Dynamic Response of Machine Foundation on Layered Soil: Cone Model Versus Experiments

This paper presents the experimental validation of analytical solution based on cone model for machine foundation vibration analysis on layered soil. Impedance functions for a rigid massless circular foundation resting on a two layered soil system subjected to vertical harmonic excitation are found using cone model. Linear hysteretic material damping is introduced using correspondence principle. The frequency-amplitude response of a massive foundation is then computed using impedance functions. To verify the solution field experiments are conducted in two different layered soil systems such as gravel layer over in situ soil and gravel layer over concrete slab (rigid base). A total 72 numbers of vertical vibration tests on square model footing were conducted using Lazan type mechanical oscillator, varying the influencing parameters such as depth of top layer, static weight of foundation and dynamic force level. The frequency-amplitude response in general and in particular the resonant frequencies and resonant amplitudes predicted by cone model is compared with the results of experimental investigation, which shows a close agreement. Thus the cone model is reliable in its application to machine foundation vibration on layered soil.     

Experimental and numerical analyses of circular footing on geogrid-reinforced granular fill underlain by soft clay

Experimental and numerical investigations into the bearing capacity of circular footing on geogrid-reinforced compacted granular fill layer overlying on natural clay deposit have been conducted in this study. A total of 8 field tests were carried out using circular model rigid footing with a diameter of 0.30 m. 3D numerical analyses were performed to simulate soil behavior using finite element program Plaxis 3D Foundation. The results from the FE analysis are in very good agreement with the experimental observations. It is shown that the degree of improvement depends on thickness of granular fill layer and properties and configuration of geogrid layers. Parameters of the experimental and numerical analyses include depth of first reinforcement, vertical spacing of reinforcement layers. The results indicate that the use of geogrid-reinforced granular fill layers over natural clay soils has considerable effects on the bearing capacity and significantly reduces the lateral displacement and vertical displacement of the footing.     

Discrete element method simulations of the seismic response of shallow foundations including soil‐foundation‐structure interaction

A novel three‐dimensional particle‐based technique utilizing the discrete element method is proposed to analyze the seismic response of soil‐foundation‐structure systems. The proposed approach is employed to investigate the response of a single‐degree‐of‐freedom structure on a square spread footing founded on a dry granular deposit. The soil is idealized as a collection of spherical particles using discrete element method. The spread footing is modeled as a rigid block composed of clumped particles, and its motion is described by the resultant forces and moments acting upon it. The structure is modeled as a column made of particles that are either clumped to idealize a rigid structure or bonded to simulate a flexible structure of prescribed stiffness. Analysis is done in a fully coupled scheme in time domain while taking into account the effects of soil nonlinear behavior, the possible separation between foundation base and soil caused by rocking, the possible sliding of the footing, and the dynamic soil‐foundation interaction as well as the dynamic characteristics of the superstructure. High fidelity computational simulations comprising about half a million particles were conducted to examine the ability of the proposed technique to model the response of soil‐foundation‐structure systems. The computational approach is able to capture essential dynamic response patterns. The cyclic moment–rotation relationships at the base center point of the footing showed degradation of rotational stiffness by increasing the level of strain. Permanent deformations under the foundation continued to accumulate with the increase in number of loading cycles. Copyright © 2011 John Wiley & Sons, Ltd.     

Dynamic Response of Footing and Machine with Spring Mounting Base

The effect of the spring mounting cushion inserted in between a machine base and its concrete footing has been examined experimentally by conducting a number of block vibrations tests. The machine was subjected to steady state vertical harmonic loading. Experiments were performed with two different stiffness values of the spring mounting cushion. The employment of the spring mounting cushion, with the stiffness much smaller than that of soil strata, offers a drastic reduction in the resonant displacement amplitudes of the footing. It also results in a significant decrease in the resonant frequency of the foundation. The resonant displacement amplitudes of both the footing and the machine were found to become lower with the smaller stiffness value of the springs. The resonant frequency for the machine base, in all the experiments, was found to be invariably the same as that of the footing.     

