Geosynthetic Reinforced Soil for Low-Volume Bridge Abutments, January 2012

This report presents a review of literature on geosynthetic reinforced soil (GRS) bridge abutments, and test results and analysis from two field demonstration projects (Bridge 1 and Bridge 2) conducted in Buchanan County, Iowa, to evaluate the feasibility and cost effectiveness of the use of GRS bridge abutments on low-volume roads (LVRs). The two projects included GRS abutment substructures and railroad flat car (RRFC) bridge superstructures. The construction costs varied from $43k to $49k, which was about 50 to 60% lower than the expected costs for building a conventional bridge. Settlement monitoring at both bridges indicated maximum settlements ≤1 in. and differential settlements ≤ 0.2 in transversely at each abutment, during the monitoring phase. Laboratory testing on GRS fill material, field testing, and in ground instrumentation, abutment settlement monitoring, and bridge live load (LL) testing were conducted on Bridge 2. Laboratory test results indicated that shear strength parameters and permanent deformation behavior of granular fill material improved when reinforced with geosynthetic, due to lateral restraint effect at the soilgeosynthetic interface. Bridge LL testing under static loads indicated maximum deflections close to 0.9 in and non-uniform deflections transversely across the bridge due to poor load transfer between RRFCs. The ratio of horizontal to vertical stresses in the GRS fill was low (< 0.25), indicating low lateral stress on the soil surrounding GRS fill material. Bearing capacity analysis at Bridge 2 indicated lower than recommended factor of safety (FS) values due to low ultimate reinforcement strength of the geosynthetic material used in this study and a relatively weak underlying foundation layer. Global stability analysis of the GRS abutment structure revealed a lower FS than recommended against sliding failure along the interface of the GRS fill material and the underlying weak foundation layer. Design and construction recommendations to help improve the stability and performance of the GRS abutment structures on future projects, and recommendations for future research are provided in this report.

Geosynthetic-Reinforced Soil Structure Built to Restore Original Geometry of a 12 m High Slope After Failure Using Local Soil

This paper presents a study case in which a geosynthetic-reinforced soil (GRS) structure was used to rebuild a 12 m high slope after its failure. The failed slope is located between the parking lot of a private company and a public school. Due to surrounding structures restrictions, this project required a solution with rapidity in execution. In addition, as a requirement established by its owner, this structure should recover the original geometry of the slope. Besides the importance regarding surrounding constructions, an interesting aspect of this study case relies on the versatility of geosynthetic materials. A woven geotextile was used as reinforcement. Five other geosynthetic materials were used in this study case. Facing comprised a geocell filled with local soil cover and grass mats, resulting in a green facing. A geonet was used to hold the grass mats in place before grass roots development. Regarding the drainage system, geocomposite drains and geopipes were installed to drain subsurface water. A nonwoven geotextile was used as filter in drainage trenches, which were placed near the structure toe. Additionally to the GRS structure, the lower portion of the slope was reinforced with soil nailing technique. The face of the nailed soil portion was covered with sandbags and shotcrete. It emphasizes the flexibility of GRS structures regarding their application with other technical options in Geotechnical Engineering. The economic aspect of this study case also deserves attention. It did not require soil transportation and other design and construction steps, e.g. concrete structures design and construction.

