Triaxial Tests Research Articles

Influence of Mixing Rubber Fibers on the Mechanical Properties of Expansive Clay under Freeze–Thaw Cycles

With the growth of the transportation industry, large volumes of waste tires are being generated, which necessitates the development of effective solutions for recycling waste tires. In this study, expansive clay was mixed with rubber fibers obtained from waste tires. Triaxial tests were conducted on the rubber fiber-reinforced expansive clay after freeze–thaw cycles. The experimental results of the unreinforced expansive clay from previous studies were used to evaluate the effect of mixing rubber fibers on the mechanical properties of rubber fiber-reinforced expansive clay under freeze–thaw cycles. The results demonstrate that the mixing of rubber fibers significantly reduces the effect of freeze–thaw cycles on the shear strength and elastic modulus of expansive clay. The shear strength and elastic modulus of the unreinforced expansive clay decrease markedly as the number of freeze–thaw cycles increases, while the shear strength and elastic modulus of the rubber fiber-reinforced expansive clay do not exhibit any remarkable change. A calculation model of the deviatoric stress–axial strain curves after freeze–thaw cycles was established. The model describes the deviatoric stress–axial strain behavior of rubber fiber-reinforced expansive clay and unreinforced expansive clay under different confining pressures and different numbers of freeze–thaw cycles.

Pre-Failure Strain Localization in Siliclastic Rocks: A Comparative Study of Laboratory and Numerical Approaches

We combined novel laboratory techniques and numerical modeling to investigate (a)seismic preparatory processes associated with deformation localization during a triaxial failure test on a dry sample of Berea sandstone. Laboratory observations were quantified by measuring strain localization on the sample surface with a distributed strain sensing (DSS) array, utilizing optical fibers, in conjunction with both passive and active acoustic emission (AE) techniques. A physics-based computational model was subsequently employed to understand the underlying physics of these observations and to establish a spatio-temporal correlation between the laboratory and modeling results. These simulations revealed three distinct stages of preparatory processes: (i) highly dissipative fronts propagated towards the middle of the sample correlating with the observed acoustic emission locations; (ii) dissipative regions were individuated in the middle of the sample and could be linked to a discernible decrease of the P-wave velocities; (iii) a system of conjugate bands formed, coalesced into a single band that grew from the center towards the sample surface and was interpreted to be representative for the preparation of a weak plane. Dilatative lobes at the process zones of the weak plane extended outwards and grew to the surface, causing strain localization and an acceleration of the simulated deformation prior to failure. This was also observed during the experiment with the strain rate measurements and spatio-temporally correlated with an increase of the seismicity rate in a similar rock volume. The combined approach of such laboratory and numerical techniques provides an enriched view of (a)seismic preparatory processes preceding the mainshock.

Experimental study of hydraulic fracturing for deep shale reservoir

Compared with shallow reservoirs of shale gas, the high stress and plasticity of shale reservoirs under deep conditions significantly impact the propagation of hydraulic fractures. The study investigates the characteristics of hydraulic fracture propagation in deep shale reservoirs by conducting true triaxial fracturing tests at different stress levels and combinations under circumstances close to the original in-situ stress of the target reservoir. Specifically, it includes comparative experiments under high and low-stress levels, variable stress combinations with equal stress differences, and experiments on the influence of maximum and minimum horizontal in-situ stress, respectively. Through a series of experimental studies, it has been shown that the fracture roughness is relatively low at high stress levels. Fractures can still generate complex and multiple fractures when subject to high-stress conditions. Amongst, natural fissures or weak surfaces still dominate the complex fracture morphology. In the case of a higher in-situ stress level with the same stress difference value brings about a more complex hydraulic fracture morphology as a result of a smaller stress-difference coefficient. The Intersection of hydraulic fractures with multiple parallel weak surfaces creates hydraulic fractures in stepped shape, which can cause drastic fluctuations in injection pressure. The research results provide a reference for on-site deep shale reservoir stimulation and optimization of a fracturing design.

