Triangular Area Research Articles

<p class="Body"><strong>A new species of <em>Pergalumna</em> (Acari: Oribatida: Galumnidae) from southeastern Iran, including a key to all species of the genus from the Palaearctic region</strong></p>

A new species of oribatid mite of the family Galumnidae, Pergalumna sistanbaluchestanica sp. nov., is described and illustrated based on adult specimens from soil in Sistan and Baluchestan province, southeastern Iran. The new species is characterized by dentate rostrum; long interlamellar setae; long, setiform, finely barbed bothridial setae; complete dorsosejugal furrow; large, nearly triangular porose areas Aa; presence of median pore in females and males; large, elongated postanal porose area and large body size. The new species is most similar morphologically to P. seminervosa Mahunka & Mahunka-Papp, 2008, however, differs from it in morphology of bothridial setae and notogastral porose areas Aa and also by the surface ornamentation of the pteromorphs and genital plates; localization of setal alveoli la and lyrifissures im and body size. An identification key to known species of Pergalumna from the Palaearctic region is given.

Cranio-Vertebral Junction Triangular Area: Quantification of Brain Stem Compression by Magnetic Resonance Images.

(1) Background: Most of the currently used radiological criteria for craniovertebral junction (CVJ) were developed prior to the popularity of magnetic resonance images (MRIs). This study aimed to evaluate the efficacy of a novel triangular area (TA) calculated on MRIs for pathologies at the CVJ. (2) Methods: A total of 702 consecutive patients were enrolled, grouped into three: (a) Those with pathologies at the CVJ (n = 129); (b) those with underlying rheumatoid arthritis (RA) but no CVJ abnormalities (n = 279); and (3) normal (control; n = 294). TA was defined on T2-weighted MRIs by three points: The lowest point of the clivus, the posterior-inferior point of C2, and the most dorsal indentation point at the ventral brain stem. Receiver operating characteristic (ROC) analysis was used to correlate the prognostic value of the TA with myelopathy. Pre- and post-operative TA values were compared for validation. (c) Results: The CVJ-pathology group had the largest mean TA (1.58 ± 0.47 cm2), compared to the RA and control groups (0.96 ± 0.31 and 1.05 ± 0.26, respectively). The ROC analysis calculated the cutoff-point for myelopathy as 1.36 cm2 with the area under the curve at 0.93. Of the 81 surgical patients, the TA was reduced (1.21 ± 0.37 cm2) at two-years post-operation compared to that at pre-operation (1.67 ± 0.51 cm2). Moreover, intra-operative complete reduction of the abnormalities could further decrease the TA to 1.03 ± 0.39 cm2. (4) Conclusions: The TA, a valid measurement to quantify compression at the CVJ and evaluate the efficacy of surgery, averaged 1.05 cm2 in normal patients, and 1.36 cm2 could be a cutoff-point for myelopathy and of clinical significance.

A redescription of Kunpania scopulusa, a bidentalian dicynodont (Therapsida, Anomodontia) from the ?Guadalupian of northwestern China

ABSTRACT Permian dicynodonts were discovered in strata exposed on the flanks of the Bogda Mountains (Xinjiang, China) in 1928. Nearly all known specimens were collected in the Guodikeng Formation (= upper Wutonggou low-order cycle); the single exception is the holotype of Kunpania scopulusa, which originated in the underlying Quanzijie Formation. The Quanzijie Formation is generally considered Capitanian in age, which would make Kunpania one of the oldest known bidentalian dicynodonts, but the type of K. scopulusa has received little attention. Here we redescribe K. scopulusa and investigate its phylogenetic relationships. Kunpania scopulusa is a valid species diagnosed by the absence of anterior palatal ridges; a robust crista oesophagea; a prominent lateral dentary shelf; a posteriorly curving projection on the angular; and a large, triangular attachment area for M. latissimus dorsi on the humerus. Our phylogenetic analysis recovered K. scopulusa as a stemward member of Dicynodontoidea and the sister taxon of the South African species Sintocephalus alticeps. Depending on the precise age of the uppermost Quanzijie Formation, three scenarios describe the potential phylogenetic implications of K. scopulusa: (1) bidentalian dicynodonts diversified before the end-Guadalupian extinction, with little of their early history preserved; (2) the main diversifications of cryptodont and dicynodontoid bidentalians occurred in the aftermath of the end-Guadalupian extinction, with K. scopulusa representing the latter; (3) K. scopulusa is a contemporary of other mid–late Wuchiapingian dicynodontoids and the initial radiation of Dicynodontoidea is not preserved in the known fossil record.

