Strip Foundation Research Articles

Calibration of resistance factors for design of shallow foundations against sliding

The design of shallow foundations typically proceeds by using the load and resistance factor design (LRFD) methodology to avoid various limit states with some probability. This paper looks at the sliding limit state of shallow foundations, and the sliding resistance factors required for the LRFD approach are estimated using reliability analyses of surface strip foundations. Cohesive and frictional soils are separately studied under wind loading conditions. Monte Carlo simulations are used to estimate the sliding failure probability of foundation designs on cohesive soils, and an analytical method is developed for frictional soils. The results indicate the existence of a “worst case” correlation length for cohesive soils, and the sliding resistance factor required to achieve target maximum lifetime failure probabilities is around 0.4–0.65 for moderate soil variability. For frictional soils, the required sliding resistance factor is about 0.5–0.85 for ν ϕ′ = 0.15. Overall, the sliding resistance factors recommended here agree well with the resistance factors of ϕ gu = 0.6 for cohesive soils and ϕ gu = 0.8 for frictional soils stipulated by geotechnical LRFD code provisions in Canada. The analyses can be used to estimate the reliability of current designs and can also aid the calibration of geotechnical design codes.

Influence of spiral anchor composite foundation on seismic vulnerability of raw soil structure

A typical single-layer raw soil structure in villages and towns in China is taken as the research object. In the probabilistic seismic demand analysis, the seismic demand model is obtained by the incremental dynamic time history analysis method. The seismic vulnerability analysis is carried out for the raw soil structure of non-foundation, strip foundation, and spiral anchor composite foundation, respectively. The spiral anchor composite foundation can reduce the seismic response and failure state of raw soil structure, and the performance level of the structure is significantly improved. Structural requirements sample data with the same ground motion intensity are analyzed by linear regression statistics. Compared with the probabilistic seismic demand model under various working conditions, the seismic demand increases gradually with the increase of intensity. The seismic vulnerability curve is summarized for comparative analysis. With the gradual deepening of the limit state, the reduction effect of spiral anchor composite foundation on the exceedance probability becomes more and more obvious, which can reduce the probability of structural failure to a certain extent.

Edged Inverted Folded Plate Shell Strip Foundation Bearing Capacity Comparison with strip footing on Sandy Soil

Using shell foundations as well as their benefits in the case of improved bearing capacity is investigated these days, especially strip folded shape. Because of more contact in soil, these type of shells have more bearing capacity than shallow foundations. In this research the behavior of Strip Inverted Folded Plate Shell Foundation is studied on sandy soil. The elastic perfectly plastic numerical analyses and experimental tests are analyzed and compared with shallow foundation. The effect of adding edge, variation in width and shell angle are considered. More than 45 geometrical shells models have been selected for research and the results are compared with common strip foundation in same width. Digital stress transducers are used for integrity of stresses and numerical model verification. The results indicate that adding edge with the same width and decreasing the B/D ratio in shell strip foundation improves the bearing capacity. Also when an edge on the toe of the foundation equivalent to the embedment depth is used the bearing capacity is improved in the range of 3-50%. Variation in shell angle with the same width results in increasing the bearing capacity up to two times. Finally, it is recommended to use a shell strip foundation with of 45o to 60o and with an edge equal to embedment depth.

Dynamic Behavior of Machine Foundations on layered sandy soil under Seismic Loadings

In this paper, a dynamic investigation is done for strip, rectangular and square machine foundation at the top surface of two-layer dry sand with various states (i.e., loose on medium sand and dense on medium sand). The dynamic investigation is performed numerically using finite element programming, PLAXIS 3D. The soil is expected as a versatile totally plastic material that complies with the Mohr-Coulomb yield criterion. A harmonic load is applied at the base with an amplitude of 6 kPa at a frequency of (2 and 6) Hz, and seismic is applied with acceleration – time input of earthquake hit Halabjah city north of Iraq. A parametric study is done to evaluate the influence of changing L/B ratio (Length=12,6,3 m and width=3 m), type of sand, and frequency of the machine for soil with two layers (dense and medium sand) and (loose and medium sand). It was noticed that the displacement decreases when the foundation is strip, and has the highest values when the foundation is square. At the same time, the maximum vertical stress of the foundation (L/B = 4 and L/B = 1) appears to be (1262) kPa and (1255) kPa, respectively, due to increasing the foundation mass as a result of increasing its dimensions. Then again, the displacement increases by 20% for vertical displacement when decreasing the relative density. In addition, it has been noticed that there is a decrease in displacement when the frequency value changes from (2 to 6) Hz.