Vertical dynamic response of a rigid foundation embedded in a poroelastic soil layer

A simplified analytical method is presented for the vertical dynamic analysis of a rigid, massive, cylindrical foundation embedded in a poroelastic soil layer. The foundation is subjected to a time‐harmonic vertical loading and is perfectly bonded to the surrounding soil in the vertical direction. The soil underlying the foundation base is represented by a single‐layered poroelastic soil based on rigid bedrock while the soil at the side of the foundation is modeled as an independent poroelastic layer composed of a series of infinitesimally thin layers. The behavior of the soil is governed by Biot's poroelastodynamic theory and its governing equations are solved by the use of Hankel integral transform. The contact surface between the foundation base and the soil is smooth and fully permeable. The dynamic interaction problem is solved following standard numerical procedures. The accuracy of the present solution is verified by comparisons with the well‐known solutions obtained from other approaches for both the elastodynamic interaction problem and poroelastodynamic interaction problem. Numerical results for the vertical dynamic impedance and response factor of the foundation are presented to demonstrate the influence of nondimensional frequency of excitation, soil layer thickness, poroelastic material parameters, depth ratio and mass ratio on the dynamic response of a rigid foundation embedded in a poroelastic soil layer. Copyright © 2008 John Wiley & Sons, Ltd.     

悬臂式刚性墙动力响应解析研究

从水平简谐振动作用下二维土?悬臂式刚性墙计算模型出发,基于波动力学理论,同时考虑土层的竖向应力和竖向位移,对二维场地中悬臂式刚性墙的动力响应特性进行了解析研究。首先对土层振动方程进行变换,得到关于体积应变? 的方程,通过分离变量法进行求解,再回代振动方程得到关于位移运动方程的非齐次方程,结合墙与土层的相互作用条件及远场边界条件得到振动方程定解,进而得到地下刚性墙墙上土压力、墙底剪力及弯矩的更为严格的解析解。将所得解与忽略竖向应力解、忽略竖向位移解进行了对比。研究表明,所得解能多反映出一个共振频率,且当土体泊松比大于0.45时,忽略竖向位移解失去意义。通过参数分析,表明激励频率与土体阻尼因子对墙体动力响应影响较大,考虑的振动模态阶数对墙体动力响应影响较小。     

A GIS and remote sensing based evaluation of groundwater potential zones in a hard rock terrain of Vaigai sub-basin, India

In this paper, remote sensing, geographic information systems (GIS) and fieldwork techniques were combined to study the groundwater conditions in Vaigai basin, Tamilnadu. Several digital image processing techniques, including standard color composites, intensity–hue–saturation transformation and decorrelation stretch were applied to map rock types. Remote sensing data were interpreted to produce lithological and lineament maps such as geology, geomorphology, soil hydrological group, land use/land cover and drainage map were prepared and analyzed using GIS Arc Map GIS Raster Calculator module as geomorphology?×?12?+?drainage?×?9?+?lineament?×?5?+?geology?×?8?+?land use?×?2?+?relief?×?4. The final cumulative map generated by applying the above equation had weight values ranging from 0.315 to 4.515. The overall results demonstrate that the use of remote sensing and GIS provide potentially powerful tools to study groundwater resources and design a suitable exploration plan, the thematic maps for the study area.     

Vertical vibration of an elastic strip footing on saturated soil

Based on Biot's dynamic coupled equations, the vertical vibration of an elastic strip footing on the surface of saturated soil is studied. Utilizing the Fourier transform, the governing dynamic differential equations for saturated poroelastic medium are solved. Considering the mixed boundary value conditions at the bottom of the foundation, a pair of dual integral equations about the vertical vibration of an elastic strip footing is derived, which can be converted to a set of linear equations by means of infinite series of orthogonal functions. The relation between the dynamic compliance coefficients and the dimensionless frequency tends to be gentle with decreasing footing rigidity, while the dimensionless frequency has only small effect on the dynamic compliance coefficients. When the dynamic permeability is large, its effect on the dynamic compliance coefficients should be taken into consideration. Furthermore, the dynamic compliance coefficients are found to be not sensitive to Poisson's ratio of the soil for footing on saturated soil. Copyright © 2007 John Wiley & Sons, Ltd.     