Deep Anti-Aliasing of Whole Focal Stack Using Slice Spectrum

The paper aims at removing the aliasing effects of the whole focal stack generated from a sparse-sampled 4D light field, while keeping the consistency across all the focal layers. We first explore the structural characteristics embedded in the focal stack slice and its corresponding frequency-domain representation, i.e., the Focal Stack Spectrum (FSS). We observe that the energy distribution of the FSS always resides within the same triangular area under different angular sampling rates, additionally, the continuity of the Point Spread Function (PSF) is intrinsically maintained in the FSS. Based on these two observations, we propose a learning-based FSS reconstruction approach for one-time aliasing removing over the whole focal stack. Moreover, a novel conjugate-symmetric loss function is proposed for the optimization. Compared to previous works, our method avoids an explicit depth estimation, and can handle challenging large-disparity scenarios. Experimental results on both synthetic and real light field datasets show the superiority of the proposed approach for different scenes and various angular sampling rates.

Sheath of distal tendon of semimembranosus muscle and it's functional significance

Introduction: Semimembranosus (SM) muscle is important in maintaining the stability of knee joint, and the distal end of it's tendon is not only complex but has been described differently in the available literature, which is quite perplexing. How a muscle with such divergent attachments can efficiently perform it's functions? Hence a detailed study of the distal semimembranosus tendon unit was undertaken. Material and Methods: One hundred lower limbs (Rt-50; lt.-50) were utilized for the present study. The posterior surface of SM was exposed and as the main tendon could not be traced to its insertion hence a vertical incision was made on the posterior surface of this tendon and this lead to the splitting of the tendon-sheath which exposed the thick shining distal tendon of SM. Results: Surprisingly, it was found that the main tendon of the SM (SMT) was surrounded by a fibrous sheath which was derived from the main muscle mass in the lower part of the thigh and in the majority of cases it was separated from it by a synovial space. Traced inferiorly it was observed that it is the sheath that spreads out to various divergent destinations described in the literature, whereas the main tendon gets attached to the groove on the posterior aspect of the medial condyle of tibia and a rough triangular area below the groove. Discussion and Conclusion: It is the nature's ingenuity that a single muscle with such divergent distal attachments can still efficiently perform its functions due to the formation of a sheath of distal tendon of SM.

Utilização de Medidas Lineares da Epífise Proximal de Tíbias Secas de Adultos na Estimativa do Sexo e Idade

A partir de exames periciais, o procedimento na identificação de pessoas tem sido relevante no que diz respeito ao esclarecimento de fatos no âmbito jurídico-social. O objetivo deste estudo é verificar o dimorfismo sexual e estimar a idade, examinando tíbias secas através de medidas lineares. Foram utilizadas 161 tíbias secas, sendo 63 do sexo feminino e 98 do sexo masculino, todas maiores de 20 anos de idade. Para o presente estudo foram tomadas as seguintes medidas lineares: distância côndilo medial ao côndilo lateral (cmcl), distância côndilo medial à tuberosidade tibial (cmt), distância côndilo lateral à tuberosidade tibial (clt) e uma área triangular a partir destas medidas (at). A análise de variância dos dados mostrou que os indivíduos do sexo masculino apresentaram médias das variáveis maiores que as do sexo feminino. De acordo com o teste t, ocorreu diferença significativa entre as médias de todas as variáveis (p:<0,0001). Através da Análise Discriminante houve índice de acerto da ordem de 76,60% para o sexo feminino e 66,33% para o sexo masculino, apresentando uma taxa total de acertos de 71,47%. Pela regressão logística, foi atingido um índice de concordância de 78,6%. De acordo com os dados, foi constatado que o modelo de predição da idade não foi significativo para as variáveis estudadas (p: 0,1358). Concluiu-se que a metodologia aplicada possa contribuir para o sucesso de pesquisas que norteiam a investigação do sexo e idade dentro do âmbito da Medicina Legal, principalmente ao ser associada com outras técnicas existentes na literatura.

