Space Research Articles

Wearable Haptics for Orthotropic Actuation Based on Perpendicularly Nested Auxetic SMA Knotting.

Smart wearable tactile systems, designed to deliver different types of touch feedback on human skin, can significantly improve engagement through diverse actuation patterns in virtual or augmented reality environments. Here, a perpendicularly nested auxetic wearable haptic interface is reported for orthotropically decoupled multimodal actuation (WHOA), capable of producing diverse tactile feedback modes with 3D sensory perception. WHOA incorporates shape memory alloy wires that are intricately knotted into an auxetic structure oriented along orthotropic dual axes. Its perpendicularly nested auxetic structure enables orthotropic actuation, allowing independent expansion and contraction along both x and y-axes, as confirmed by force-strain and displacement-time performance tests. Additionally, the perylene coating provides orthogonal electrical isolation to WHOA, allowing for stripe-specific localized actuation and enabling multiple tactile feedback modes. As an orthotropic wearable haptic interface, WHOA distinguishes between x-axis and y-axis directions and ultimately delivers multi-dimensional information regarding movements in 3D space through tactile feedback. As a result, when worn on the foot or arm, WHOA naturally delivers spatiotemporal tactile information to the user, facilitating navigation and teleoperation with 3D sensory perception.

Joint Design of Transmit Waveform and Altitude for Unmanned Aerial Vehicle-Enabled Integrated Sensing and Wireless Power Transfer Systems

Recently, unmanned aerial vehicle (UAV)-enabled wireless power transfer (WPT) has received great attention as a promising technology for providing stable power to energy-constrained devices by navigating three-dimensional (3D) space, particularly in challenging environments such as maritime networks and smart cities. Additionally, UAV-enabled radar sensing has gained significant attention as a key technology for future 6G networks, as it enables high-accuracy sensing for various applications, such as target detection and tracking, surveillance, and environmental monitoring, as well as autonomous UAV operation. In this regard, we investigated UAV-enabled integrated sensing and wireless power transfer (ISWPT) systems that combine radar sensing and WPT operations on a unified hardware platform, sharing the same spectrum of resources. In order to accurately sense multiple targets and efficiently transfer power to multiple devices at the same time, we propose a method for jointly designing the transmit waveform and UAV altitude, taking into account the fundamental trade-off between radar sensing performance with the desired beam pattern and WPT performance with the desired harvested power of the devices. We first developed an effective method to obtain the optimal waveform and altitude by solving a challenging non-convex optimization problem. Based on this, we developed another efficient, low-complexity method by exploring a novel transmit waveform and optimizing its parameters to reduce computational complexity and thereby lower power consumption in UAVs. The numerical results verify that the proposed method significantly improves both radar sensing and WPT performance, as well as substantially reduces computational complexity.

Nonlinear analysis of three-dimensional hyperelastic problems using radial point interpolation method

Hyperelastic materials are primarily common in real life as well as in industry applications, and studying this kind of material is still an active research area. Naturally, the characteristic of hyperelastic material will be expressed when it undergoes large deformation, so the geometrical nonlinear effect should be considered. To analyze the behavior of hyperelastic material, the Neo-Hookean model is imposed in this study because of its simplicity. The model shows the nonlinear behavior when the deformation becomes large due to the nonlinear displacement-strain relation. This constitutive relation also gives a good correlation with experimental data. This study performs a meshless method, namely the radial point interpolation method (RPIM), to analyze the nonlinear behavior of Neo-Hookean hyperelastic material under a finite deformation state in three-dimensional space. The standard Newton-Raphson technique is applied to obtain the nonlinear solutions. Unlike mesh-based approaches, the meshless method shows its advantages in large deformation problems due to its mesh independence. In this paper, the numerical results of three-dimensional problems that undergo large deformation will be calculated and validated with solutions derived from previous studies. By investigating the obtained results, the superior ability of RPIM in hyperelastic problems can be proved.

