivalence of ensembles in nonequilibrium systems.

The strength characteristics and progressive failure mechanism of soft rock-coal combination samples with consideration given to interface effects

The coal-measure rock masses of China's Ordos Basin are mainly composed of typical soft rock with low strength, which bear loads together with the coal seams during coal mining activities. Accurately determining the mechanical behaviors of combination soft rock and coal masses can provide a basis for underground coal engineering designs. First, uniaxial compression tests were conducted on medium sandstone samples, coal samples, and coal-rock combination samples. It was observed that the peak axial strain, uniaxial compressive strength, stress-strain curve shape, and elastic modulus of the combination samples were closer to those of the coal samples, indicating that the mechanical characteristics of soft rock-coal combination samples were mainly affected by the coal. Then, using the static equilibrium and deformation continuous conditions, along with the Griffith strength criterion, the ultimate compressive strength of materials at different positions in a combination model was analyzed. The results revealed that the interface constraint effects had reduced the strength of the sandstone near the interface and improved that of the coal near the interface. The interface constraint effects were verified by comparing the generalized Poisson's ratio of materials at different positions with those of the standard coal and sandstone samples. Finally, based on the final failure modes, and the temporal characteristics of the acoustic emission (AE) count rate and peak frequency, the progressive failure mechanism of the soft rock-coal combination samples was studied. This failure process was found to be characterized by the synergistic failure of the material and structure. Furthermore, the effect of coal-rock height ratio on the strength of materials at different positions was discussed, which interpreted the experimental results observed in the previous related studies, namely, with the increase in the rock-coal height ratio, the strength of the combination samples had increased, and the impact tendency had been significantly enhanced.

Martensitic transformation in a two‐dimensional polycrystalline shape memory alloys using a multi‐phase‐field elasticity model based on pairwise rank‐one convexified energies at small strain

AbstractFor modeling the solid‐solid transformation using the phase‐field method, we need to describe the phase‐fields strain and stress fields in the interfacial regions which are necessary to define the mechanical driving force density of the phase‐fields motion. Seeking quantitative modeling, we introduce briefly a multi‐phase‐field elasticity model based on the rank‐one convexification of the pairwise energies which satisfies the pairwise interfacial static equilibrium and kinematic compatibility conditions. As an application, we simulate the martensitic transformation in a two‐dimensional polycrystalline SMAs at small strains. The finial evaluated microstructure consists of stress‐free laminates meeting the theoretical expectations.

Study on the Cable Traversing Robot on Spatially Structured Cableway

This paper describes the kinematics, motion planning and mechanism optimization of the dual-arm type cable traversing robot on spatially-structured cable way. Since the inverse kinematics cannot be perfectly defined due to one of the orientation parameters is determined by static condition, its inverse kinematics algorithm utilizing both the kinematics of 3R serial spherical mechanism and the static equilibrium condition of the whole system was developed. The motion planning method to traverse cable node is based on the kinematics and Spherical Linear Interpolation using quaternion. Furthermore, mechanism optimization for avoidance of collision with cables and improvement of characteristics is also conducted.

Improved general slice method of limit equilibrium for slope stability analysis

For traditional slice methods of limit equilibrium used to analyze slope stability, some hypothetical conditions on interslice force are generally introduced to solve the problem. In order to reduce the defect theoretically due to the related hypothesis, more rigorous constraints of interslice force are completely considered in light of static equilibrium conditions and energy dissipation principle of the interface between two adjacent slices. Without hypothesis of interslice force, the slope stability analysis is transformed consistently into a non-linear programming problem to be solved. So, a generally improved solution of slice method of limit equilibrium to slope stability is put forward. In particular, influence of the dilation angle of soil on slope stability can be involved in the method. The proposed method can be utilized for any slopes with arbitrary slip surfaces.