Numerical Prediction of Hydrodynamic Performance of Planing Trimaran with a Wave-Piercing Bow

The central hull is the most important structure in the planing trimaran. In order to gain insight into the relationship between hydrodynamic performance and main hull shape, experimental tests and numerical simulations were carried out for volume Froude Number (FrΔ) ranging from 1.31 to 4.98. Dynamic sinkage and trim in the Dynamic Fluid Body Interaction (DFBI) six-degree-of-freedom model were considered. A validation study carried out by comparison of experimental test results with numerical results showed good consistency. To analyze the process of tunnel penetration and pressure change at the bottom of the boat, numerical simulation results for free surface, bottom streamline, and pressure distribution around the hull are given. A large triangular high-pressure area was observed in the front of the main hull for all volume Froude numbers. Consequently, the central drainage body, in reference to the profile of single planing craft with distinctive resistance performance, was redesigned into a wave-piercing shape. Total resistance, sinkage, and trim angle of the new model were then predicted by numerical method. The results show that the central drainage body has a significant impact on the hydrodynamic performance of the planing trimaran. Furthermore, the wave-piercing shaped main hull has a drag reduction effect.

Numerical Simulation of Explosion of Late-excavated Tunnel Parts of Double-arch Tunnel without Middle Drift

Compared with the construction method of a tunnel with a middle drift, the construction method of a tunnel without a middle drift is a more advanced, novel, efficient, and energy efficient. Moreover, the blasting excavation of late-excavated tunnel parts exerts a vibration impact on the lining structure of early excavated tunnel parts. To analyze and predict the influence of late-excavated tunnel blasting on an early excavated tunnel and surrounding rocks in a triangular area, this study uses the Ansys LS-DYNA software to build a three-dimensional tunnel model simulating multihole blasting and the fluid–solid interaction method to assess the interaction of different materials. In addition, the different working conditions of surrounding rock levels and explosive equivalents are simulated. The distribution law of peak particle vibration velocity and maximum principal stress peak value of surrounding rocks and the lining along the transverse and longitudinal directions of the early excavated tunnel are generalized based on the numerical simulation results. The influence of the blasting of a late-excavated tunnel on the initial lining, secondary lining, and the middle triangular area of a double-arch tunnel is analyzed. The relationship between the surrounding rock level, explosive equivalent, and vibration velocity peak value is concluded. The field experiment-measured vibration velocities from the double-arch tunnel without a middle drift in the Chenjiachong tunnel of the Chuyao expressway in Yunnan Province, China, are in satisfactory agreement with the numerical simulation results. The results of this study are verified by the field blasting vibration data of the Chenjiachong and Changba tunnels and can provide reference and guidance for the blasting engineering practices of late-excavated double-arch tunnels without a middle drift.

Articulatory activity of the tongue, jaw, and lips during the second passaggio acoustic transition of female singers

Sopranos typically exhibit an acoustic modification between 600 and 700 Hz (on /a/) during which second resonance (R2) tracking of the second harmonic (2fo) changes to first resonance (R1) tracking of the fundamental (fo). To quantify the alteration, the sound pressure level difference between the first two harmonics (L1-L2) was measured for chromatic scales sung between C5◻ and G5◻ (523 to 784 Hz) by 17 sopranos (9 judged by the first author as “techniqued” and 8 as “un-techniqued” and confirmed by perceptual experiment). Techniqued sopranos shifted from negative to positive values of L1-L2 as early as D5◻ (587 Hz), while the least techniqued singers did not make the change at all. Articulatory correlates were measured using ultrasound of the tongue and optical tracking. Head-corrected tongue contours showed the most critical articulatory factor to be the size of a triangular area between two points on the hard palate and the most anterior tongue point. Sopranos who made the change earliest exhibited the largest anterior oral cavities whereas sopranos who never made the acoustic change had significantly smaller anterior cavities. Larger anterior oral cavities appear to accommodate lower frequencies of R2, presumably lowering L2 and increasing L1-L2. [Work supported by NIH grant DC-002717.]

Specific Formation of the Bermuda and Dragon Triangles as a Result of a Change in the Axis of the Earth’s Rotation

The Bermuda Triangle is located in the area of the archipelago between North and South America and the Dragon Triangle is located in the area of the archipelago in Southeast Asia. There is a great resemblance between these two triangular areas; both were formed following special geological and tectonic conditions. It is herein proposed that their creation stems from the change in location of the axis of rotation of the earth and, accordingly, the change in the location of the equator.

