Uniform Rigidity Research Articles

Optimization of column-in-column system based on non-conventional TMD concept

Previous studies showed that the non-conventional tuned mass damper (TMD) with large mass ratio outperforms the traditional one in respect to the structural vibration control efficiency and robustness. The authors recently proposed a novel control system based on the non-conventional TMD concept, namely the column-in-column (CIC) system, which was composed of a primary column, a secondary column and a series of interconnected springs/dashpots. In this novel system, the secondary column connected to the primary one with springs/dashpots could act as a large TMD to attenuate adverse vibration of the primary structure, and its control effectiveness was preliminarily verified through numerical investigations. However, the control robustness was found not sufficient based on the existing optimal formulae in the literature for CIC optimization. This paper presents a new design method for optimizing the CIC system for better harnessing its control effectiveness and robustness in reducing structural response. The CIC system consists of two columns with distributed mass and uniform flexural rigidity, connected by springs along the column height. The effective modal mass and modal stiffness of a specific vibration mode of the system can be straightforwardly calculated by using the Euler-Bernoulli beam theory. Considering the fundamental vibration mode of the system as the target response mode for vibration control, the multiple degree-of-freedom (DOF) CIC is simplified into a two DOF with three springs (2DOF3S) structural model, the design parameters, i.e., the optimal tuning frequency ratio and damping ratio of this system are derived to minimize the displacement response of the primary structure. To demonstrate the proposed design method, the effectiveness and robustness of the CIC system in controlling seismic induced structural vibrations are assessed in both the frequency and time domains. Results show that the derived optimum formulae are applicable for optimizing the TMD system with consideration of the distributed mass and deformation of the mass damper, i.e., a column in this study. The optimized CIC system has good control robustness even if the CIC is mistuned with its design parameters deviate from the optimal values by ±50 %. The conventional TMD system with lumped mass as the mass damper is a special case of the proposed CIC system. The optimized CIC system has favorable control efficiency in mitigating the seismic responses of structures with reduction ratios averagely varying within the range of 15 % ∼ 55 % with a probability of 92.67 %. It is concluded that the proposed method is reliable and can be used for the optimum design and control of the CIC system.

Measure-theoretic equicontinuity and rigidity of group actions

Let ( G , X ) be a G-system, which means that X is a compact Hausdorff space and G is an infinite topological group continuously acting on X, and let μ be a G-invariant measure of ( G , X ) . In this paper, we introduce the concepts of rigidity, uniform rigidity and μ-Ω-equicontinuity of ( G , X ) with respect to an infinite sequence Ω of G and the notions of μ-Ω-equicontinuity and μ-Ω-mean-equicontinuity of a function f ∈ L 2 ( μ ) with respect to an infinite sequence Ω of G. Then we give some equivalent conditions for f ∈ L 2 ( μ ) and ( G , X ) to be rigid, respectively. In addition, if G is commutative and X satisfies the first axiom of countability, we present some equivalent conditions for ( G , X ) to be uniformly rigid.

Time-Independent Grid-Based Forecast Model for M ≥6.0 Earthquakes in Southeastern Tibetan Plateau Using GNSS Strain Rates and Seismicity

ABSTRACT Earthquake forecasting models play a vital role in earthquake occurrence assessment. Despite improved availability of seismic and geodetic data and processing techniques to produce high-resolution catalogs and deformation history, the implementation of earthquake forecasting models with seismic and geodetic data remains a challenge. In this study, we utilize seismicity and Global Navigation Satellite Systems (GNSS) data to propose time-independent grid-based regional earthquake likelihood models for southeastern Tibetan plateau (RELM-TibetSE). First, we solve the GNSS velocity field and strain rates from 1999 to 2017, deriving geodetic moment rates and introducing empirical correction coefficients to balance them with historical seismic moment rate. Subsequently, we employ a truncated Gutenberg–Richter law and Poisson process to calculate time-independent probabilities for M ≥ 6 earthquakes in 0.2° × 0.2° cells. The grid-based forecasting models indicate that the 30-year probability for M ≥ 6 earthquakes exceeds 1% in more than one-third of the entire study area, highlighting prominently higher earthquake occurrence in these regions. Probability distribution exhibits significant spatial variations. Finally, the predictive performance of the forecasting models is validated based on historical seismicity. The validation indicates that all RELM-TibetSE exhibit good predictive capability relative to a spatially uniform model. The RELM-TibetSE incorporating principal strain rates outperforms those involving maximum shear strain rate in forecasting seismicity. And the differences in forecasting performance between the RELM-TibetSE accounting for spatially varied seismogenic thickness and rigidity and those with uniform thickness and rigidity are not significant. The forecasting models also exhibit better predictive performance for seismic source areas than for epicenters. Moreover, the optimal model highlights zones with higher earthquake occurrence, including the zones about 50 km wide across the Ninglang fault, the zones across the southwestern segment of the Lijiang–Xiaojinhe fault, the China–Myanmar borderland north of the Nantinghe fault, and so on. Therefore, it is justified to conduct multidisciplinary rigorous observations to capture the potential nucleation process of future large earthquakes in these zones.