Performance of Gabion Faced Reinforced Earth Retaining Walls

Gabion faced re.taining walls are essentially semi rigid structures that can generally accommodate large lateral and vertical movements without excessive structural distress. Because of this inherent feature, they offer technical and economical advantage over the conventional concrete gravity retaining walls. Although they can be constructed either as gravity type or reinforced soil type, this work mainly deals with gabion faced reinforced earth walls as they are more suitable to larger heights. The main focus of the present investigation was the development of a viable plane strain two dimensional non linear finite element analysis code which can predict the stress - strain behaviour of gabion faced retaining walls - both gravity type and reinforced soil type. The gabion facing, backfill soil, In - situ soil and foundation soil were modelled using 20 four noded isoparametric quadrilateral elements. The confinement provided by the gabion boxes was converted into an induced apparent cohesion as per the membrane correction theory proposed by Henkel and Gilbert (1952). The mesh reinforcement was modelled using 20 two noded linear truss elements. The interactions between the soil and the mesh reinforcement as well as the facing and backfill were modelled using 20 four noded zero thickness line interface elements (Desai et al., 1974) by incorporating the nonlinear hyperbolic formulation for the tangential shear stiffness. The well known hyperbolic formulation by Ouncan and Chang (1970) was used for modelling the non - linearity of the soil matrix. The failure of soil matrix, gabion facing and the interfaces were modelled using Mohr - Coulomb failure criterion. The construction stages were also modelled.Experimental investigations were conducted on small scale model walls (both in field as well as in laboratory) to suggest an alternative fill material for the gabion faced retaining walls. The same were also used to validate the finite element programme developed as a part of the study. The studies were conducted using different types of gabion fill materials. The variation was achieved by placing coarse aggregate and quarry dust in different proportions as layers one above the other or they were mixed together in the required proportions. The deformation of the wall face was measured and the behaviour of the walls with the variation of fill materials was analysed. It was seen that 25% of the fill material in gabions can be replaced by a soft material (any locally available material) without affecting the deformation behaviour to large extents. In circumstances where deformation can be allowed to some extents, even up to 50% replacement with soft material can be possible.The developed finite element code was validated using experimental test results and other published results. Encouraged by the close comparison between the theory and experiments, an extensive and systematic parametric study was conducted, in order to gain a closer understanding of the behaviour of the system. Geometric parameters as well as material parameters were varied to understand their effect on the behaviour of the walls. The final phase of the study consisted of developing a simplified method for the design of gabion faced retaining walls. The design was based on the limit state method considering both the stability and deformation criteria. The design parameters were selected for the system and converted to dimensionless parameters. Thus the procedure for fixing the dimensions of the wall was simplified by eliminating the conventional trial and error procedure. Handy design charts were developed which would prove as a hands - on - tool to the design engineers at site. Economic studies were also conducted to prove the cost effectiveness of the structures with respect to the conventional RCC gravity walls and cost prediction models and cost breakdown ratios were proposed. The studies as a whole are expected to contribute substantially to understand the actual behaviour of gabion faced retaining wall systems with particular reference to the lateral deformations.

RELIBILITY ANALYSIS OF SIMPLE SLOPES AND SOIL-STRUCTURES WITH LINEAR LIMIT STATES

The first objective of this research was to develop closed-form and numerical probabilistic methods of analysis that can be applied to otherwise conventional methods of unreinforced and geosynthetic reinforced slopes and walls. These probabilistic methods explicitly include random variability of soil and reinforcement, spatial variability of the soil, and cross-correlation between soil input parameters on probability of failure. The quantitative impact of simultaneously considering the influence of random and/or spatial variability in soil properties in combination with cross-correlation in soil properties is investigated for the first time in the research literature. Depending on the magnitude of these statistical descriptors, margins of safety based on conventional notions of safety may be very different from margins of safety expressed in terms of probability of failure (or reliability index). The thesis work also shows that intuitive notions of margin of safety using conventional factor of safety and probability of failure can be brought into alignment when cross-correlation between soil properties is considered in a rigorous manner. The second objective of this thesis work was to develop a general closed-form solution to compute the true probability of failure (or reliability index) of a simple linear limit state function with one load term and one resistance term expressed first in general probabilistic terms and then migrated to a LRFD format for the purpose of LRFD calibration. The formulation considers contributions to probability of failure due to model type, uncertainty in bias values, bias dependencies, uncertainty in estimates of nominal values for correlated and uncorrelated load and resistance terms, and average margin of safety expressed as the operational factor of safety (OFS). Bias is defined as the ratio of measured to predicted value. Parametric analyses were carried out to show that ignoring possible correlations between random variables can lead to conservative (safe) values of resistance factor in some cases and in other cases to non-conservative (unsafe) values. Example LRFD calibrations were carried out using different load and resistance models for the pullout internal stability limit state of steel strip and geosynthetic reinforced soil walls together with matching bias data reported in the literature.

Estudo do efeito da face sobre o equilíbrio de estruturas de contenção de solo reforçado sob condições de trabalho

