Three-dimensional limit variation analysis on the ultimate pullout capacity of the anchor cables based on the Hoek-Brown failure criterion

Only simplified two-dimensional model and a single failure mode are adopted to calculate the ultimate pullout capacity(UPC)of anchor cables in most previous research.This study focuses on a more comprehensive combination failure mode that consists of bond failure of an anchorage body and failure of an anchored rock mass.The three-dimensional ultimate pullout capacity of the anchor cables is calculated based on the Hoek-Brown failure criterion and variation analysis method.The numerical solution for the curvilinear function in fracture plane is obtained based on the finite difference theory,which more accurately reflects the failure state of the anchor cable,as opposed to that being assumed in advance.The results reveal that relying solely on a single failure mode for UPC calculations has limitations,as changes in parameter values not only directly impact the UPC value but also can alter the failure model and thus the calculation method.

Effects of loading rate on root pullout performance of two plants in the eastern Loess Plateau,China

Root pullout performance of plants is an important mechanical basis for soil reinforcement by plant roots in the semi-arid areas.Studies have shown that it is affected by plant factors(species,ages,root geometry,etc.)and soil factors(soil types,soil moisture,soil bulk densities,etc.).However,the effects of loading rates on root pullout performance are not well studied.To explore the mechanical interactions under different loading rates,we conducted pullout tests on Medicago sativa L.and Hippophae rhamnoides L.roots under five loading rates,i.e.,5,50,100,150,and 200 mm/min.In addition,tensile tests were conducted on the roots in diameters of 0.5-2.0 mm to compare the relationship between root tensile properties and root pullout properties.Results showed that two root failure modes,slippage and breakage,were observed during root pullout tests.All M.sativa roots were pulled out,while 72.2%of H.rhamnoides roots were broken.The maximum fracture diameter and fracture root length of H.rhamnoides were 1.22 mm and 7.44 cm under 100 mm/min loading rate,respectively.Root displacement values were 4.63%(±0.43%)and 8.91%(±0.52%)of the total root length for M.sativa and H.rhamnoides,respectively.The values of maximum pullout force were 14.6(±0.7)and 17.7(±1.8)N under 100 mm/min for M.sativa and H.rhamnoides,respectively.Values of the maximum pullout strength for M.sativa and H.rhamnoides were 38.38(±5.48)MPa under 150 mm/min and 12.47(±1.43)MPa under 100 mm/min,respectively.Root-soil friction coefficient under 100 mm/min was significantly larger than those under other loading rates for both the two species.Values of the maximum root pullout energy for M.sativa and H.rhamnoides were 87.83(±21.55)mm•N under 100 mm/min and 173.53(±38.53)mm•N under 200 mm/min,respectively.Root pullout force was significantly related to root diameter(P<0.01).Peak root pullout force was significantly affected by loading rates when the effect of root diameter was included(P<0.01),and vice versa.Except for the failure mode and peak pullout force,other pullout parameters,including root pullout strength,root displacement,root-soil friction coefficient,and root pullout energy were not significantly affected by loading rates(P>0.05).Root pullout strength was greater than root tensile strength for the two species.The results suggested that there was no need to deliberately control loading rate in root pullout tests in the semi-arid soil,and root pullout force and pullout strength could be better parameters for root reinforcement model compared with root tensile strength as root pullout force and pullout strength could more realistically reflect the working state of roots in the semi-arid soil.

Influence of soil moisture content on pullout properties of Hippophae rhamnoides Linn. roots

Plant root system plays an important role in preventing soil erosion and improving slope stability.However,its performance is significantly affected by soil moisture content,and the role of soil moisture in root reinforcement is not fully understood.In this study,the influence of soil moisture on root pullout properties was studied by experiments.Vertical in-situ pullout tests under four different levels of soil matric suction(12 kPa,18 kPa,24 kPa,30 kPa)were carried out on roots of sea buckthorn plants(Hippophae rhamnoides Linn.)which were artificially cultivated for 7 months.Diameter and length of the root system of sea buckthorn were investigated.The results showed that a very significant correlation was observed between root diameter(D)and root length(L)(P<0.01),and root diameter decreased with soil depth.When soil bulk density was constant,peak pullout force(F)and friction coefficient of root-soil interface(μ)decreased with increasing gravimetric soil moisture content in power functions.Soil moisture content significantly affected root pullout resistance because the increase of soil moisture content decreased the friction coefficient between the roots and soil.Root diameter at breakage point(Db)and length of root segment left in soil(Lb)were increased with soil moisture content.In addition,peak pullout force of the roots increased in a power function with root diameter at the soil surface(D0)and in a linear function with total root length(L).The results provided an experimental basis for quantifying the effects of soil moisture content on soil reinforcement by plant roots.