Instability mechanism of shear-layered fluid in the presence of a floating elastic plate

In this study, linear stability analysis in the two-dimensional Cartesian coordinate system is used to analyze the flow dynamics underneath a large floating elastic plate over a slippery surface in the presence of external shear. For both viscous and inviscid flows, the Orr–Sommerfeld equation and the Rayleigh equation, respectively, are obtained using normal mode analysis. The Chebyshev collocation method is used to solve both equations numerically. Analysis of the growth rate and energy distributions is performed to understand the flow instability at various flow and structural parameters. The study reveals that the flow below the floating elastic plate dampens for larger uniform mass and structural rigidity in the viscous fluid. On the other hand, there is no effect of structural rigidity on the flow stability in the case of inviscid flow. However, the plate of larger uniform mass stabilizes the growing disturbance generated due to the externally imposed shear at the surface of the plate. The present study is analogous to the simple geographical model of external shearing on the surface of a large ice cover zone caused by atmospheric air. This study can be extended to understand the flow stability below other large floating structures like a floating island and a floating airport.

Topological equicontinuity and topological uniform rigidity for dynamical system

In this paper, we study topological equicontinuity, topological uniform rigidity and their properties. For a dynamical system, on a compact, T3 space, we study relations among the set of recurrent points of the map, the set of non-wandering points of the map and the intersection of the range sets of all iterations of the map. We define topological version of uniform rigidity and show that on a compact and T3 space any dynamical system is topologically uniformly rigid if it is first countable, almost topologically equicontinuous and transitive or it is second countable, topologically equicontinuous and has a dense set of periodic points. We show that a topologically uniformly rigid dynamical system, on a compact, Hausdorff space, has zero topological entropy. Moreover, we provide necessary examples and counterexamples.

On uniform and coarse rigidity of $L^p([0,1])$

If $X$ is an almost transitive Banach space with amenable isometry group (for example, if $X=L^p([0,1])$ with $1\leq p \lt \infty $) and $X$ admits a uniformly continuous map $X\overset \phi \longrightarrow E$ into a Banach space $E$ satisfying $$ \inf _{

Flexural gravity wave scattering due to a pair of asymmetric rectangular trenches

The research presented here investigates the interaction of oblique flexural gravity waves with a pair of asymmetric trenches. The fluid considered here is bounded above by an infinite thin uniform ice sheet of particular flexural rigidity. Velocity potential describing the motion in the fluid is obtained explicitly in terms of non-orthogonal eigenfunctions. The mode-coupling relations satisfied by the eigenfunction are given. Using matching conditions along the vertical boundaries of the trench walls the problem is transformed into a system of singular integral equations. The unknown functions involved in the integral equations are calculated numerically using multi-term Galerkin approximations involving ultraspherical Gegenbauer polynomials. The reflection and transmission coefficients are obtained numerically and depicted in the number of figures for both symmetric and asymmetric cases. The energy balance relation satisfied by the reflection and transmission coefficients is obtained. The results are analyzed for various non-dimensional parameters describing the model. The results using the present method are compared with previously published works available in the literature. It is found that a thin ice sheet of uniform flexural rigidity has a significant effect on the scattering behavior of the wave in presence of wide trenches.

