Elastic Energy Dissipation Research Articles

Design and Analysis of a 3D Frictional Mechanical Metamaterial for Efficient Energy Dissipation

AbstractThis study introduces a novel frictional mechanical metamaterial composed of a central hexagon or re‐entrant honeycomb frame, a lower section with four tapered columns, and an upper portion with a blade shape. When subjected to an external uniaxial force, the 3D structure of the metamaterial utilizes sliding interactions to dissipate frictional energy. The mechanical properties of the proposed metamaterial, such as load‐displacement relationships, hysteresis area, and peak force, can be fine‐tuned by adjusting geometric parameters and constituent materials. Extensive analysis is conducted through experimental compression tests, finite element (FE) simulations, and theoretical modeling. Comparative assessments of the metamaterial's energy dissipation performance demonstrated a good agreement between experimental and simulation results, with minor variations observed for deeper compression cycles. The proposed metamaterial offers the potential for superior elastic energy absorption and dissipation, making it a promising solution for applications requiring repeated energy dissipation or damping under cyclical loads while maintaining a lightweight profile.

Experimental Investigation of High-performance Fiber-reinforced Cementitious Composite and its Effect on RC Beams by Numerical Method

In the present study, experimental investigations were initially conducted on high-performance fiber-reinforced cementitious composite (HPFRCC). A total of 9 samples were examined and subjected to a 4-point bending test. The sample lengths were standardized at 500 and 1700 mm. The variables under scrutiny included the impact of Micro Steel, Macro Steel, and polyvinyl alcohol fibers. Furthermore, the models were scrutinized under two conditions: with and without glass fiber reinforced polymer (GFRP) bars. The number of samples was 9. In the second part of the article, subsequent to verifying the experimental samples from the current study alongside a concrete beam, numerical analyses were carried out to assess the influence of HPFRCC on the behavior of RC beams. Similarly, the impact of GFRP diameter, as well as the height of HPFRCCs, on the seismic performance of RC beams, was investigated by conducting 36 numerical analyses. The analyses were carried out using nonlinear static methods, with monotonic loading. The model outputs encompass elastic stiffness, ultimate strength, relative stiffness, and energy dissipation. The experimental results showed that the use of macro steel fibers in models without GFRP rebars has better results on the flexural behavior of HPFRCC. Moreover, by reinforcing RC beams with HPFRCC, a 70% increase in energy dissipation was observed. The elastic stiffness and ultimate strength of the strengthened beam are directly proportional to the ratio of the HPFRCC's elastic flexural stiffness to that of the original beam. These results increase proportionally as this ratio rises.

The Fluvial Battering Ram: Collisional Experiments Reveal the Importance of Particle Impact Energies on Bedrock Erosional Efficiency

AbstractThe battering of bedrock by bedload collisions is the primary mechanism by which bedrock rivers erode and landscapes evolve. The energy imparted via impacts acts to detach bedrock via the growth and intersection of surface fractures. We present impact experiments designed to test the influence of particle impact energy on bedrock erosion rates. We found that erosional efficiency increased with increasing impact energy. Notably, these increases in efficiency are not captured by a widely‐used mechanistic bedrock erosion model. Observed increases in erosional efficiency were linked with enhanced elastic energy dissipation captured by differences in the coefficient of restitution. We suggest that this increase in energy dissipation is indicative of enhanced crack extension for high velocity impacts. Our experiments indicate a clear energy‐dependence for bedrock detachment processes that is not yet captured by bedrock incision models but may be integrated into long‐term erosion rates and landscape evolution.

