The accurate prediction of the friction angle of clays is crucial for assessing slope stability in engineering applications.This study addresses the importance of estimating the friction angle and presents the develop...The accurate prediction of the friction angle of clays is crucial for assessing slope stability in engineering applications.This study addresses the importance of estimating the friction angle and presents the development of four soft computing models:YJ-FPA-MLPnet,YJ-CRO-MLPnet,YJ-ACOC-MLPnet,and YJCSA-MLPnet.First of all,the Yeo-Johnson(YJ)transformation technique was used to stabilize the variance of data and make it more suitable for parametric statistical models that assume normality and equal variances.This technique is expected to improve the accuracy of friction angle prediction models.The friction angle prediction models then utilized multi-layer perceptron neural networks(MLPnet)and metaheuristic optimization algorithms to further enhance performance,including flower pollination algorithm(FPA),coral reefs optimization(CRO),ant colony optimization continuous(ACOC),and cuckoo search algorithm(CSA).The prediction models without the YJ technique,i.e.FPA-MLPnet,CRO-MLPnet,ACOC-MLPnet,and CSA-MLPnet,were then compared to those with the YJ technique,i.e.YJ-FPA-MLPnet,YJ-CRO-MLPnet,YJ-ACOC-MLPnet,and YJ-CSA-MLPnet.Among these,the YJ-CRO-MLPnet model demonstrated superior reliability,achieving an accuracy of up to 83%in predicting the friction angle of clay in practical engineering scenarios.This improvement is significant,as it represents an increase from 1.3%to approximately 20%compared to the models that did not utilize the YJ transformation technique.展开更多
Surrounding rocks at different locations are generally subjected to different stress paths during the process of deep hard rock excavation.In this study,to reveal the mechanical parameters of deep surrounding rock und...Surrounding rocks at different locations are generally subjected to different stress paths during the process of deep hard rock excavation.In this study,to reveal the mechanical parameters of deep surrounding rock under different stress paths,a new cyclic loading and unloading test method for controlled true triaxial loading and unloading and principal stress direction interchange was proposed,and the evolution of mechanical parameters of Shuangjiangkou granite under different stress paths was studied,including the deformation modulus,elastic deformation increment ratios,fracture degree,cohesion and internal friction angle.Additionally,stress path coefficient was defined to characterize different stress paths,and the functional relationships among the stress path coefficient,rock fracture degree difference coefficient,cohesion and internal friction angle were obtained.The results show that during the true triaxial cyclic loading and unloading process,the deformation modulus and cohesion gradually decrease,while the internal friction angle gradually increases with increasing equivalent crack strain.The stress path coefficient is exponentially related to the rock fracture degree difference coefficient.As the stress path coefficient increases,the degrees of cohesion weakening and internal friction angle strengthening decrease linearly.During cyclic loading and unloading under true triaxial principal stress direction interchange,the direction of crack development changes,and the deformation modulus increases,while the cohesion and internal friction angle decrease slightly,indicating that the principal stress direction interchange has a strengthening effect on the surrounding rocks.Finally,the influences of the principal stress interchange direction on the stabilities of deep engineering excavation projects are discussed.展开更多
The ruin of several civil engineering works occurs due to shear rupture of the ground. When the stress is greater than the shear resistance, the internal friction angle and the cohesion of the soil loosen and rupture ...The ruin of several civil engineering works occurs due to shear rupture of the ground. When the stress is greater than the shear resistance, the internal friction angle and the cohesion of the soil loosen and rupture occurs. Cement and lime are often used to stabilize soils and improve soil strength. The costs and environmental problems of these technologies raise concerns and challenge researchers to innovate with clean, inexpensive materials, accessible to the most disadvantaged social classes. The question that this study seeks to answer is whether the binders derived from plant tannins, which also stabilize soils, improve the shear resistance of these soils. To do this, we determined for silty sand the shear parameters, notably the cohesion and the angle of internal friction in the non-stabilized state and when they are stabilized with the powder of the bark of the Bridelia under different water states. The results show that the addition of Bridelia powder to silty sand increases the cohesion of the soil by nearly 70.71% and the friction angle by 4.31%. But in unfavourable water conditions, the cohesion and internal friction angle of the silty sand material improved with Bridelia bark powder drops drastically by nearly 81.56%. but does not dissolve completely as for the same material. When it is not stabilized. This information is an invaluable contribution in the search for solutions to increase the durability of earthen constructions by improving the water-repellent properties of soils.展开更多
Although friction characteristics of fault gouge are important to understand reactivation of fault,behavior of earthquake,and mechanism of slope failure,analysis results of fault gouge have low accuracy mostly than th...Although friction characteristics of fault gouge are important to understand reactivation of fault,behavior of earthquake,and mechanism of slope failure,analysis results of fault gouge have low accuracy mostly than those of soils or rocks due to its high heterogeneity and low strength.Therefore,to improve the accuracy of analysis results,we conducted simple regression analysis and structural equation model analysis and selected major influential factors of friction characteristics among many factors,and then we deduced advanced regression model with the highest coefficient of determination(R^(2)) via multiple regression analysis.Whereas most coefficients of determination in simple regression analysis are below0.3-0.4,coefficient of determination in multiple regression analysis is remarkably large as 0.657.展开更多
Severe faults have caused many earthquakes around the world throughout history.More recently,earthquakes have occurred in Taiwan,China(Chi-Chi fault),and elsewhere,causing loss of lives and destroying many buildings a...Severe faults have caused many earthquakes around the world throughout history.More recently,earthquakes have occurred in Taiwan,China(Chi-Chi fault),and elsewhere,causing loss of lives and destroying many buildings and structures.These tectonic movements have gained attention from engineers,and in the past 15 years,the focus has been on faulting mechanisms.In this study,a physical model(1 g)was fabricated and used to evaluate the impact of a reverse fault in a field with a tunnel.In the 1 g model,researchers installed additional gauges on the tunnel,so that all the displacements could be adjusted,and all the responses could be monitored during faulting.An experimental study of various soil properties(cohesion and friction angles)in reverse faults on the tunnel lining were carried out and are described herein.A comparison of results for different levels of soil cohesion revealed that it can dramatically reduce the displacement by as much as 40%,and that friction angles of 27ºcan record approximately 60%more displacements than at 37º.Furthermore,a comparison of fault angles of 30ºand 60ºindicates that the displacements can be different by more than 43%in cohesionless soil and about 64%for a friction angle of 27º.展开更多
