• Geomechanics and Engineering
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• 제18권3호
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• pp.225-234
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• 2019

A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass is investigated, which is compatible with Mohr-Coulomb and generalized Hoek-Brown failure criteria. Based on finite difference method, plastic region is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium and compatibility equations, the material parameters of the rock or soil mass are assumed to be the same in each ring. For the strain-softening behavior, the strength parameters are assumed to be a linear function of deviatoric plastic strain (${\gamma}p^*$) for each ring. Increments of stress and strain for each ring are calculated with the finite difference method. Assumptions of large-strain for soil mass and small-strain for rock mass are adopted, respectively. A new numerical stepwise approach for limited pressure and plastic radius are obtained. Comparisons are conducted to validate the correctness of the proposed approach with Vesic's solution (1972). The results show that the perfectly elasto-plastic model may underestimate the displacement and stresses in cavity expansion than strain-softening coefficient considered. The results of limit expansion pressure based on the generalised H-B failure criterion are less than those obtained based on the M-C failure criterion.

• 한국지반공학회논문집
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• 제35권11호
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• pp.63-74
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• 2019

동적원심모형 시험 결과를 기준으로 액상화모델과 응답이력해석 절차에 대한 검증을 시행하였다. 사용된 동적원심모형시험 결과는 LEAP-2017(Liquefaction Experiments Analysis Project)의 일환으로 시행된 결과이다. 시험을 위한 모형지반은 오타와 F-65모래를 이용하여 강성토조 내부 수면아래 상대밀도 55%, 표면경사 5°로 조성되었다. 진폭이 변화하는 주파수 1Hz 사인파형 입력운동을 강성토조 하단에 가진하였다. 수치해석은 원심모형시험의 원형스케일에 대해서 2차원 유한차분 해석기법을 이용하여 수행되었다. 지반은 전단파괴 이전 이력감쇠를 나타내며 전단 파괴기준은 Mohr-Coulomb 모델을 따르도록 모델링 되었다. 정적평형 후 반복하중으로 인한 간극수압의 변화를 묘사하기 위하여 Byrne의 액상화 모델을 적용하였다. 액상화 해석에 적합한 흐름조건을 확인을 위하여 수치해석은 배수 및 비배수 조건으로 시행하였으며, 비배수 해석조건에서 시행된 수치해석결과가 원심모형시험과 유사한 결과를 제시함을 알 수 있었다.

• 한국강구조학회 논문집
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• 제13권5호
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• pp.567-575
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• 2001

구조해석에 사용되는 확률변수들의 통계적 특성들을 고려하기 위해 기존의 접근방법은 경험에 근거한 안전계수를 사용하여 구조물의 안전성을 평가하여왔다. 또한 실제 구조물들은 하중 재료적 특성 및 부재 치수들의 불확실량을 포함한 형태로 해석되어져 왔다. 그러나 구조 해석을 정확히 하기 위해서는 불확실량이 체계적으로 고려되어야 한다. 기존의 구조 설계 개념에 의한 방법으로는 구조물의 안전성을 정확히 파악할 수 없기 때문에 최근에는 확률이론에 근거한 신뢰성이론을 적용하여 구조물의 안전성을 판단하는 시도가 이루어지고 있다. 따라서 본 연구에서는 기존의 유한요소방법에 확률이론을 도입한 확률 유한요소법을 개발하였다. 이 연구에서는 3개의 한계상태방정식 즉 Von-Mises, Tresca, Mohr-Coulomb의 파괴조건 식들을 이용하여 개선된 1계2차모멘트방법에 의해 평면응력 구조물의 신뢰성을 평가하였다. 본 연구 결과의 검증은 Von-Mises의 항복기준으로 Monte Carlo Simulation 방법을 사용하였으며, 본 연구 결과의 파괴확률과는 1.2% 차이가 있었다. 본 연구의 장점은 Monte Carlo Simulation 방법에서 사용된 16만번의 반복계산을 PFEM은 3번으로 줄여 해석시간이 대단히 짧아진 것과 설계변수가 파괴확률에 미치는 영향을 알 수 있다는 것이다. 셀계변수가 파괴확률에 미치는 영향을 분석해 본 결과 가장 민감한 변수는 부재두께와 하중순이었다.