Yielding behaviour of chemically treated Pseudomonas fluorescens biofilms

The mechanics of biofilms are intrinsically shaped by their physicochemical environment. By understanding the influence of the extracellular matrix composition, pH and elevated levels of cationic species on the biofilm rheology, novel living materials with tuned properties can be formulated. In this study, we examine the role of a chaotropic agent (urea), two divalent cations and distilled deionized water on the nonlinear viscoelasticity of a model biofilm Pseudomonas fluorescens. The structural breakdown of each biofilm is quantified using tools of non-linear rheology. Our findings reveal that urea induced a softening response, and displayed strain overshoots comparable to distilled deionized water, without altering the microstructural packing fraction and macroscale morphology. The absorption of divalent ferrous and calcium cations into the biofilm matrix resulted in stiffening and a reduction in normalized elastic energy dissipation, accompanied by macroscale morphological wrinkling and moderate increases in the packing fraction. Notably, ferrous ions induced a predominance of rate dependent yielding, whereas the calcium ions resulted in equal contribution from both rate and strain dependent yielding and structural breakdown of the biofilms. Together, these results indicate that strain rate increasingly becomes an important factor controlling biofilm fluidity with cation-induced biofilm stiffening. The finding can help inform effective biofilm removal protocols and in development of bio-inks for additive manufacturing of biofilm derived materials.

Dynamic Mechanical Performance of Sulfate-Bearing Soils Stabilized by Magnesia-Ground Granulated Blast Furnace Slag

Sulfate soils often caused foundation settlement, uneven deformation, and ground cracking. The distribution of sulfate-bearing soil is extensive, and effective stabilization of sulfate-bearing soil could potentially exert a profound influence on environmental protection. Ground granulated blast furnace slag (GGBS)–magnesia (MgO) can be an effective solution to stabilize sulfate soils. Dynamic cyclic loading can be used to simulate moving vehicles applied on subgrade soils, but studies on the dynamic mechanical properties of sulfate-bearing soil under cyclic loading are limited. In this study, GGBS-MgO was used to treat Ca-sulfate soil and Mg-sulfate soil. The swelling of the specimens was analyzed by a three-dimensional swelling test, and the change in compressive strength of the specimens after immersion was analyzed by an unconfined test. The dynamic elastic properties and energy dissipation of GGBS-MgO-stabilized sulfate soils were evaluated using a fatigue test, and the mineralogy and microstructure of the stabilized soils were investigated by X-ray diffraction and scanning electron microscopy. The results showed that the maximum swelling percentage of stabilized Ca-sulfate soil was achieved when the GGBS:MgO ratio was 6:4, resulting in an expansion rate of 14.211%. In contrast, stabilized Mg-sulfate soil exhibited maximum swelling at GGBS:MgO = 9:1, with a swelling percentage of 5.127%. As the GGBS:MgO ratio decreased, the dynamic elastic modulus of stabilized Ca-sulfate soil diminished from 2.8 MPa to 2.69 MPa, and energy dissipation reduced from 0.02 MJ/m3 to 0.019 MJ/m3. Conversely, the dynamic elastic modulus of stabilized Mg-sulfate soil escalated from 2.16 MPa to 6.12 MPa, while energy dissipation decreased from 0.023 MJ/m3 to 0.004 MJ/m3. After soaking, the dynamic elastic modulus of Ca-sulfate soil peaked (4.01 MPa) and energy dissipation was at its lowest (0.012 MJ/m3) at GGBS:MgO = 9:1. However, stabilized Mg-sulfate soil exhibited superior performance at GGBS:MgO = 6:4, with a dynamic elastic modulus of 0.74 MPa and energy dissipation of 0.05 MJ/m3. CSH increased significantly in the Ca-sulfate soil treated with GGBS-MgO. The generation of ettringite increased with the decrease in the GGBS-MgO ratio after immersion. MSH and less CSH were formed in GGBS-MgO-stabilized Mg-sulfate soil compared to Ca-sulfate soils. In summary, the results of this study provide some references for the improvement and application of sulfate soil in the field of road subgrade.

