Determination of passive earth pressure with lower bound finite elements limit analysis and modified pseudo-dynamic method

ABSTRACT

The present study deals with the determination of passive earth pressure under seismic condition by following the lower bound finite elements limit analysis and modified pseudo-dynamic methodology. In accordance with the lower bound finite elements formulation, the stress field was modelled using a three-noded triangular elements, while the passive pressure was determined via linear optimisation. The parametric study was performed, for a vertical rigid retaining wall, by varying the magnitude of seismic acceleration in horizontal direction (k_h) between 0 and 0.3, while the vertical seismic acceleration (k_v) was kept equal to 0 or 0.5 k_h. Furthermore, the damping coefficient for dry cohesionless backfill was kept ξ = 10%. The obtained results in various cases were found to be in good agreement with those found in the literature. It is expected that this method can be further used for solving other important geotechnical stability problems.     

Stability of a long unsupported circular tunnel in soils with seismic forces

By using the lower-bound finite element limit analysis, the stability of a long unsupported circular tunnel has been examined with an inclusion of seismic body forces. The numerical results have been presented in terms of a non-dimensional stability number (γH/c) which is plotted as a function of horizontal seismic earth pressure coefficient (k _h) for different combinations of H/D and ?; where (1) H is the depth of the crest of the tunnel from ground surface, (2) D is the diameter of the tunnel, (3) k _h is the earthquake acceleration coefficient and (4) γ, c and ? define unit weight, cohesion and internal friction angle of soil mass, respectively. The stability numbers have been found to decrease continuously with an increase in k _h. With an inclusion of k _h, the plastic zone around the periphery of the tunnel becomes asymmetric. As compared to the results reported in the literature, the present analysis provides a little lower estimate of the stability numbers. The numerical results obtained would be useful for examining the stability of unsupported tunnel under seismic forces.     

Pseudo Static Seismic Stability Analysis of Reinforced Soil Structures

The paper pertains to the pseudo-static seismic stability analysis of reinforced soil structures. Using limit equilibrium method and assuming the failure surface to be logarithmic spiral, analysis has been conducted to maintain internal stability against both tensile and pullout failure of the reinforcements. The external stability of the reinforced earth wall is also assessed in terms of its sliding, overturning, eccentricity and bearing modes of failure. The influence of the intensity of the surcharge load placed on the backfill is also considered in the analysis. The obtained results are validated by comparing the same with those reported in literature. Studies have also been made regarding the influence of backfill soil friction angle, horizontal and vertical seismic accelerations, surcharge load, the tensile strength of reinforcement, pullout length of the reinforcement and number of reinforcement layers on the seismic stability against various failure modes as mentioned earlier.     

Seismic Bearing Capacity of Shallow Strip Footing with Coulomb Failure Mechanism using Limit Equilibrium Method

In this paper, an effort is made to evaluate the seismic bearing capacity of shallow strip footing resting on c–ф soil. The formulation is developed to get a single coefficient of bearing capacity for simultaneous resistance of weight, surcharge and cohesion. Limit equilibrium method in Pseudo-static approach with Coulomb mechanism is applied here to evaluate the seismic bearing capacity. The seismic bearing capacity of footing (q_uE) is expressed in terms of single coefficient N_γE. The effect of various parameters viz. angle of internal friction of soil (ф), angle of wall friction (δ), cohesion (c), ratio of depth to width of footing (d_f/B₀), seismic acceleration (k_h, k_v) are studied on the variation of seismic bearing capacity co-efficients.     

Risk Factor Based Design of Cantilever Retaining Walls

Sensitivity analysis of geotechnical random variables on potential failure modes (overturning, sliding, bearing capacity and eccentricity) of a cantilever retaining wall reveals that high sensitivity of a particular variable on a particular mode of failure does not necessarily imply a remarkable contribution to the overall failure probability. The present paper aims to combine probability of failure (P _f ) of each failure mode and sensitivity of the random variables to these failure modes and introduces a new factor, called Probabilistic Risk Factor (R _f ) for each random variable. P _f is calculated by Monte Carlo Simulation and sensitivity analysis of each random variable is calculated based on normalized F-Statistics value. R _f is a reduction factor which takes into account the variations of random variables and hence can be directly implemented in design by the designers. The random variables (friction angle and unit weight of backfill soil; and friction angle, unit weight and cohesion of foundation soil), when divided by R _f and applied in design, yield a structure which is safe against variations of the random variables. It is observed that R _f of friction angle (φ ₁ ) of backfill increases and cohesion (c ₂ ) of foundation soil decreases with an increase in variation of φ ₁ , while R _f for unit weights (γ ₁ and γ ₂ ) of both the soil and friction angle of foundation soil (φ ₂ ) remains almost constant. Finally, design guidelines for different variations of φ ₁ are provided based on the proposed methodology, which proves to be cost effective.     