The shear strength of sand-foam mixtures plays a crucial role in ensuring successful earth pressure balance(EPB)shield tunneling.Since the sand-foam mixtures are constantly sheared by the cutterhead and the screw conv...The shear strength of sand-foam mixtures plays a crucial role in ensuring successful earth pressure balance(EPB)shield tunneling.Since the sand-foam mixtures are constantly sheared by the cutterhead and the screw conveyor with varied rotation speeds during tunneling,it is non-trivial to investigate the effect of shear rates on the undrained shear strength of sand-foam mixtures under chamber pressures to extend the understanding on the tunneling process.This study conducted a series of pressurized vane shear tests to investigate the role of shear rates on the peak and residual strengths of sand-foam mixtures at different pore states.Different from the shear-rate characteristics of natural sands or clay,the results showed that the peak strength of sand-foam mixtures under high vertical total stress(σ_(v)≥200 kPa)and low foam injection ratio(FIR30%)decreased with the increase in shear rate.Otherwise,the peak strength was not measurably affected by shear rates.The sand-foam mixtures in the residual state resembled low-viscous fluid with yield stress and the residual strength increased slightly with shear rates.In addition,the peak and residual strengths were approximately linear with vertical effective stress regardless of the total stress and FIR.The peak effective internal friction angle remained almost invariant in a low shear rate(γ′<0.25 s1)but decreased when the shear rate continued increasing.The residual effective internal friction angle was lower than the peak counterpart and insensitive to shear rates.This study unveiled the role of shear rates in the undrained shear strength of sand-foam mixtures with various FIRs and vertical total stresses.The findings can extend the understanding of the rate-dependent shear characteristics of conditioned soils and guide the decision-making of soil conditioning schemes in the EPB shield tunneling practice.展开更多
Currently,the application of the Yellow River silt in subgrade,especially in expressway subgrade,has not been widely promoted.The main reason is that the research on the mechanical characteristics of the Yellow River ...Currently,the application of the Yellow River silt in subgrade,especially in expressway subgrade,has not been widely promoted.The main reason is that the research on the mechanical characteristics of the Yellow River silt used for subgrade filling is extremely limited.In this study,the static shear test of the Yellow River silt under drained condition was carried out using Global Digital Systems(GDS)triaxial apparatus,and the effects of confining pressure,relative density and shear rate on the strength and deformation behavior of the Yellow River silt were investigated.The cohesive force of the Yellow River silt is low,and the friction angle is the main factor determining the shear strength.Friction angle at phase transformation stateφpt,friction angle at peak stateφps,friction angle at critical stateφcs,were obtained via the observation on the evolution law of mobilized friction angle during the whole shearing process.The friction angles corresponding to three different characteristic states have the following magnitude relationship,namelyφps>φcs>φpt.The strength parameters for low-grade subgrade and highgrade subgrade were chosen to be 29.33°and 33.75°.The critical state line(CSL),envelop of phase transformation(EOP),and envelop of dilatancy(EOD)for three different characteristic states were determined.The critical stress ratio M,the phase transformation stress ratio Mptand the dilatancy stress ratio Mdof the Yellow River silt are 1.199,1.235,1.152,respectively.These results provide a basis for the mechanical analysis of the Yellow River silt subgrades and the subsequent establishment of dynamic constitutive model of the Yellow River silt.展开更多
Fine-grained silt is widely distributed in the Huanghe River Delta(HRD)in China,and the sedimentary structure is complex,meaning that the clay content in the silt is variable.The piezocone penetration test(CPTu)is the...Fine-grained silt is widely distributed in the Huanghe River Delta(HRD)in China,and the sedimentary structure is complex,meaning that the clay content in the silt is variable.The piezocone penetration test(CPTu)is the most widely approved in situ test method.It can be used to invert soil properties and interpret soil behavior.To analyse the strength properties of surface sediments in the HRD,this paper evaluated the friction angle and its inversion formula through the CPTu penetration test and monotonic simple shear test and other soil unit experiments.The evaluation showed that the empirical formula proposed by Kulhawy and Mayne had better prediction and inversion effect.The HRD silts with clay contents of 9.2%,21.4%and 30.3%were selected as samples for the CPTu variable rate penetration test.The results show as follows.(1)The effects of the clay content on the tip resistance and the pore pressure of silt under different penetration rates were summarized.The tip resistance Q_t is strongly dependent on the clay content of the silt,the B_(q)value of the silt tends to 0 and is not significantly affected by the change of the CPTu penetration rate.(2)Five soil behavior type classification charts and three soil behavior type indexes based on CPTu data were evaluated.The results show that the soil behavior type classification chart based on soil behavior type index ISBT,the Robertson 2010 behavior type classification chart are more suitable for the silty soil in the HRD.展开更多
This paper focuses on the development of the mathematical model of shear stress by direct shear test for compressible soil of the littoral region, which will be a great tool in the hand of geotechnical engineers. The ...This paper focuses on the development of the mathematical model of shear stress by direct shear test for compressible soil of the littoral region, which will be a great tool in the hand of geotechnical engineers. The most common use of a shear test is to determine the shear strength which is the maximum shear stress that a material can withstand before the failure occurs. This parameter is useful in many engineering designs such as foundations, roads and retaining walls. We carried out an experimental laboratory test of ten samples of undisturbed soil taken at different points of the border of Wouri river of Cameroon. The samples were collected at different depths and a direct shear test was conducted. The investigations have been performed under constant vertical stresses and constant sample volume with the aim to determine the frictional angle and the cohesion of the compressible soil which are so important to establish the conditions of buildings stability. Special care was taken to derive loading conditions actually existing in the ground and to duplicate them in the laboratory. Given that the buildings constructed in this area are subjected to settlement, landslide, and punch break or shear failure, the cohesion and the frictional angle are determined through the rupture line after assessed the mean values of the shear stress for the considered ten samples. The bearing capacity of the soil, which is the fundamental soil parameter, was calculated. From the laboratory experimental results, the least squared method was used to derive an approximated mathematical model of the shearing stress. Many optimizations methods were then considered to reach the best adjustment.展开更多