Mechanical Behavior of the Special Segment Structure during Upward Shield Tunnel Construction

The upward shield method in horizontal tunnels has the advantages of small ground space occupation, low construction cost, and short construction period, which expresses substantial economic benefits. The special segments of horizontal shield tunnels corresponding to the upward shield method construction area have special design requirements, and different internal force calculations and analyses should be carried out. To determine the mechanical behavior of the special segment structure of horizontal shield tunnels during the construction of upward shield tunnels, the theoretical calculation formula of the internal force of the special segment structure is deduced based on the average uniform rigidity ring method. Moreover, the bending moment and axial force of special segments are numerically simulated and analyzed using Midas GTS NX software. Finally, the theoretical formula and finite element calculation results are compared and analyzed. The results show that the internal force values of the open segment ring and the adjacent segment ring of the special segment are quite different during upward shield tunnel construction. Furthermore, compared with the arch crown and arch bottom of the segment ring, the stress at the arch waist of the segment ring is the most unfavorable. The stress difference between the open segment ring and the adjacent segment ring may cause unbalanced deformation, leading to damage to the segment ring radial joint. In the design and construction, attention should be given to the shear strength of the segment ring radial joint and the bending stiffness of the ring joint at the arch waist.

Dynamic Properties Comparison of 1D, 2D, and 3D Model for Concrete Box-Girder Bridge of 40-meter Span

Concrete box-girder structure is considered the thin-walled structure, undergoing deformation and forces, as well as having structural rigidity in three dimensional directions. However, it’s commonly modeled as 1D structure for the sake of design practicality, which influences the numerical result of its dynamic properties when compared to both real time SHMS and field test result. To see how far the difference of the dynamic properties between 1D, 2D, and 3D model of concrete box-girder structure, the concrete box-girder structure is modeled as 1D (frame), 2D (shell), and 3D (solid) element with MIDAS Civil 2019. Considering the allowable deflection and stress limited by design code, concrete box-girder structure is modeled and analyzed as linearly elastic material. The dynamic properties obtained from these 3 models were compared with those obtained from real time SHMS and field test. These results indicate that both natural frequency and period of 2D and 3D models are close to those of real time SHMS and field test. However, the natural frequency of 1D model is slightly larger than the real SHMS and field test, indicating that 1D model gives the slightly overestimate natural frequency and structural rigidity compared to the reality. Unlike 2D and 3D model, the structure is accounted to have the uniform sectional rigidity along transversal direction in 1D model. This is why 1D model seems to have higher structural rigidity compared to 2D and 3D model, which subsequently yields the higher natural frequency than 2D and 3D model. This research proves that the designers’ discretion is advised if 1D model is used for the sake of design practicality.

General Uniform Roe algebra rigidity

We generalize all known results on rigidity of uniform Roe algebras to the setting of arbitrary uniformly locally finite coarse spaces. For instance, we show that isomorphism between uniform Roe algebras of uniformly locally finite coarse spaces whose uniform Roe algebras contain only compact ghost projections implies that the base spaces are coarsely equivalent. Moreover, if one of the spaces has property A, then the base spaces are bijectively coarsely equivalent. We also provide a characterization for the existence of an embedding onto hereditary subalgebra in terms of the underlying spaces. As an application, we partially answer a question of White and Willett about Cartan subalgebras of uniform Roe algebras.

On the uniform torsional rigidity of square concrete-filled steel tubular (CFST) sections

There are a number of scenarios in which structural members experience torsion, including under the direct application of torsional loading, when transverse loading is applied at an eccentricity to the shear centre and as a second order effect arising from lateral torsional instability. To date, the torsional rigidity of concrete-filled steel tubular (CFST) sections has yet to be fully explored; hence a study into the uniform torsional rigidity of square CFST sections is presented herein. First, the strain energy of square CFST sections is formulated, in which the longitudinal warping displacement is assumed to have an undetermined constant. The undetermined constant is then deduced by means of the principle of minimum strain energy, and thus an analytical expression for the uniform torsional rigidity of square CFST sections is obtained. The accuracy of the derived formula is verified against existing theoretical solutions for simplified scenarios, test data and the results of numerical simulations. Finally, the influence of the key parameters in the derived formula for the torsional rigidity of square CFST sections are analysed, and a simplified design formula is presented.

Algorithm for an Effective Ratio of the Transverse Bending Rigidity Based on the Segment Joint Bending Stiffness

An algorithm for calculating the effective ratio of the transverse bending rigidity is established based on the segment longitudinal joint bending stiffness. With the knowledge of this effective ratio, the bending rigidity of a modified uniform rigidity ring is fully defined. To verify this developed algorithm, the effective ratios and convergence deformations of the modified uniform rigidity rings obtained with different methods are compared. Moreover, the responses of the modified uniform rigidity ring model under loading obtained from this algorithm are compared to those obtained with the existing generally accepted beam-spring model. The results show that although the bending moments obtained from these two models are different, the axial forces, horizontal convergent deformations, and vertical convergent deformations are quite consistent with each other. The modified uniform rigidity ring model built on the developed effective ratio algorithm is applicable for the analysis of the tunnel convergence deformation and the interaction between the tunnel structure and the ground during operation. This modified uniform rigidity ring model is simpler and easier to use than the beam-spring model; thus, the significance of the developed algorithm for the effective ratio of the transverse bending rigidity is demonstrated.