Interaction of rigid shallow foundation with dip-slip normal fault rupture outcrop: effective parameters and retrofitting strategies

Devastating influences of fault rupture outcrop on various geo-structures during past earthquakes have revealed the necessity of more detailed and comprehensive studies on the fault-foundation interaction. In this study, the interaction between the normal fault and shallow surface/embedded strip foundations is rigorously examined through a well-established upper bound limit analysis formulation in conjunction with the finite element discretization and linear programming technique. The adopted upper bound FELA method is shown to be efficient and cost-effective with high predictive capability, which can be easily implemented in any common computational platforms, like MATLAB. The accuracy of the adopted numerical method is first verified against some findings in the literature. Using this validated numerical approach, a comprehensive parametric study is performed to examine the interaction of the normal fault rupture outcrop with the surface and embedded shallow foundations. Accordingly, the influences of various parameters including the foundation breadth, the service footing pressure, the internal friction angle of the soil deposit, the foundation embedment depth, the fault throw and the relative distance between the fault rupture and shallow foundation, on the normal fault-footing interaction are systematically investigated and discussed. In addition, as an efficient retrofitting strategy to protect the shallow foundation against the fault outcrop, rigid mitigating barrier walls with different filling materials are proposed so as to divert the mainstream of the fault rupture and thus reduce its destructive effects on the overlying superstructures. In this regard, another parametric survey is carried out to explore the effects of wall-related geometric parameters, such as its depth, width, filling material and relative position, on the reduction of the destructive consequences of the normal fault rupture emergence at the ground surface. The results generally show that applying a rigid concrete wall with suitable height, width and distance from the foundation leads to the significant reduction in the amount of surface footing rotation subjected to normal fault rupture outcrop.

An analytical approach to the ultimate bearing capacity of smooth and rough strip foundations on rock mass considering three-dimensional (3D) strength

An analytical approach to the ultimate bearing capacity qu of strip foundations on rock mass under both smooth and rough base conditions is presented. To consider the three-dimensional (3D) stress state, a 3D version of the Hoek-Brown (HB) criterion is combined with equilibrium equations to derive the governing equations by using the characteristics method. Then, a finite difference-based approach is used to solve the stresses below the foundation. Finally, integration of the vertical stress on the foundation base is performed to determine the qu of a strip foundation with different base conditions. Validation of the proposed approach is performed through comparisons with model test results and the effect of 3D strength is investigated by comparing the proposed approach with a two-dimensional HB criterion-based solution. Finally, parametric analyses are conducted to study the effects of rock constant mi, unconfined compression strength of intact rock, geological strength index, Poisson’s ratio of rock mass, and foundation width on the qu, failure zone, and vertical stress on the base. The results show that ignoring 3D strength and unit weight of rock leads to underestimations of qu and it is important to consider the different factors when designing a strip foundation on rock mass.

STUDY ON APPLICATION OF MUNICIPAL SOLID BOTTOM ASH REPLACING SAND CUSHION BELOW STRIP FOUNDATIONS ON WEAK GROUND

So far, several publications on physical and mechanical properties of solid bottom ash have been reported, in which proposals on utilizing the bottom ash to produce lightweight concrete, backfill materials behind retaining walls, asphalt concrete additives and road embankment materials are also pointed out. In this study, series of laboratory experiments were carried out to determine the mechanical properties of the municipal solid bottom ash collected from Thanh Quang - Dan Phuong - Hanoi. Based on the results of the experiments, FEM analyses of a strip foundation on the bottom ash cushion which partially replaces the underlying soft soil layer were conducted. It is derived from the numerical results that the bottom ash could be used to replace the sand cushion in reinforcing of weak ground below foundation.

Modification of Schmertmann-Hartman-Brown method to estimate immediate (elastic) settlement of shallow foundations

One of the methods intensively employed in many practical projects to estimate the immediate (elastic) settlement of shallow foundations is the Schmertmann-Hartman-Brown method (1978). In the method, two approaches are given as a function of type of the shallow foundation either a square/circular (axisymmetric condition) or a strip (plain strain condition) foundation. Thus, two sets of equations are provided to estimate the settlements for these types of shallow foundations. If a shallow foundation has a shape of rectangular, some approximations are suggested in the technical literature to estimate the elastic settlement of rectangular based shallow foundations. These approximations are tedious and time consuming. In this study, the Schmertmann – Hartman – Brown method (1978) is modified and only one set of equations used for any type (square, circular, rectangular, and strip) of shallow foundations is introduced. The modified method estimates the immediate settlement as precise as the original form of the method that is more complicated. Also, some hypothetical cases are considered to figure out the effect of width and length/width ratios of foundations on elastic settlement.