The effect of combined use of plybamboo sheathings and self-tapping screws in enhancing wood-frame shear wall performance

ABSTRACT Plybamboo panels are renewable and eco-friendly structural panels with high strength, good dimensional stability, and affordability, making them highly suitable for wood-frame construction. This study presents an experimental investigation of the wood-frame shear wall constructed with plybamboo-sheathing panels with self-tapping screws (STSs) subjected to monotonic and cyclic loadings. Performance parameters including shear strength, elastic shear modulus, ductility ratio, stiffness degradation, and energy dissipation were evaluated. Results indicate that the combined use of plybamboo sheathings and STSs can substantially reduce failures due to the tearing of sheathing, fastener head pull-through, and fastener withdrawal. The plybamboo-sheathed wood-frame shear walls with STSs had over 1.8 times shear strength and 1.4 times ultimate displacement than those of comparable wood-frame shear walls with nails, respectively, maintaining over 80% of their maximum lateral load capacity at a drift level over 4%. Moreover, the influence of aspect ratio and screw spacing on the elastic shear modulus, shear strength, and stiffness degradation of the plybamboo-sheathed wood-frame shear walls with STSs are consistent with those for common wood-frame shear walls.

Influence of key design variables on dynamic material properties of iron tailing porous concrete under impact loading

Iron tailing porous concrete (ITPC) is a new foamed concrete material that using iron ore tailing powder to partially replace the cement. Previous investigations on ITPC primarily focused on its mechanical properties under static loads or low strain rate conditions, leaving a significant gap in its impact resistance performance at high strain rates. This study employed the split Hopkinson pressure bar (SHPB) to test ITPC specimens under impact loading with strain rate around 120 s−1. Density, water-binder (W/B) ratio, iron tailing powder content, polypropylene fiber length and content were taken as key design variables to prepare the ITPC specimens with different mix ratios and study their effects on the dynamic material properties of ITPC. Specifically, the failure modes, stress-strain relations, elastic moduli, compressive strengths and energy dissipation densities of the ITPC specimens with various design variables were recorded and compared. The test results indicate that the material density, fiber length and content have strong influences on the impact failure modes of ITPC. The elastic modulus, compressive strength and energy dissipation density of ITPC exhibit exponential growth with the material density. These parameters, however, show an initial growth followed by a decrease with the rising W/B ratio, fiber length and fiber content, and they reach the peak values at around 0.70, 9 mm and 2.0%, respectively. Moreover, the iron tailing powder content of 25% is recommended for ITPC for maintaining good impact resistance.

In-silico simulation of nanoindentation on bone using a 2D cohesive finite element model

This study proposed and validated a 2D finite element (FE) model for conducting in-silico simulations of in-situ nanoindentation tests on mineralized collagen fibrils (MCF) and the extrafibrillar matrix (EFM) within human cortical bone. Initially, a multiscale cohesive FE model was developed by adapting a previous model of bone lamellae, encompassing both MCF and EFM. Subsequently, nanoindentation tests were simulated in-silico using this model, and the resulting predictions were compared to AFM nanoindentation test data to verify the model's accuracy. The FE model accurately predicted nanoindentation results under wet conditions, closely aligning with outcomes obtained from AFM nanoindentation tests. Specifically, it successfully mirrored the traction/separation curve, nanoindentation modulus, plastic energy dissipation, and plastic energy ratio obtained from AFM nanoindentation tests. Additionally, this in-silico model demonstrated its ability to capture alterations in nanoindentation properties caused by the removal of bound water, by considering corresponding changes in mechanical properties of the collagen phase and the interfaces among bone constituents. Notably, significant changes in the elastic modulus and plastic energy dissipation were observed in both MCF and EFM compartments of bone, consistent with observations in AFM nanoindentation tests. These findings indicate that the proposed in-silico model effectively captures the influence of ultrastructural changes on bone's mechanical properties at sub-lamellar levels. Presently, no experimental methods exist to conduct parametric studies elucidating the ultrastructural origins of bone tissue fragility. The introduction of this in-silico model presents an invaluable tool to bridge this knowledge gap in the future.