ВИПАДКОВІСТЬ У СИСТЕМІ НАУКОВОГО ЗНАННЯ: СВІТОГЛЯДНИЙ ТА МЕТОДОЛОГІЧНИЙ АСПЕКТИ

In the article the author's attention is focused on modern scientific interpretations of the phenomenon of chance. The author also focused on the generalization of the results of research by scientists of nonlinear processes of self-organization of complex systems. The main goal of the article is to study the phenomenon of the so-called "nonlinear thinking" in science. Of particular interest was the philosophical assessment of the very subject of this thinking. The author tried to reveal the essence in the interpretation of statistical laws. He also sought to prove that these patterns represent a more fundamental aspect of reality than the laws of dynamics. The choice of the topic of the article, the application of its theoretical and methodological approaches is determined by the very subject of thought and the nature of the tasks. So it turned out that many dynamical systems – physical, chemical, biological – fall under nonlinear dynamic equations. Here they are quite predictable. However, they become unpredictable if they appear at the macro level. After all, individual systems are considered "normal" and function according to deterministic laws only up to a certain time. This is the period between situations of bifurcation. Here their "behavior" can be fully predicted. However, in their own development, they can come to certain extreme changes. To overcome them further, two variants of the quality state appear. Each of them can happen first. This happens when an object passes through so-called tipping points. It is impossible to predict which variant will achieve ontological legitimation. The object experiences microwaves between the two physical alternatives for some time. But with an increase in the value of the key parameter of one of the alternatives, further complication of the state occurs. This process is a sequential bifurcation, similar to the alternation of two existing states. It is characterized by periods of instability. In this case, it is impossible to predict the state of development of the object. Here, as you know, "His Majesty the case" enters the scene. The case in such systems cannot be neglected. After all, here the relationship between necessity and chance, between fluctuations and deterministic algorithms, is different than in a stationary environment. Not far from the bifurcation nodes, micro-fluctuations or chances reign supreme. Whereas in the distance there is a deterministic order of things. Even more effective is the study of the phenomenon of non-determinism in relation to the space-time models of the behavior of systems. Through scientific research, it has been reliably established that at the bifurcation points of such a medium, successive microchanges reach large values. Their scale is sometimes compared to the system itself. Here the system changes due to fluctuations, up to the appearance of a new quality. A deep understanding of the significance of the new style of scientific thinking is closely related to a radical revision of the idea of self- organization of matter in nature. This ability to change has previously been studied only in the framework of macroscopic statistical equilibrium states. This is a new style of scientific thinking and a new picture of the world. They are related to the study of nonlinear and unbalanced open systems. All this demonstrates a non-trivial understanding of matter itself and its ability to self-organize. Matter takes on new forms of existence. Their appearance is due to their own internal forces and properties of matter itself. The worldview generalizations of such discoveries are important here. After all, they allow you to see the world more clearly, which is self-organizing as a single whole and is at different levels of its existence. The generalized results of studying the topic give grounds to draw the following conclusion. The subject of the new style of scientific thinking is the nonlinear processes of self-organization of matter. This style of thinking, as well as the discoveries of nonlinear natural science, allow us to understand the nature of the surrounding world in a new way. Namely – the ability of a substance to self-organize as a whole and at various levels of its own being. This is due to the internal forces and properties of this world. However, to fully understand the nature of this world, it is necessary to comprehend randomness. After all, it is precisely chance that is an essential part of reality. That is, randomness is that part of reality that gives a more perfect picture of the surrounding world.

Analiza kretanja i stabilnosti holonomnog mehaničkog sistema u proizvoljnom polju sila

In order to give an insight into the work of the machine before the production and assembly and to obtain good analysis, this paper presents detailed solutions to the specific problem occured in the field of analytical mechanics. In addition to numerical procedures in the paper, a review of the theoretical foundations was made.Various types of analysis are very common in mechanical engineering, due to the possibility of an approximation of complex machines. For the proposed system, Lagrange's equations of the first kind, covariant and contravariant equations, Hamiltons equations and the generalized coordinates, as well as insight in Coulumb friction force are provided.Also, the conditions of static equilibrium are solved numerically and using intersection of the two curves. Finally, stability of motion for the disturbed and undisturbed system was investigated.