Effect of cracked section properties on the resilience based seismic performance evaluation of a building

The importance of performance based design lies with detailed examination of the seismic performance of a structure in terms of its desired performance levels, damage ratio’s and ductility demand with respect to various ground motions. It is evident that all the buildings will not have uniform rigidity due to various construction errors, environmental conditions etc., which leads to the degradation of the concrete member stiffness that affects the rigidity of the structure. Though several codes proposed the cracking coefficient to account stiffness degradation of the structural members in the analysis, the Indian Standard was silent on these aspects. In the latest revision of IS: 1893–2016, the reduced gross moment of inertia for the structural members that can be considered during the structural analysis was included which indirectly consider the cracking effect on concrete members. This reduction in the stiffness can affect the functionality of the building which in turns affects seismic performance as well as the most important design parameter called resilience. However, the code is silent on these aspects. In this study, a high rise reinforced concrete building of G + 10 storey with gross and cracked section was considered. The building was subjected to different ground motions with Peak Ground Acceleration (PGA) varies from 0.10 g to 1.70 g. For the concrete members like beams and columns, the cracking coefficients of 0.35 and 0.70, respectively were considered. It has been observed that due to stiffness reduction, there is a significant loss of ductility demand and resilience of the building. Also, in case of building with cracked section, the damage ratio increases at higher PGA level as compared to building with gross section case, which ultimately altered the performance level of the building to the sudden collapse stage.

Effect of Increase in Swayload on Unsymmetrically Loaded Portal Frame Structure at Lekki Using Slope Deflection Method

This research work involves the study on the effect of increase in lateral load by 0.5kN on the slopes (θ), linear displacement (∆), Xmax and the bending moments of an unsymmetrically loaded portal frames structures with uniform flexural rigidity (E.I = constant) using the slope deflection method, also the results was obtained and represented graphically. In this study, the discussion will be restricted to one story building under differential settlement and also the analysis will be carried out on an unsymmetrical loaded portal frame structure using the slope deflection method of analysis. The slope B (θB) decreases positively as the lateral load increases by 0.5kN while slope C (θC) increases negatively as the sway load increases. The linear displacement (∆) increases negatively as the sway load increases while the Xmax, Mmax, MAB, MBA andMCB increases positively as the sway load increases by 0.5kN. MDC decreases negatively as the sway load increases by 0.5kN. The proposed method of analysis offers a number of relative simple expressions from which the lateral sway, slopes, Xmax values and the bending moments can be easily calculated for the portal frame structure under increase in lateral loads that is saving time and attractive for use in preliminary design and studying structures subjected to dynamic loads. The present analysis describes the relation between the increase in lateral load on linear displacements, slopes, Xmax values and the bending moments of the portal frame structure. The maximum sway depends mainly in the contribution of the increase in lateral load, bending moment and the slope of the portal frame structure, the bending moment in columns and the beams which represent the contribution of the moment of inertia of columns, beams and their cross sectional areas. The contribution of the normal forces in the portal frame is approximately equal to zero which represent the contribution of the cross sectional area of the portal frame. The great advantages of the slope deflection method of analysis are the determination of the lateral sway by using hand calculations only (without the use of computer computations) or by using simple spread sheet program {Excel program}. Slope deflection equation was derived for one storey residential building under collapse due to sideway or linear displacement. The dead loads and live loads were applied as uniformly distributed load on beam and sway force on column of the portal frame. This research work will serve as a useful interactive material for teaching structural engineering students and a valuable tool for practicing structural engineers.