• Geomechanics and Engineering
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• 제11권3호
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• pp.439-455
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• 2016

This paper presented solutions of displacement and stress for a circular opening which is reinforced with grouted rock bolt. It satisfies the Mohr-Coulomb (M-C) or generalized Hoek-Brown (H-B) failure criterion, and exhibits elastic-brittle-plastic or strain-softening behavior. The numerical stepwise produce for strain-softening rock mass reinforced with grouted rock bolt was developed with non-associative flow rules and two segments piecewise linear functions related to a principle strain-dependent plastic parameter, to model the transition from peak to residual strength. Three models of the interaction mechanism between grouted rock bolt and surrounding rock proposed by Fahimifar and Soroush (2005) were adopted. Based on the axial symmetrical plane strain assumption, the theoretical solution of the displacement and stress were proposed for a circular tunnel excavated in elastic-brittle-plastic and strain-softening rock mass compatible with M-C or generalized H-B failure criterion, which is reinforced with grouted rock bolt. It showed that Fahimifar and Soroush's (2005) solution is a special case of the proposed solution for n = 0.5. Further, the proposed method is validated through example comparison calculated by MATLAB programming. Meanwhile, some particular examples for M-C or generalized H-B failure criterion have been conducted, and parametric studies were carried out to highlight the influence of different parameters (e.g., the very good, average and very poor rock mass). The results showed that, stress field in plastic region of surrounding rock with considering the supporting effectiveness of the grouted rock bolt is more than that without considering the effectiveness of the grouted rock bolt, and the convergence and plastic radius are reduced.

• Design & Manufacturing
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• 제13권4호
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• pp.10-16
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• 2019

Semiconductor chip is bonded to the substrate by melting solder bumps. In general, the chip bonding is applied by a Reflow process or a Thermo-Compression(TC) bonding process. In this paper, we introduce a Laser Assisted Thermo-Compression bonding (LATCB) process to improve the anxiety of the existing process(Reflow, TC bonding). In the LATCB process, the chip is bonded to the substrate by irradiating a laser with a uniform energy density in the same area as the chip to melt only the solder bumps and press the chip with a Transparent Compression Module (TCM). The TCM consists of a fused silica header for penetrating the laser and pressurizing the chip, and a piezoelectric actuator (P.A.) coupled to both ends of the header for micro displacement control of the header. In addition, TCM is a structure that can pressurize the chip and deliver it to the chip and solder bumps without losing the energy of the laser. Fused silica, which is brittle, is vulnerable to deformation, so the header may be damaged when an external force is applied for pressurization or a displacement differenced is caused by piezoelectric actuators at both ends. On the other hand, in order to avoid interference between the header and the adjacent chip when pressing the chip using the TCM, the header has a notch at the bottom, and breakage due to stress concentration of the notch is expected. In this study, the thickness and notch length that the header does not break when the external force (500 N) is applied to both ends of the header are optimized using structural analysis and Coulomb-Mohr failure theory. In addition, the maximum displacement difference of the P.A.s at both ends where no break occurred in the header was derived. As a result, the thickness of the header is 11 mm, and the maximum displacement difference between both ends is 8 um.

• Geomechanics and Engineering
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• 제3권4호
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• pp.291-321
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• 2011

The paper describes a simple numerical FLAC model that was developed to simulate the dynamic response of two instrumented reduced-scale model reinforced soil walls constructed on a 1-g shaking table. The models were 1 m high by 1.4 m wide by 2.4 m long and were constructed with a uniform size sand backfill, a polymeric geogrid reinforcement material with appropriately scaled stiffness, and a structural full-height rigid panel facing. The wall toe was constructed to simulate a perfectly hinged toe (i.e. toe allowed to rotate only) in one model and an idealized sliding toe (i.e. toe allowed to rotate and slide horizontally) in the other. Physical and numerical models were subjected to the same stepped amplitude sinusoidal base acceleration record. The material properties of the component materials (e.g. backfill and reinforcement) were determined from independent laboratory testing (reinforcement) and by back-fitting results of a numerical FLAC model for direct shear box testing to the corresponding physical test results. A simple elastic-plastic model with Mohr-Coulomb failure criterion for the sand was judged to give satisfactory agreement with measured wall results. The numerical results are also compared to closed-form solutions for reinforcement loads. In most cases predicted and closed-form solutions fall within the accuracy of measured loads based on ${\pm}1$ standard deviation applied to physical measurements. The paper summarizes important lessons learned and implications to the seismic design and performance of geosynthetic reinforced soil walls.

• Geomechanics and Engineering
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• 제24권4호
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• pp.307-321
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• 2021

In an earlier publication (Serrano et al. 2014), the theoretical basis for evaluating the shear strength in rock joints was presented and used to derive an equation that governs the relationship between tangential and normal stresses on the joint during slippage between the joint faces. In this paper, the theoretical equation is applied to two non-linear failure criteria by using non-associated flow laws, including the modified Hoek and Brown and modified Mohr-Coulomb equations. The theoretical model considers the geometric dilatancy, the instantaneous friction angle, and a parameter that considers joint surface roughness as dependent variables. This model uses a similar equation structure to the empirical law that was proposed by Barton in 1973. However, a good correlation with the empirical values and, therefore, Barton's equation is necessary to incorporate a non-associated flow law that governs breakage processes in rock masses and becomes more significant in highly fractured media, which can be induced in a rock joint. A linear law of dilatancy is used to assess the importance of the non-associated flow to obtain very close values for different roughness states, so the best results are obtained for null material dilatancy, which considers significant changes that correspond to soft rock masses or altered zones of weakness.