Effectiveness of Random Field Approach in Serviceability Limit State Analysis of Strip Foundation

This work conducts a probabilistic inquiry on how the variability of the parameter defining soil deformability affects the settlement of the foundation located on the soil. The analysis addresses the random foundation model to relevantly estimate the probability of allowable deflection exceedance. The constitutive model parameter is based either on a single random variable or a random field. The computations incorporate direct Monte Carlo sampling and the variance reduction techniques, i.e. Stratified Sampling and Latin Hypercube Sampling. The work focuses on soil parameter modelling by random fields defined by various correlation functions. One of the analytical means is the application of a non-homogeneous function capable of reflecting the soil strata. The probabilistic methods proposed in the paper are tested on a standard example of a foundation strip featuring load eccentricity. It is proved that the modelling mode of the soil—a single variable or a random field—substantially affects the results, i.e. foundation settlements. It was detected that incorporating random fields in soil analysis allows for a valid reliability assessment of a foundation in respect to Serviceability Limit State. The relevantly adjusted correlation functions of random fields allow for a realistic subsoil analysis even in the case of a limited in situ measurement database.

Vertical vibration of a rigid strip footing on a half-space of unsaturated porous soil

This study presents an analytical solution to the compliance coefficient of rigid strip footings lying on an unsaturated porous soil half-space when subjected to vertical vibration. Using the Fourier transform techniques, the complex interaction between unsaturated soils and rigid strip foundations is transformed into a mixed boundary-value problem based on the developed framework of Biot’s model. The wavenumber domain auxiliary function and boundary conditions are used to convert the governing equations to a pair of dual integral equations. To yield the compliance function, the integral equations are transformed into a system of inhomogeneous linear equations by utilizing hypergeometric polynomials and Bessel functions. The proposed analytical solution is verified against existing solutions to interactions between foundations and saturated soil or single-phase soil by adjusting the parameters in the unsaturated soil model. Additionally, the impacts of soil skeleton saturation, intrinsic permeability, and Poisson’s ratio of unsaturated soil on the dynamic compliance coefficient of rigid strip footings are examined. It is shown that the Poisson’s ratio of the soil skeleton and the soil saturation at critical saturation have a significant effect on the dynamic compliance coefficient, but have a negligible effect on the intrinsic permeability.

Spatially variable soils affecting geotechnical strip foundation design

Natural soil variability is a well-known issue in geotechnical design, although not frequently managed in practice. When subsoil must be characterized in terms of mechanical properties for infrastructure design, random finite element method (RFEM) can be effectively adopted for shallow foundation design to gain a twofold purpose: (1) understanding how much the bearing capacity is affected by the spatial variability structure of soils, and (2) optimisation of the foundation dimension (i.e. width B ). The present study focuses on calculating the bearing capacity of shallow foundations by RFEM in terms of undrained and drained conditions. The spatial variability structure of soil is characterized by the autocorrelation function and the scale of fluctuation ( δ ). The latter has been derived by geostatistical tools such as the ordinary Kriging (OK) approach based on 182 cone penetration tests (CPTs) performed in the alluvial plain in Bologna Province, Italy. Results show that the increase of the B / δ ratio not only reduces the bearing capacity uncertainty but also increases its mean value under drained conditions. Conversely, under the undrained condition, the autocorrelation function strongly affects the mean values of bearing capacity. Therefore, the authors advise caution when selecting the autocorrelation function model for describing the soil spatial variability structure and point out that undrained conditions are more affected by soil variability compared to the drained ones. • RFEM is able to consider the soil variability structure in strip foundation design. • Bearing capacity mean value is affected by soil spatial variability. • Bearing capacity is affected by autocorrelation function model. • Coefficient of variation COV reduces as the foundation size increases. • Both drained and undrained soil conditions show similar COV reduction.

Load and resistance factor design versus reliability-based design of shallow foundations

ABSTRACT The load and resistance factor design (LRFD) approach employed in geotechnical design codes is often calibrated using the reliability-based design (RBD) method. However, the LRFD may not achieve the target safety level exactly. This paper makes comparisons between the LRFD and RBD by considering the ultimate and serviceability limit state design of strip foundations. The RBD is carried out via the Random Finite Element Method. It is found that the failure probability and the resulting foundation width for ULS obtained using the RBD increase with the soil spatial correlation length, gradually reaching a plateau. The comparison between the LRFD and RBD results for ULS suggests that the LRFD is conservative for low to medium soil variability, particularly at smaller correlation lengths. The reliability-based SLS design is less dependent on the soil correlation length, particularly for lower coefficients of variation of the soil elastic modulus. However, a resistance factor of 1.0 for SLS is unconservative, and resistance factors of 0.65, 0.7 and 0.8 are better aligned with the RBD when the target failure probabilities are 1×10−3, 1×10−2 and 1×10−1. The current study can be used to guide the design of shallow foundations and the calibration of the LRFD approach.