It is of great significance for safety reason to obtain the triaxial compressive properties of cemented tailings backfill(CTB).The influence of cement content,curing age and confining pressure on strength and deformat...It is of great significance for safety reason to obtain the triaxial compressive properties of cemented tailings backfill(CTB).The influence of cement content,curing age and confining pressure on strength and deformation properties of CTB was examined and discussed.Results indicate that the triaxial compressive and deformation behavior of CTB is strongly affected by the cement content,curing age and confining pressure.The increase in cement content,curing age and confining pressure leads to a change in stress−strain behavior and an increase in the axial strain at failure and post-peak strength loss.The cohesion of CTB rises as the curing age and cement content increase.However,the enhancement in internal friction angle is trivial and negligible.It should be noted that the failure pattern of CTB samples in triaxial compression is mainly along a shear plane,the confining pressure restrains the lateral expansion and the bulging failure pattern is dominantly detected in CTB samples as curing age length and cement content increase.The results will help to better understand the triaxial mechanical and deformation behavior of CTB.展开更多
This paper aims to study the shear interaction mechanism of one of the critical geosynthetic interfaces,the geotextile/geomembrane, typically used for lined containment facilities such as landfills. A largedirect shea...This paper aims to study the shear interaction mechanism of one of the critical geosynthetic interfaces,the geotextile/geomembrane, typically used for lined containment facilities such as landfills. A largedirect shear machine is used to carry out 90 geosynthetic interface tests. The test results show a strainsoftening behavior with a very small dilatancy （〈0.5 mm） and nonlinear failure envelopes at a normalstress range of 25e450 kPa. The influences of the micro-level structure of these geosynthetics on themacro-level interface shear behavior are discussed in detail. This study has generated several practicalrecommendations to help professionals to choose what materials are more adequate. From the threegeotextiles tested, the thermally bonded monofilament exhibits the best interface shear strength underhigh normal stress. For low normal stress, however, needle-punched monofilaments are recommended.For the regular textured geomembranes tested, the space between the asperities is an important factor.The closer these asperities are, the better the result achieves. For the irregular textured geomembranestested, the nonwoven geotextiles made of monofilaments produce the largest interface shear strength.展开更多
The constant m_(i) in the Hoek-Brown(H-B) criterion is a fundamental parameter required for determining the compressive strength of rock. In this paper, drilling parameters provide a new basis for determining the cons...The constant m_(i) in the Hoek-Brown(H-B) criterion is a fundamental parameter required for determining the compressive strength of rock. In this paper, drilling parameters provide a new basis for determining the constant mi. An analytical relationship between the drilling parameters and constant miis established in consideration of the contact response between the drilling bit and the cut rock in the crushed zone.New models are developed to predict the triaxial compressive strength(TCS), internal friction angle φand cohesion c of rock. Drilling tests are carried out on 6 rock types to study the correlation between φ and m_(i). A comparison between the predicted values of rock mechanical properties and the measured values from the laboratory is performed to verify the accuracy of the proposed model(yielding an error less than 10%). The TCSs and constant m_(i) values of fifteen rocks are cited to validate the accuracy of the proposed model. The result shows that the proposed model predicts the TCS and constant m_(i) within a maximum error of 20%. The method can be conveniently applied to the rock mechanical properties.展开更多
Using a new low-temperature dynamic triaxial apparatus, the influence law of freezing-thawing cycles on clay shear strength is studied. In this research, the concept of correction coefficients of freezing-thawing cycl...Using a new low-temperature dynamic triaxial apparatus, the influence law of freezing-thawing cycles on clay shear strength is studied. In this research, the concept of correction coefficients of freezing-thawing cycles on clay static strength, cohesion and internal friction angles is proposed, and the change patterns, correction curves and regressive formulae of clay static strength, cohesion and internal friction angles under freezing-thawing cycles are given. The test results indicate that with increasing numbers of freezing-thawing cycles, the clay static strength and cohesion decrease exponentially but the internal friction angle increases exponentially. The performance of static strength, cohesion and internal friction angles are different with increasing numbers of freezing-thawing cycles, i.e., the static strength decreases constantly until about 30% of the initial static strength prior to the freezing-thawing cycling and then stays basically stable. After 5-7 freezing-thawing cycles, the cohesion decreases gradually to about 70% of the initial cohesion. The internal friction angle increases about 20% after the first freezing-thawing cycle, then increases gradually close to a stable value which is an increase of about 40% of the internal friction angle. The freezing-thawing process can increase the variation of the density of the soil samples; therefore, strict density discreteness standards of frozen soil sample preparation should be established to ensure the reliability of the test results.展开更多
The effect of geosynthetic reinforcing on bearing capacity of a strip footing resting on georeinforced clayey slopes was investigated.The results of a series of numerical study using finite element analyses on strip f...The effect of geosynthetic reinforcing on bearing capacity of a strip footing resting on georeinforced clayey slopes was investigated.The results of a series of numerical study using finite element analyses on strip footing upon both reinforced and unreinforced clayey slopes were presented.The objectives of this work are to:1) determine the influence of reinforcement on the bearing-capacity of the strip footings adjacent slopes,2) suggest an optimum number of reinforcement and 3) survey the effect of friction angle in clayey soils reinforced by geogrids.The investigations were carried out by varying the edge distance of the footing from slope.Also different numbers of geosynthetic layers were applied to obtaining the maximum bearing capacity and minimum settlement.To achieve the third objective,two different friction angles were used.The results show that the load?settlement behavior and ultimate bearing capacity of footing can be considerably improved by the inclusion of reinforcing layer.But using more than one layer reinforcement,the ultimate bearing capacity does not change considerably.It is also shown that for both reinforced and unreinforced slopes,the bearing capacity increases with an increase in edge distance.In addition,as the soil friction angle is increased,the efficiency of reinforcing reduces.展开更多