Characteristics of root pullout resistance of Caragana korshinskii Kom.in the loess area of northeastern Qinghai-Tibet Plateau,China

Roots exert pullout resistance under pullout force,allowing plants to resist uprooting.However,the pullout resistance characteristics of taproot-type shrub species of different ages remain unclear.In this study,in order to improve our knowledge of pullout resistance characteristics of taproot systems of shrub species,we selected the shrub species Caragana korshinskii Kom.in different growth periods as the research plant and conducted in situ root pullout test.The relationships among the maximum pullout resistance,peak root displacement,shrub growth period,and aboveground growth indices(plant height and plant crown breadth)were analyzed,as well as the mechanical process of uprooting.Pullout resistance of 4-15 year-old C.korshinskii ranged from 2.49(±0.25)to 14.71(±4.96)kN,and the peak displacement ranged from 11.77(±8.61)to 26.50(±16.09)cm.The maximum pullout resistance and the peak displacement of roots increased as a power function(R^(2)=0.9038)and a linear function(R^(2)=0.8242)with increasing age,respectively.The maximum pullout resistance and the peak displacement increased with increasing plant height;however,this relationship was not significant.The maximum pullout resistance increased exponentially(R^(2)=0.5522)as the crown breadth increased.There was no significant relationship between the peak displacement and crown breadth.The pullout resistance and displacement curve were divided into three stages:the initial nonlinear growth,linear growth,and nonlinear stages.Two modes of failure of a single root occurred when the roots were subjected to vertical loading forces:the synchronous breakage mode and the periderm preferential breakage mode.These findings provide a foundation for further investigation of the soil reinforcement and slope protection mechanisms of this shrub species in the loess area of northeastern Qinghai-Tibet Plateau,China.

Pullout behavior of polymeric strip in compacted dry granular soil under cyclic tensile load conditions

Assessment of the reinforcement behavior of soil under cyclic and monotonic loads is of great impor- tance in the safe design of mechanically stabilized earth walls, In this article, the method of conducting a multistage pullout （MSP） test on the polymeric strip （PS） is presented, The post-cyclic behavior of the reinforcement can be evaluated using a large-scale pullout apparatus adopting MSP test and one-stage pullout （OSP） test procedures, This research investigates the effects of various factors including load amplitude, load frequency, number of load cycles and vertical effective stress on the peak apparent coefficient of friction mobilized at the soil-PS interface and the pullout resistance of the PS buried in dry sandy soil. The results illustrate that changing the cyclic tensile load frequency from 0,1 Hz to 0,5 Hz does not affect the pullout resistance. Moreover, the influence of increasing the number of load cycles from 30 to 250 on the peak pullout resistance is negligible. Finally, the effect of increasing the cyclic tensile load amplitude from 20% to 40% on the monotonic pullout resistance can be ignored. The peak apparent coefficient of friction mobilized at the soil-PS interface under monotonic and cyclic load conditions decreases with the increase in vertical effective stress.