Critical state behaviour of an unsaturated kaolin mixture

In this paper, a series of suction-controlled triaxial tests were conducted to investigate the hydromechanical behaviour of an unsaturated kaolin mixture. The studied variables included the mean net stress, suction, and initial dry density. The suction was controlled over a wide range – in the span of 0–390 MPa using the axis translation method and the vapour equilibrium technique, aiming to holistically study the mechanical response of unsaturated soils. The discussion focused on the critical state behaviour and dilatancy characteristics of the tested soil. The experimental results indicate that the ductility of the soil decreases and shifts towards brittleness with increasing suctions. The critical state stress ratio (Ma) of the soil exhibits a significant increase with suction, and this increase becomes more pronounced with higher initial dry density. Conversely, the impact of suction on the critical state line in the specific volume-mean net stress plane (v-lnpnet plane) diminishes with higher initial dry density. Furthermore, suction notably influences the stress-dilatancy relationship of kaolin mixtures, while the effect of confining pressure appears to be marginal. The influence of suction on the stress-dilatancy relationship primarily stems from its impact on the critical stress ratio (Ma), which can be normalized by dividing the stress ratio by the critical state stress ratio. Lastly, the stress-dilatancy equation of the modified Cam-clay model is extended to capture the effect of suction on the dilatancy characteristics of unsaturated soils.

DEM simulation of microscopic structure and macroscopic mechanical behavior of clay in oedometer and triaxial compression tests

An updated DEM simulation scheme for clay is implemented by incorporating convex polygon shaped platelets and robust algorithm for physico-chemical–mechanical interaction between clay platelets. Clays with two typical microscopic structures, i.e., card-house structure and book-house structure, are simulated in oedometer test and triaxial compression test. Virtual Mercury Intrusion Porosimetry (MIP) and pore segmentation algorithms are utilized to extract pore statistics from the numerical samples. The simulation results and experimental results from the literature are thoroughly compared at both macroscopic and microscopic scales. It is found that the implemented DEM simulation scheme can satisfactorily reproduce the experimentally observed macroscopic behavior of clay. Especially, in triaxial compression tests, the critical state behavior, stress-dilatancy relationship and over-consolidation effects are generally consistent with existing experimental results. General consistency in pore size, orientation and shape distributions in DEM simulations and experiments can be observed. Clay platelets tend to rotate to align their normal directions along the major principal stress direction, while pores tend to align their long-axis directions in the confinement direction, leading to dynamically evolving fabric anisotropy. In the book-house structure clay, clay domains experience multiple deformation modes, including uniaxial compaction, shear distortion, spatial spin, and their combinations.

Microscopic deformation mechanism and characteristics of carbonaceous slate during the creep process

Carbonaceous slate exhibits a significant creep deformation that seriously affects the construction and operation of underground projects. To investigate the microstructural changes characteristics and reveal the microscopic deformation mechanism of the carbonaceous slate during the creep process, multiple methods were performed, including the triaxial creep test, SEM and MIP. The following conclusions were drawn: The rock samples underwent three stages during the creep test: microporosity closure at a low-stress level, material densification at an intermediate stress level, and microcracks emerging and expanding to failure at the high stress. The creep deformation was particularly significant in the first and third processes. The lamellar particles are compressed or bent under stress in parallel and vertical directions, showing the anisotropic properties of deformation. The deformation of the rock sample is related to the angle between the bedding and the orientation of major principal stress, and the effect of the anisotropy decreases with the increased stress level. The sprouting and expansion of microfractures occur at high-stress levels, showing pressure dissolution of mineral particles, migration of very fine particles, and cement damage between lamellar particles. Finally, the horizontal samples formed a combined rupture surface composed of the laminar surface and the fracture surface intersecting it, showing brittle damage, while the vertical samples formed a fracture surface parallel to the laminar surface, showing a ductile damage pattern. Those results could provide the basis for a further understanding of the mechanical properties of carbonaceous slate and the improvement of its creep model and parameters. It was significant for the stability analysis and deformation prediction of engineering structures using numerical simulation.

