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By Mauricio Terceros, Martin Achmus, Freddy Lopez

The massive use of deep foundations had a remarkable influence in the building industry in the 20th century. Piles and micropiles made possible to erect thousands of civil structures around the world, changing quintessentially the urban and rural landscapes. Especially in urban areas, the ongoing development requires not only new infrastructure, but also to increase the capacity and/or to extend the serviceability of existing structures (buildings, bridges, etc.). Factors such as the change of use of existing facilities or the requirement to comply with updated building regulations confront Civil Engineers with the question, whether to tear down and build new structures, or to reinforce the existing structures from their foundations. Micropiling has enabled designers to come up with technical feasible solutions to retrofit the existing deep foundations, making the structural reinforcement a real option, even under considerable changes in the loading conditions. The following article presents an overview of an intervention project, where micropiles were designed to reinforce the original pile foundation of an existing building, enabling it to be reused with a different structural function. This paper will focus mainly on the analysis of the interaction between the existing piles and the reinforcing micropiles, especially in terms of settlements’ compatibility. Finally, the adopted solution, with its correspondent design considerations and execution process will be presented.

Jan 1, 2018

By Daniel A. Thome, Robert C. Janke

"Installation of permanent soil nails through distressed mechanically stabilized earth retaining walls is a cost effective and aesthetically pleasing solution when using the appropriate equipment and drilling methods for installation. A forensic investigation was performed on an existing mechanically stabilized earth retaining wall to determine the possible causes for the excessive horizontal displacements and visual structural flaws found along a portion of the wall. Reports concluded that the visual shifting was due to a number of factors including improper drainage in the vicinity of the wall and unsuitable compaction of the backfill material. Conceptual designs were proposed to the owner and the installation of permanent soil nails through the existing precast panels was determined to be the most practical solution. A total of ninety-three permanent soil nails were installed to lengths of up to 40 feet (12 m) through sand backfill and silty day fill using a hydraulic rotary percussion drill attached to a tract mounted excavator.IntroductionThe Illinois State Toll Highway Authority awarded Contract RR-03-5144 in the summer of 2004. Construction work for the project consisted of the rehabilitation of two existing concrete culverts and approximately 100 linear feet (31 m) of mechanically stabilized earth (MSE) retaining wall. The retaining wall is located below the southbound lanes of the Tri-State Tollway near the intersection of Federal Highway 41 in Wadsworth, Illinois as shown in Figure 1.Reports were prepared by Applied Technologies in cooperation with Giles Engineering Associates to determine the condition of the MSE wall and recommended conceptual designs to extend the service life of the wall.Nicholson Construction Company (Nicholson) wasselected as the design-build geotechnical subcontractor to install the recommended permanent soil nails through the existing precast concrete panels of the MSE wall. Rehabilitation of the wall involved the installation of ninety-three permanent soil nails through the existing wall, along with soil nail verification tests and proof tests on production nails."

Jan 1, 2005

By Ricardo Dobry, Alain Pecker, George E. Leventis, Ralph B. Peck

"This year’s DFI Outstanding Project Award is for the design and construction of the foundation scheme for the largest cable-stayed bridge in the world. In 1993, Gefyra, SA (a French/Greek consortium led by VINCI of Paris, France) was awarded a €750 million ($1billion+ USD) Concession Contract to design, build, fi nance, operate and maintain a three-span cable-stayed suspension bridge connecting the Peloponnese, Greece’s southernmost peninsula, with the mainland across the Gulf of Corinth. The contract extends over a 42-year period, 7 years for design and construction and 35 years for operation. The project was fi nanced through a combination of public funds, private equity and bank loans. Alternative foundation concepts that were considered included traditional driven piles, deeply embedded caissons and soil improvement. PROJECT CHALLENGESThe extreme technical challenges faced included:??Weak foundation soils composed of soft alluvial deposits consisting of interbedded layers of granular and cohesive materials with thin layers and lenses of gravel and liquefi able sand pockets; rock is believed to be at a depth of 1,000 m (3,500 ft) or more.??A very deep seabed exceeding 60 m (200 ft).??The requirement to withstand the collision of 180,000-ton tankers traveling at 16 knots.??Maximum wind forces of 250 km/hour (155 mi/hour).??Design seismic forces corresponding to Richter magnitudes of 7.0+ with peak ground accelerations of 0.48 g at seabed.??Design tectonic movements of 2 m (7 ft) in any direction between any two adjacent bridge pier foundations/pylons.Considering subsurface conditions and local seismicity and water depths, foundation design and construction methods were the key drivers for this project. In large part, the success of the project is owed to the unprecedented partnering and collaboration between all partners involved fostered under the leadership of Jean Paul Teyssandier and Gilles De Maublanc of VINCI Group (France) who served as lead Concessionaire and General Contractor. The joint venture’s lead Greek partners were Elliniki Technodomiki/AKTOR and J&P/AVAX. Alain Pecker of Geodynamique et Structure (France) served as lead Geotechnical Consultant/ Designer while Buckland and Taylor (Canada) served as Design Checkers with Ralph Peck and Ricardo Dobry (U.S.) as Special Advisors on foundation issues, Langan International/Langan Engineering and Environmental Services P.C. (George E. Leventis, Gregory Biesiadecki and Diane Fiorelli) served as Technical Advisor on geotechnical, geodynamic and foundation/marine construction issues."