Laboratory large-scale pullout investigation of a new reinforcement ofcomposite geosynthetic strip

In this paper,more than 70 large-scale pullout tests were performed to evaluate the performance of an innovative composite geosynthetic strip(CGS)reinforcement in sandy backfill.The CGS reinforcement is composed of a geosynthetic strip(GS)and parts of a scrap truck tire as transverse members.The experimental pullout results for the CGS reinforcement were compared with the suggested theoretical equations and ordinary reinforcements,including the GS,the steel strip(SS),and the steel strip with rib(SSR).The pullout test results show that adding three transverse members to the GS reinforcement(CGS3)with S/H?6.6(where S and H are the space and height of the transverse members,respectively)increases pullout resistance by more than 120%,170%,and 50%compared to the GS,the SS,and the SSR,respectively.This result shows that the CGS3(CGS with three transverse members)reinforcement needs at least 55.5%,63%,and 33.3%smaller length compared to the GS,the SS,and the SSR,respectively.In general,implementation of mechanically stabilized earth wall(MSEW)with the proposed strip may help geotechnical engineers prevent costly designs and solve the problem of MSEW implementation in cases where there are limitations of space.

Studying the mechanical properties of the soil-root interface using the pullout test method

It is important to quantify the effect of the root diameter, the embedment length of the root and load speed on the soil-root interface mechanical properties for studying the root anchorage. The soilroot interface mechanical properties can be obtained through the pullout force and root slippage curve(F-S curve). About 120 Pinus tabulaeformis single roots whose diameters ranged from 1 mm to 10 mm divided into 6 groups based on different root embedment length(50 mm, 100 mm and 150 mm) and different load velocity(10 mm·min^(-1), 50 mm·min^(-1), 100 mm·min^(-1) and 300 mm·min^(-1)) were investigated using the pullout method. This study aims to explore the mechanical properties of the soil-root interface in the real conditions using the pullout test method. The results showed two kinds of pullout test failure modes during the experimental process: breakage failure and pullout failure. The results showed that the roots were easier to be broken when the root diameter was smaller or the loading speed was larger. The relationship between the maximum anchorage force and root diameter was linear and the linearly dependent coefficient(R^2) was larger than 0.85. The anchorage force increased with the root embedment length. An increase of 10%^(-1)5% for the maximumanchorage force was found when load speed increased from 10 to 300 mm.min^(-1). The mean peak slippage of the root was from 13.81 to 35.79 mm when the load velocity varied from 10 to 300 mm.min^(-1). The study will be helpful for the design of slopes reinforced by vegetation and in predicting risk of uprooting of trees, and will have practical benefits for understanding the mechanism of landslide.

Variation analysis of ultimate pullout capacity of shallow horizontal strip anchor plate with 2-layer overlying soil based on nonlinear M-C failure criterion

Based on the nonlinear Mohr-Coulomb failure criterion and an associated flow rule,a kinematic admissible velocity field of failure mechanism of the 2-layer soil above a shallow horizontal strip anchor plate is constructed.The ultimate pull-out force and its corresponding failure mechanism through the upper bound limit analysis according to a variation principle are deduced.When the 2-layer overlying soil is degraded into single-layer soil,the model of ultimate pullout force could also be degraded into the model of single-layer soil.And the comparison between results of single-layer soil variation method and those calculated by rigid limit analysis method proves the correctness of our method.Based on that,the influence of changes of geotechnical parameters on ultimate pullout forces and failure mechanism of a shallow horizontal strip anchor with the 2-layer soil above are analyzed.The results show that the ultimate pull-out force and failure mechanism of a shallow horizontal strip anchor with the 2-layer soil above are affected by the nonlinear geotechnical parameters greatly.Thus,it is very important to obtain the accurate geotechnical parameters of 2-layer soil for the evaluation of the ultimate pullout capacity of the anchor plate.

Upper bound analysis of ultimate pullout capacity of shallow 3-D circular plate anchors based on nonlinear Mohr-Coulomb failure criterion

Based on the nonlinear Mohr-Coulomb failure criterion and the associated flow rules,the three-dimensional(3-D)axisymmetric failure mechanism of shallow horizontal circular plate anchors that are subjected to the ultimate pullout capacity(UPC)is determined.A derivative function of the projection function for projecting the 3-D axisymmetric failure surface on plane is deduced using the variation theory.By using difference principle,the primitive function of failure surface satisfying boundary condition and numerical solution to its corresponding ultimate pullout capacity function are obtained.The influences of nonlinear Mohr-Coulomb parameters on UPC and failure mechanism are studied.The result shows that UPC decreases with dimensionless parameter m and uniaxial tensile strength increases but increases when depth and radius of plate anchor,surface overload,initial cohesion,geomaterial density and friction angle increase.The failure surface is similar to a symmetrical spatial funnel,and its shape is mainly determined by dimensionless parameter m;the surface damage range expands with the increase of radius and depth of the plate anchor as well as initial cohesion but decreases with the increase of dimensionless parameter m and uniaxial tensile strength as well as geomaterial density.As the dimensionless parameter m=2.0,the numerical solution of UPC based on the difference principle is proved to be feasible and effective through the comparison with the exact solution.In addition,the comparison between solutions of UPC computed by variation method and those computed by upper bound method indicate that variation method outperforms upper bound method.