Bubble drag in electrolytically generated microbubble swarms with bubble-vortex interactions

Air bubbles entrained in ocean breaking waves play various roles in air–sea gas transfer, wave energy dissipation, and surface layer mixing. While sub-mm bubbles dominate the distribution of sizes observed in bubble plumes created by breaking waves, the dynamics of such microbubbles in a swarm are poorly understood, and most previous experimental and computational studies have focused on the behavior of homogeneous swarms of larger mm-scale bubbles for industrial applications. Here, we propose novel probabilistic empirical models of rise velocity and bubble drag for a microbubble swarm incorporating bubble–vortex interactions. These are based on image measurements of the motion of electrolytically generated microbubbles. We found that convective interactions between bubbles and vortex-induced flows, that is, Rayleigh–Taylor instability caused by density difference near the electrodes, induce counter-rotating vortices that accelerate bubbles and align them along paths in the flow induced between them, resulting in an increase in rise velocity and its variance in the statistical equilibrium state. We describe the statistical features of bubble rise in such swarms in our proposed empirical model and deduce its optimal parameters. We anticipate our findings being a starting point for understanding behaviors of oceanic bubbles possessing an analogous size distribution to the present electrolytically generated microbubbles.

On ride-pooling and traffic congestion

Ridesourcing platforms, such as Uber, Lyft and Didi, are now launching commercial on-demand ride-pooling programs that enable their affiliated drivers to serve two or more passengers in one ride. It is generally expected that successful designs of ride-pooling programs can reduce the required vehicle fleet size, and achieve various societally beneficial objectives, such as alleviating traffic congestion. The reduction in traffic congestion can in turn save travel time for both ridesourcing passengers and normal private car users. However, it is still unclear to what extent the implementation of ride-pooling affects traffic congestion and riders’ travel time. To this end, this paper establishes a model to describe the ridesourcing markets with congestion effects, which are explicitly characterized by a macroscopic fundamental diagram. We compare the time cost (sum of travel time and waiting time) of ridesourcing passengers and normal private car users (background traffic) in the ridesourcing markets without ride-pooling (each vehicle serves one passenger) and with ride-pooling (each vehicle serves one or more passengers). It is found that, a win-win situation can be achieved under some scenarios such that the implementation of on-demand ride-pooling reduces the time cost for both ridesourcing passengers and private car users. Furthermore, we find that the matching window is a key decision variable the platform leverages to affect the stationary equilibrium state. As the matching window increases, passengers are expected to wait for longer time, but the pool-matching probability (the proportion of passengers who are pool-matched) increases, which further alleviates traffic congestion and in turn reduces passengers’ travel time. It is interesting to find that, there is a globally optimal matching window for achieving the minimum time cost for ridesourcing passengers in the normal flow regime.

Rotational Low-Impedance Physical Human–Robot Interaction Using Underactuated Redundancy

Abstract This paper extends the concept of underactuated redundancy for physical human–robot interaction (pHRI) in a context of industrial assembly by introducing a novel 1-dof gravity balanced rotational manipulator. The proposed architecture consists of a rotational active counterweight with a passive joint equipped with an encoder. The proposed architecture is first described, and the static equilibrium conditions are used to describe the operation of the mechanism. Then, alternative architectures are briefly introduced. Finally, an experimental validation is provided to demonstrate the viability of the concept for rotational low impedance pHRI.

Estimation of the stable frozen zone volume and the extent of contrast for a therapeutic substance.