Negative stiffness metamaterial with elastic energy dissipation based on conical shell: theoretical solution and experimental study

Negative stiffness (NS) metamaterials with the capability of elastic energy dissipation have gained substantial attention for their potential in shock absorption and vibration control. However, their practical application is often limited by their strength and stiffness. This study investigates an NS material that generates the NS phenomenon based on stretching and rotation of conical shells, akin to coned disk springs. This approach enhances the strength and loading capacity of the material compared to metamaterials based on conventional beam or shell structures. To fully understand the behavior of this material, a theoretical framework is presented, followed by a comprehensive validation process involving tests and numerical simulations. The applicability and constraints of the theoretical solution are discussed, and a parametric analysis is undertaken based on the solution. Finally, NS metamaterials based on the proposed mechanism are fabricated and tested, which showcases their strength and elastic energy dissipation capacity.

Effects of initial unloading level on the mechanical, micro failure and energy evolution characteristics of stratified rock mass under triaxial unloading confining pressure

In order to study the strength, micro crack distribution and energy evolution characteristics of stratified rock mass under unloading confining pressure conditions, triaxial compression tests and triaxial unloading confining pressure tests at different initial unloading levels were carried out. The experimental results indicated that the triaxial unloading confining pressure plus axial stress is a stress path between the stress state of uniaxial compression and triaxial compression. With the increasing initial unloading level, the specimen is closer to the stress state of triaxial compression, the peak stress, peak axial strain, peak circumferential strain and peak volume strain increase linearly, Poisson’s ratio decreases linearly, failure type of specimens shows 4 typical characteristics. When the bedding plane inclination is 45°, 3D reconstruction and quantitative characterization of micro cracks of stratified rock mass specimens are conducted based on CT scanning results. Variations of area fraction along the specimen height show 3 typical characteristics. The stratified rock mass mainly stores and dissipates energy before the peak stress, and mainly releases and dissipates energy after the peak stress under different conditions. With the increasing initial unloading level, the input energy, elastic energy, dissipative energy and energy dissipation rate at the peak stress increase approximately linearly.

Enhanced Semi-active piezoelectric vibration control method with shunt circuit by energy dissipations switching

Piezoelectric vibration control holds the advantages of lightweight and anti-electromagnetic interference, and has broad application prospects in fields such as aerospace and mechanical engineering. A semi-active control method based on a piezoelectric smart cantilever beam with a passive shunt circuit is proposed for vibration control. The contribution is that the proposed semi-active control method is used to achieve energy dissipations switching by changing the piezoelectric electrical boundary conditions. The open-circuit state of piezoelectric materials corresponds to higher stiffness and dissipation of elastic potential energy, while the short-circuit state is accompanied by lower stiffness and dissipation of electrical energy. Firstly, the stiffness difference of different electrical boundary conditions of the piezoelectric materials is derived and its effect on the vibration characteristics is analyzed. Then, the proposed passive shunt circuit for the vibration control principle is analyzed, and the modeling of the piezoelectric smart cantilever beam with the passive shunt circuit is developed. Finally, a prototype is manufactured and the measurement system is constructed. The correctness and the feasibility of the semi-active vibration control method are verified by experiments, and the logarithmic damping coefficient is 0.8919. The superiority of the proposed shunt circuit is demonstrated experimentally with the comparison groups including depolarized comparison group and the common shunt circuits.