Untangling the influence of soil moisture on root pullout property of alfafa plant

Root pullout property of plants was of key importance to the soil reinforcement and the improvement of slope stability. To investigate the influence of soil moisture on root pullout resistance and failure modes in soil reinforcement process, we conducted pullout tests on alfalfa(Medicago sativa L.) roots at five levels(40, 30, 20, 10 and 6 kPa) of soil matric suction, corresponding to respectively 7.84%, 9.66%, 13.02%, 19.35% and 27.06% gravimetric soil moisture contents. Results showed that the maximal root pullout force of M. sativa decreased in a power function with increasing soil moisture content from 7.84% to 27.06%. Root slippage rate increased and breakage rate decreased with increasing soil moisture content. At 9.66% soil moisture content, root slippage rate and breakage rate was 56.41% and 43.58%, respectively. The threshold value of soil moisture content was about 9.00% for alfalfa roots in the loess soil. The maximal pullout force of M. sativa increased with root diameter in a power function. The threshold value of root diameter was 1.15 mm, because root slipping force was greater than root breaking force when diameter >1.15 mm, while diameter ≤1.15 mm, root slipping force tended to be less than root breaking force. No significant difference in pullout forces was observed between slipping roots and breaking roots when they had similar diameters. More easily obtained root tensile force(strength) is suggested to be used in root reinforcement models under the condition that the effect of root diameter is excluded as the pullout force of breaking roots measured in pullout tests is similar to the root tensile force obtained by tensile tests.

Numerical modelling of pullout of helical soil nail

An investigation into the pullout response of helical soil nail using finite element subroutine Plaxis 2D is presented.The numerical modelling of actual pullout response is achieved by axisymmetric and horizontal loading condition.The effect of varying number of helical plates,helical plate spacing and helical plate diameter is studied to understand the pullout capacity behaviour.The failure surfaces for various helical soil nail configurations and their pullout mechanisms are also analysed and discussed.The pullout capacity is found to increase with increase in number of helical plates.The helical plate spacing ratio（s/D;） and diameter ratio（D;/D;） are found to increase the pullout only up to a critical value.The response of helical soil nail using axisymmetric finite element simulation is found similar to the uplift behaviour of helical piles and helical soil anchors.In the absence of literature regarding numerical modelling of helical soil nail,simulation results are validated with uplift responses of helical piles and soil anchors.A good agreement in their comparative study for pullout response is also observed.

FINITE-ELEMENT MODELLING OF SOIL-GEOGRID INTERACTION DEALING WITH THE PULLOUT BEHAVIOUR OF GEOGRIDS

To predict the behavior of geogrids embedded in sand under pullout loading conditions, the two dimensional plane-stress finite element model was presented. The interactions between soil and geogrid were simulated as non-linear springs, and the stiffness of the springs was determined from simple tests in the specially designed pullout box. The predicted behavior of the geogrid under pullout load agrees well with the observed data including the load-displacement properties, the displacement distribution along the longitudinal direction and the mobilization of the frictional and bearing resistance. (Edited author abstract) 8 Refs.