Jan 1, 2007

By Bas R. Hemmen

GeoBrain is a facility at GeoDelft with the purpose to provide society with all relevant geo-engineering knowledge and experience in a structured way. On the basis of the available knowledge and experience engineers, decision makers and construction supervisors can come to a fast, reproducible and objective choice, taking into account the consequences. The paper presents examples from the GeoBrain experience databases and forecasting models developed for foundation engineering and directional drilling, or: "GeoBrain Foundations" and "GeoBrain Drilling". GeoBrain is closing the gap between theory and practice. It is aimed directly at reducing uncertainty and the costs of failure, thereby increasing the quality of profession and minimising the risk in geo-engineering works.

Jan 1, 2006

By Frank Rausche

Since the early 1980s, when the Road Construction Authority of Victoria authorized the dynamic proof testing of roughly 100 drilled shafts of 1.5 m diameter and typically 60 m length in Melbourne Australia, dynamic load testing has been applied worldwide for quality control of drilled shafts. Today, test capacities of 4000 tons or more are not unusual. On numerous occasions the authors have been involved in similar tests in the United States and test engineers from other countries have reported on experiences in many different countries. Without doubt, generating high test loads is most economically accomplished by dynamic load testing and this method is particularly well suited for testing piles founded in rock because of the rocks low energy dissipation. However, deep foundation professionals have on occasion expressed reservations about subjecting a drilled shaft to impact loadings fearing, for example, a degradation of the shaft ? rock interface properties or potential error sources due to uncertain concrete properties or shaft geometry. This paper will present numerous case studies, demonstrating the performance of rock socketed drilled shafts under dynamic loads. It will discuss the mechanics of the dynamic tests and the method of data interpretation, addressing the concerns stated above and investigating the limitations of the test method. The paper will formulate a set of recommendations for the design and execution of these tests.

Jan 1, 2006

By Tracy Brettmann

Equipment ? Hollow Stem Auger ? Drill Bits ? Leads/Torque Arm ? Hydraulic Gearbox ? Hydraulic Power Unit ? Grout Pump ? Crawler Crane

Jan 1, 2004

By Y. M. Ha, T. D. Nguyen, D. T. Nguyen, H. K. Choi

Conventionally, cement deep mixing (CDM) columns are designed to have constant diameters over the improved depth as this facilitates the construction procedures. However, this design pattern may be inefficient in cases of spread footings or shallow foundations. This paper first briefly introduces principles of an improved CDM method that can create head-enlarged CDM (termed PF) columns. A simple analysis approach was introduced to obtain optimal shape of PF columns that results in minimum settlement. The effectiveness of this improved method over the conventional CDM method was then illustrated by settlement analysis for an actual footing in a case study using two recommended analytical methods in the literature. Analysis results from the case indicated that by using the same amount of soil-cement mixed volumes, settlement from a footing on PF columns can reduce up to 10 % compared with that from the same footing on CDM columns. In addition, a material quantity comparison for the case indicated that to have the same settlement values the volume of each PF column can be reduced of around 10% compared with that of the CDM column. INTRODUCTION The cement deep mixing (CDM) method is one of the most popular methods in ground improvement works. Details on the method such as construction procedures, necessary equipment and recommendations are described in many references or manuals (e.g. Bruce et al. 2013, BS EN 2015, Kitazume and Terashi 2013). Conventionally, CDM columns are designed to have constant diameters over the improved depth as this facilitates the construction procedures. However, this design pattern is found inefficient in cases of spread footings or shallow foundations as the upper soil layers are naturally weaker than the deeper ones but are subjected to larger amount of induced stress from the superstructures.