How does lead selection impact diagnosis through AI? Implications for continuous monitoring systems using convolutional neural networks

Abstract Background and Objectives Recently, there has been a surge in non-invasive diagnosing methods leveraging the dipolar 12-lead ECG information using Convolutional Neural Networks (CNNs). However, the traditional ECG contains 12 projections of the cardiac dipole in a three-dimensional space can result in redundancy. Furthermore, in continuous monitoring systems such as Holter and wearables, not all 12 leads are consistently available. This study aims to quantify redundancy and determine the best lead configuration for improved classification results using a CNN. It evaluates the level of redundancy in ECG leads and its impact on CNN classification. Methods The degree of redundancy was quantified by means of lead entropies (H) as depicted in Figure 1.A. The standard 12-lead ECG was chosen as the baseline input. From it, various subsets of leads were selected (6, 3, 1 leads) with the objective of attaining maximal orthogonality between leads while minimizing redundancy (Figure 1.B). A 2D-CNN model was trained for multiclass classification: Hypertension (HYP), ST-T interval Changes (STTC), Conduction Disturbances (CD), Myocardial Infarction (MI) and Normal (NORM). The designed inputs were employed to evaluate how redundancy impacts the performance of the CNN (see Figure 1.C). Results Reducing redundancy in input leads led to notable improvements in model prediction for all pathological conditions in terms of Area Under the Curve (AUC). Reducing to 6 and 8 leads were the most suitable input for the CNN (Table 1) increasing by 1.18% in HYP, 0.23% in STTC, 0.52% in CD, and 0.33% in MI. However, a significant reduction in redundancy may result in the loss of essential clinical information for classification, as observed in scenarios involving only 3 or 1 leads. Conclusions When diagnosing pathologies with systems featuring fewer leads, its combinations should aim for maximum orthogonality to reduce redundancy while preserving unique information. By strategically selecting a set of leads with reduced input redundancy, the effectiveness of the standard 12-lead ECG can be improved, thereby enhancing the utility of such continuous monitoring systems for automated diagnosis and also decreasing training and prediction times.

Speeding up echocardiographic examination by automated generation of 2D imaging views from 3D volumetric data using machine learning

Abstract Background 3D echocardiographic data contain infinite 2D echocardiographic planes generated by multiplanar reconstruction, but the process is labor-intensive and time-consuming. Artificial intelligence (AI) utilizing cutting-edge machine learning techniques may improve the accuracy and efficiency of the process. In the study, we developed and validated an AI software that automatically reconstructs 7 2D views recommended by the American Society of Echocardiography from 3D echocardiographic data. Method Convolutional neural network (CNN) architecture utilizing Spatial Configuration Net was used as the machine learning model. We identify a minimum of 3 key feature landmarks on each 2D cross-sectional plane, with the 3D coordinates representing 2D cross-sectional planes accordingly. Subsequently, these landmarks are accurately labeled within a 3D space. 31 landmarks were identified across 7 2D cross-sectional planes and a total of 472 3D volume data were labelled. The performance of the model is evaluated by Root Mean Square Error (RMSE) of the predicted landmark coordinates. Results The mean RMSE over 31 predicted landmarks evaluated in testing is 2.70% for the input 3D volume dimensions. The average time used to generate the 7 2D imaging views was 19.91±3.19 seconds (figure). Conclusion The AI algorithm can efficiently convert 3D echocardiographic data into guideline-recommended 2D images, which shortens the length of echo examination but still preserves the accuracy.AI generation of 2D views from 3D echo

The covariant functoriality of graph algebras

AbstractIn the standard category of directed graphs, graph morphisms map edges to edges. By allowing graph morphisms to map edges to finite paths (path homomorphisms of graphs), we obtain an ambient category in which we determine subcategories enjoying covariant functors to categories of algebras given by constructions of path algebras, Cohn path algebras, and Leavitt path algebras, respectively. Thus, we obtain new tools to unravel homomorphisms between Leavitt path algebras and between graph C*‐algebras. In particular, a graph‐algebraic presentation of the inclusion of the C*‐algebra of a quantum real projective plane into the Toeplitz algebra allows us to determine a quantum CW‐complex structure of the former. It comes as a mixed‐pullback theorem where two ‐homomorphisms are covariantly induced from path homomorphisms of graphs and the remaining two are contravariantly induced by admissible inclusions of graphs. As a main result and an application of new covariant‐induction tools, we prove such a mixed‐pullback theorem for arbitrary graphs whose all vertex‐simple loops have exits, which substantially enlarges the scope of examples coming from noncommutative topology.