Pullout of soil nail with circular discs: A three-dimensional finite element analysis

An internal failure mode for a soil-nailed system consists of failure at nail heads,slope facing,nail strength,along groutesoil interface and pullout failure.A better understanding of pullout of soil nail thus becomes important to assess the stability of a soil-nailed system.In the present study,an investigation into the pullout behaviour of soil nail with circular discs along the shaft has been carried out by a threedimensional finite element analysis using Abaqus/Explicit routine.A total of 67 simulations have been performed to accurately predict the pullout behaviour of soil nail.The soil nail under study has circular discs along its shaft varying in numbers from 1 to 4.The pullout of this soil nail in a pullout test box has been simulated with a constant overburden pressure of 20 kPa acting on the nail.The pullout load edisplacement characteristics,stresses around soil nail and failure mechanism during pullout are studied.Variations of dimensionless factors such as normalised pullout load factor and bearing capacity factor have been obtained with different combinations of parameters in terms of relative disc spacing ratio,anchorage length ratio,embedment ratio,diameter ratio and displacement ratio.From the results of analyses,it is found that nail with more circular discs requires higher pullout load.There are critical relative disc spacing ratio and diameter ratio which significantly affect the pullout behaviour of nail.

Visualization of pullout behaviour of geogrid in sand with emphasis on size effect of protrusive junctions

Geogrid has been extensively used in geotechnical engineering practice due to its effectiveness and economy. Deep insight into the interaction between the backfill soil and the geogrid is of great importance for proper design and construction of geogrid reinforced earth structures. Based on the calibrated model of sand and geogrid, a series of numerical pullout tests are conducted using PFC^(3D) under special considerations of particle angularity and aperture geometry of the geogrid. In this work, interface characteristics regarding the displacement and contact force developed among particles and the deformation and force distribution along the geogrid are all visualized with PFC^(3D) simulations so that new understanding on how geogrid-soil interaction develops under pullout loads can be obtained. Meanwhile, a new variable named fabric anisotropy coefficient is introduced to evaluate the inherent relationship between macroscopic strength and microscopic fabric anisotropy. A correlation analysis is adopted to compare the accuracy between the newly-proposed coefficient and the most commonly used one. Furthermore, additional pullout tests on geogrid with four different joint protrusion heights have been conducted to investigate what extent and how vertical reinforcement elements may result in reinforcement effects from perspectives of bearing resistance contribution, energy dissipation, as well as volumetric response. Numerical results show that both the magnitude and the directional variation of normal contact forces govern the development of macroscopic strength and the reinforcing effects of joint protrusion height can be attributed to the accelerated energy dissipation across the particle assembly and the intensive mobilization of the geogrid.

Analytical analysis of pullout resistance of the hydraulic expansion rockbolts on a frictionally coupled model

This paper proposes an empirical formula to estimate the shear strength of hydraulic expansion rockbolts.The field experimental results were obtained from eleven pullout tests to evaluate the results computed by the proposed formula.It was found that shear resistance of hydraulic expansion rockbolts significantly depends on the uniaxial compressive strength and elastic modulus of rock,with high correlation coefficients of 0.7651 and0.8587,respectively.The developed formula enables estimation of the maximum pullout load in an analytical process without pullout tests in the field.Conversely,due to the poor interlocking at the initial pullout load,the measured displacements were higher than the estimated ones.To reduce the interlocking effects between bolt and rock,we recommend preloading of 29.4 kN.Preload allows reducing the distance between the measured and estimated displacement and making two load-displacement curves practically identical with marginal differences of 1.1 to 1.5 mm at the maximum pullout load.

Investigations on pullout behavior of geogrid-granular trench using CANAsand constitutive model

Experimental and numerical investigations have been carried out on behavior of pullout resistance of embedded circular plate with and without geogrid reinforcement layers in stabilized loose and dense sands using a granular trench.Different parameters have been considered,such as the number of geogrid layers,embedment depth ratio,relative density of soil and height ratio of granular trench.Results showed that,without granular trench,the single layer of geogrid was more effective in enhancing the pullout capacity compared to the multilayer of geogrid reinforcement.Also,increasing the soil density and embedment depth ratio led to an increase in the uplift capacity.When soil was improved with the granular trench,the uplift force significantly increased.The granular trench improved the uplift load in dense sand more,as compared to the same symmetrical plate embedded in loose sand.Although it was observed that,in geogrid-reinforced granular trench condition,the ultimate pullout resistance at failure increased as the number of geogrid layers increased up to the third layer,and the fifth layer had a negligible effect in comparison with the third layer of reinforcement.Finite element analyses with hardening soil model for sand and CANAsand constitutive model for granular trench were conducted to investigate the failure mechanism and the associated rupture surfaces utilized.The response of granular material in the proposed model is an elastoplastic constitutive model derived from the CANAsand model,which uses a non-associated flow rule along with the concept of the state boundary surface possessing a critical and a compact state.It was observed that the granular trench might change the failure mechanism from deep plate to shallow plate as the failure surface can extend to the ground surface.The ultimate uplift capacity of anchor and the variation of surface deformation indicated a close agreement between the experiment and numerical model.