Jan 1, 2019

By M. Mets

Pile foundations have been used in Estonia since the beginning of 1960's. To evaluate the capacity of piles nearly 2,500 pile tests and 1,800 pile loading tests Have been carried out. The pile foundations of nearly 150 houses are under settlement observations.

Jan 1, 2000

By Paolo Heiniger

The aim of this paper is to present the operative solutions devised and then adopted to implement the underexcavation (soil extraction) of the Tower of Pisa, by means of soil extraction. The intervention has been performed by the Consorzio Progetto Torre di Pisa, a joint venture made of five qualified Italian companies (Trevi S.p.A. , Rodio S.p.A., Italsonda S.p.A., Ismes -Enel Hydro S.p.A., Bonifica S.p.A.), selected for their experience in the field of monitoring and restoration of monuments, structural design, foundation engineering and specialised works in underground conditions. Since 1991 the Consorzio has been charged with the specific task of implementing, within the contractual frame of a Concession, all the decisions made by the International Multidisciplinary Commission appointed by the Italian Government the previous year, with the aim at solving the «problem» of the Tower, strengthening the structure and stabilising its foundation. The Trevi Group, which is represented by Trevi S.p.A. in the above mentioned Consorzio, has given and is giving its direct and constant contribution and is engaged in supplying the special equipment to the operation and the drilling technology which has been successfully adopted to date.

Jan 1, 2000

By D. Mohan

Soft to medium dense silty and clayey soils are found in many parts of India and conventional friction piles have normally been used for foundations of high rise buildings and other structures on such soils. The author investigated the use of Bored Compaction Piles and these have been used on these soils achieving substantial economies in cost over conventional friction piles. Similarly highly expansive clays, commonly known as Indian Black Cotton Soils occupy about 20 percent of the Indian land area. Short bored underreamed piles have been developed for such soils and a very large construction of various types of buildings and other structures have come up on such piles over the last thirty years in various parts of the country. The paper describes investigations leading to the design and development of both these type of foundations.

Jan 1, 1989

By B. N. Hira

A multistoreyed residential complex was at the penultimate stage of construction by ONGC at Nazira, Assam. The site was situated at high earthquake zone. The subsoil was very weak and contained soft to medium clay with water table almost at the ground level. The bearing capacity of soil was quite poor particularly with predicted settlement beyond permissible limit. In this situation, the conventional shallow and deep foundations were found uneconomical and ground improvement with granular piles was considered as the viable solution. ONGC approached the Central Building Research Institute with the request to design granular piles along with R.C.C. foundation and other suitable cost effective measures. CBRI collected relevant geotechnical informations and supplimented the data by conducting field tests at site and laboratory tests at Roorkee. Rational design of 30 cm dia. and 5.00 meter deep granular piles were suggested with isolated and combined RCC footings over the reinforced soil. In addition to several structural and geotechnical advantages, the granular pile foundation provided considerable economy in the cost of construction. The paper presents the salient geotechnical and structural informations of the challenging project and provides the design details of the innovative granular pile-system. It also furnishes the design approach of the RC footings and other elements of the foundation.

Jan 1, 1996

By Bernardo J. Jiménez Vega, Edy L. T. Montalvan

During the last phase of the Circunvalacion Norte project in San Jose, Costa Rica, preliminary designs for an underpass structure of over 16 km (10 miles) considered drilled shafts as an earth retaining system. Since the project’s execution was delayed and close to the deadline, it was necessary to optimize this structure, with the drilled shafts being the most critical aspect. The key element in order to obtain an improved design was characterizing the job site with a specific site study for seismic demand, and the use of advanced numerical modelling, considering soil-structure interaction. The site investigation comprised the CPT, PMT, MASW geophysical tests, deep exploration drilling, and triaxial compression tests. The terrain was modeled using an advanced constitutive model with hardening plasticity calibrated from the triaxial tests. Plaxis software was used to calibrate the seismic model for the terrain and for the dynamic analysis. Two conditions were considered for the retaining structure: free-head and fixed head. A parametric study with drilled shafts of 1.0 m (3.3 ft) and 1.2 m (3.9 ft) in diameter, and center-to-center spacing of 1.3 m (4.3 ft) and 3.0 m (9.8 ft) was conducted in order to obtain an optimized structure. For each condition of the drilled shaft wall, the computed deformations were compared for two spectrum designs: site-specific spectrum and seismic code generic spectrum. Finally, a dynamic analysis was performed to check the performance of the drilled shafts with optimized spacing using a control earthquake. Based upon seismic performance curves, the analysis showed the possibility of greater spacing for the drilled shafts compared to the original design, obtaining a 32% reduction in the total length of the drilled shafts in the project.