Os métodos de análise de estruturas de contenção de solo reforçado sob condições de trabalho, em geral, desconsideram a contribuição da face para o equilíbrio da estrutura. Visando estudar a influência do peso específico da face e das propriedades relacionadas à rigidez da mesma sobre o desempenho das estruturas de solo reforçado, são realizadas simulações numéricas de diversas estruturas, utilizando a versão de dupla precisão do programa CRISP92-SC. Avalia-se, também, o emprego de diferentes tipos de elementos para a representação da face. Verifica-se que a face rígida impõe redução significativa das solicitações máximas de tração nos reforços e dos deslocamentos das estruturas de solo reforçado. A influência do peso específico da face sobre a estabilidade interna dos maciços reforçados mostrase desprezível e constata-se que a rigidez à flexão e a rigidez axial da face, função da sua geometria e do seu módulo de Young, são parâmetros influentes no comportamento das estruturas de contenção de solo reforçado. As variações da tração no reforço e da resultante de força cortante na face, em decorrência do enrijecimento da face, são analisadas e propõe-se uma relação entre elas. Quanto à forma de representação de uma face com rigidez expressiva, na simulação de uma estrutura de solo reforçado com o CRISP92-SC, é observado que a representação da face, seja por elementos de viga, seja por elementos quadriláteros, não altera os resultados da análise.

Estruturas de Suporte de Terras Executadas com Pneus - Modelo à Escala Reduzida

Mestrado em Engenharia Civil – Ramo de Estruturas

Estruturas de Suporte de Terras Executadas Com Pneus. Estudo Paramétrico e Conceção de Protótipo

No presente trabalho descreve-se o estudo realizado no Instituto Superior de Engenharia do Porto (ISEP) com o objetivo de comprovar a viabilidade da utilização de pneus em fim de vida em estruturas de solo reforçado. As estruturas de suporte de terras materializadas com pneus preenchidos com solo são usadas em alguns países, sobretudo em estruturas do tipo gravidade. Investiga-se neste trabalho o seu desempenho em estruturas de solo reforçado. Com a finalidade de prever o comportamento da construção, foi utilizado um software desenvolvido pela empresa Canadiana Rocscience, denominado Phase2. Com este software foi possível fazer uma análise paramétrica da secção transversal do modelo, avaliando os esforços e os deslocamentos que se desenvolvem no interior da estrutura, através da utilização do Método dos Elementos Finitos. Foi efetuada uma campanha de ensaios laboratoriais, realizados com amostras de solo retiradas do local de construção do protótipo, com o intuito de caracterizar os parâmetros do solo A definição destes parâmetros tem como objetivo tornar a simulação o mais fidedigna possível. Estruturas de Suporte de Terras Executadas Com Pneus. Estudo Paramétrico e Conceção de Protótipo Como validação da modelação realizada no programa Phase2, o protótipo será devidamente instrumentado com equipamentos de monitorização; a informação recolhida receberá um tratamento posterior e permitirá a calibração do modelo numérico. No presente trabalho define-se o plano de monitorização a instalar no protótipo.

Modelação numérica de uma solução de reforço de solos para fundações de aerogeradores

Dissertação de mestrado integrado em Engenharia Civil

Highway Applications for Rammed Aggregate Piers in Iowa Soils, TR-443, 2003

This report describes a study to evaluate Geopier® soil reinforcement technology in transportation construction. Three projects requiring settlement control were chosen for evaluation—an embankment foundation, a box culvert, and a bridge approach fill. For each project, construction observations, in situ soil testing, laboratory material characterization, and performance monitoring were carried out. For the embankment foundation project, Geopier elements were installed within and around an abutment footprint for the new I-35 overpass at the US Highway 5/Interstate 35 interchange in Des Moines, Iowa. Although the main focus of this investigation was to evaluate embankment foundation reinforcement using Geopier elements, a stone column reinforced soil provided an opportunity to compare systems. In situ testing included cone penetration tests (CPTs), pressuremeter tests (PMTs), Ko stepped blade tests, and borehole shear tests (BSTs), as well as laboratory material testing. Comparative stiffness and densities of Geopier elements and stone columns were evaluated based on full-scale modulus load tests and standard penetration tests. Vibrating wire settlement cells and total stress cells were installed to monitor settlement and stress concentration on the reinforcing elements and matrix soil. Settlement plates were also monitored by conventional optical survey methods. Results show that the Geopier system and the stone columns performed their intended functions. The second project involved settlement monitoring of a 4.2 m wide x 3.6 m high x 50 m long box culvert constructed beneath a bridge on Iowa Highway 191 south of Neola, Iowa. Geopier elements were installed to reduce total and differential settlement while ensuring the stability of the existing bridge pier foundations. Benefits of the box culvert and embankment fill included (1) ease of future roadway expansion and (2) continual service of the roadway throughout construction. Site investigations consisted of in situ testing including CPTs, PMTs, BSTs, and dilatometer tests. Consolidated drained triaxial compression tests, unconsolidated undrained triaxial compression test, oedometer tests, and Atterberg limit tests were conducted to define strength and consolidation parameters and soil index properties for classification. Vibrating wire settlement cells, total stress cells, and piezometers were installed for continuous monitoring during and after box culvert construction and fill placement. This project was successful at controlling settlement of the box culvert and preventing downdrag of the bridge foundations, but could have been enhanced by reducing the length of Geopier elements at the ends of the box culvert. This would have increased localized settlement while reducing overall differential settlement. The third project involved settlement monitoring of bridge approach fill sections reinforced with Geopier elements. Thirty Geopier elements, spaced 1.8 m apart in six rows of varying length, were installed on both sides of a new bridge on US Highway 18/218 near Charles City, Iowa. Based on the results of this project, it was determined that future applications of Geopier soil reinforcement should consider extending the elements deeper into the embankment foundation fill, not just the fill itself.