Numerical study on strength and failure characteristics of rock samples with different hole defects

In a rock mass, holes of various sizes and geometries naturally occur, which in turn can affect the mechanical properties of the rock mass. These defects often cause engineering problems in subsurface construction. In this study, PFC2D was used to perform uniaxial compression tests on a rock mass containing ten different types of hole defects to analyze their failure behavior and mechanical properties. Four failure modes were determined, and crack propagation and stress field evolution were studied. The results show that the hole defect reduces the uniaxial compressive strength, peak strain, and elastic modulus of a rock mass. Also, these defects accelerate the generation of cracks and promote the destruction of the rock. The failure modes can be classified as Y-type, inverted Y-type, upper left to lower right type, and upper right to lower left type. Before cracks are generated, the compressive stress concentration area is located on the left and right sides of the hole and distributed as a butterfly shape, and the tensile stress concentration area is located in the upper and lower parts of the hole. A zone where stress is decreasing is located near the tip of the tensile stress triangular area. The magnitude and concentration area of compressive and tensile stresses are greatly affected by various hole geometries. Finally, the maximum principal compressive stress decreases instantly after a crack coalesces. Overall, the hole shape has a noticeable influence on the stress distribution surrounding the hole, and a hole defect reduces the degree of failure of a rock mass.

Screw dislocations on pyramidal planes induced by Vickers indentation in HVPE GaN

The dislocation structure around the Vickers indentation on a hydride vapor-phase epitaxy GaN wafer was observed by multi-photon photoluminescence imaging and cross-sectional scanning transmission electron microscopy. Straight dislocation lines parallel to the six equivalent directions, i.e. a rosette pattern, were observed in the subsurface. Below the rosette pattern, a flower-like pattern similar to dislocation loops expanded in the six equivalent directions. Under the flower-like pattern, an inverted triangular dark area composed of dislocations on pyramidal planes was observed. This structure did not vary with load (20–980 mN) or crack formation. The inverted triangular dark area contained screw dislocations with a slip system and an estimated density of 2 × 109 cm−2. The penetration depth of the screw dislocation on the pyramidal plane was found to be proportional to the length of the diagonal indentation line.

A rock mechanics calculation model for identifying bed separation position and analyzing overburden breakage in mining

During coal seam mining, the overlying rock can deform, break, and produce a large number of fractures, including horizontal and vertical fractures; the horizontal fractures are also known as bed separation. A bed separation water disaster (BSWD) is a destructive release of roof water, and preventing BSWDs requires accurate location of bed separation positions. A calculation model for overburden deformation and fracture analysis during mining is therefore needed. First, the deformation and breakage area of overlying rock above an active mining face were reduced to a triangular overburden deformation area (TODA), based on the results of similar material simulation experiments. Second, the hierarchy comparison merging method (HCMM) was proposed to analyze the combination and separation of rock layers in the overlying strata. The triangular calculation model (TCM), which can be used to identify bed separation locations and analyze overlying strata breakage, was then obtained by combining TODA with HCMM, and the discriminant principle and related calculation formulas of the model were given. Finally, the model was applied and validated using a mining case, showing that the TCM is a practical tool for analyzing bed separation position and overburden breakage during mining.

Conservation recommendations for Oryza rufipogon Griff. in China based on genetic diversity analysis

Over the past 30 years, human disturbance and habitat fragmentation have severely endangered the survival of common wild rice (Oryza rufipogon Griff.) in China. A better understanding of the genetic structure of O. rufipogon populations will therefore be useful for the development of conservation strategies. We examined the diversity and genetic structure of natural O. rufipogon populations at the national, provincial, and local levels using simple sequence repeat (SSR) markers. Twenty representative populations from sites across China showed high levels of genetic variability, and approximately 44% of the total genetic variation was among populations. At the local level, we studied fourteen populations in Guangxi Province and four populations in Jiangxi Province. Populations from similar ecosystems showed less genetic differentiation, and local environmental conditions rather than geographic distance appeared to have influenced gene flow during population genetic evolution. We identified a triangular area, including northern Hainan, southern Guangdong, and southwestern Guangxi, as the genetic diversity center of O. rufipogon in China, and we proposed that this area should be given priority during the development of ex situ and in situ conservation strategies. Populations from less common ecosystem types should also be given priority for in situ conservation.