Oct 1, 2022

By R. Heath Forbes

The route of a new, 4-mile long, electrical transmission line passed through residential neighborhoods and commercial areas of a small town in the South Carolina Coastal Plain. The new line consisted of 54 new poles and a one-mile underground section. Most of the new poles were constructed within 50 ft of existing structures, and in some cases, within 8 ft to 20 ft. A widely-space subsurface exploration consisting of 20 cone penetration test soundings indicated the subsurface conditions along the alignment generally consisted of saturated, loose to medium dense, fine slightly silty to silty sand. The pole foundations consisted of 20 to 30 ft long, prefabricated ?caissons? (essentially an open-end pipe pile with a prefabricated connection system at the top) with diameters of 28 to 56 inches. The steel caissons were installed with vibratory pile hammers. To help prevent damage and defend against possible allegations from nearby property owners, vibration and settlement monitoring was performed during all foundation installation activities. Limited structural condition assessments were also performed before and after foundation installation. For 53 of the 54 foundations, the ground vibrations recorded at distances coincident with the nearest structure locations ranged from 0.05 inches per second to 1.46 inches per second. With consideration of the dominant frequency, the majority of these values were below the commonly used USBM vibration limits. For a foundation installation that was only 8 ft from the nearest structure, a peak particle velocity of 3.06 inches per second was recorded, which exceeded the USBM limits. For all cases, the measured ground surface settlement was negligible (i.e., less than ¾ inch). Several spurious claims alleging vibration-induced damage were made, but the monitoring program provided an adequate defense. One claim involving artwork that fell to the floor during foundation installation at a distance of 8 ft from the house was deemed legitimate.

Jan 1, 2011

By Nikolaus Schneider

"Abstract: The combination of failure in joints of diaphragm walls and their exposure to water pressure may have far reaching effects ranging from water leakage to the risk of catastrophic loss of stability for the retaining wall and civil structures behind it. Investigations of imperfect joints in diaphragm walls have led to the development and testing of a quality tool to monitor the joint integrity of diaphragm walls during construction. By applying independent mechanical sensors (“joint inspector”) to the steel frame of hydraulic or mechanical grabs, it is now possible to record the surface conditions of exposed primary joints during the construction of secondary panels. This allows for the implementation of corrective action during the construction process should joint quality not indicate a watertight connection to the adjacent panel. The joint inspector, used for different types of stop ends, was tested on a full scale test field at several construction sites. The implementation of this new quality tool drives a new quality standard for deep excavations in inner city areas.General introduction to diaphragm wallsDiaphragm walls are reinforced concrete elements constructed using bentonite slurry to temporarily support an open trench in the ground. They are used in two main fields of application in civil construction, as foundation elements for vertical and horizontal loads (barrettes) and as retaining walls for excavation pits.Particularly for deep excavation pits in inner city areas, diaphragm walls are used as temporary or permanent walls of retaining walls. Alternative retaining wall systems would be secant pile walls, sheet piles or soldier piles, but these have disadvantages in structural strength when compared to diaphragm walls. If the vertical load of existing buildings next to the excavation pit has to be accommodated, the most practical solution can be found using diaphragm walls supported by prestressed anchors, steel struts or slabs."