The fracture initiation behavior for hydraulic fracturing treatments highlighted the necessity of proposing fracture criteria that precisely predict the fracture initiation type and location during the hydraulic fract...The fracture initiation behavior for hydraulic fracturing treatments highlighted the necessity of proposing fracture criteria that precisely predict the fracture initiation type and location during the hydraulic fracturing process.In the present study,a Mohr-Coulomb criterion with a tensile cut-off is incorporated into the finite element code to determine the fracture initiation type and location during the hydraulic fracturing process.This fracture criterion considers the effect of fracture inclination angle,the internal friction angle and the loading conditions on the distribution of stress field around the fracture tip.The results indicate that the internal friction angle resists the shear fracture initiation.Moreover,as the internal friction angle increases,greater external loads are required to maintain the hydraulic fracture extension.Due to the increased pressure of the injected water,the tensile fracture ultimately determines the fracture initiation type.However,the shear fracture preferentially occurs as the stress anisotropy coefficient increases.Both the maximum tensile stress and equivalent maximum shear stress decrease as the stress anisotropy coefficient increases,which indicates that the greater the stress anisotropy coefficient,the higher the external loading required to propagate a new fracture.The numerical results obtained in this paper provide theoretical supports for establishing basis on investigating of the hydraulic fracturing characteristics under different conditions.展开更多
Mechanical properties of methane hydrate- bearing-sediments （MHBS） are basic parameters for safety analysis of hydrate exploration and exploitation. Young＇s modulus, cohesion, and internal friction angle of hydrate...Mechanical properties of methane hydrate- bearing-sediments （MHBS） are basic parameters for safety analysis of hydrate exploration and exploitation. Young＇s modulus, cohesion, and internal friction angle of hydrate- bearing sediments synthesized in laboratory, are investigated using tri-axial tests. Stress-strain curves and strength parameters are obtained and discussed for different compositions and different hydrate saturation, followed by empirical expressions related to the cohesion, internal friction angle, and modulus of MHBS. Almost all tested MHBS samples exhibit plastic failure. With the increase of total saturation of ice and methane hydrate （MH）, the specimens＇ internal friction angle decreases while the cohesion increases.展开更多
This work presents a study on the behaviors of diatomaceous soils. Although studies are rarely reported on these soils, they have been identified in Mexico City, the Sea of Japan, the northeast coast of Australia,the ...This work presents a study on the behaviors of diatomaceous soils. Although studies are rarely reported on these soils, they have been identified in Mexico City, the Sea of Japan, the northeast coast of Australia,the equatorial Pacific, and the lacustrine deposit of Bogota(Colombia), among other locations. Features of this kind of soil include high friction angle, high initial void ratio, high compressibility index, high liquid limit, and low density. Some of these features are counterintuitive from a classical soil mechanics viewpoint. To understand the geotechnical properties of the diatomaceous soil, a comprehensive experimental plan consisting of more than 2400 tests was performed, including physical tests such as grain size distribution, Atterberg limits, density of solid particles, and organic matter content; and mechanical tests such as oedometric compression tests, unconfined compression tests, and triaxial tests.Laboratory tests were complemented with scanning electron microscope(SEM) observations to evaluate the microstructure of the soil. The test results show that there is an increase in liquid limit with increasing diatomaceous content, and the friction angle also increases with increasing diatomaceous content. In addition, several practical correlations were proposed for this soil type for shear strength mobilization and intrinsic compression line. Finally, useful correlations were presented, such as the relationship between the state consistency and the undrained shear strength, the friction angle and the liquid limit, the void ratio at 100 kPa and the liquid limit, the plasticity index and the diatomaceous content, among others.展开更多
The shear strength and dilatancy of typical uncemented calcareous sand from the South China Sea are investigated by soil lab tests.According to drained triaxial tests at various relative densities and confining stress...The shear strength and dilatancy of typical uncemented calcareous sand from the South China Sea are investigated by soil lab tests.According to drained triaxial tests at various relative densities and confining stresses,it is found that the constant volume friction angle is approximated as 39°and the traditional Bolton’s equations can be modified to estimate the peak friction angle and dilation angle.The reliability of the equation proposed for the peak friction angle is verified in terms of calcareous sands from more onshore and offshore sites worldwide,while the errors of the predicted dilation angles scatter in a relatively large range.Totally,the dilation angles of sands in the South China Sea are estimated by the equation presented with an error of±30%.The peak friction angle measured by the undrained is similar to that by the drained tests as the relative density smaller than 60%,while the former is slightly lower for denser samples.展开更多
Application of cemented rockfilling to underground mining could not be separated from the corresponding backfill’s shear strength properties. The shear of cemented rockfill(CRF)-rock wall and the shear interaction oc...Application of cemented rockfilling to underground mining could not be separated from the corresponding backfill’s shear strength properties. The shear of cemented rockfill(CRF)-rock wall and the shear interaction occurring within CRFs both have some disadvantageous failure chances. In this study,we tried to investigate the complete shear properties of CRFs using direct shear and triaxial tests of cemented granite rockfill. Large-scale triaxial testing was held to accommodate the large CRF sample.Direct shear testing on the prepared flat and smooth surfaces was assessed with brief conversions and their corrections were used to approximate the shear strength envelopes of CRF joint interfaces. Two types of CRFs with the same aggregate size and distribution but different unconfined compressive strengths(UCSs) due to different mixture designs indicated insignificant differences between their basic friction angles, and also their asperity inclination angles. Nevertheless, investigation between direct shear test and triaxial test showed that the specimen with higher UCS tended to have a slightly lower friction angle but a higher cohesion than the other one.展开更多
More accurate and reliable estimation of residual strength friction angle(/r)of clay is crucial in many geotechnical engineering applications,including riverbank stability analysis,design,and assessment of earthen dam...More accurate and reliable estimation of residual strength friction angle(/r)of clay is crucial in many geotechnical engineering applications,including riverbank stability analysis,design,and assessment of earthen dam slope stabilities.However,a general predictive equation for/r,with applicability in a wide range of effective parameters,remains an important research gap.The goal of this study is to develop a more accurate equation for/r using the Pareto Optimal Multi-gene Genetic Programming(POMGGP)approach by evaluating a comprehensive dataset of 290 experiments compiled from published literature databases worldwide.A new framework for integrated equation derivation proposed that hybridizes the Subset Selection of Maximum Dissimilarity Method(SSMD)with Multi-gene Genetic Programming(MGP)and Pareto-optimality(PO)to find an accurate equation for/r with wide range applicability.The final predictive equation resulted from POMGGP modeling was assessed in comparison with some previously published machine learning-based equations using statistical error analysis criteria,Taylor diagram,revised discrepancy ratio(RDR),and scatter plots.Base on the results,the POMGGP has the lowest uncertainty with U95=2.25,when compared with Artificial Neural Network(ANN)(U95=2.3),Bayesian Regularization Neural Network(BRNN)(U95=2.94),Levenberg-Marquardt Neural Network(LMNN)(U95=3.3),and Differential Evolution Neural Network(DENN)(U95=2.37).The more reliable results in estimation of/r derived by POMGGP with reliability 59.3%,and resiliency 60%in comparison with ANN(reliability=30.23%,resiliency=28.33%),BRNN(reliability=10.47%,resiliency=10.39%),LMNN(reliability=19.77%,resiliency=20.29%)and DENN(reliability=27.91%,resiliency=24.19%).Besides the simplicity and ease of application of the new POMGGP equation to a broad range of conditions,using the uncertainty,reliability,and resilience analysis confirmed that the derived equation for/r significantly outperformed other existing machine learning methods,including the ANN,BRNN,LMNN,and DENN equations。展开更多