Numerical and analytical investigation of U-shape dampers and its effect on steel frames

Yielding dampers are one of the structural systems which dissipate a portion of the seismic force via premature yielding. The numerical and analytical methods were used in this study to investigate the behavior of the U-Shape Damper (USD) and its effect on steel frames. For this purpose at first, extensive parametric studies were performed using calibrated USD model. The parametric studies involved investigating the effect of USD dimensions on its elastic stiffness, strength, effective stiffness, and equivalent viscous damping ratio. Finite element models were analyzed under cyclic loading using nonlinear static analysis. An analytical equation was then presented to estimate seismic parameters of the USD. In the second part, the effect of this damper on the steel frame was investigated using push over analysis. The seismic parameters of the frame, including elastic stiffness, strength, ductility, and energy dissipation, were investigated through 56 numerical models to determine the effects of the number of USDs and the axial force of the column. The results indicated that reducing the radius and increasing the thickness of the damper led to an increase in effective stiffness, energy dissipation, and strength, while reducing the equivalent viscous damping ratio. Furthermore, the results obtained from the steel frame equipped with a USDs revealed that the addition of the damper mitigates the adverse effects of axial force on the frame.

Porous-Solid Metaconverters for Broadband Underwater Sound Absorption and Insulation

Existing solid composite structures composed of several viscoelastic materials and metals mainly exploit diverse resonances, damping, and scattering to realize underwater acoustic wave functionalities. However, low-frequency broadband underwater sound absorption and insulation are still hard to capture with an acoustic coating possessing subwavelength thickness and lightweight nature simultaneously. This paper reports the systematic simulated and experimental validations of a porous-solid underwater metaconverter, consisting of a rubber layer and a topology-optimized elastic metasurface to exhibit broadband functionalities of sound absorption and insulation caused by the strong reflective and transmitted longitudinal-to-transverse wave conversion, while sustaining broadband impedance matching. Various results confirm the predicted capabilities of underwater broadband high-efficiency sound absorption (>80%) or insulation (20 dB) within the range of 2–10 kHz for a large- and limited-size sample, providing an estimate of the energy-converting effect and phenomenon. The present study provides possibilities for elastic wave energy dissipation, harvesting, and underwater acoustic stealth via metasurfaces.4 MoreReceived 9 December 2022Revised 3 February 2023Accepted 28 February 2023DOI:https://doi.org/10.1103/PhysRevApplied.19.044074© 2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAcoustic metamaterialsAcoustic wave phenomenaArchitectural acousticsCloakingMechanical & acoustical propertiesUnderwater acousticsPhysical SystemsPorous mediaTechniquesSound wave techniquesCondensed Matter, Materials & Applied Physics

Shock Wave Formation and Cloaking in Hyperelastic Rods

The analysis of propagating an initially harmonic acoustic pulse in a semi-infinite hyperelastic rod obeying the Yeoh strain energy potential reveals attenuation with distance of the wave amplitudes caused by the elastic energy dissipation due to forming and propagation of the shock wave fronts and heat production. The observed attenuation of harmonic waves results in a broadband cloaking of fairly remote regions. The analysis is based on solving a nonlinear equation of motion by an explicit Lax–Wendroff time-difference scheme combined with the finite element discretization in the spatial domain. The revealing phenomena are applicable to studies of acoustic wave propagation in various elastomeric rubberlike materials modeled by the Yeoh hyperelastic potentials.

In-plane seismic performance of an innovative steel modular reinforcement system for URM walls

An experimental and numerical research, aimed at evaluating the in-plane seismic performance of an innovative steel modular system for the reinforcement of load-bearing masonry walls (named "Resisto 5.9", designed by Progetto Sisma s.r.l.), is currently underway at the EUCENTRE Foundation in Pavia. Two different masonry typologies, representing common solutions in Italian existing buildings, were considered in this campaign: one made up with solid clay bricks and lime mortar, with "header bond" pattern, and the other with a typical Italian hollow clay "doppio UNI" unit and cement-lime mortar, assembled in a "Flemish bond" pattern. The experimental tests included first the complete mechanical characterization of units, mortars, masonry typologies and of the strengthening system components (i.e. steel elements and anchors). In-plane quasi-static tests were performed on different batches of full--scale specimens to investigate the influence of the proposed reinforcement system on the lateral in-plane response of the walls, compared to their unreinforced conditions. The cyclic behaviour of the masonry piers was analysed in terms of elastic stiffness, lateral strength, displacement capacity and energy dissipation, depending on the achieved damage mechanism. The numerical study of the ongoing campaign consisted of a series of parametric analyses on advanced discontinuous models based on the Distinct Element Method (DEM), considering different wall dimensions, vertical load levels and boundary conditions, in addition to those tested experimentally. Moreover, the numerical campaign was extended also to other possible masonry typologies, varying the bond pattern and the mechanical properties with respect to the experimentally tested solutions. In this paper, the results of the experimental tests on solid brick masonry together with a preliminary overview of the findings of the numerical study, still ongoing, were reported.