Piezomagnetic fields associated with a dislocation source in a layered elastic medium

SUMMARYThe piezomagnetic effect is defined as a change in magnetization with applied stress. Changes in the geomagnetic field caused by the piezomagnetic effect, referred to as the piezomagnetic field, have been theoretically estimated and compared by previous studies to interpret observed variations in the geomagnetic field. However, the piezomagnetic field estimated in previous studies may not provide an accurate estimation because they ignored spatial variations in elasticity, leading to only a rough approximation of the properties of Earth's crust. In this paper, a semi-analytical procedure for calculating the piezomagnetic field arising from a point dislocation source embedded in a layered elastic medium is derived. Following a well-established method of the vector surface harmonic expansion, all of the governing equations written in partial differential equations in a real domain, together with the linear constitutive law of the piezomagnetic effect, are converted to a set of ordinary differential equations in a wavenumber domain. Equations in the wavenumber domain are solved analytically, and each component of the piezomagnetic field in the real domain is obtained after applying the Hankel transform. By using the derived procedure, the piezomagnetic and displacement fields due to a finite fault with strike-slip, dip-slip, and tensile-opening mechanisms are estimated for media with layered elasticity structures. Results for a finite fault are obtained by integrating the point source solution over the fault plane. The results of the numerical analysis allow the effect of heterogeneities in rigidity on the piezomagnetic effect to be examined and implications for the findings of previous investigations to be drawn. In cases where the moment-release at the dislocation source is fixed, the effect of the rigidity differences between upper and lower layers on the piezomagnetic field is minor even in the case where the Curie point depth is near the source of dislocation. This result is in contrast to a previous study that assumed the Mogi model and suggested that heterogeneities in the horizontal direction may be of importance when combined with layered rigidity structures. A contrast is seen between the piezomagnetic and displacement fields corresponding to models with layered rigidity structures: the piezomagnetic field is roughly proportional to the moment-release on a source fault, whereas the displacement field is proportional to slip or opening of the fault. Provided that the rigidity of the crust increases with increasing depth, the calculated piezomagnetic field is likely to have been underestimated in many earlier studies, which assumed uniform rigidity and a geodetically inverted size of slip.

Experimental Study on the Transverse Effective Bending Rigidity of Segmental Lining Structures

The transverse effective rigidity ratio is a key parameter when the uniform rigidity ring model is adopted to design or numerically analyse segmental lining structures commonly used on a shield‐driven tunnel. Traditionally, the transverse effective rigidity ratio η is treated as a constant, which can be evaluated through theoretical analysis and model tests. In this study, scale models were designed and tested to investigate the variation of the transverse effective rigidity ratio in the segmental linings’ flattening deformation process. The test results suggested that in the elastic stage, the transverse effective rigidity ratio fluctuated between 0.667 and 0.734 for the stagger‐jointed rings and fluctuated between 0.503 and 0.642 for the straight‐jointed rings. When segmental linings were squashed and started to crack at the circumferential joints, the transverse effective rigidity ratio decreases sharply. Then, a regression equation was obtained to fit the variation trend of η with the increase of horizontal convergence to the outer‐diameter ratio (ΔD/Dout). Finally, in a case study, the regression equation was adapted to determine the value of η of an operated shield tunnel which was once surcharged accidentally and deformed severely so as to numerically predict the prospective deformation induced by the upcoming adjacent excavation. Numerical results indicated that as the value of η decreases, the horizontal convergences of shield tunnel induced by adjacent excavation increase significantly and even more than doubled in the case study. Comparatively, through taking account of the operating tunnels’ exiting transverse deformation, the predicted deformation tends to be unfavourable.

Stability Analysis of Compression Member on Elastic Springs

Part of the large parametric study focused on the stability behaviour of compression single members and the member structures with various loadings and boundary conditions is presented here. This part relates to the stability analysis of the compression member on elastic springs. The span of the member L = nℓ, where ℓ is the length of the field which equals to the distance between the neighbouring elastic springs. The members under investigation have seven various numbers of the fields n = 2, 3, 4, 5, 6, 7 and ∞. The members have uniform bending rigidity EI, uniform normal force N and (n – 1) elastic springs with equal spring stiffness Cw. The results are presented in the form of eight diagrams. The curves of diagrams were replaced by the straight lines to be able derived approximate formulae for calculation of the critical force. It is shown that approximate formulae give the values of the critical forces Fcr.a which differ from diagram values Fcr less than 3.3 %, being slightly on the safe side. The values of the critical forces Fcr obtained from the solution of the stability equation are verified by comparisons with results Fcr.IQ of the computer program IQ 100. Excellent agreement is achieved between Fcr.IQ and Fcr. The presented solution of the compression member on elastic springs may be used also for the calculation of the critical force of the compression member on elastic foundation. The solution given in the paper creates scientific background needed in the design of the semi-through bridge trusses.