文摘The accurate prediction of the friction angle of clays is crucial for assessing slope stability in engineering applications.This study addresses the importance of estimating the friction angle and presents the development of four soft computing models:YJ-FPA-MLPnet,YJ-CRO-MLPnet,YJ-ACOC-MLPnet,and YJCSA-MLPnet.First of all,the Yeo-Johnson(YJ)transformation technique was used to stabilize the variance of data and make it more suitable for parametric statistical models that assume normality and equal variances.This technique is expected to improve the accuracy of friction angle prediction models.The friction angle prediction models then utilized multi-layer perceptron neural networks(MLPnet)and metaheuristic optimization algorithms to further enhance performance,including flower pollination algorithm(FPA),coral reefs optimization(CRO),ant colony optimization continuous(ACOC),and cuckoo search algorithm(CSA).The prediction models without the YJ technique,i.e.FPA-MLPnet,CRO-MLPnet,ACOC-MLPnet,and CSA-MLPnet,were then compared to those with the YJ technique,i.e.YJ-FPA-MLPnet,YJ-CRO-MLPnet,YJ-ACOC-MLPnet,and YJ-CSA-MLPnet.Among these,the YJ-CRO-MLPnet model demonstrated superior reliability,achieving an accuracy of up to 83%in predicting the friction angle of clay in practical engineering scenarios.This improvement is significant,as it represents an increase from 1.3%to approximately 20%compared to the models that did not utilize the YJ transformation technique.
基金the financial support from the National Natural Science Foundation of China(Grant Nos.51839003 and 42207221).
文摘Surrounding rocks at different locations are generally subjected to different stress paths during the process of deep hard rock excavation.In this study,to reveal the mechanical parameters of deep surrounding rock under different stress paths,a new cyclic loading and unloading test method for controlled true triaxial loading and unloading and principal stress direction interchange was proposed,and the evolution of mechanical parameters of Shuangjiangkou granite under different stress paths was studied,including the deformation modulus,elastic deformation increment ratios,fracture degree,cohesion and internal friction angle.Additionally,stress path coefficient was defined to characterize different stress paths,and the functional relationships among the stress path coefficient,rock fracture degree difference coefficient,cohesion and internal friction angle were obtained.The results show that during the true triaxial cyclic loading and unloading process,the deformation modulus and cohesion gradually decrease,while the internal friction angle gradually increases with increasing equivalent crack strain.The stress path coefficient is exponentially related to the rock fracture degree difference coefficient.As the stress path coefficient increases,the degrees of cohesion weakening and internal friction angle strengthening decrease linearly.During cyclic loading and unloading under true triaxial principal stress direction interchange,the direction of crack development changes,and the deformation modulus increases,while the cohesion and internal friction angle decrease slightly,indicating that the principal stress direction interchange has a strengthening effect on the surrounding rocks.Finally,the influences of the principal stress interchange direction on the stabilities of deep engineering excavation projects are discussed.
文摘The ruin of several civil engineering works occurs due to shear rupture of the ground. When the stress is greater than the shear resistance, the internal friction angle and the cohesion of the soil loosen and rupture occurs. Cement and lime are often used to stabilize soils and improve soil strength. The costs and environmental problems of these technologies raise concerns and challenge researchers to innovate with clean, inexpensive materials, accessible to the most disadvantaged social classes. The question that this study seeks to answer is whether the binders derived from plant tannins, which also stabilize soils, improve the shear resistance of these soils. To do this, we determined for silty sand the shear parameters, notably the cohesion and the angle of internal friction in the non-stabilized state and when they are stabilized with the powder of the bark of the Bridelia under different water states. The results show that the addition of Bridelia powder to silty sand increases the cohesion of the soil by nearly 70.71% and the friction angle by 4.31%. But in unfavourable water conditions, the cohesion and internal friction angle of the silty sand material improved with Bridelia bark powder drops drastically by nearly 81.56%. but does not dissolve completely as for the same material. When it is not stabilized. This information is an invaluable contribution in the search for solutions to increase the durability of earthen constructions by improving the water-repellent properties of soils.
基金supported by Postdoctoral Fellowship Program funded by the Ministry of Education of the Republic of Korea through the Chungbuk National University in 2020。
文摘Although friction characteristics of fault gouge are important to understand reactivation of fault,behavior of earthquake,and mechanism of slope failure,analysis results of fault gouge have low accuracy mostly than those of soils or rocks due to its high heterogeneity and low strength.Therefore,to improve the accuracy of analysis results,we conducted simple regression analysis and structural equation model analysis and selected major influential factors of friction characteristics among many factors,and then we deduced advanced regression model with the highest coefficient of determination(R^(2)) via multiple regression analysis.Whereas most coefficients of determination in simple regression analysis are below0.3-0.4,coefficient of determination in multiple regression analysis is remarkably large as 0.657.
文摘Severe faults have caused many earthquakes around the world throughout history.More recently,earthquakes have occurred in Taiwan,China(Chi-Chi fault),and elsewhere,causing loss of lives and destroying many buildings and structures.These tectonic movements have gained attention from engineers,and in the past 15 years,the focus has been on faulting mechanisms.In this study,a physical model(1 g)was fabricated and used to evaluate the impact of a reverse fault in a field with a tunnel.In the 1 g model,researchers installed additional gauges on the tunnel,so that all the displacements could be adjusted,and all the responses could be monitored during faulting.An experimental study of various soil properties(cohesion and friction angles)in reverse faults on the tunnel lining were carried out and are described herein.A comparison of results for different levels of soil cohesion revealed that it can dramatically reduce the displacement by as much as 40%,and that friction angles of 27ºcan record approximately 60%more displacements than at 37º.Furthermore,a comparison of fault angles of 30ºand 60ºindicates that the displacements can be different by more than 43%in cohesionless soil and about 64%for a friction angle of 27º.