The stress regime in a Rotliegend reservoir of the Northeast German Basin

In-situ stresses have significant impact, either positive or negative, on the short and long term behaviour of fractured reservoirs. The knowledge of the stress conditions are therefore important for planning and utilization of man-made geothermal reservoirs. The geothermal field Groß Schönebeck (40 km north of Berlin/Germany) belongs to the key sites in the northeastern German Basin. We present a stress state determination for this Lower Permian (Rotliegend) reservoir by an integrated approach of 3D structural modelling, 3D fault mapping, stress ratio definition based on frictional constraints, and slip-tendency analysis. The results indicate stress ratios of the minimum horizontal stress S _hmin being equal or increasing 0.55 times the amount of the vertical stress S _V (S _hmin ≥ 0.55S _V ) and of the maximum horizontal stress S _Hmax ≤ 0.78–1.00S _V in stress regimes from normal to strike slip faulting. Thus, acting stresses in the 4,100-m deep reservoir are S _V  = 100 MPa, S _hmin = 55 MPa and S _Hmax = 78?100 MPa. Values from hydraulic fracturing support these results. Various fault sets of the reservoir are characterized in terms of their potential to conduct geothermal fluids based on their slip and dilatation tendency. This combined approach can be adopted to any other geothermal site investigation.     

Reliability Based Earthquake Resistant Design for Internal Stability of Reinforced Soil Structures

This paper presents a method to evaluate reliability for internal stability of reinforced soil structures using reliability based design optimization. Using limit equilibrium method and assuming the failure surface to be logarithmic spiral, analysis is conducted to maintain internal stability against both tensile and pullout failure of the reinforcements. Properties of backfill soil and strength of the geosynthetic reinforcement are considered as random variables. For the seismic conditions, reliability indices of all the geosynthetic layers in relation to tension and pullout failure modes are determined for different magnitudes of seismic accelerations both in the horizontal and vertical directions, surcharge load and design strength of the reinforcement. The efforts have been made to obtain the number of layers, pullout length and total length of the reinforcement at each level for the desired target reliability index values against tension and pullout modes of failure. The influence of horizontal and vertical earthquake acceleration, surcharge load, design strength of the reinforcement, coefficient of variation of soil friction angle and design strength of the reinforcement on number of layers, pullout length and total length of the reinforcement needed for the stability at each level is discussed.     

Dynamic active earth pressure on cantilever retaining walls

In normal practice, the active earth pressure on cantilever retaining wall is evaluated with different procedures relating to an ideal vertical plane passing through the heel of the wall. If the wall presents a long heel, failure planes do not interfere with the vertical stem, so that the limit Rankine conditions can develop freely in the backfill. The inclination of lateral actions along the ideal plane is assumed to be constant and depends on the geometry of the ground level and on the friction angle φ. The Authors recently proposed a new method to evaluate the active earth pressure coefficient due to seismic loading with a pseudo-static stress plasticity solution. The present paper describes the application of this method to a retaining wall supporting a φ soil backfill with an irregular surface. For two different configurations of wall-soil system, the behaviour is also studied by continuum FDM dynamic analyses, utilising four Italian accelerometric time-histories scaled at the same peak ground acceleration. The comparison between different procedures is also analysed.     

In Situ Stress Measurements in the Lhasa Terrane, Tibetan Plateau, China

Tectonic activities are frequent in the Lhasa terrane because of the ongoing collision between the India and Eurasia plates. Knowledge of the stress state is critical to evaluate the crustal stability and the design of underground excavations. Because of the limitations imposed by natural conditions,little research has been performed on the present crustal in situ stress in the Tibetan Plateau,and further study is imperative. In this study,hydraulic fracturing measurements were conducted in Nyching County(LZX) and Lang County(LX),Lhasa terrane to characterize the shallow crustal stress state. The results indicate that the stress state in the LZX borehole is markedly different from that in the LX borehole,in both magnitude and orientation. At the same measurement depths,the magnitudes of horizontal principal stresses in the LX borehole are 1.5–3.0 times larger than those in the LZX borehole. The stress regime in the LX borehole favors reverse faulting characterized by SHShSv,where SH,Sh,and Sv are maximum horizontal,minimum horizontal,and vertical principal stresses,respectively. The SH and Sh values are approximately three and two times greater than Sv. Fracture impression results reveal that SH in the LX borehole are predominantly N–S,while in the LZX borehole the maximum horizontal principal stress is mainly in the NNE-direction. The heterogeneity of the regional stress state might be a result of the population and distribution of local structures and seismic activities. The stress state in the LX borehole has exceeded the critical state of failure equilibrium,and there is an optimally orientated pre-existing fault near the borehole. It can be concluded that the optimally orientated fault is likely to be active when the stress has built up sufficiently to destroy the frictional equilibrium; it is suggested that research focus should be placed on this in future. The stress states in boreholes LZX and LX indicate uniformity of the regional stress field and diversity of the local stress fields resulting from the interactions among regional dynamic forces,tectonic stress field,and geological structures.     