In-depth morphological and functional analysis of ATTR-CA myocardial cells and niche by electron microscopic 3D reconstruction

Abstract Background Cell-cell interactions and interplay with extracellular matrix are known to be important in the steady state and pathological conditions, including wild-type transthyretin cardiac amyloidosis (wtATTR-CA). However, alterations of the microstructure of cardiomyocytes (CMs) and cardiac niches have not been well analyzed. Normal histological staining is usually limited in resolution, and 2D electron microscopy cannot capture stereoscopic images or the distribution of target particles and organelles in intra- and extracellular 3D space, so novel methods are being attempted. Methods and Results Using Serial Block Face-Scanning Electron Microscopy (SBF-SEM) and a 3D structural reconstruction system, we for the first time investigated the microstructure of human myocardial tissue from control hypertrophied heart (hypertensive heart disease) and wtATTR-CA patients. The microstructure of myocardial niche, cell morphology/numbers, and the distribution of intracellular organelles such as intercalated discs (ICDs) were compared to control endomyocardial biopsy (EMB) samples (2 controls vs 5 wtATTR-CA patients). In all wtATTR-CA samples, amyloid fibers were deposited originating around the capillary structures with various electron densities, compressing myocardial cells not only from the periphery but also dividing them from the center of the cell body, and CMs showed degeneration and dwarfing according to the severity of amyloid fiber deposition (Figure 1). The capillary structures showed degeneration and narrowing with stratified basement membrane, and rarefaction (3378±216.5 vs 1448±116.8/mm2, p<0.0001). Notably, the stromal cells (pericytes, fibroblasts, macrophages) were more likely buried by amyloid fibers than CMs, and their numbers were also reduced, indicating a loss of adjacent and intercellular interaction with capillaries and CMs (Fig. 2, 1892±194.4 vs 1189±107.4 mm2, p=0.0043). This method can also be used to analyze intracellular organelles and microstructures in CMs. In ATTR-CA, morphological abnormalities were observed in ICDs (Figure 3) and mitochondria. Conclusion In the ATTR-CM patients, there was a significant decrease in the number of capillaries in accordance with the deposition of myocardial amyloid fibers, as well as a decrease in stromal cells. These results support the hypothesis that amyloid fibril deposition not only causes chronic myocardial ischemia, but also reduces the number of niche cells, which play a supportive role for CM function and entirely exacerbate the damage. The SBF-SEM is an innovative tool for 3D imaging and quantitative analysis of myocardial ultrastructure and functions.Methods & Figure 1Figure 2 and Figure 3

Naked-eye 3D visualization of cultural relics based on integrated imaging

AbstractDigital technology has become crucial for the protection of cultural relics, enabling their acquisition, preservation, exhibition, and dissemination in a non-contact manner.At present, the three-dimensional(3D) visualization technology of cultural relics focuses on the research of non-true 3D visualization, which cannot provide continuous viewing angle and takes a long time to render. This paper focuses on the acquisition and reproduction of digital information related to cultural relics, and proposes to achieve the true 3D display of cultural relics from a continuous perspective based on integrated imaging(InIm). Building up on traditional InIm, an Element image array (EIA) generation algorithm based on local depth template matching is designed by using spatial geometry relation. Experimental results show that the algorithm not only enables naked-eye 3D visualization of cultural relics, but also the generation speed is more than twice that of the compared 3D display data source generation algorithm.

Experimental Elucidation of a Cubane Water Cluster in the Hydrophobic Cavity of UiO-66.

Nanoscale water plays a pivotal role in determining the properties and functionalities of materials, and the precise control of its quantity and atomic-scale ordered structure is a focal point in nanotechnology and chemistry. Several studies have theoretically discussed the nano-ordered ice within one- or two-dimensional space and without confinement through hydrogen bonds. In particular, the water cluster has been predicted to play a significant role in biomolecules or functional nanomaterials; however, there has been little experimental evidence for their presence in hydrophobic cavities. In this study, the cubane water octamer - the most stable isomer among small water clusters - was detected within the hydrophobic cavities of UiO-66 metal-organic frameworks, revealing the presence of the smallest ice in their hydrophobic cavity, in the absence of hydrogen bonding. This observation contrasts earlier examples of water clusters confined within nanocavities through hydrogen bonds and provides experimental evidence for water-cluster capturing within hydrophobic cavities. Consequently, our renewed understanding of hydrophilicity and hydrophobicity warrants a design re-evaluation of materials for chemical applications, including fuel cells, water harvesting, catalysts, and batteries.