BackgroundIn biomedical science and clinical practice, an estimation of the stable frozen zone volume and distribution of concentration fields of injected diagnostic and healing solutions in the tissues of living organisms is of great importance and does not currently have any mathematical solution aimed at its precise evaluation.ObjectiveThe aim of this research is the estimation of the stable frozen zone volume at ultra-low temperatures as well as the distribution of temperature areas and concentration fields of injected diagnostic and healing substances in vitro. The results can improve our understanding of the stable frozen zone volume and the extent of contrast for a therapeutic substance.Materials and methodsA cryogenic zone (ice ball) was generated at -180°C using liquid nitrogen without any difficulties in vitro. The effects of freeze-thaw processes using ultra-low temperature and the cryogenic response of a 1.5% gelatin solution in water (%g/v) kept at a constant temperature of 20°C and continuously stirred were mathematically analyzed. The stable frozen zone volume was illustrated in vitro and measured in terms of its length, depth and cryogenic margin using a standard medical ruler and Vernier caliper after a freezing period at -180°C, using liquid nitrogen to provide cooling and freezing of a small portion of this solution in the vessel at room temperature (20°C). Round-shaped cryoprobes with diameters of 15 mm and 50 mm were applied to create a frozen zone volume in vitro. A single cryoprobe was used per procedure. The sample exposure time was 3 min. After this time, the volume of the frozen region remains unchanged, which indicates that the equilibrium stationary state has been reached. The experimental design, cryogenic procedure and freeze-thaw processes of the hemisphere were described and illustrated in vitro item by item. The statistical analysis manifested significant differences that were found between the 50 mm and 15 mm cryoprobes with regards to the freezing diameter, depth, and cryogenic margin (P < 0.001).ResultsAn illustrated analytical mathematical solution of equations determined the stable frozen zone volume and the radius of the sphere of the frozen medium in the equilibrium stationary state. The resulting assessment provided the basis for the creation of mini- and micro-cryoprobes as well as cryoneedles for local tissue freezing in living biological structures. A solution to the equations was obtained under the boundary conditions with a set stable temperature value on the boundary surface of the cryoprobe as well as at the surface well-away from it, where the temperature is equal to the stable temperature of the environment. For example, this solution gives that in the case of a hemispherical cryoprobe radius of 1 mm, the frozen zone volume was more than three orders of magnitude greater than the volume of the cryoprobe itself and was equal to approximately 4 cm3. The determination of the fractal dimension can consider the individual characteristics of the spread of the contrast medium or therapeutic substance(s) in living tissue. Based on fractal theory, our innovative mathematical formulas allow for the assessment of the effective distribution of contrast medium in living biological structures, specifically for tissues assessed for diagnostic purposes, and they enable the selection of an optimal treatment strategy in medical practice.ConclusionA simple mathematical approach to solving the problems of assessing the stable frozen zone volume and distribution of temperature areas and concentration fields of injected diagnostic and healing substances in living biological structures, particularly living tissue in vitro, is presented in this study. The expressed quantitative mathematical formulas determine the stable stationary frozen zone volume and provide the basis for the creation of mini- and micro-cryoprobes. The application of fractal theory is proposed for assessing the distribution efficiency of contrast medium and therapeutic substance(s) in living biological structures for diagnostic purposes and for selecting a compassionate treatment strategy in medical professional practice.

Random-walk model of cotransport.

We present a statistical mechanical model to describe the dynamics of an arbitrary cotransport system. Our starting point was the alternating access mechanism, which suggests the existence of six states for the cotransport cycle. Then we determined the 14 transition probabilities between these states, including a leak pathway, and used them to write a set of Master Equations for describing the time evolution of the system. The agreement between the asymptotic behavior of this set of equations and the result obtained from thermodynamics is a confirmation that leakage is compatible with the static head equilibrium condition and that our model has captured the essential physics of cotransport. In addition, the model correctly reproduced the transport dynamics found in the literature.

Numerical Validation of Heat Conduction in 2D Binary Granular Mixtures under Mechanical Loading

This study set out to investigate numerical simulations of heat conduction to validate existing experimental results of two-dimensional binary granular mixtures subjected to mechanical loading. Data for this study were collected using molecular dynamics (henceforth MD) method. Three different configurations of the granular composite samples were systematically prepared under similar experimental conditions. A confined mechanical loading was applied to the granular samples. The fields of normalized temperature change of each particle were plotted for an individual sample. The results were statistically analyzed under a static equilibrium condition. The results indicate that simulation is in good correlation with the experiments in terms of statistical analysis via the probability of the distributions of the normalized temperature change. It also revealed that the normalized temperature changes which are greater than the average temperature distributes as an exponential decreasing for all tested samples. This study is in line with other studies that are related to force distribution of law. Less than 50% of particle numbers that have the normalized temperature changes, which are greater than the average value, is also explored. Besides, localizations of the temperature were found in the individual sample.