A study of ground‐structure interaction in dynamic plate load testing

A mathematical treatment is presented for the forced vertical vibration of a padded annular footing on a layered viscoelastic half‐space. On assuming a depth‐independent stress distribution for the interfacial buffer, the set of triple integral equations stemming from the problem is reduced to a Fredholm integral equation of the second kind. The solution method, which is tailored to capture the stress concentrations beneath footing edges, is highlighted. To cater to small‐scale geophysical applications, the model is used to investigate the near‐field effects of ground‐loading system interaction in dynamic geotechnical and pavement testing. Numerical results indicate that the uniform‐pressure assumption for the contact load between the composite disc and the ground which is customary in dynamic plate load testing may lead to significant errors in the diagnosis of subsurface soil and pavement conditions. Beyond its direct application to non‐intrusive site characterization, the proposed solution can be used in the seismic analysis of a variety of structures involving annular foundation geometries. Copyright © 2002 John Wiley & Sons, Ltd.     

Effects of base geogrid on geocell-reinforced foundation beds

The effect of a base geogrid layer below the geocell mattress in sand, sand overlying soft clay, and soft clay foundation beds has been studied using a series of laboratory scale load tests. A rigid circular model footing was used to apply static monotonic loading on the foundation beds with and without geocell reinforcement. The model test results show that the provision of an additional layer of planar geogrid at the base of the geocell mattress further increases the performance of the footing in terms of bearing capacity and reduction in surface heave of the foundation bed. It is also observed that the beneficial effect of the base geogrid layer becomes negligible with increasing height of the geocell mattress beyond the influence of the depth of the footing. Strain measurements in the base geogrid layer indicate that it is more effective with the limited heights of the geocell mattress. The earth pressure cells embedded in the subgrade soil provide evidence that when the base geogrid is provided below the geocell mattress, the footing pressure is distributed more uniformly over an extended area.     

Characterization of the shallow groundwater system in an alpine watershed: Handcart Gulch,Colorado, USA

Water-table elevation measurements and aquifer parameter estimates are rare in alpine settings because few wells exist in these environments. Alpine groundwater systems may be a primary source of recharge to regional groundwater flow systems. Handcart Gulch is an alpine watershed in Colorado, USA comprised of highly fractured Proterozoic metamorphic and igneous rocks with wells completed to various depths. Primary study objectives include determining hydrologic properties of shallow bedrock and surficial materials, developing a watershed water budget, and testing the consistency of measured hydrologic properties and water budget by constructing a simple model incorporating groundwater and surface water for water year 2005. Water enters the study area as precipitation and exits as discharge in the trunk stream or potential recharge for the deeper aquifer. Surficial infiltration rates ranged from 0.1–6.2×10^?5 m/s. Discharge was estimated at 1.28×10^?3 km³. Numerical modeling analysis of single-well aquifer tests predicted lower specific storage in crystalline bedrock than in ferricrete and colluvial material (6.7×10^?5–2.0×10^?3 l/m). Hydraulic conductivity in crystalline bedrock was significantly lower than in colluvial and alluvial material (4.3×10^?9–2.0×10^?4 m/s). Water budget results suggest that during normal precipitation and temperatures water is available to recharge the deeper groundwater flow system.     

Chloride as tracer of solute transport in the aquifer–aquitard system in the Pearl River Delta,China

A 1D numerical model is constructed to investigate the impact of sedimentation and sea level changes on transport of Cl^? in the aquifer–aquitard system in the Pearl River Delta (PRD), China. The model simulates the evolution of the vertical Cl^? concentration profiles during the Holocene. Sedimentation is modeled as a moving boundary problem. Chloride concentration profiles are reconstructed for nine boreholes, covering a wide area of the PRD, from northwest to southeast. Satisfactory agreement is obtained between simulated and measured Cl^? concentration profiles. Diffusion solely is adequate to reproduce the vertical Cl^? concentration profiles, which indicates that diffusion is the regionally dominant vertical transport mechanism across the aquitards in the PRD. The estimated effective diffusion coefficients of the aquitards range from 2.0?×?10^–11 to 2.0?×?10^–10 m²/s. The effective diffusion coefficients of the aquifers range from 3.0?×?10^–11 to 4.0?×?10^–10 m²/s. Advective transport tends to underestimate Cl^? concentrations in the aquitard and overestimate Cl^? concentrations in the basal aquifer. The results of this study will help understand the mechanisms of solute transport in the PRD and other deltas with similar geological and hydrogeological characteristics.     