Jan 1, 2014

By Priyadharshini M. R., Premalatha K

"Abstract With the development in the construction of heavily loaded structures, the necessity of pile foundations has increased. For the transfer of heavy loads, it is mandatory that the piles need to be socketed in the underlying rock strata. The load transfer in bored rock socketed piles is by end resistance or the combination of shaft and end resistance which in turn depends on the length of the rock socket. The determination of socketing length of the pile at present is mostly based on a few factors which affect the pile load transfer mechanism. The effect of all the possible factors involved, need to be studied in proposing guidelines for the design of rock socketing length of the pile. Analyses are carried out using finite element analysis software (PLAXIS 3D Foundation) to understand the influence of the thickness of overlying strata for different socket lengths of piles in weak rock. From the load settlement curves, the influence of the overlying soil on the rock socket length isobserved and an effective rock socket length is proposed.IntroductionThe determination of socketing length of the pile at present is mostly based on a few factors affecting the pile load transfer mechanism, which sometimes give a better design and sometimes an uneconomical design. Too much socketing length results in more construction time and higher costs. Therefore, the effect of all possible factors involved need to be studied in proposing guidelinesfor the design of t h e r o c k socket length of the pile.The factors that affect the termination criteria of the rock socketed pile are the capacity requirement, thickness and properties of the overlying soil, characteristics of the founding strata, drilling tools used, roughness of the rock socket and nature of loading.A comprehensive study was performed to understand all the above mentioned factors in different types of rocks. In this paper discussion is made on the settlement results, specifically the influence of overlying sand of different densities above a weak rock. The influence of stress developed is not discussed, keeping in mind the size of the paper under study."

Jan 1, 2014

By Hee-suk Yun, Dae-jin Hwang, Jeong-woo Seok, Myoung-mo Kim

"In this paper, the accuracy of the data measured by a newly developed displacement measuring system, DPRMs (Digital Pile Penetration and Rebound Monitoring system) and its applicability as a quality control tool were verified by field measurements of pile penetration and rebound for pile driving performed at 3 construction sites and 1 test site. The DPRMs data were found to be much better than handwork data. A new dynamic formula for pile capacities is proposed uses the results of a pilot dynamic load test and the final pile penetration. The ratios of pile capacities obtained by the new formula to those by the dynamic load test were 94%±7.4% in the contrast with 123±28.3% by the 5S formula and 68±24.0% by Hiley's formula. This result shows the superiority of the new formula. The ratios of the maximum compressive stresses calculated by using DPRMs to those calculated by using PDA (Pile Driving Analyzer) were about 90-110±10%. This result confirms the applicability of DPRMs as an overdriving monitoring tool. Two sets of DPRMs were used to measure the 3-D displacement behavior of a pile head at the test site. The more the pile head moves laterally, the less the final set values were expected because of the loss of driving energy, but this trend was not obvious within the limited data obtained at the test site.INTRODUCTIONPile construction monitoring consists of two parts. In the first part, enough capacity of the pile is secured to stand the design load. In the other part, pile damage during driving is prevented. Although several methods can be applied to achieve the first part, PDA is nearly the only tool for measuring pile stress.Several methods such as a static load test, a dynamic load test, an Osterberg cell, and numerous driving equations can determine the pile capacity. Among them, the static load test and the dynamic load test are most widely used. The static load test is advantageous because it has the highest reliability. The disadvantages are as follows: it is costly and time-consuming. Also, the capacity of the pile under construction cannot be evaluated. The dynamic load test has lower reliability than the static load test, but it is cheaper than the static load test, is reliable enough to determine the pile capacity, can evaluate the capacity of a pile during construction, and can offer information about construction conditions such as the pile integrity and the pi le stress during driving. The dynamic load test takes a relatively short time and is low cost compared with the static load test. However, it is still costly, time-consuming, and unnecessary to apply to all piles in the field as a construction measurement tool. Therefore, driving resistance (blowcounts) is commonly measured to confirm the pile capacity at construction sites."

Jan 1, 2005

By D. Waite

The Chairman opened the session by wondering why so few papers on Maritime Structures had been received for this conference. Perhaps because the marine environment is so hostile and the access so difficult that engineers tend to be more prudent about new ideas and designs. Dennis Waite noted the number of grey hairs in the room - grey hairs which could be equated with experience gained the hard way. He hoped that this experience would be passed on in the discussion period of this session. The Chairman was delighted to welcome two authors from China, Mr Sun and Mr Liang. He was most grateful on behalf of the conference for their efforts both in preparing their papers and for being able to present them. He regretted that Messrs Noce and Fedolino were not able to present their paper and then welcomed Mr Christensen from Denmark who would present the first paper.