• 자원환경지질
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• 제38권3호
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• pp.305-317
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• 2005

본 연구는 도로 절취사면에 대한 사면안정 연구로서 삼량진과 밀양을 연결하는 1022호 지방도 중 천태산 부근에 위치한 약 4km의 연속적인 절취사면에서 수행되었다. 연구지역은 유문암질 회류응회암, 강하응회암, 유문암 및 안산암 등의 백악기 화산암류로 구성되어 있으며, 거의 전 구간에 걸쳐 $70^{\circ}$이상의 사면각으로 형성된 절취암반은 높은 빈도의 불연속면을 포함하고 있다. 암반사면의 불안정 요인으로 작용하는 불연속면의 기하학적 분포특성을 파악하기 위하여 8개 지점에서 선형조사선 조사를 실시하였으며, 조사 자료에 대하여 운동학적 해석 및 블록이론해석을 적용하여 대상 도로절취사면의 안정성을 검토하였다. 각각의 선형조사선에서 조사된 개별 불연속면에 대한 중력 재하의 평면 파괴, 쐐기 파괴, 및 전도 파괴 등에 대한 최대안전사면각을 산정한 결과, 평면파괴에 대한 최대안전사면각은 대부분의 개별 불연속면에서 $65^{\circ}$이상으로 나타났으며, 쐐기파괴에 대한 최대안전사면각은 $45^{\circ}$이상으로 산정되었다. 또한, 전도파괴에 대해서는 대부분의 개별 불연속면에서 $80^{\circ}$이상으로 산정되었다. 블록이론을 적용한 결과 SL4, SL5, SL6 및 SL8 지점에 존재하는 잠재적 키블록(Type II)을 확인하였다. 블록이론에 의해 구분된 잠재적 키블록에 대하여 한계평형해석을 수행한 결과 중력재하에서는 1보다 큰 안전율이 확보되었으나 집중호우 시 나타날 수 있는 간극수압과 같은 외적 사면 불안정 요인에 따라 안전율이 크게 저하될 수 있음을 도출하였다. 또한, 한계평형해석 시 적용되는 Mohr-Coulomb 및 Barton 등의 전단강도 기준식에 따른 안전율의 변화를 제시하였다.

• 자원환경지질
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• 제10권1호
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• pp.37-48
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• 1977

The earth's crust is unceasingly undergoing deformations because of the forces acting upon it. The relationship between the tectonic forces and the resulting deformations are found from the states of stresses in the earth's crust induced by these forces. The study has been attempted to analyze the deformations of the overlying sedimentary layers, which are deformed by the magma intrusion along its lower boundary. The elastic model is constructed to analyze the geologic structures, by means of the theory of elasticity, and then the appropriate boundary conditions are given. The solution of the Airy stress function which satisfies the given boundary conditions is derived from the analytic method. The internal stress distributions of the deformed elastic model layer are portrayed by principal stress trajetories, and then the corresponding potential faults and joints systems are predicted from the Coulomb-Mohr failure criterion. The internal displacement distributions are shown by the calculated displacement components vectors, namely horizontal, vertical and net components. Results of the numerical calculations show the developments of some geologic structures as follows; (1) one set of shear joints and or two sets of shear joints which are oppisite directions, and one set of extension joints parallel to the ${\sigma}_1$ direction, (2) one set of high angle thrusts and normal faults, (3) symmetric fold; both limbs are dipping in opposite direction with low angle. The field work at the Wall-A San area, located near Jinju City, in southern Korea, had accomplished to compare the field structures with the predicted ones. The results of the comparison exhibits the developments of joint and fault systems satisfactorily consistent with each others. But the area does not show any type of folding, in spite of the intrusion of a granodiorite massif, this fact is one of the important features of the whole Kyungsang sedimentary basins of Mesozoic age distributed at the south-eastern parts of Korea. For this reason, it is thought that the magma intrusion had occurred with extremly low pressure. The geologic structures have been modified by the erosion and weathering throughout the geologic time, and the conditions of the sedimentary layers (width, thickness and radius of magma) are not the same as before, being intruded by the magma. To enlighten this, it is preferable to study these geologic structures with analyses of various types of rheological models.