Investigation of fracture-plugging wellbore strengthening: Large scale true tri-axial experiments and field tests

Lost circulation caused by developed natural fracture occurs frequently in tight sandstone formations located in Sichuan Basin, China. Fracture-plugging wellbore strengthening by lost circulation materials (FPWSLCM) is a widely applied fluid loss control technique globally. The upper limit of the pressure-bearing capacity treated using FPWSLCM and the relevant engineering influencing factors needs to be investigated further. In this paper, a self-designed large-scale true tri-axial cell was developed to simulate the fracturing and sealing processes in a cubic sandstone sample (30 cm × 30 cm×30 cm) under anisotropic stress to investigate the effect of lost circulation materials (LCM) and the experimental processes on the formation pressure-bearing capacity. Three homogeneous cubic tight sandstone samples taken from Xujiahe Formation in Sichuan Basin with a central hole were used for the wellbore strengthening experiments with FPWSLCM, which was used to eliminate the heterogeneity effect of the rock. SRIPE (SINOPEC Research Institute of Petroleum Engineering) bridge plugging materials were used as LCM. The results show that the formation pressure-bearing capacity after treatment by FPWSLCM was affected by the initial injection pressure, the intrusion amount of LCM, the pressure holding time, and the injection rate. The formation pressure-bearing capacity did not decrease consistently with the increase of plugging zone instability times, but showed an obvious characteristic of fluctuations; the formation pressure-bearing capacity exceeded the fracturing pressure in some cases. The experimental results could be explained by the stress cage theory. Finally, the modified FPWSLCM was applied as a lost circulation control approach by drilling into the tight sandstone formation in the Shunbei oil field, which has a history of severe loss of fluid circulations. The result of the field test indicated that the modified approaches were more successful than the previous approaches used in other wells in this block. The research results are of great significance for improving the success rate of lost circulation control and a reduction in drilling costs.

Study on dynamic and failure characteristics of sand and anti-floating safety of tunnel structures under long-term vibration loads of the Beijing subway

Most research into sand liquefaction has predominantly focused on the effects of earthquake ground motion, with a limited exploration into the possibility of sand liquefaction induced under long-term train vibration loads. Therefore, in order to explore the possibility of saturated sand liquefaction under long-term vibration loads of the Beijing subway, this article selected Tongzhou sand to conduct dynamic triaxial tests and obtained the dynamic and failure characteristics of saturated sand under different confining pressures and dynamic stresses. The test results showed that the confining pressure has a greater impact on sand liquefaction. When the confining pressure exceeds 100 kPa, the possibility of liquefaction of Tongzhou sand is fairly limited. Furthermore, a numerical model of an operating tunnel under the influence of long-term train vibration loads is established, and the dynamic response characteristics of the saturated sand and tunnel structure are studied. Numerical simulation results show that the local liquefaction of sand caused by train vibration will not cause the tunnel structure to float. Under local liquefaction conditions at the extremely shallow tunnel base, the soil did not completely lose its bearing capacity, and the displacement of the soil and structure was still dominated by settlement. Changes in tunnel burial depth have a greater impact on segment structure than train vibration loads. Tunnels with a more than 10 m burial depth will not liquefy in saturated sand within one year, and the segment structure is safe. The research results can provide a reference for the anti-floating safety of tunnel structures in similar saturated sand strata.

The use of a nonlocal critical state model in modelling triaxial and plane strain tests on overconsolidated clays

When modelling the phenomenon of strain localisation in strain-softening soils with the finite element (FE) method, nonlocal approaches have been commonly employed to avoid mesh dependency and numerical instability. This paper first presents the FE formulation of a critical state model for highly overconsolidated clays incorporating a nonlocal method. The performance of the nonlocal strain regularisation is subsequently assessed through a series of coupled hydro-mechanical (HM) analyses of undrained and drained triaxial compression tests on London clay. The mechanism behind the evolution of strain localisation in triaxial tests is investigated and a comparison with equivalent plane strain analyses is discussed. Finally, a comprehensive sensitivity study is presented, investigating the influence of the two nonlocal parameters, in the adopted nonlocal algorithm, on the predicted stress–strain responses. A key outcome is the derived linear relationship between the two parameters, which enables a unique stress–strain response to be achieved in either axisymmetric or plane strain analyses with multiple combinations of the two parameters. Such a modelling capability is essential in applications of the proposed nonlocal strain regularisation in large scale boundary value problems in which restrictions on element size exist.