Foundation bearing capacity estimation on unsaturated soil slope under transient flow condition using slip line method

In this paper, an analytical method is proposed for estimating the bearing capacity of soil within the framework of slip line theory. The method incorporates a closed-form solution taking account the transient unsaturated vertical flow conditions. The proposed framework is validated for both level and sloping ground scenarios considering saturated and unsaturated soil conditions. More specifically, the bearing capacity of a strip foundation located on an unsaturated soil slope under the influence of different rainfall infiltration conditions is evaluated. A comprehensive parametric study is also conducted taking account the influence of the rainfall influx, rainfall duration, slope angle, foundation setback distance, soil type, and the depth of the ground water table. In addition, the contribution of matric suction towards the bearing capacity under transient flow conditions is evaluated. Results of this study provide a rigorous understanding of the performance of foundations on sloping ground extending the mechanics of unsaturated soils.

Train-induced environmental vibrations by considering different building foundations along curved track

Comparing with the straight track, the curved track accounts for a large proportion with the rapid development of metro networks. The train-induced horizontal vibrations, which can’t be ignored, are close to the vertical vibrations. The residents and the service of building structures adjacent to the curved subway lines are greatly affected by the train-induced horizontal vibrations and vertical vibrations. Meanwhile, subway lines inevitably pass through the sensitive areas which have the requirements for vibration control, and the effect of soil-structure interaction on vibration propagation from the ground to upper building structures are not clear so far. Thus, this paper presents a numerical method to study the vibration propagation laws in the ground soil and the effect of soil-structure interactions on building vibrations along a curved subway segment. The method consists of a train-track coupled model and a finite-infinite model. The train-track coupled model could obtain both vertical and horizontal forces of inner and outer wheel-rail, and they are the dynamic loads applying at the finite-infinite numerical model. Then, the numerical method is verified by comparing with the situ measurements, which have been performed along a curved track of Guangzhou metro. Finally, building with pile, raft, or strip foundations was modeled to study the impact of soil-structure interactions. The numerical results show that the horizontal and vertical vibrations along the curved track are larger than the corresponding vibrations induced by train operation on the straight track. The soil-structure interaction has a significant effect on vibration propagation both in the ground soil and from the ground soil into the upper building. A building with a pile foundation can alleviate the vibration of the upper structure, especially in high-frequency band.

Dynamic analysis of eccentrically loaded rigid strip foundation on layered transversely isotropic poroelastic media

This paper presents an analytical method for analyzing vertical and rocking motions of a rigid strip foundation on layered transversely isotropic poroelastic media. The extended precise integration method is employed to obtain the plain strain dynamic responses of layered poroelastic media due to the reaction force from the rigid strip. Then, the contact stresses for dynamic soil-structure interactions (SSI) are modelled by the Bessel series expansions, and a set of linear equations can be developed from the dual integral equations of mixed boundary value problems. The explicit expressions for the contact stresses are further obtained by solving these linear equations. Finally, the presented method is verified, and numerical examples are provided to demonstrate the effects of stratifications, transverse isotropy and permeability of media on the dynamic responses of eccentrically loaded rigid strip foundation.

Analytical Prediction of Strip Foundation Building Response to Shallow Tunneling Considering the Tunneling Process

This paper presents an analytical method to predict the response of a strip foundation building to shallow tunneling based on the two-stage method. The existing building is simplified as a Euler–Bernoulli beam resting on the Pasternak model. The tunneling process and different relative positions between the tunnel and the existing building can be considered in the proposed method. The accuracy of the proposed method is verified through comparisons with results from the finite element and finite difference methods. The results indicate that the differential settlement of the building reaches a maximum and the rotation angles are symmetric with respect to the building centerline when the tunnel face arrives at the middle of the building. The maximum bending moments occur at the middle of the building, while the maximum shear forces occur at about one-fifth and four-fifths of the building length when the tunnel face is located at the two ends of the building. According to the parametric analysis, the alignment angle, elastic modulus and Poisson’s ratio of the soil, bending stiffness, and gap parameter greatly affect the building response.