Energy Based Design of Rc Staging in Elevated Service Reservoir

Elevated service reservoirs (ESRs) are inverted pendulum structures and are often categorized under lifeline structures. They are expected to remain functional after the earthquake to provide essential drinking water and water for post-earthquake firefighting. The current code-based design procedure of ESR in India is similar to the design procedure of other structures and does not explicitly provide insight into its post-earthquake behavior. Energy-Based Design (EBD) can provide a better and more reliable alternative to overcome the deficiencies of code-based design. EBD considers a coherent approach to estimate the input energy, the elastic energy dissipation, and the plastic energy dissipation, taking into account the inelastic behavior of structural members. In the present research, various issues of the EBD for frame staging of the ESR have been identified and assessed using linear and nonlinear analysis. A comparison of the seismic behavior of the ESR according to the Indian code and the EBD has been made. Besides, the structural design procedure based on the column tree method (CTM) has been modified to suit the specific behavior of the ESR.

Temperature-dependent compressive stress-strain behaviors of alkali-activated slag-based ultra-high strength concrete

In this work, the uniaxial compressive behaviors of alkali-activated slag-based ultra-high strength concrete (AAS-UHSC) subjected to different temperatures were investigated, with an emphasis on the temperature-dependent stress-strain relation. To this end, 104 cylinder specimens with three steel fiber contents (0.5%, 1.0%, and 1.5%) and two water-to-binder (W/B) ratios (0.20 and 0.25) were tested upon the monotonic and cyclic compression performed at ambient temperature (20 ℃) and four elevated temperatures (200, 400, 600, and 800 ℃). The test results showed that the mechanical properties of AAS-UHSC in terms of elastic modulus, ultimate strength, energy dissipation, and post-peak softening can be effectively improved with the fiber inclusion, regardless of the W/B ratio. Moreover, AAS-UHSC exhibited a quite different plastic strain evolution law featured as two discontinuous stages due to the damage localization and possessed better energy dissipation capacity compared to OPC-based concretes. After being exposed to elevated temperatures, a consistent decline in compressive strength was observed as the temperature increased, with residual strength at 800 ℃ remaining around 10% of the ultimate compressive strength at 20 ℃. Based on the test results, a unified empirical temperature-dependent model was proposed to capture the main features of the constitutive compressive stress-strain relations of AAS-UHSC. The fairly good comparisons between test results and model predictions in different loading scenarios demonstrated a compromise between the accuracy and the generality of the model and contributed a beneficial addition to the understanding of nonlinear responses of AAS-UHSC.

The relationship between storage-dissipation-release of coal energy and intensity of induced charge