Effects of particle overall regularity and surface roughness on fabric evolution of granular materials: DEM simulations

AbstractParticle shape irregularity is a notable feature of granular materials that exerts a profound influence on their mechanical behavior. This study examines the effects of particle overall regularity and surface roughness on the fabric evolution of granular materials using the Discrete Element Method (DEM). By connecting multiple spheres with varying sizes and positions, a diversity of clump particles characterized by distinct overall regularity () and surface roughness () are generated. A series of DEM simulations on drained triaxial compression tests have then been performed on granular assemblies with varying shapes, whereby their characteristics of contact intensity and the anisotropy of various fabric entities defined by contact normal, branch vector, and particle orientation, have been thoroughly investigated. The results show that increasing particle shape irregularity, indicated by smaller values of and , is generally associated with an enhanced internal structure within the granular assembly, exhibiting a higher mechanical coordination number and a greater fabric anisotropy. Conversely, in granular assemblies with relatively high overall regularity, the fabric anisotropy is notably reduced, and this reduction cannot be compensated by enhancements in particle surface roughness. The evolution of two contact‐related fabric anisotropies is analyzed in relation to particle orientation‐based fabric anisotropy, which is more profoundly influenced by particle overall regularity, underscoring its significant role in fabric evolution of granular materials.

Small-strain shear modulus and liquefaction resistance of calcareous sand with non-plastic fines

Incorporation of non-plastic fines can dramatically affect the liquefaction resistance and stiffness of sands. In this study, the aim is to evaluate the influence of non-plastic fines on the liquefaction resistance and small-strain shear modulus of calcareous sand under cyclic loading. Forty-seven sets of undrained cyclic triaxial tests and companion bender element tests are conducted on reconstituted specimens. The cyclic behaviour of clean sand and silty sand with varying fines content is examined with respect to the global void ratio, relative density and granular skeleton void ratio. The findings demonstrate that the microscopic contacts between coarse and fine grains have a significant impact on the macroscopic behaviour of sand–fines mixtures. The experimental findings are evaluated using the equivalent granular skeleton void ratio, which has been recognised as a suitable parameter to describe the overall effect of fines. The findings on calcareous sand with fines are supplemented and compared with published data in accordance with the semiempirical simplified approach for liquefaction triggering based on shear wave velocity.

Static liquefaction as a form of material instability in element test simulations of granular soil

Static liquefaction is a form of unstable behaviour of granular soil. It is most common in saturated loose sands under monotonically loaded undrained conditions. Predicting static liquefaction using an elastic-plastic model that incorporates the non-associated plastic flow rule and strain hardening is possible. The article briefly describes the unstable behaviour of saturated sand in undrained conditions under a monotonic load. A simple elastic-plastic model with deviatoric hardening and a Drucker–Prager load surface is presented. The constitutive relationships were programmed in a Python script. Simulations of triaxial tests under mixed stress-strain control demonstrated the model’s ability to predict various undrained sand responses, including fully stable responses (no liquefaction) and partial and complete liquefaction under triaxial compression and tension. Predicting static liquefaction is possible by properly selecting the proportions of the parameters involved in plastic potential and loading functions and the parameter A used in the deviatoric hardening rule of hyperbolic type.

Photogrammetry-Based Method for Measuring Volume Changes of Soil Specimens During Critical Phases of Triaxial Testing

Triaxial tests has been routinely used to measure the stress–strain relationship for geomaterials. During triaxial testing, many sources of errors that cannot be completely avoided but are often ignored or approximated using empirical equations. This paper presents a systematic investigation of soil volume change, volume strain nonuniformity, and cross-sectional calculation along the specimen during triaxial testing using a photogrammetry-based method. Consolidated drained triaxial tests were performed in which two parallel measurements were taken: (1) relative volume using the conventional triaxial testing and (2) absolute volume using the photogrammetry-based method. The difference in the observed volume and void ratio measurements between the two methods highlighted the importance of absolute soil volume over the relative volume method. The results revealed the effect of soil volume change in the interpretation of triaxial testing findings. Various preparation steps and procedures during triaxial testing have influenced the initial measured volume and thus caused deviation of the subsequent associated measurements. This method would present a quality control approach for different aspects of triaxial testing to improve the test simulations to accurately measure the soil behavior. The proposed method is important for more refined simulations and identification of setup-induced errors. Additional applications of the current research would allow correct determination of the stress path followed during triaxial testing, the critical-state soil mechanics parameters, and the stress–strain relationship, including deformation and strength parameters.