Seismic Pullout Capacity of Inclined Anchor Plates in Sand

By using the lower bound finite elements limit analysis, the pullout capacity of an inclined strip anchor plate embedded in a cohesionless soil medium has been computed with an inclusion of pseudo-static horizontal earthquake body forces. The variation of the pullout capacity factor (F _γ ) with changes in horizontal earthquake acceleration co-efficient (α _h ) has been computed by varying the inclination angle (β) of the anchor plate between 0° and 90°. The results clearly reveal that the pullout capacity factor (F _γ ) decreases significantly with an increase in the value of α _h . The reduction in the pullout resistance due to seismic forces (1) becomes much more extensive for a vertical anchor plate as compared to the horizontal anchor, (2) decreases generally with increases in the soil friction angle (?) and (3) increases with an increase in friction angle between soil and anchor plate (δ). The developments of the failure zone around the anchor plate were also examined by varying α _h and β. The results obtained from the analysis compare well with the solutions reported in literature.     

Estimation of velocity function parameters in unconsolidated sands using semblance velocity analysis

To properly understand seismic wave propagation in unconsolidated sand layers, it is important to estimate the parameters of their continuous velocity–depth functions. This study proposes a procedure to estimate the V ₀ and k parameters of a specific velocity function, where V ₀ is the direct P-wave velocity at the ground surface and k is the velocity gradient. The V ₀ and k parameters are generally independent of each other. However, it is possible to relate them numerically because both depend strongly on the porosity (?) and water saturation (S _w). The proposed procedure starts by tabulating V ₀ and k for 0.05?≤???≤?0.5 sampled at Δ??=?0.05 and S _w?=?0.6, so that only V ₀ is needed for fitting. Then, time–distance (T-X) type curves of the direct arrival are calculated for the corresponding values of V ₀ and k parameters values. The type curves are fitted then to the observed shot gather through a modification of the classic semblance velocity analysis method. Once the best-fit V ₀ value is found, the corresponding k, ?, and S _w values are picked from a V ₀–k–? lookup table. The procedure is applied on synthetic shot gathers with various amounts of additive Gaussian random noise. Results show that the method is robust and tolerant to low to moderate amounts of noise.     

Tectonic stress field in the epicentral zone of the Latur earthquake of 1993

In situ stress measurements by hydraulic fracturing were carried out in the 617 m deep borehole specially drilled in the epicentral zone of the 1993 Latur earthquake for the purpose of research. The stress measurements carried out at 592 m depth in this borehole are the deepest of all such measurements made so far in the Indian shield. The maximum and minimum principal horizontal stresses (S _H max andS _h min) have been derived from the hydrofracture data using the classical method. TheS _{H max} andS _h min are found to be 16.5 and 9.6 MPa at 373 m depth, and 25.0 and 14.1 MPa at 592 m depth, indicating that the vertical gradients ofS _hmax andS _hmin in the epicentral zone are 39 MPa/km and 21 MPa/km respectively. The principal horizontal stresses in the epicentral zone are comparable with those at Hyderabad and 30% higher than in most other comparable intra-continental regions. Analysis of the results indicate that the stresses in the focal region of the 1993 Latur earthquake have not undergone any significant change following its occurrence and this is in agreement with a similar inference drawn from the seismic data analysis. It appears that the Latur earthquake was caused due to rupturing of the overpressured fault segment at the base of the seismogenic zone.     