QPOs from charged particles around magnetized black holes in braneworlds

Quasiperiodic oscillations (QPOs) are a powerful tool for testing gravity theories, probing gravitational and electromagnetic field properties, and obtaining constraints on the black hole and field parameters. This work considers charged particle dynamics near uniformly magnetized black holes in braneworlds. First, we obtain the solution of the Maxwell equation for magnetic fields and calculate the radial and angular magnetic field components. We derive and analyze the effective potential of charged particles for circular orbits and investigate the energy and angular momentum for the circular orbits. We also analyze the combined effects of magnetic interaction and braneworlds on the charged particles’ innermost stable circular orbits (ISCOs). We calculate the angular momentum of charged particles in Keplerian orbits in the presence of an external magnetic field and braneworlds. Also, we investigate frequencies of the particle oscillations along vertical and angular directions. We applied our studies on particle oscillations to the QPO studies in the relativistic precession model. Finally, we obtain constraints on magnetic interaction and braneworld parameters together with the black hole mass and QPO orbits using Monte Carlo Markov Chain (MCMC) simulation in the four-dimensional parameter space for the QPOs observed in the microquasars XTE J1550-564, GRO J1655-40 & GRS 1915-105, and at the center of galaxies M82 and Milky Way.

An efficient Protocol for Enhanced Flynet Communication in Presence of Partitioning

This paper presents an adaptive fault-tolerant resource allocation protocol tailored for FlyNet, a dynamic aerial network characterized by its mobility and three-dimensional operational space. Addressing the challenges of network partitioning and resource allocation in aerial networks, the proposed algorithm dynamically adjusts to the network's changing topology, ensuring consistent and efficient resource management. Through robust fault tolerance mechanisms, the protocol enhances FlyNet's reliability, maintaining seamless communication and optimal resource utilization even amid node mobility and disruptions. Simulation results demonstrate the algorithm's effectiveness in adapting to dynamic environments, maximizing resource utilization, and minimizing communication delays.

Effect of attention on ensemble perception: Comparison between exogenous attention, endogenous attention, and depth.

Ensemble perception is an important ability of human beings that allows one to extract summary information for scenes and environments that contain information that far exceeds the processing limit of the visual system. Although attention has been shown to bias ensemble perception, two important questions remain unclear: (1) whether direct manipulations on different types of spatial attention could produce similar effects on ensembles and (2) whether factors potentially influencing the attention distribution, such as depth perception, could evoke an indirect effect of attention on ensemble representation. This study aims to address these questions. In Experiments 1 and 2, two types of precues were used to evoke exogenous and endogenous attention, respectively, and the ensemble color perceptions were examined. We found that both exogenous and endogenous attention biased ensemble representation towards the attended items, and the latter produced a greater effect. In Experiments 3 and 4, we examined whether depth perception could affect color ensembles by indirectly influencing attention allocation in 3D space. The items were separated in two depth planes, and no explicit cues were applied. The results showed that color ensemble was biased to closer items when depth information was task relevant. This suggests that ensemble perception is naturally biased in 3D space, probably through the mechanism of attention. Computational modeling consistently showed that attention exerted a direct shift on the ensemble statistics rather than averaging the feature values over the cued and noncued items, providing evidence against an averaging process of individual perception.

A novel model for low-permeability reservoir numerical simulation considering dynamic capillary force

ABSTRACT Capillary force is not only affected by water saturation but also affected by fluid flow velocity, which is necessary to modify the prior numerical simulation methods. First, a dynamic capillary force testing device was developed, then, an experimental procedure was adopted to measure the dynamic capillary force curve. Three dynamic capillary force curves were obtained under different displacement velocity conditions. Finally, the dynamic capillary force was introduced into the flow equation of low-permeability reservoir numerical simulation. The oil-phase equation and water-phase equation were discretized in three-dimensional space, and the IMPES method was used to solve the water saturation and pressure difference. The calculation results between the traditional numerical simulation method and the novel method under heterogeneous and inhomogeneous conditions were analyzed. The results reveal that the difference in water cut is mainly reflected in the rapid rise of water cut. In the early stage of rapid increase, the water cut calculated by the new method is slightly higher than traditional method. When the water cut is more than 65%, the water cut calculated by the new method is slightly lower than the traditional method.