New Model for Predicting the Bearing Capacity of Large Strip Foundations on Soil under Combined Loading

The bearing capacity of large strip foundations under combined loading is an important issue in geotechnical engineering, which is related to the design and stability analysis of foundations such as gravity dams, retaining walls, and ground anchorages of bridges. Herein, a new model for predicting the bearing capacity of large strip foundations under combined loading was proposed. First, a series of numerical simulation analyses of a large strip foundation resting on the surface of the soil were conducted to investigate the shape of the failure envelope in the V–M–H (vertical load, overturning moment, and horizontal load) loading space, and an improved form of failure equation was proposed. Second, the main factors influencing Vmax (the vertical ultimate bearing capacity) and the shape of the failure envelope were determined. Last, an applicable empirical equation of the failure envelope in the V–M–H loading space was presented. The results show that the deflection angle of the ellipse (θ), which is considered as a certain constant by previous studies, varies with the vertical load (V); the width of the foundation (B), the depth of the foundation (D), the cohesion of the soil (c), and the internal friction angle of the soil (φ) are the main factors influencing Vmax and the shape of the failure envelope; only parameters B, D, c, φ, and γ are needed to determine, in a unique way, the empirical equation of the failure envelope in the V–M–H loading space. The proposed model provides a convenient means of calculating the bearing capacity of large strip foundations on soil under combined loading.

Effect of Partial Saturation on Ultimate Bearing Capacity of Skirted Foundations

Skirted foundations are one of the solutions proposed to increase the bearing capacity of the soil. They assist in increasing the load and depth of failure in weak ground or soils with low shear resistance and reducing the foundation settlement if a soil improvement method cannot be applied or the cost of implementing deep foundations increases. This study examined and investigated the extent of soil bearing of skirted foundations on sandy soils and studied the effect of soil saturation cases and three cases of water content reduction to measure the matric suction value of unsaturated soil. A physical model was created to simulate the strip foundation and compare these cases (dry-fully saturated-partially saturated). It was found that the soil load carrying capacity in the case of unsaturated soil is the highest, where matric suction is at a depth of 450 mm, followed by the dry case and then the saturated case as it represents the weakest state of the soil.

Comparing bearing capacity factor Nγ of finite element method with analytical methods for sandy soils

Shallow strip footings are essential to carry loads from structures. Load bearing capacity factors can be calculated both by the field tests (plate load test) and numerically. Bearing capacity factors are the main parameters that affect the bearing capacity of any foundations. Nγ, one of these factors, have significant impact. Increase in internal frictional angle (ϕ), causes enhance the Nγ value. However, after ϕ value reaches 30°, dramatic increase is observed. This make the bearing capacity values complicated. In this study, strip foundation on surface resting on sandy soils were designed with a Geostudio 2012 software. Various foundation width (1, 1.25, 1.5, 1.75 and 2 m) and internal friction angle (29°, 31°, 33°, 35°, 37°, 39°, and 41°) was selected. Bearing capacity values were calculated with both numerical (software) and analytical methods. After, Nγ values of analytical methods were compared to results obtained from software. Results indicate that, Biarez 1961 has the average Nγ values while Terzaghi (1943) and Michalowski (1997) have the maximum. Nγ value obtained from numerical analysis (finite element method) increased with an increase in foundation width also. Values from finite element method is average of other analytical methods when B = 1.25 m, while Nγ values of numerical methods are the biggest when B = 2 m.

Field monitoring of vertical stress distribution in GRS-IBS with full-height rigid facings

This paper presents a case study of the first geosynthetic reinforced soil-integrated bridge system (GRS-IBS) with full-height rigid facings in China. Open graded gravel and biaxial geogrid were used for the GRS-IBS. Steel frames and three-dimensional (3D) vegetation nets were used as temporary facing support during construction of the GRS abutments. Full-height rigid facings were cast in place on strip foundations. Field monitoring results of vertical stress distribution for different construction stages and loading conditions are presented and discussed. For both bridge dead load and truck loads, measured incremental vertical stresses under the beam seat increase significantly with increasing elevation, especially for higher applied vertical stress. The calculated incremental vertical soil stresses using the Boussinesq solution are in reasonable agreement with the measured values, while the 2 : 1 stress distribution method overestimates the incremental stresses in the lower section of the abutment. The transferred vertical stresses from bridge load application for the GRS abutment with full-height rigid facing are larger than those for the GRS abutment with modular block facing near the top of the abutment, but are smaller near the bottom.