Modeling of fatigue behaviors of rock materials subjected to cyclic loads with fractional-order plastic flow rule

Compressive cyclic loads induce a progressive failure in rock materials, and the long-term stability can not be guaranteed by the strength under monotonic load. To this end, the present study aims at establishing an elastoplastic fractional fatigue damage model for predicting the accumulative deformation of rock materials in a unified framework. A fractional-order plastic flow rule is introduced to describe volume transformation of rock sample from compression to expansion, eliminating the need for plastic potential functions. And a hardening function with an equivalent plastic shear strain is adopted. Concerning the fatigue effects, the progressive deterioration of material due to cyclic loads is intricately linked to microstructural degradation, depicted by a convolution law. In the context of creep deformation, loading cycle serves as an equivalent time measure, connecting the plastic deformation with the fatigue damage. In order to verify the accuracy, the proposed model is numerically implemented by a returning mapping procedure simulate the mechanical responses of three types of rocks in both uniaxial and triaxial cyclic tests. Comparative analysis with associated fatigue model is also provided to evaluate the accumulative deformation and damage evolution of concerned rocks.

Effect of pore-bearing fluids on the mechanical behavior of siliceous cemented sandstones containing different clay contents and types

The clay minerals contained in the reservoir rock of CO2 geological storage formations can adsorb fluids and swell, which weakens the rock and promotes deformation. This phenomenon has not been widely investigated due to the complexity of the mineral components of the rock. To study the relationship between fluids in rock pores and the mechanical behavior of clay-bearing reservoir rocks, three types of siliceous cemented sandstones mainly composed of clay minerals and quartz, both dry and saturated with various fluids (i.e. N2, scCO2, H2O), were subjected to conventional triaxial compression tests. The results show that the fluids weakened the mechanical strength of the sandstones, and the degree of weakening depended on the clay composition and the type of fluid, with no significant relationship to the clay content. For the sandstone containing montmorillonite, compared to the dry condition, scCO2 and H2O reduced the peak strength by up to 7.16% and 15.33%, respectively, while for the sandstone containing only kaolinite as clay component, scCO2 and H2O reduced the peak strength by 3.34% and 3.18%, respectively. As a control, N2 weakened the strength of the three types of sandstones between 1.46% and 4.04%. By considering the failure characteristics of sandstone at the macro- and microscales, the failure mechanism of the sandstones was explained from two perspectives: the intercrack surface energy reduction and the swelling of clay. This study offers new perspectives for assessing the mechanical stability of fluid-bearing reservoirs and clarifies the role of clay in the connection between fluids in rock pores and the mechanical behavior of rocks.

Study on water–rock interaction failure mechanism and constitutive model of mudstone damaged by pre-peak disturbance

The mudstone disturbed by engineering has been damaged to varying degrees before the peak strength, which is often ignored in the existing research. To reveal the failure mechanism and mechanical characteristics of mudstone under the combined action of water and damage. Firstly, this study proposed a pre-peak damage variable (Da) to characterize the degree of damage before peak stress. Then, triaxial tests were conducted to assess the mechanical properties under different Da and the water–rock interaction. The failure mechanisms of mudstone were revealed from both macro and micro perspectives. Finally, a statistical damage constitutive model for mudstone was constructed, and the rationality of the model was verified using experimental results. The results indicate: (1) The reduction of strength parameters caused by engineering disturbance and water rock coupling is the main reason for the instability of mudstone slope after construction. (2) Mudstone strength decreases gradually and then sharply with increasing Da. The Da reduces mudstone strength by 10%-20% on the original conditions. The Da firstly reduces the cohesion, and then the friction angle. (3) The undamaged mudstone mainly exhibits a multiple-failure-plane mode, while damaged mudstone consists of a single-failure-plane mode. The reason is that the damage zone of mudstone is more likely to infiltrate water molecules, leading to lubrication and softening of the mineral particle skeleton, resulting in a single fracture surface failure mode. (4) The constitutive model for mudstone considering the water weakening and Da effectively describes the stress–strain relationship of damaged mudstone under the water–rock interaction. The research provides new insights into the evolution of soft rock damage considering disturbances and water weakening.