基金the National Outstanding Youth Science Fund Project of the National Natural Science Foundation of China(Grant No.52022112)the Hunan Provincial Innovation Foundation for Postgraduate of China(Grant No.2020zzts152)are acknowledged.
文摘The shear strength of sand-foam mixtures plays a crucial role in ensuring successful earth pressure balance(EPB)shield tunneling.Since the sand-foam mixtures are constantly sheared by the cutterhead and the screw conveyor with varied rotation speeds during tunneling,it is non-trivial to investigate the effect of shear rates on the undrained shear strength of sand-foam mixtures under chamber pressures to extend the understanding on the tunneling process.This study conducted a series of pressurized vane shear tests to investigate the role of shear rates on the peak and residual strengths of sand-foam mixtures at different pore states.Different from the shear-rate characteristics of natural sands or clay,the results showed that the peak strength of sand-foam mixtures under high vertical total stress(σ_(v)≥200 kPa)and low foam injection ratio(FIR30%)decreased with the increase in shear rate.Otherwise,the peak strength was not measurably affected by shear rates.The sand-foam mixtures in the residual state resembled low-viscous fluid with yield stress and the residual strength increased slightly with shear rates.In addition,the peak and residual strengths were approximately linear with vertical effective stress regardless of the total stress and FIR.The peak effective internal friction angle remained almost invariant in a low shear rate(γ′<0.25 s1)but decreased when the shear rate continued increasing.The residual effective internal friction angle was lower than the peak counterpart and insensitive to shear rates.This study unveiled the role of shear rates in the undrained shear strength of sand-foam mixtures with various FIRs and vertical total stresses.The findings can extend the understanding of the rate-dependent shear characteristics of conditioned soils and guide the decision-making of soil conditioning schemes in the EPB shield tunneling practice.
基金National Natural Science Foundation of China(Grant Nos.5217836952109140)+4 种基金Key Projects of High Schools of Henan province of China(20A560021)Natural Science Foundation of Henan Province of China(202300410424)Youth Talent Promotion Project of Henan Province of China(2021HYTP016)Key Specialized Research and Development Breakthrough in Henan Province of China(212102310977)China Postdoctoral Science Foundation(2019M662533)。
文摘Currently,the application of the Yellow River silt in subgrade,especially in expressway subgrade,has not been widely promoted.The main reason is that the research on the mechanical characteristics of the Yellow River silt used for subgrade filling is extremely limited.In this study,the static shear test of the Yellow River silt under drained condition was carried out using Global Digital Systems(GDS)triaxial apparatus,and the effects of confining pressure,relative density and shear rate on the strength and deformation behavior of the Yellow River silt were investigated.The cohesive force of the Yellow River silt is low,and the friction angle is the main factor determining the shear strength.Friction angle at phase transformation stateφpt,friction angle at peak stateφps,friction angle at critical stateφcs,were obtained via the observation on the evolution law of mobilized friction angle during the whole shearing process.The friction angles corresponding to three different characteristic states have the following magnitude relationship,namelyφps>φcs>φpt.The strength parameters for low-grade subgrade and highgrade subgrade were chosen to be 29.33°and 33.75°.The critical state line(CSL),envelop of phase transformation(EOP),and envelop of dilatancy(EOD)for three different characteristic states were determined.The critical stress ratio M,the phase transformation stress ratio Mptand the dilatancy stress ratio Mdof the Yellow River silt are 1.199,1.235,1.152,respectively.These results provide a basis for the mechanical analysis of the Yellow River silt subgrades and the subsequent establishment of dynamic constitutive model of the Yellow River silt.
基金The National Natural Science Foundation of China under contract No.U2006213。
文摘Fine-grained silt is widely distributed in the Huanghe River Delta(HRD)in China,and the sedimentary structure is complex,meaning that the clay content in the silt is variable.The piezocone penetration test(CPTu)is the most widely approved in situ test method.It can be used to invert soil properties and interpret soil behavior.To analyse the strength properties of surface sediments in the HRD,this paper evaluated the friction angle and its inversion formula through the CPTu penetration test and monotonic simple shear test and other soil unit experiments.The evaluation showed that the empirical formula proposed by Kulhawy and Mayne had better prediction and inversion effect.The HRD silts with clay contents of 9.2%,21.4%and 30.3%were selected as samples for the CPTu variable rate penetration test.The results show as follows.(1)The effects of the clay content on the tip resistance and the pore pressure of silt under different penetration rates were summarized.The tip resistance Q_t is strongly dependent on the clay content of the silt,the B_(q)value of the silt tends to 0 and is not significantly affected by the change of the CPTu penetration rate.(2)Five soil behavior type classification charts and three soil behavior type indexes based on CPTu data were evaluated.The results show that the soil behavior type classification chart based on soil behavior type index ISBT,the Robertson 2010 behavior type classification chart are more suitable for the silty soil in the HRD.
文摘This paper focuses on the development of the mathematical model of shear stress by direct shear test for compressible soil of the littoral region, which will be a great tool in the hand of geotechnical engineers. The most common use of a shear test is to determine the shear strength which is the maximum shear stress that a material can withstand before the failure occurs. This parameter is useful in many engineering designs such as foundations, roads and retaining walls. We carried out an experimental laboratory test of ten samples of undisturbed soil taken at different points of the border of Wouri river of Cameroon. The samples were collected at different depths and a direct shear test was conducted. The investigations have been performed under constant vertical stresses and constant sample volume with the aim to determine the frictional angle and the cohesion of the compressible soil which are so important to establish the conditions of buildings stability. Special care was taken to derive loading conditions actually existing in the ground and to duplicate them in the laboratory. Given that the buildings constructed in this area are subjected to settlement, landslide, and punch break or shear failure, the cohesion and the frictional angle are determined through the rupture line after assessed the mean values of the shear stress for the considered ten samples. The bearing capacity of the soil, which is the fundamental soil parameter, was calculated. From the laboratory experimental results, the least squared method was used to derive an approximated mathematical model of the shearing stress. Many optimizations methods were then considered to reach the best adjustment.