Toward a Generic Framework for Mission Planning and Execution with a Heterogeneous Multi-Robot System

This paper presents a comprehensive framework for mission planning and execution with a heterogeneous multi-robot system, specifically designed to coordinate unmanned ground vehicles (UGVs) and unmanned aerial vehicles (UAVs) in dynamic and unstructured environments. The proposed architecture evaluates the mission requirements, allocates tasks, and optimizes resource usage based on the capabilities of the available robots. It then executes the mission utilizing a decentralized control strategy that enables the robots to adapt to environmental changes and maintain formation stability in both 2D and 3D spaces. The framework’s architecture supports loose coupling between its components, enhancing system scalability and maintainability. Key features include a robust task allocation algorithm, and a dynamic formation control mechanism, using a ROS 2 communication protocol that ensures reliable information exchange among robots. The effectiveness of this framework is demonstrated through a case study involving coordinated exploration and data collection tasks, showcasing its ability to manage missions while optimizing robot collaboration. This work advances the field of heterogeneous robotic systems by providing a scalable and adaptable solution for multi-robot coordination in challenging environments.

Multiple dimensions of immorality

ABSTRACT We conducted a four-part study to map out the conceptual space of a diverse set of immoral items, including those that are extreme and/or intergroup (e.g. child sex abuse, genocide, slavery), with the goal of identifying attributes spontaneously used in moral judgment. In Part 1, we identified 56 immoral items. In Part 2, participants completed a similarity-based card sort task of the 56 immoral items. Multidimensional scaling (MDS) indicated that three-dimensional space was needed to capture the perceived differences among the items. In Part 3, regression analysis indicated that perceived similarity among the immoral items related to their commonness, objectivity, forgivability, and legality. In Part 4, regression analysis indicated that the configuration of immoral items corresponded to the amount of anger and disgust the items elicited and items’ perceived harmfulness. We attempt to synthesize these results and answer questions about the roles of anger, disgust, and harm in moral judgment.

A Clustering Approach to Unveil User Similarities in 6-DoF Extended Reality Applications

The advent in our daily life of Extended Reality (XR) technologies, such as Virtual and Augmented Reality, has led to the rise of user-centric systems, offering higher level of interaction and presence in virtual environments. In this context, understanding the actual interactivity of users is still an open challenge and a key step to enabling user-centric system. In this work, our goal is to construct an efficient clustering tool for 6 Degree-of-Freedom (DoF) navigation trajectories by extending the applicability of existing behavioural tool. Specifically, we first compare the navigation in 6-DoF with its 3-DoF counterpart, highlighting the main differences and novelties. Then, we investigate new metrics aimed at better modelling behavioural similarities between users in a 6-DoF system. More concretely, we define and compare 11 similarity metrics which are based on different distance features ( i.e. , user positions in the 3D space, user viewing directions) and distance measurements ( i.e. , Euclidean, Geodesic, angular distance). Our solutions are validated and tested on real navigation paths of users interacting with dynamic volumetric media in both 6-DoF Virtual Reality and Augmented Reality conditions. Results show that metrics based on both user position and viewing direction better perform in detecting user similarity while navigating in a 6-DoF system. Such easy-to-use but robust metrics allow us to answer a fundamental question for user-centric systems: “how do we detect if users look at the same content in 6-DoF?”, opening the gate to new solutions based on users interactivity, such as viewport prediction, live streaming services optimised based on users behaviour but also for user-based quality assessment methods.