Dynamic properties of alkali residue-based foamed concrete under cyclic load

Alkali residue-based foamed concrete (A-FC), consisting of cement, alkali residue, blast furnace slag, and foam, has great potential for application in subgrade engineering. A series of dynamic triaxial tests were conducted, and the influences of confining pressure, vibration frequency, and curing age on the dynamic properties of A-FC was revealed. Test results indicated that the backbone curves of A-FC exhibit a hyperbolic shape, effectively captured by the H-D model. After 7 days of curing, A-FC possessed robust dynamic bearing capacity. As the dynamic strain increases, the dynamic elastic modulus of A-FC exhibits an initial rise followed by a gradual decline. Concurrently, the damping ratio demonstrates an initial decrease and subsequent gradual increase. Elevated confining pressure, prolonged curing age, and higher vibration frequency were found to contribute to a progressive increase in the dynamic elastic modulus of A-FC. Throughout the damping ratio growth stage, the increasing curing age and confining pressure led to the decrease of damping ratio, with minimal influence from vibration frequency. A calculation model for the maximum dynamic elastic modulus of A-FC was proposed, considering confining pressure, vibration frequency, and curing age. This research underscores the capacity of A-FC to withstand cyclic loading, thereby offering valuable support for its engineering applications.

Equivalent state parameter dependency on gradation properties of medium sand-fines mixtures

Multiple studies confirm that determining the liquefaction resistance of sand-silt mixtures is more intricate compared to pure sand. Furthermore, it has been observed that the global void ratio fails to accurately predict the behavior of silty sand soils due to the fines particles, which can occupy voids between sand grains without significantly contributing to resisting external forces. To address this, a new parameter called equivalent void ratio (e*) has been proposed to better forecast the response of medium sand-fines mixtures. To investigate this further, a series of compression triaxial tests were conducted on mixtures comprising medium sand with low plastic fines. These mixtures were prepared in the laboratory with an initial relative density and subjected to varying confining pressures. The test results were utilized to assess the undrained shear strength of medium sand-silt mixtures based on the equivalent void ratio (e*) and to establish the equivalent granular steady-state line, which serves as a reference for calculating the equivalent state parameter (ψ*). Analysis of the obtained data suggests a correlation between the equivalent void ratio (e*) and the equivalent state parameter (ψ*) with the grading characteristics (such as D10, D50, Cu, D10R, D50R, and CUR) of the medium silty sand.

Multiscale mechanical analysis of Frozen Clay: Triaxial testing and discrete element modeling

The macroscopic and microscopic mechanical characteristics of subgrade soil in cold regions play an important role in the stability of embankment engineering in cold regions. In this study, we conduct triaxial tests and isotropic loading-unloading tests on frozen clay in the cold region subgrade. The tests are conducted under different temperatures and confining pressures to obtain its macroscopic strength and deformation characteristics. Meanwhile, we establish a discrete element model of frozen clay based on the Discrete Element Method (DEM) to simulate conventional triaxial and isotropic loading-unloading tests, and analyze its mechanical characteristics from a microscopic perspective. The results of the study indicate that the strength and deformation of frozen clay are greatly affected by the cooling temperature and confining pressure. As the cooling temperature decreases, the cohesion of the specimen significantly increases, and the internal friction angle slightly increases, along with the elastic moduli. Under low confining pressure, the specimen exhibits significant volumetric expansion, while under high confining pressure, the specimen mainly undergoes volumetric contraction. Through discrete element numerical simulation, we obtain the microscopic mechanical characteristics of frozen clay, explain the “bulging” phenomenon of the specimen from a microscopic perspective, and verify the applicability of the flexible membrane. Meanwhile, the influence rules of various microscopic parameters on the mechanical properties of frozen clay are also obtained through a series of parameter calibration works.

A quantitative study of the effects of physical properties and external loads on the liquefaction of saturated sand based on an intelligent numerical cyclic triaxial test system

ABSTRACT Soil liquefaction would cause significant damage to the safety of cargo transportation. The aim of this article is to conduct a quantitative study of the influence of the main physical characteristic parameters of saturated sand and external loads on its liquefaction. On the basis of the physical cyclic triaxial test (CTT), the finite element simulation model and PSO-BP neural network prediction model and importance analysis model were optimised in this study. Based on this, an innovative intelligent numerical CTT system for saturated sand was constructed. The research results indicate the influence of external load, effective internal friction Angle and plasticity index on the liquefaction of saturated sand is significant, and the average weight is 40.15%, 29.15% and 25.05%, respectively. In this paper, the relevant research provides a theoretical basis for effective control of sand liquefaction and provides new ideas and feasible solutions for subsequent research on sand liquefaction.