基金Projects(2018YFC0808403,2018YFE0123000)supported by the National Key Technologies Research&Development Program of ChinaProject(800015Z1185)supported by the Yueqi Young Scholar Project,ChinaProject(2020YJSNY04)supported by the Fundamental Research Funds for the Central Universities,China。
文摘It is of great significance for safety reason to obtain the triaxial compressive properties of cemented tailings backfill(CTB).The influence of cement content,curing age and confining pressure on strength and deformation properties of CTB was examined and discussed.Results indicate that the triaxial compressive and deformation behavior of CTB is strongly affected by the cement content,curing age and confining pressure.The increase in cement content,curing age and confining pressure leads to a change in stress−strain behavior and an increase in the axial strain at failure and post-peak strength loss.The cohesion of CTB rises as the curing age and cement content increase.However,the enhancement in internal friction angle is trivial and negligible.It should be noted that the failure pattern of CTB samples in triaxial compression is mainly along a shear plane,the confining pressure restrains the lateral expansion and the bulging failure pattern is dominantly detected in CTB samples as curing age length and cement content increase.The results will help to better understand the triaxial mechanical and deformation behavior of CTB.
基金an extensive research project sponsored by the Company Ferrovial S.A.(Spain)conducted by the Geotechnical Group at the School of Civil Engineering,the University of Cantabria(Spain)
文摘This paper aims to study the shear interaction mechanism of one of the critical geosynthetic interfaces,the geotextile/geomembrane, typically used for lined containment facilities such as landfills. A largedirect shear machine is used to carry out 90 geosynthetic interface tests. The test results show a strainsoftening behavior with a very small dilatancy （〈0.5 mm） and nonlinear failure envelopes at a normalstress range of 25e450 kPa. The influences of the micro-level structure of these geosynthetics on themacro-level interface shear behavior are discussed in detail. This study has generated several practicalrecommendations to help professionals to choose what materials are more adequate. From the threegeotextiles tested, the thermally bonded monofilament exhibits the best interface shear strength underhigh normal stress. For low normal stress, however, needle-punched monofilaments are recommended.For the regular textured geomembranes tested, the space between the asperities is an important factor.The closer these asperities are, the better the result achieves. For the irregular textured geomembranestested, the nonwoven geotextiles made of monofilaments produce the largest interface shear strength.
基金sponsored by the National Natural Science Foundation of China (Nos. 42177158, 11902249 and 11872301)Natural Science Foundation of Shaanxi Province (Shaanxi Province Natural Science Foundation) (No. 2019JQ395)Education Bureau of Shaanxi Province | Scientific Research Plan Projects of Shaanxi Education Department in China (No. 20JS093)。
文摘The constant m_(i) in the Hoek-Brown(H-B) criterion is a fundamental parameter required for determining the compressive strength of rock. In this paper, drilling parameters provide a new basis for determining the constant mi. An analytical relationship between the drilling parameters and constant miis established in consideration of the contact response between the drilling bit and the cut rock in the crushed zone.New models are developed to predict the triaxial compressive strength(TCS), internal friction angle φand cohesion c of rock. Drilling tests are carried out on 6 rock types to study the correlation between φ and m_(i). A comparison between the predicted values of rock mechanical properties and the measured values from the laboratory is performed to verify the accuracy of the proposed model(yielding an error less than 10%). The TCSs and constant m_(i) values of fifteen rocks are cited to validate the accuracy of the proposed model. The result shows that the proposed model predicts the TCS and constant m_(i) within a maximum error of 20%. The method can be conveniently applied to the rock mechanical properties.
基金Scientific Research Fund of Institute of Engineering Mechanics,China Earthquake Administration under Grant No.2018D12National Natural Science Foundation of Heilongjiang Province under Grant No.E 2016045+1 种基金National Natural Science Foundation of China under Grant No.5137816451508140
文摘Using a new low-temperature dynamic triaxial apparatus, the influence law of freezing-thawing cycles on clay shear strength is studied. In this research, the concept of correction coefficients of freezing-thawing cycles on clay static strength, cohesion and internal friction angles is proposed, and the change patterns, correction curves and regressive formulae of clay static strength, cohesion and internal friction angles under freezing-thawing cycles are given. The test results indicate that with increasing numbers of freezing-thawing cycles, the clay static strength and cohesion decrease exponentially but the internal friction angle increases exponentially. The performance of static strength, cohesion and internal friction angles are different with increasing numbers of freezing-thawing cycles, i.e., the static strength decreases constantly until about 30% of the initial static strength prior to the freezing-thawing cycling and then stays basically stable. After 5-7 freezing-thawing cycles, the cohesion decreases gradually to about 70% of the initial cohesion. The internal friction angle increases about 20% after the first freezing-thawing cycle, then increases gradually close to a stable value which is an increase of about 40% of the internal friction angle. The freezing-thawing process can increase the variation of the density of the soil samples; therefore, strict density discreteness standards of frozen soil sample preparation should be established to ensure the reliability of the test results.
文摘The effect of geosynthetic reinforcing on bearing capacity of a strip footing resting on georeinforced clayey slopes was investigated.The results of a series of numerical study using finite element analyses on strip footing upon both reinforced and unreinforced clayey slopes were presented.The objectives of this work are to:1) determine the influence of reinforcement on the bearing-capacity of the strip footings adjacent slopes,2) suggest an optimum number of reinforcement and 3) survey the effect of friction angle in clayey soils reinforced by geogrids.The investigations were carried out by varying the edge distance of the footing from slope.Also different numbers of geosynthetic layers were applied to obtaining the maximum bearing capacity and minimum settlement.To achieve the third objective,two different friction angles were used.The results show that the load?settlement behavior and ultimate bearing capacity of footing can be considerably improved by the inclusion of reinforcing layer.But using more than one layer reinforcement,the ultimate bearing capacity does not change considerably.It is also shown that for both reinforced and unreinforced slopes,the bearing capacity increases with an increase in edge distance.In addition,as the soil friction angle is increased,the efficiency of reinforcing reduces.
基金Project(2017YFC1503102)supported by the National Key Research and Development ProgramProjects(51874065,U1903112)supported by the National Natural Science Foundation of China。
文摘The fracture initiation behavior for hydraulic fracturing treatments highlighted the necessity of proposing fracture criteria that precisely predict the fracture initiation type and location during the hydraulic fracturing process.In the present study,a Mohr-Coulomb criterion with a tensile cut-off is incorporated into the finite element code to determine the fracture initiation type and location during the hydraulic fracturing process.This fracture criterion considers the effect of fracture inclination angle,the internal friction angle and the loading conditions on the distribution of stress field around the fracture tip.The results indicate that the internal friction angle resists the shear fracture initiation.Moreover,as the internal friction angle increases,greater external loads are required to maintain the hydraulic fracture extension.Due to the increased pressure of the injected water,the tensile fracture ultimately determines the fracture initiation type.However,the shear fracture preferentially occurs as the stress anisotropy coefficient increases.Both the maximum tensile stress and equivalent maximum shear stress decrease as the stress anisotropy coefficient increases,which indicates that the greater the stress anisotropy coefficient,the higher the external loading required to propagate a new fracture.The numerical results obtained in this paper provide theoretical supports for establishing basis on investigating of the hydraulic fracturing characteristics under different conditions.