Effect of porous Cu addition on the microstructure and mechanical properties of SnBi-xAg solder joints

The effects of porous copper (P-Cu) on the microstructure, hardness, and shear strength of SnBi, SnBi-0.4Ag, and SnBi-1Ag solder joints were investigated in this paper. The experimental results show that P-Cu frames distribute in the solder bulks and form triangular areas. The addition of P-Cu leads to the microstructural refinement in the enclosed areas by the P-Cu frames in the solder bulks. The average hardness here is increased due to the fine grain strengthening mechanism. The SnBi-1Ag@P-Cu solder bulk shows smaller Bi-rich grains but larger β-Sn dendrites than the other two P-Cu-enhanced solder bulks. Porous Cu exists as a frame structure in the solder joints, which hinders the initiation and propagation of cracks and has a positive effect on the improvement of joint strength. Compared to the SnBi and SnBiAg solder joints, the shear strength of the P-Cu-enhanced solder joints is increased by 15%. The average shear strength of the SnBi-0.4Ag@P-Cu solder joint is 79.34 MPa, which is the highest among all the solder joints investigated in this study.

Scale Dependence of Waviness and Unevenness of Natural Rock Joints through Fractal Analysis

The scale dependence of surface roughness is critical in characterising the hydromechanical properties of field-scale rock joints but is still not well understood, particularly when different orders of roughness are considered. We experimentally reveal the scale dependence of two-order roughness, i.e., waviness and unevenness through fractal parameters using the triangular prism surface area method (TPM). The surfaces of three natural joints of granite with the same dimension of 1000 mm×1000 mm are digitised using a 3D laser scanner at three different measurement resolutions. Waviness and unevenness are quantitatively separated by considering the area variation of joint surface as grid size changes. The corresponding fractal dimensions of waviness and unevenness in sampling window sizes ranging from 100 mm×100 mm to 1000 mm×1000 mm at an interval of 100 mm×100 mm are determined. We find that both the fractal dimensions of waviness and unevenness vary as the window size increases. No obvious stationarity threshold has been found for the three rock joint samples, indicating the surface roughness of natural rock joints should be quantified at the scale of the rock mass in the field.

"Trazar una bóveda cónica cuadrada" La trompa volada de Tomás Vicente Tosca

<div data-canvas-width="82.4750337835114"><p>The squinches isa very versatile construction type in the field of stonework. It is defined in its most elementary case as the covering of a triangular area with a conical surface, but, nevertheless, there are an infinite number of variants increasing the complexity of the layout and its execution.The studied case in this paper is the development of the layout of the "square conical vault" (actually, a cantilevered vault), in the treatise on stonework by Tomás Vicente Tosca, published in 1727. This author's work reflectsthe tradition of the local area (which comes mainly from the brilliant episode of the 15th century in Valencia), but it is also part of the pre-illustrated cultural trends of the time. The traces that appear are the result of combining ancient graphic habits with the development, to a certain extent, already scientific, of geometry and mathematics.All this leads, in the case of the "conical-square vault", to the development of a fundamentally descriptive trace, result of a mentality that is more analytical than practical, but that does not manage to emancipate itself from the old building tradition, as this study makes evident, and also the detected graphic habits.The research is also based on other examples of a documentary nature, such as the cantilevered domes of Vandelvira, Philibert de l'Orme, Gelabert, and on a built example; the squinch of the palace of the Generalitat de Valencia.</p></div><div data-canvas-width="145.94326164079826"> </div>

Extended Level IV Neck Dissection for Limited Prophylactic Clearance of Level V in Node-Positive Papillary Thyroid Carcinoma: a Homogenous Study Population.