Jan 1, 1991

By D. G. Bishop

This paper is intended as a review and update of the use of Pressure Injected Footings as deep foundation units in North America. We will discuss various aspects of this pile and then discuss a particular project - the Mobile Alabama Convention Centre which is currently under construction. Pressure Injected Footing is a generic name used to describe a foundation unit that has been in use around the world for some 80 years. It has been used on all types of structures. It is an excellent pile in both compression and tension. It is particularly economic where a layer of granular soils can be found at relatively shallow depths. Other types of piles would penetrate these layers. Caissons are often difficult to construct in these soils because of their lack of cohesion and the often present water table. PIFs can density these shallow layers and carry relatively heavy building loads on them.

Jan 1, 1992

By F. Z. Suo

Baoahan Iron and Steel Complex is situated at lower beaches of the Yangtze River. The subsoils 50~70 M below the surface is a deposite of Yangtze River delta, consisting mainly of weak silty clay and loam, with low soil bearing capacity. Consequently, to build on such a weak soil a grant iron and steel integrated works weak soil improvement at the Complex, pile foundation is the effective type. It is estimated that at the first stage of Baoshan project 60,000 piles have been driven, of which 60% are steel pipe piles and 40% reinforced concrete piles. To provide reliable basis for pile foundation design, on-site loading tests were carried out for long reinforced concrete piles 27,45 60 M in length ,with strain gauges on the chief reinforcement of pile shaft and strain rod on pile tip. Based on loading tests, the paper discusses and analyses some issues, including determination of load transfer mechanism distribution of frictional resistance. Tests show that as far as long friction piles in soft clay are concerned, regardless of the properties of pile tip's bearing stratum, loads are mainly carried by shaft frictional resistance which it is effective to determine pile capacity in terms of P ~ S relationship.

Jan 1, 2010

By Kirk Ellison, Sherif Elfass, Ramin Motamed, Kevin V. Stanton

"The determination of accurate load transfer curves are essential for estimating deep foundation loadsettlement response using t-z style analyses. While recently developed semi-empirical methods from Ashour et al. (2010) and Ashour & Helal (2012) have shown promise in preliminary studies, they have not yet been thoroughly benchmarked against a more widely accepted approach. To address this issue, these recent procedures are implemented in the computer program CGI-DFSAP to predict the results of four Osterberg-cell (O-Cell) load tests. These predictions are compared to outcomes obtained following the recommendations from Reese & O’Neill (1988) for t-z analyses of drilled shafts in sand and clay which are carried out with the program TZ-PILE. Overall, the results suggest that the new approach offers improved accuracy regarding predictions of drilled shaft response to axial loading.INTRODUCTIONThe behavior of axially loaded deep foundations is often analyzed using a technique known as the t-z method. In this method, deep foundation elements are broken into multiple segments which are supported by discrete nonlinear springs to capture the contribution of both side-friction (t-z springs) and end-bearing (Q-z springs). Hence, the t-z and Q-z relationships dictate the predicted load-settlement response. A number of different approaches have been developed to estimate load-transfer curves with some relying solely on empirical data from laboratory and field experiments (i.e. Coyle & Reese, 1966; Vijayvergiya, 1977) and others based mainly on analytical frameworks (i.e. Kraft et al., 1981; Randolph, 1994). Reese & O’Neill (1988) provide recommendations which are widely used for developing t-z and Q-z curves for analyzing drilled shafts. This method is hereafter referred to as Method 1 (M1). It should be noted that these empirically derived relationships are only applicable for problems associated with drilled shafts and are therefore not appropriate for developing load-transfer curves for other types of deep foundations (i.e. driven piles). This is because of the difference in the frictional resistance which can be developed between a circular concrete-soil interface as opposed to that of other materials (i.e. steel) and/or different cross sectional geometries.The M1 load-transfer curves form the basis for the t-z analysis of drilled shafts implemented in the computer program TZ-PILE (Ensoft, 2014). In light of this, TZ-PILE is employed herein as a reference to compare against the capabilities of another method of implementing t-z style analyses. This method is based on a semi-empirical framework for soil behavior developed by Norris (1986) and is implemented using the program CGI-DFSAP (Computers & GeoEngineering Inc., 2011). More information concerning this approach, hereafter referred to as Method 2 (M2), is given in subsequent sections."

Jan 1, 2017