基金supported by the National Natural Science Foundation of China (11102209 and 11072245)the National High Technology Research and Development Program of China (863)the Key Program of Chinese Academy of Sciences (KJCX2-YW-L02)
文摘Mechanical properties of methane hydrate- bearing-sediments （MHBS） are basic parameters for safety analysis of hydrate exploration and exploitation. Young＇s modulus, cohesion, and internal friction angle of hydrate- bearing sediments synthesized in laboratory, are investigated using tri-axial tests. Stress-strain curves and strength parameters are obtained and discussed for different compositions and different hydrate saturation, followed by empirical expressions related to the cohesion, internal friction angle, and modulus of MHBS. Almost all tested MHBS samples exhibit plastic failure. With the increase of total saturation of ice and methane hydrate （MH）, the specimens＇ internal friction angle decreases while the cohesion increases.
文摘This work presents a study on the behaviors of diatomaceous soils. Although studies are rarely reported on these soils, they have been identified in Mexico City, the Sea of Japan, the northeast coast of Australia,the equatorial Pacific, and the lacustrine deposit of Bogota(Colombia), among other locations. Features of this kind of soil include high friction angle, high initial void ratio, high compressibility index, high liquid limit, and low density. Some of these features are counterintuitive from a classical soil mechanics viewpoint. To understand the geotechnical properties of the diatomaceous soil, a comprehensive experimental plan consisting of more than 2400 tests was performed, including physical tests such as grain size distribution, Atterberg limits, density of solid particles, and organic matter content; and mechanical tests such as oedometric compression tests, unconfined compression tests, and triaxial tests.Laboratory tests were complemented with scanning electron microscope(SEM) observations to evaluate the microstructure of the soil. The test results show that there is an increase in liquid limit with increasing diatomaceous content, and the friction angle also increases with increasing diatomaceous content. In addition, several practical correlations were proposed for this soil type for shear strength mobilization and intrinsic compression line. Finally, useful correlations were presented, such as the relationship between the state consistency and the undrained shear strength, the friction angle and the liquid limit, the void ratio at 100 kPa and the liquid limit, the plasticity index and the diatomaceous content, among others.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.U1806230 and 42025702).
文摘The shear strength and dilatancy of typical uncemented calcareous sand from the South China Sea are investigated by soil lab tests.According to drained triaxial tests at various relative densities and confining stresses,it is found that the constant volume friction angle is approximated as 39°and the traditional Bolton’s equations can be modified to estimate the peak friction angle and dilation angle.The reliability of the equation proposed for the peak friction angle is verified in terms of calcareous sands from more onshore and offshore sites worldwide,while the errors of the predicted dilation angles scatter in a relatively large range.Totally,the dilation angles of sands in the South China Sea are estimated by the equation presented with an error of±30%.The peak friction angle measured by the undrained is similar to that by the drained tests as the relative density smaller than 60%,while the former is slightly lower for denser samples.
基金the University of Alberta Mining Department teams for their support and guidancethe Indonesia Endowment Fund for Education scholarship (Grant No. 20151112014754/LPDP/2015) for the authors’ financial assistance
文摘Application of cemented rockfilling to underground mining could not be separated from the corresponding backfill’s shear strength properties. The shear of cemented rockfill(CRF)-rock wall and the shear interaction occurring within CRFs both have some disadvantageous failure chances. In this study,we tried to investigate the complete shear properties of CRFs using direct shear and triaxial tests of cemented granite rockfill. Large-scale triaxial testing was held to accommodate the large CRF sample.Direct shear testing on the prepared flat and smooth surfaces was assessed with brief conversions and their corrections were used to approximate the shear strength envelopes of CRF joint interfaces. Two types of CRFs with the same aggregate size and distribution but different unconfined compressive strengths(UCSs) due to different mixture designs indicated insignificant differences between their basic friction angles, and also their asperity inclination angles. Nevertheless, investigation between direct shear test and triaxial test showed that the specimen with higher UCS tended to have a slightly lower friction angle but a higher cohesion than the other one.
文摘More accurate and reliable estimation of residual strength friction angle(/r)of clay is crucial in many geotechnical engineering applications,including riverbank stability analysis,design,and assessment of earthen dam slope stabilities.However,a general predictive equation for/r,with applicability in a wide range of effective parameters,remains an important research gap.The goal of this study is to develop a more accurate equation for/r using the Pareto Optimal Multi-gene Genetic Programming(POMGGP)approach by evaluating a comprehensive dataset of 290 experiments compiled from published literature databases worldwide.A new framework for integrated equation derivation proposed that hybridizes the Subset Selection of Maximum Dissimilarity Method(SSMD)with Multi-gene Genetic Programming(MGP)and Pareto-optimality(PO)to find an accurate equation for/r with wide range applicability.The final predictive equation resulted from POMGGP modeling was assessed in comparison with some previously published machine learning-based equations using statistical error analysis criteria,Taylor diagram,revised discrepancy ratio(RDR),and scatter plots.Base on the results,the POMGGP has the lowest uncertainty with U95=2.25,when compared with Artificial Neural Network(ANN)(U95=2.3),Bayesian Regularization Neural Network(BRNN)(U95=2.94),Levenberg-Marquardt Neural Network(LMNN)(U95=3.3),and Differential Evolution Neural Network(DENN)(U95=2.37).The more reliable results in estimation of/r derived by POMGGP with reliability 59.3%,and resiliency 60%in comparison with ANN(reliability=30.23%,resiliency=28.33%),BRNN(reliability=10.47%,resiliency=10.39%),LMNN(reliability=19.77%,resiliency=20.29%)and DENN(reliability=27.91%,resiliency=24.19%).Besides the simplicity and ease of application of the new POMGGP equation to a broad range of conditions,using the uncertainty,reliability,and resilience analysis confirmed that the derived equation for/r significantly outperformed other existing machine learning methods,including the ANN,BRNN,LMNN,and DENN equations。