地震条件下悬臂式挡墙主动土压力的极限分析方法

为确定地震条件下悬臂式挡土墙主动土压力,考虑假想坦墙墙背的可能不同位置,给出了墙后填土5种可能的失稳破坏模式;在此基础上,采用拟静力法,基于极限分析上限定理,推导了作用于坦墙墙背上的地震主动土压力计算公式,包括填土性质、填方坡面倾角、踵板长度、墙体高度、水平及竖向地震影响系数等多因素,其中除填土黏聚力与竖向地震影响系数与该土压力呈线性相关性外,其余因素呈非线性影响。实例分析表明,基于本方法地震土压力而计算的墙体抗滑与抗倾稳定系数,多数情况下均比经典的Mononobe-Okabe法略偏大;在填土中存在第二破裂面情况下,以踵板下边缘作为假想墙背端点的计算模式相对略偏不安全;竖直假想墙背模式相应的土压力计算值最小,但相应的墙体稳定系数却不一定最大。     

Experimental and analytical investigations on bearing capacity of strip footing in reinforced sand backfills and flexible retaining wall

This study focuses on the experimental and analytical investigations of small-scale physical model tests. For this purpose, a set of tests were conducted with and without reinforcement on the top of the backfill. The specimens were different in terms of parameters like the number of geotextile layers, the vertical distance between layers and the strip footing distance from the wall. Soil failure in the bearing capacity step and the backfill shear zones was analysed using particle image velocimetry methods. Bearing capacity of the strip footings was studied using analytical procedures. The results indicate that a reinforcing top zone of the flexible retaining structures may be more appropriate than unreinforced case. The ultimate bearing capacity and wall deflection can be significantly improved by increasing the number of reinforcement layers. When the three layers of reinforcement are used, there is an optimum vertical spacing of the layers at which the bearing capacity is the greatest (h/H?=?0.12, d/H?=?0.33 and u?=?B). The study shows that the analytical solution and the results from the experimental models are in good agreement.     

Comparison of the magnetic properties of leading and following spots and the overlying ultraviolet emission

SDO/HMI and SDO/AIA data for the 24th solar-activity cycle are analyzed using a quicker and more accurate method for resolving π ambiguities in the transverse component of the photospheric magnetic field, yielding new results and confirming some earlier results on the magnetic properties of leading and following magnetically connected spots and single spots. The minimum inclination of the field lines to the positive normal to the solar surface α _min within umbrae is smaller in leading than in following spots in 78% of the spot pairs considered; the same trend is found for the mean angle 〈α〉 in 83% of the spot pairs. Positive correlations between the α _min values and the 〈α〉 values in leading and following spots are also found. On average, in umbrae, the mean values of 〈B〉, the umbra area S, and the angles α _min and 〈α〉 decrease with growth in the maximum magnetic field B _max in both leading and following spots. The presence of a positive correlation between B _max and S is confirmed, and a positive correlation between 〈B〉 and S in leading and following spots has been found. Themagnetic properties of the umbrae of magnetically connected pairs of spots are compared with the contrast of the He II 304 emission above the umbrae, C ₃₀₄. Spots satisfying certain conditions display a positive correlation between C _304?L and 〈α _L 〉 for the leading (L) spots, and between C _304?L /C _304?F and l _L /l _F , where l _L (l _F ) are the lengths of the field lines connecting leading (L) or following (F) spots from the corresponding spot umbrae to the apex of the field line.     

Review: Geothermal heat as a tracer of large-scale groundwater flow and as a means to determine permeability fields

A review of coupled groundwater and heat transfer theory is followed by an introduction to geothermal measurement techniques. Thereafter, temperature-depth profiles (geotherms) and heat discharge at springs to infer hydraulic parameters and processes are discussed. Several studies included in this review state that minimum permeabilities of approximately 5?×?10^?17?<?k _min <10^?15?m² are required to observe advective heat transfer and resultant geotherm perturbations. Permeabilities below k _min tend to cause heat-conduction-dominated systems, precluding inversion of temperature fields for groundwater flow patterns and constraint of permeabilities other than being <k _min. Values of k _min depend on the flow-domain aspect-ratio, faults and other heterogeneities, anisotropy of hydraulic and thermal parameters, heat-flow rates, and the water-table shape. However, the k _min range is narrow and located toward the lower third of geologic materials, which exhibit permeabilities of 10^?21?<?k?<?10^?7?m². Therefore, a wide range of permeabilities can be investigated by analyzing subsurface temperatures or heat discharge at springs. Furthermore, temperature is easy and economical to measure and because thermal material properties vary far less than hydraulic properties, temperature measurements tend to provide better-constrained groundwater flow and permeability estimates. Aside from hydrogeologic insights, constraint of advective/conductive heat transfer can also provide information on magmatic intrusions, metamorphism, ore deposits, climate variability, and geothermal energy.     