Vertical vibration of a rigid strip footing on viscoelastic half-space

This paper presents an analytical method for modeling the dynamic response of a rigid strip footing subjected to vertical-only loads. The footing is assumed to rest on the surface of a viscoelastic half-space; therefore, effects of hysteretic soil damping on the impedance of the foundation and the generated ground vibrations are considered in the solution. To solve the mixed boundary value problem, we use the Fourier transform to cast a pair of dual integral equations providing contact stresses, which are solved by means of Jacobi orthogonal polynomials. The resulting soil and footing displacements and stresses are obtained by means of the Fourier inverse transform. The solution provides more realistic estimates of footing impedance, compared to existing solutions for elastic soil, as well as of the attenuation of ground vibrations with distance of the footing. The latter is important for the estimation of machine vibration effects on nearby structures and installations.     

Layered elastic model for analysis of Cone Penetration Testing

A layered elastic model is adopted in the paper for the analysis of soil layering effects on the results of Cone Penetration Testing (CPT). Analytical solutions associated with the layered elastic CPT model and obtained via numerically integrating the fundamental singular solution for layered elastic solids due to the action of a body force concentrated on a circular ring. The soil layering effects on the CPT tip and friction resistance are examined in detail using the layered elastic CPT model. These examinations include parametric studies, influence of soil compressibility, comparisons with theoretical results given in the literature, verification with experimental data and simulation of field trial results. The examinations lead to the conclusions that the layered elastic CPT model can be used to analyse soil layering effects on CPT results and to estimate relative shear modulus strength of soil layers. Copyright © 1999 John Wiley & Sons, Ltd.     

Bearing capacity of square footings on reinforced layered soil

In the present study, an approximate method has been suggested to calculate the ultimate bearing capacity of a square footing resting on reinforced layered soil. The soil is reinforced with horizontal layers of reinforcement in the top layer of soil only. The pre requisite to the method is the ultimate bearing capacity of unreinforced layered soil, which can be determined from the methods already available in literature. The results have been validated with the model tests conducted on two layered soil compacted at different densities and the top layer reinforced with horizontal layers of geogrid reinforcement.     

Stability of eccentrically loaded footings on slopes

The stability of eccentrically loaded strip footings on slopes was investigated using the method of finite element analysis based on the theory of elasto-plasticity. The analysis was done for two different soils involving three levels of slope angle, six footing locations, and two levels of load eccentricity plus central vertical loading. The strip footing analysed was a 3-ft (0.9 m) wide reinforced concrete footing embedded to a depth of 3 ft (0.9 m). The analysis focused on footing settlement, plastic yielding of soil, and ultimate bearing capacity. The results of analysis show that the influence of load eccentricity on footing pressure vs. footing centre settlement is negligibly small. However, the progressive soil yielding and ultimate bearing capacity are greatly affected by load eccentricity. Furthermore, the effect of load eccentricity differs considerably with the load location relative to the footing centre and slope crest. The ultimate bearing capacity for the eccentric load located on the slope side is significantly greater than that for the load located on the other side of the footing centre. For a 2(H): 1(V) slope in silty clay, the effect of slope on footing stability decreases with increasing footing location from slope crest as would be expected, and diminishes when the footing is located from the crest at about 5-times the footing width.     

Estimating hydraulic conductivity using grain-size analyses, aquifer tests, and numerical modeling in a riverside alluvial system in South Korea

Hydraulic conductivity (K) for an alluvial system in a riverbank filtration area in Changwon City, South Korea, has been studied using grain-size distribution, pumping and slug tests, and numerical modeling. The alluvial system is composed of layers: upper fine sand, medium sand, lower fine sand, and a highly conductive sand/gravel layer at the base. The geometric mean of K for the sand/gravel layer (9.89?×?10^?4 m s^?1), as determined by grain-size analyses, was 3.33 times greater than the geometric mean obtained from pumping tests (2.97?×?10^?4 m s^?1). The geometric mean of K estimates obtained from slug tests (3.08?×?10^?6 m s^?1) was one to two orders of magnitude lower than that from pumping tests and grain-size analyses. K estimates derived from a numerical model were compared to those derived from the grain-size methods, slug tests and pumping tests in order to determine the degree of deviation from the numerical model. It is considered that the K estimates determined by the slug tests resemble the uppermost part of the alluvial deposit, whereas the K estimates obtained by grain-size analyses and pumping tests are similar to those from the numerical model for the sand/gravel layer of the riverside alluvial system.     