There is near consensus that prophylactic lateral neck dissection has no role in the management of differentiated thyroid cancer, but the extent of lateral neck dissection in differentiated thyroid cancer remains controversial, especially whether level V should be addressed or not. There is lot of heterogeneity in reporting of the management of level V in papillary thyroid cancer. We at our Institute address the lateral neck positive papillary thyroid cancer with selective neck dissection involving levels II-IV, performing extended level IV dissection with inclusion of the triangular area delineated by the sternocleidomastoid muscle, the clavicle, and the perpendicular line drawn to the clavicle from the point where the horizontal line at the level of cricoid cuts the posterior border of sternocleidomastoid muscle. Retrospective analysis of the departmental data set related to thyroidectomy with lateral neck dissection from 2013 to mid-2019 for papillary thyroid cancer, was carried out. Patients with recurrent papillary thyroid cancer were excluded as were patients with involvement of level V. Data related to the demography of patients, histological diagnosis, and postoperative complications were compiled and summarized. Note was made of the incidence of ipsilateral neck recurrence and the neck level involved with recurrence noted. Data was analyzed for fifty-two patients of non-recurrent papillary thyroid cancer who had undergone total thyroidectomy and lateral neck dissection involving levels II-IV, with extended dissection at level IV. It should be noted that none of the patients had clinical involvement of level V. Only two patients had lateral neck recurrence, both the recurrences were in level III, one on the ipsilateral side and the other on the contralateral side. Recurrence in the central compartment was noted in two patients, with one of these patients also having ipsilateral level III recurrence. One of the patients had distal metastasis to the lungs. Transient paresis of the unilateral vocal cords was noted in seven patients which got resolved within 2months in all of them. Transient hypocalcemia was noted in four patients. Although our series has a small sample size with limited follow-up, it is one of the few studies in which prophylactic level V dissection has been studied in a homogenous study population of non-recurrent papillary thyroid cancer. Our study has shown that prophylactic dissection of level V may have a limited role, but further large multi-institutional studies need to be carried out to come up with a definite answer.

Statistical modeling of longitudinal medical cost trajectory: renal cell cancer care cost analyses.

Estimating the current cost of cancer care is important to health policy makers. An indispensable step in cost projection is to estimate cost trajectories from an incident cohort of cancer patients using longitudinal medical cost data, accounting for terminal events such as death, and right censoring due to loss of follow-up. Since the cost of cancer care and survival are correlated, a scientifically meaningful quantity for inference in this context is the mean cost trajectory conditional on survival. We propose a two-stage semiparametric approach to estimate the longitudinal cost trajectories from a joint model of longitudinal medical costs and survival. The longitudinal cost trajectories corresponding to various survival times form a bivariate surface in a triangular area. The cost trajectories are estimated using the tensor products of discretized measurement time and survival, as well as effective ridge penalties for data in 2D arrays. The proposed approach balances the practical considerations of model flexibility, statistical efficiency, and computational tractability. We used the proposed method to estimate the cost trajectories of renal cell cancer patients using the Surveillance, Epidemiology, and End Results-Medicare linked database.

Computation of direction dependent joint surface parameters through the algorithm of triangular prism surface area method: A theoretical and experimental study

Grasselli’s (2001) methodology on the quantification of the “shear-induced potential contact zones” is fundamentally very strong at properly dealing with the physics of the shear phenomenon. However, the high precision measurement system and the triangulation algorithm he used may not be easily accessible for everyone due to its industrial characteristics. Therefore, a simple technique called “the modified shear-induced potential contact zones” is introduced in the present work. By executing this technique on the surface coordinates of a large number of rock joints digitized through a specially developed mechatronic surface scanning device, “maximum possible and total potential contact areas” (A0 and Aθ*) and “directional surface parameters” (θ*max: maximum apparent dip angle, c2 : shape parameter, θ*max/c2 : change of angularity) are calculated in a specified direction. Ratio A0/c2 is proposed for a new directional roughness parameter. Surface roughness is also characterized by fractal dimension (Dtp), alternatively. Using a specially developed shear box, shear tests are performed in the direction of parameter calculation. Then, by a series of quantitative comparisons between the directional surface parameters and both the fractal dimensions and the shear strengths, the ability of the parameters to relate with the surface roughness and the shear strength is examined. In general, the results are satisfactory for the reliability of the modified technique. The main advantage of the introduced technique is its algorithmic simplicity facilitating direct applicability for basic 2D data sets, [z = f (x, y)], which can be practically acquired via easily accessible and cost-effective surface measurement systems. Additionally, another simple recipe is also introduced predicting contact zones visually prior to shearing. Then, total potential contact areas predicted in the shear direction are visually compared with the actual images of contacts observed in the tests. The best match is obtained when the threshold apparent inclination (θ*cr) is chosen equal to the experimental dilation angle (id) unique for the applied normal load. This clearly proves the validity of Grasselli’s (2001) “threshold apparent dip angle” concept.