Field Measurements and Pullout Tests of Reinforced Earth Retaining Wall

In this paper, field measurements and pullout tests of a new type of reinforced earth retaining wall, which is reinforced by trapezoid concrete blocks connected by steel bar, are described. Field measurements included settlements of the earth fill, tensile forces in the ties and earth pressures on the facing panels during the construction and at completion. Based on the measurements, the following statements can be made: (1) the tensile forces in the ties increased with the height of backfill above the tie and there is a tensile force crest in most ties; (2) at completion, the measured earth pressures along the wall face were between the values of the active earth pressures and the pressures at rest; (3) larger settlements occurred near the face of the wall where a zone of drainage sand and gravel was not compacted properly and smaller settlements occurred in the well-compacted backfill. The results of field pullout tests indicated that the magnitudes of pullout resistances as well as tensile forces induced in the ties were strongly influenced by the relative displacements between the ties and the backfill, and pullout resistances increased with the height of backfill above the ties and the length of ties.

Study on Ultimate Pullout Force of Grouting Anchors of the Anchor-Pull Retaining Wall

Determination of the grouting anchor pullout force is a key step during the design of anchor-pull retaining wall, but it is mostly determined relied on empirical formula at present, and the rationality and the safety cannot be effectively guaranteed. Based on the engineering case of the gravity retaining wall of Qinglin Freeway, the model test was designed, and combined with the results of the ABAQUS finite element numerical analysis, it was analyzed that how the anchor axial pulling force distributes. The results showed that the force of the anchor near the wall bolt was large and which far from the wall was small and the ultimate pullout force was proportional to the length, diameter and shear strength. When the end tension of the anchor was small, the top load played a leading role on the anchor tension. This conclusion confirmed the calculation formula of ultimate pullout force was and provided a theoretical basis for anchor-pull retaining wall design and calculation.

Pullout Behavior of Large-diameter Collapsed Double-walled Carbon Nanotubes

The pullout behavior of large-diameter collapsed double-walled carbon nanotubes（DWCNT） was studied by molecular dynamics simulations and compared with those in the circular cross-sectioned state. The pullout force-displacement curves of both are in good agreement with the same mean value of the pullout force during the steady pullout stage. The pullout force was mainly due to the formation of new surfaces; the friction between nested walls was negligible. The effects of different chiral combinations and inter-wall spacings on the pullout behavior for both section situations were investigated. The commensurate（zigzag/zigzag or armchair/armchair） bi-tube systems have a larger fluctuation in the pullout force. The smaller interspacing implies lower mean pullout force with stronger fluctuations.

Pullout of the Cylindrical Helicoidal Fiber

The multi-layer cylindrical helicoidal fiber structure(MCHFS)exists widely in biological materials such as bone and wood at the microscale.MCHFSs typically function as reinforcing elements to enhance the toughness of materials.In this study,we establish a shear lag-based pullout model of the cylindrical helicoidal fiber(CHF)for investigating interlayer stress transfer and debonding behaviors,with implications regarding the underlying toughening mechanism of MCHFS.Based on the shear lag assumptions,analytical solutions for the stress and displacement fields of the MCHFS during the pullout are derived by considering the CHF as a cylindrically monoclinic material and verified through the 3D finite element simulation.It is found that the helical winding of CHF results in both axial and hoop interlayer shear stresses.Both the helical winding angle and the elastic moduli of the fiber and matrix have significant influences on interlayer stress transfer.This work reveals a new interlayer stress transfer mechanism in the MCHFS existing widely in biological materials.