Key Technology of Port Pile Foundation Construction Based on Mechanical Analy

Zhou, L., 2020. Key technology of port pile foundation construction based on mechanical analysis. In: Yang, Y.; Mi, C.; Zhao, L., and Lam, S. (eds.), Global Topics and New Trends in Coastal Research: Port, Coastal and Ocean Engineering. Journal of Coastal Research, Special Issue No. 103, pp. 402–406. Coconut Creek (Florida), ISSN 0749-0208.In view of the poor structural stability of port pile foundation at present, the key technology research of port pile foundation construction based on mechanical analysis is put forward. According to the construction characteristics of ports, the settlement-displacement relationship of soil mass on pile side is analyzed. The pile-soil contact model is constructed based on the settlement calculation results of single pile. The ultimate Punching Strength of the bearing layer at the end of the pile is determined by considering the punching failure of the hard bearing layer and the strength failure of the soft underlying layer. Suitable proportional value is obtained by static equilibrium condition calculation, and key technology research of port pile foundation construction based on mechanical analysis is completed. The experimental results show that the soil pressure exertion coefficient of the pile foundation structure designed by the proposed technology is stable, and the change trend of the passive soil pressure coefficient is basically the same as that of the active soil pressure coefficient. It can be verified that the stability of the designed pile foundation structure is significantly improved compared with the structure designed by the comparison methods.

Compliant Manipulation Method for a Nursing Robot Based on Physical Structure of Human Limb

Nursing robots can be a good substitute to do nursing works for severely disabled patients who have completely lost the ability of movement. In order to improve the safety and comfort of human-robot interaction, we propose a novel compliant manipulation method for a nursing robot based on physical structure of human limb, which is applicable to severely disabled patients and can reduce the high performance requirements of sensors in existing human-robot interaction systems. The method aims to obtain the optimal manipulative force in static and dynamic manipulations. In the aspect of static calculation, static equilibrium conditions are used to obtain optimal static manipulative force. And in the aspect of dynamic calculation, lagrangian method is used to obtain optimal dynamic manipulative force based on predefined movement trajectory. Adams simulations and experiments are executed by manipulating limb model to conduct rehabilitation movements. Experimental results show that the proposed method can provide compliant manipulation method for a nursing robot.

Numerical study on a possible cause of the ‘strange tide’ in the coastal area of Jiangsu Province, China

There are many eyewitness reports on unexpected water level change called ‘strange tide’ around the area of the radial sand ridges off the coast of Jiangsu Province, China, which has caused several fatal accidents in history. This study aims to prove whether a fast-moving atmospheric pressure disturbance can be a possible cause of the ‘strange tide.’ Based on the nonlinear shallow water model, a large number of scenarios for waves induced by a fast-moving pressure disturbance are numerically simulated and the maximum of the wave amplification ratio in each scenario is discussed. In each scenario, we assume an idealized pressure disturbance passing through the concerned area. The heading angle and translational speed of atmospheric disturbances are considered as variables. The results show that a fast-moving pressure disturbance can induce large wave level fluctuation in this area. In some special situations, the water level rise can be amplified more than 40 times than the water level change caused by a pressure disturbance with equivalent intensity under static equilibrium state. Both the heading angle and translational speed of atmospheric disturbances play a very important role in the occurrence of dangerous situation. The most dangerous combination of the two parameters is discussed, and the disaster prone locations in this area are identified considering the historical accidents and the numerical experiments.

Experimental observations on fine sand winnowing from immobile gravel substrate

Introduction of fine sand into gravel-bed rivers has surged tremendously as a result of human activities. The ecological concerns for river habitats have called for suitable management strategies for cleaning these particles from gravel bed rivers. This paper is concerned with determining movement threshold of fine sand initially entrapped in the spaces between large immobile elements resembling a coarse riverine substrate with flow depths comparable to non-erodible element sizes. Static equilibrium condition was reached during an experimental run by maintaining a zero-supply condition for sand. It was assumed that the flow condition corresponding to this sand level was representative of critical conditions for onset of sand motion. A nonlinear regression curve was fitted between the level of the sand and associated critical shear stress. The flow field measurements using an ultrasonic Doppler rofiler delineate main features of the shallow flow over large roughness elements such as sharp velocity gradients near the crest of the immobile elements, and also a deviation of instantaneous velocity probability density function from normal distribution very close to the sand level.