Constraining dark matter from strong phase transitions in a U1Lμ−Lτ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ extrm{U}{(1)}_{L_{\\mu }-{L}_{\ au }} $$\\end{document} model: implications for neutrino masses and muon g − 2

In this paper, we study a non-minimal gauged U1Lμ−Lτ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ extrm{U}{(1)}_{L_{\\mu }-{L}_{\ au }} $$\\end{document} model, where we add two complex singlet scalars, three right-handed Majorana neutrinos (RHN), and a vector-like dark fermion to the Standard Model (SM), all non-trivially charged under the extra gauge symmetry. The model offers an easy resolution to the muon (g – 2) anomaly, which fixes the scale of spontaneous symmetry breaking. Furthermore, the two-zero minor structure in the RHN mass matrix provides successful predictions for neutrino oscillation parameters, including the Dirac phase. The extended scalar sector can easily induce first-order phase transitions. We identify all possible phase transition patterns in the three-dimensional field space. We quantify the associated gravitational waves from the sound wave source and demonstrate that the signatures can be observed in future space-based experiments. We find that strong first-order phase transitions require large values of scalar quartic couplings which constrain the scalar dark matter (DM) relic density to a maximum of 10−2 and 10−5 when we consider the DM direct detection bound. Nonetheless, the model successfully explains the DM relic density via contribution from the vector-like dark fermion. We show the allowed range of the model parameters that can address all the beyond SM issues targeted in this study.

Hydroxyapatite/Silk Fibroin Composite Scaffold with a Porous Structure and Mechanical Strength Similar to Cancellous Bone by Electric Field-Induced Gel Technology.

Repair and regeneration of bone tissue defects is a multidimensional process that has been highly challenging to date. The artificial bone scaffold materials, which play a core role, still face the conflict that a biofriendly porous structure will reduce the mechanical performance and accelerate degradation. Herein, a multistage porous structured hydroxyapatite (HA)/silk fibroin (SF) composite scaffold (e-HA/SF) was successfully constructed by cleverly utilizing electric field-induced gel technology. The results indicated that the prepared e-HA/SF scaffolds possess biomimetic hierarchical porous structures with a suitable porosity similar to that of cancellous bone. The HA nanocrystals were uniformly encapsulated in the three-dimensional space of the composite scaffold, thus endowing the e-HA/SF composite scaffolds with an enhanced mechanical performance. Notably, the maximum compression stress and Young's modulus of e-HA/SF-2 scaffolds can reach 24.66 ± 0.88 and 28.91 ± 3.19 MPa, respectively, which are equivalent to those of cancellous bone. Such mechanical performance enhancement was previously unattainable through conventional freeze-drying strategies. Moreover, the introduction of bioactive nano-HA can trigger the optimal cell response in both static and dynamic cell culture experiments in vitro. The e-HA/SF composite scaffold developed in this study can better balance the conflict between the porous structure and mechanical and degradation properties of porous scaffolds.

Evolutive 3D Urban Data Representation through Timeline Design Space

AbstractCities are constantly changing to adapt to new societal and environmental challenges. Understanding their evolution is thus essential to make informed decisions about their future. To capture these changes, cities are increasingly offering digital 3D snapshots of their territory over time. However, existing tools to visualise these data typically represent the city at a specific point in time, limiting a comprehensive analysis of its evolution. In this paper, we propose a new method for simultaneously visualising different versions of the city in a 3D space. We integrate the different versions of the city along a new way of 3D timeline that can take different shapes depending on the needs of the user and the dataset being visualised. We propose four different shapes of timelines and three ways to place the versions along it. Our method places the versions such that there is no visual overlap for the user by varying the parameters of the timelines, and offer options to ease the understanding of the scene by changing the orientation or scale of the versions. We evaluate our method on different datasets to demonstrate the advantages and limitations of the different shapes of timeline and provide recommendations so as to which shape to chose.

Numerical Modeling of Soil and Structure Behavior for Tunneling in Different Types of Soil

This note studies the correlation between surface and tunnel volume loss in various types of dry soil via finite element method. The effect of small strain stiffness, the buoyancy effect of soil, and tunnel overburden depth are considered in the 2D tunneling model. The results show that both surface volume loss ratio and settlement trough width parameter in the empirical solution can be expressed as a linear equation of tunnel volume loss ratio for 1D overburden shallow tunnels. Furthermore, the surface volume loss ratio can be presented as a non-linear polynomial equation of overburden depth and tunnel volume loss ratio in a 3D space, and this equation holds in different types of soil. The ranges of required fitting parameters and upper and lower bounding surfaces are suggested for various types of soil. Knowledge of this correlation between surface and tunnel volume loss is valuable, as it can be employed in practice for preliminary tunnel design in the absence of tunneling induced maximum ground settlement.