Development of a Darcy-Brinkman model to simulate water flow and tracer transport in a heterogeneous karstic aquifer (Val d’Orléans, France)

Darcy’s law is the equation of reference widely used to model aquifer flows. However, its use to model karstic aquifers functioning with large pores is problematic. The physics occurring within the karstic conduits requires the use of a more representative macroscopic equation. A hydrodynamic model is presented which is adapted to the karstic aquifer of the Val d’Orléans (France) using two flow equations: (1) Darcy’s law, used to describe water flow within the massive limestone, and (2) the Brinkman equation, used to model water flow within the conduits. The flow equations coupled with the transport equation allow the prediction of the karst transfer properties. The model was tested by using six dye tracer tests and compared to a model that uses Darcy’s law to describe the flow in karstic conduits. The simulations show that the conduit permeability ranges from 5?×?10^?6 to 5.5?×?10^?5?m² and the limestone permeability ranges from 8?×?10^?11 to 6?×?10^?10?m². The dispersivity coefficient ranges from 23 to 53 m in the conduits and from 1 to 5 m in the limestone. The results of the simulations carried out using Darcy’s law in the conduits show that the dispersion towards the fractures is underestimated.     

Study of radium content and radon exhalation rates in soil samples of northern India

Radon is a radioactive hazardous and ubiquitous gas. It has been recognized to be one of the major contributors to natural radiation even causing lung cancer if present at enhanced levels. There are large variations in data available in the literature for radium content and radon exhalation rates of various materials. It is a well-documented fact that radon exhalation from the ground surface depends upon a number of parameters such as soil grain size, soil porosity and radium content. For this purpose, in this study the so-called can technique has been used to measure radium content and exhalation rates of radon in soil samples collected from different places of Aligarh, Etah and Mathura districts of Uttar Pradesh??a province in northern India. These districts lie within the subtropical region of the Indo-Gangetic plains. The values of effective radium content are found to vary from 8.11 to 112.83?Bq?kg^?1 with a mean value of 33.21?Bq?kg^?1 and a standard deviation of 28.15. The values of mass exhalation rates of radon vary from 0.76?×?10^?6 to 15.80?×?10^?6?Bq?kg^?1?day^?1 with a mean value of 4.21?×?10^?6?Bq?kg^?1?day^?1, while the surface exhalation rates vary from 1.97?×?10^?5 to 41.03?×?10^?5?Bq?m^?2?day^?1 with a mean value of 10.93?×?10^?5?Bq?m^?2?day^?1.     

Soil organic carbon within the vadose zone of a floodplain

Past studies have focused on carbon variation in the upper 1 m of the soil profile. However, there is limited information on carbon variation at deeper depths (e.g., 0–4 m) and mathematical functions to extrapolate carbon content at these depths. The objective of this study was therefore to assess the vertical variation in SOC (reached 4 m) of the Tarim River floodplain in northwestern China. The vertical distribution in SOC was described by exponential and power functions based on (1) soil depth, (2) soil depth and silt content, (3) soil depth and SOC at the shallowest and deepest depths, (4) soil depth, silt content, and SOC at the shallowest and deepest depths, and (5) soil depth and SOC at the shallowest depth. We found SOC content decreased with depth from 6.82 g kg^?1 at 0–0.2 m to?<?1.0 g kg^?1 below 3.2–3.4 m averaged across five locations along the floodplain. Both the power and exponential functions provided a good fit to the measured data in the upper 1 m of the soil profile, whereas the power function provided a better fit to the data when extrapolating to a depth of 3–4 m. The power function describing SOC as a function of soil depth, silt content, and SOC at the shallowest and deepest depths best portrayed the distribution in SOC with depth. Considering the cost and labor in measuring soil properties, our results suggest that SOC at the shallowest depth can provide good estimates of the vertical distribution in SOC in a floodplain.