Using uniaxial compression experiments, the evolution characteristics between energy and induced charge in each stage of coal deformation and failure are studied. Further, the relationship of energy conversion in the process of coal failure is analyzed. The calculation methods of energy storage, dissipation, and release of coal are proposed. The relationships between induced charge intensity and factors, including storage of elastic strain energy, increment of elastic strain energy, increment of dissipated energy, released energy, accumulated dissipated-released energy, are studied. A theoretical model of induced charge based on dissipated energy and released energy is established. The monitoring test of induced charge under the mine is conduced. The results show that the induced charge intensity is not related to the accumulation of elastic strain energy, but positively correlated to the dissipation and release of elastic strain energy. The induced charge intensity is not significantly correlated with the cumulative dissipated-released energy, but is significantly correlated with the slope of the cumulative dissipated-released energy curve and its variations. Especially when the escalation effect shows, the induced charge intensity accordingly increases in an abrupt manner. When the increment of dissipated energy rises to a certain degree, the intensity of induced charge suddenly increases. When the released energy suddenly increases, if the major part converts into the kinetic energy of coal chips and particles, a violent ejection phenomenon occurs, the induced charge intensity suddenly increases. The induced charge intensity is positively correlated with the increment of dissipated energy and the sudden increase of released energy. The higher the stress concentration degree and the greater the influence of mining for coal-rock, the larger amount of energy is dissipated and released, and thus the greater intensity of induced charge is monitored. The study can provide a theoretical basis for the monitoring and early warning of coal-rock dynamic disaster.

Study of Energy Evolution Law and Damage Characteristics during Uniaxial Cyclic Loading and Unloading of Sandstone

Using the rock mechanics test (RMT) and acoustic emission acquisition system (DS9), based on the energy principle, uniaxial compression, uniaxial cyclic loading, and unloading tests are used to study the energy transformation characteristics of the process of sandstone absorbing axial strain energy, accumulating and releasing elastic strain energy, plastic deformation, and crack extension dissipation energy. The study results show the increase of loading rate, rock fracture surface increases, number of fragments increases, and size of fragments decreases; the sandstone damage process causes: shear damage to tensile shear damage and then splitting damage for change; the input energy and elastic energy increase nonlinearly with an increase of stress, and the dissipative energy is larger at the beginning of loading. After a small decrease, it enters the nonlinear growth stage, and the input energy density grows the fastest. The elastic energy density is the second fastest, and the dissipative energy density grows the slowest; with an increase of loading rate, in any deformation stage, the elastic energy density and dissipation energy density are increased, proportion of elastic energy density is decreased, and proportion of dissipation energy density is increased. Near the peak stress stage, the proportion of elastic energy decreases, and the proportion of dissipative energy increases; the damage variable stress curve of sandstone is “weakly concave”, which is consistent with the logistic function, and the damage evolution process has chaotic dynamics properties; the acoustic emission energy of sandstone in cyclic loading and unloading test has a similar variation with the theoretical calculation of dissipated energy. The cumulative energy curve shows a step-up law, and the stress corresponding to the step point is near the historical maximum stress.

Energy dissipation models of soil nails for 3D upper bound analyses of steep reinforced slopes

Analytical energy dissipation models of nail-soil systems under the ultimate limit state are rare. In this study, a rigorous plastic energy dissipation model (RPEDM) is employed and a pseudo-plastic energy dissipation model (PPEDM) of nails is proposed to analyze the stability of nailed slopes. In the RPEDM, the energy dissipation rate of nails was assumed to be independent of nail-grout interaction. However, in the PPEDM, the nail-soil interaction was analytically accounted for. Based on the upper bound of the plastic theorem, the RPEDM and PPEDM are then incorporated into a three-dimensional discretized failure mechanism to analyze the stability of steep nailed slopes. External work rates and energy dissipation rates are computed to formulate the work rare balance equation, followed by a global search of the critical factors of safety (FS). A comparison with numerical simulations and existing solutions demonstrated that: (1) the RPEDM obeyed the basic principle of the plastic theorem but the estimated FSs had a significant discrepancy with numerical simulations; (2) the PPEDM could predict more accurate FSs and variation of axial forces mobilized within nails compared with the RPEDM but the FSs obtained by PPEDM did not provide rigorous upper bound solutions since “elastic energy dissipation” was factored in the analysis; (3) the PPEDM can degrade into RPEDM if the width of the nail-soil interaction zone is equal to zero. In the end, the RPEDM and PPEDM were used to explore the effects of the layout and the size of nails on the FSs of steep nailed slopes.