Physical properties of calcium aluminates from vibrational spectroscopy

Heat capacity (C_V) and entropy (S) as a function of temperature were calculated for phases in the CaO-Al₂O₃ system from vibrational spectra using a quasi-harmonic model. Calculated values of C_V at 298 K for the calcium aluminates may have uncertainties as small as ±1%, based on comparison with published calorimetric data for CaO, Al₂O₃, and CaAl₂O₄. For hibonite (CaAl₁₂O₁₉), we predict C_P as 519.3 J/mol-K and S as 391.7 J/mol-K, at 298 K. For grossite (CaAl₄O₇), calculated values of C_P as 195.9 J/mol-K and of S as 172.0 J/mol-K are slightly smaller than the available calorimetric data at 298 K, consistent with calorimetric data having been obtained from samples containing ∼10 wt% hibonite impurities. Thermal conductivity at 298 K (k₀) is predicted from peak widths of the vibrational modes using the damped harmonic oscillator model of a phonon gas. Calculations of k₀ for CaO and Al₂O₃ differ from the measurements by 17% and 5%, respectively. The discrepancy for lime is larger due to uncertainties in its peak widths. This comparison suggests that our results for the calcium aluminates should be more accurate than conventional measurements of k₀ which are commonly uncertain by ∼25%.     

绿色翡翠颜色分布规律研究

采用国际照明委员会CIE LAB色度坐标,定量描述了翡翠的绿色,分析了颜色的分布情况,总结其分布规律,建立起翡翠绿色L^*、a^*、b^*、C^*、h_ab的分布关系。当明度较小时,色调角几乎不变,彩度和明度呈现近似的线性相关;当明度变大时,色调角的变化幅度稍大,彩度值在明度中等偏低时变为最大。这些信息将在很大程度上对翡翠绿色分级的细化起到积极作用,可以用来指导翡翠色卡的制备。     

Effect of Model Scale and Particle Size Distribution on PFC3D Simulation Results

This paper investigates the effect of model scale and particle size distribution on the simulated macroscopic mechanical properties, unconfined compressive strength (UCS), Young’s modulus and Poisson’s ratio, using the three-dimensional particle flow code (PFC3D). Four different maximum to minimum particle size (d _max/d _min) ratios, all having a continuous uniform size distribution, were considered and seven model (specimen) diameter to median particle size ratios (L/d) were studied for each d _max/d _min ratio. The results indicate that the coefficients of variation (COVs) of the simulated macroscopic mechanical properties using PFC3D decrease significantly as L/d increases. The results also indicate that the simulated mechanical properties using PFC3D show much lower COVs than those in PFC2D at all model scales. The average simulated UCS and Young’s modulus using the default PFC3D procedure keep increasing with larger L/d, although the rate of increase decreases with larger L/d. This is mainly caused by the decrease of model porosity with larger L/d associated with the default PFC3D method and the better balanced contact force chains at larger L/d. After the effect of model porosity is eliminated, the results on the net model scale effect indicate that the average simulated UCS still increases with larger L/d but the rate is much smaller, the average simulated Young’s modulus decreases with larger L/d instead, and the average simulated Poisson’s ratio versus L/d relationship remains about the same. Particle size distribution also affects the simulated macroscopic mechanical properties, larger d _max/d _min leading to greater average simulated UCS and Young’s modulus and smaller average simulated Poisson’s ratio, and the changing rates become smaller at larger d _max/d _min. This study shows that it is important to properly consider the effect of model scale and particle size distribution in PFC3D simulations.     

Seismic vertical uplift capacity of horizontal strip anchors using pseudo-dynamic approach

This paper presents the pseudo-dynamic analysis to determine the seismic vertical uplift capacity of a horizontal strip anchor using upper bound limit analysis. However, in the literature, the pseudo-static approach was used by few researchers to compute the seismic vertical pullout resistance, where the real dynamic nature of earthquake accelerations cannot be considered. Under the seismic conditions, the values of the unit weight component of uplift factor f_γE are determined for different magnitudes of soil friction angle, soil amplification, embedment ratio and seismic acceleration coefficients both in the horizontal and vertical directions. It is observed that the uplift factor f_γE decreases significantly with the increase in seismic accelerations and amplification but increases with the increase in embedment ratio. The results are compared with the existing values in the literature and the significance of the present methodology for designing the horizontal strip anchor is discussed. In presence of vertical earthquake acceleration and amplification of vibration, the present values of f_γE compare reasonably well with the existing pseudo-static values obtained by modifying the horizontal acceleration coefficient.