Specific Features of Fluoroplastic Band Bending with Due Account of Various Modularity of Material

The paper considers a technological process for production of sealing rings by winding a band work-piece on a cylindrical caliber mandrel with subsequent endurance under load and further cutting of a spiral in rings and also studies the possibility to obtain products while using a method for cold forming of a work-piece which excludes thermal stabilization operation. Taking into account the fact that fluorine plastic is a high-plastic material even at very low temperatures such technology looks quite real. Therefore winding of a band on a mandrel, endurance of a spiral work-piece without heating but under conditions of force action within the time which is necessary for completion of relaxation processes, and the subsequent cutting in rings will allow to obtain finished ring products of the required size. However fluoroplastic has specific mechanical properties and a number of specific features which are revealed during deformation process. Its deformation behavior considerably differs from behavior of low-molecular materials and therefore it requires a solid approach while using the existing theoretical base and developing calculation methodologies. While taking into consideration the fact that fluorine plastic is high density material and has structure with high degree of crystallinity, the mechanism of deformation behavior in it under conditions of a force field is mainly similar to metal behavior that allows to use methods and approaches for calculation of fluoroplastic products which are accepted in mechanics of solid bodies. However the applied calculating formulae require a certain correction and adaptation to specific features of mechanical fluoroplastic properties, one of which is its various rigidity at stretching and compression that is revealed in case of winding band work-piece on a mandrel. Fluorine plastic is a material with various modularity and its rigidity is higher during compression than under stretching and consequently in the case of band bending a neutral axis of section is displaced from the center of gravity to the area of compressed fibers, and the area of stretching is increasing. High elasticity at stretching and increase of this area lead to large accumulation of elastic deformations causing springing after unloading and changes in size of a finished product. These facts must be taken into account while calculating and designing a mandrel tool, it is also necessary to keep in mind various modularity of a material and possibility that a section being led to an uniform rigidity may take some other shape due to this. Calculation methodologies have been developed by the authors for both versions of section that take into consideration directly or indirectly a material with various modularity and which do not contradict each other and which are rather precisely proved by experimental data.

Stability Analysis of Compression Member on Elastic Supports

Part of the large parametric study focused on the stability behavior of compression single members and the member structures with various loadings and boundary conditions is presented here. The presented part relates to the stability analysis of the compression member on elastic springs and elastic foundation. The span of the member L = nℓ, where ℓ is the length of the field which equals to the distance between the neighboring elastic springs. The members under investigation have seven various numbers of the fields n = 2, 3, 4, 5, 6, 7 and ∞. The members have uniform bending rigidity EI, uniform normal force N and (n – 1) elastic springs with equal spring stiffness Cw. The results are presented in the form of 4 diagrams. The curves of diagrams were replaced by the straight lines to be able derived approximate formulae for calculation of the critical force. It is shown that approximate formulae give the values of the critical forces Fcr.a which differ from exact diagram values Fcr less than 3.3 %, being slightly on the safe side. The exact values of the critical forces Fcr obtained from the solution of the stability equation are verified by comparisons with results Fcr.IQ of the computer program IQ 100. Excellent agreement is achieved between Fcr.IQ and Fcr. The presented solution of the compression member on elastic springs may be used also for the calculation of the critical force of the compression member on elastic foundation. The solution given in the paper creates scientific background needed in the design of the semi-through bridge trusses. Stability of the beams on elastic foundation is solved for three different boundary conditions too.

Experimental Research on the Transverse Effective Bending Rigidity of Shield Tunnels

The uniform rigidity ring model is commonly used to design the segmented structures of shield tunnels. However, model tests have been primarily used to study the transverse effective rigidity ratio η with a concentrated force, which is notably different from realistic loading patterns. To obtain more reasonable η values, in this study, tests were performed with a concentrated load on an experimental bench and with a realistic loading pattern in sandy soil in a rigid steel tank. Three types of segmental ring models were designed and tested: straight‐jointed, stagger‐jointed, and uniform rings. The test results indicated that the η values of the stagger‐jointed assembly mode were clearly larger than those of the straight‐jointed assembly mode under both loading patterns. η increased as the load increased under the realistic loading conditions, whereas η decreased as the load increased under the concentrated load. More importantly, the η values derived from the realistic load tests were considerably larger than those derived from the concentrated load tests for both assembly modes (i.e., 0.423–0.672 and 0.587–0.761 for the straight‐jointed and stagger‐jointed assembly modes, respectively), and the former should be recommended for practical engineering applications. Furthermore, formulas relating η to the ratio of the cover depth to the tunnel diameter were proposed for sandy soil.