Utilisation of Coir Geotextiles for Unpaved Roads and Embankments

The increasing tempo of construction activity the world over creates heavy pressure on existing land space. The quest for new and competent site often points to the needs for improving existing sites, which are otherwise deemed unsuitable for adopting conventional foundations. This is accomplished by ground improvement methods, which are employed to improve the quality of soil incompetent in their natural state. Among the construction activities, a well-connected road network is one of the basic infrastructure requirements, which play a vital role for the fast and comfortable movement of inter- regional traffic in countries like India.One of the innovative ground improvement techniques practised all over the world is the use of geosynthetics, which include geotextiles, geomembranes, geogrids, etc . They offer the advantages such as space saving, enviromnental sensitivity, material availability, technical superiority, higher cost savings, less construction time, etc . Because of its fundamental properties, such as tensile strength, filtering and water permeability, a geotextile inserted between the base material and sub grade can function as reinforcement, a filter medium, a separation layer and as a drainage medium. Though polymeric geotextiles are used in abundant quantities, the use of natural geotextiles (like coir, jute, etc.) has yet to get momentum. This is primarily due to the lack of research work on natural geotextilcs for ground improvement, particularly in the areas of un paved roads. Coir geotextiles are best suited for low cost applications because of its availability at low prices compared to its synthetic counterparts. The proper utilisation of coir geotextilcs in various applications demands large quantities of the product, which in turn can create a boom in the coir industry. The present study aims at exploring the possibilities of utilising coir geotextiles for unpaved roads and embankments.The properties of coir geotextiles used have been evaluated. The properties studied include mass per unit area, puncture resistance, tensile strength, secant modulus, etc . The interfacial friction between soils and three types of coir geotextiles used was also evaluated. It was found that though the parameters evaluated for coir geotextiles have low values compared to polymeric geotextiles, the former are sufficient for use in unpaved roads and embankments. The frictional characteristics of coir geotextile - soil interfaces are extremely good and satisfy the condition set by the International Geosynthetic Society for varied applications.The performance of coir geotextiles reinforced subgrade was studied by conducting California Bearing Ratio (CBR) tests. Studies were made with coir geotextiles placed at different levels and also in multiple layers. The results have shown that the coir geotextile enhances the subgrade strength. A regression analysis was perfonned and a mathematical model was developed to predict the CBR of the coir geotextile reinforced subgrade soil as a function of the soil properties, coir geotextile properties, and placement depth of reinforcement.The effects of coir geotextiles on bearing capacity were studied by perfonning plate load tests in a test tan1e This helped to understand the functioning of geotextile as reinforcement in unpaved roads and embankments. The perfonnance of different types of coir geotextiles with respect to the placement depth in dry and saturated conditions was studied. The results revealed that the bearing capacity of coir-reinforced soil is increasing irrespective of the type of coir geotextiles and saturation condition.The rut behaviour of unreinforced and coir reinforced unpaved road sections were compared by conducting model static load tests in a test tank and also under repetitive loads in a wheel track test facility. The results showed that coir geotextiles could fulfill the functions as reinforcement and as a separator, both under static and repetitive loads. The rut depth was very much reduced whik placing coir geotextiles in between sub grade and sub base.In order to study the use of Coir geotextiles in improving the settlement characteristics, two types of prefabricated COlf geotextile vertical drains were developed and their time - settlement behaviour were studied. Three different dispositions were tried. It was found that the coir geotextile drains were very effective in reducing consolidation time due to radial drainage. The circular drains in triangular disposition gave maximum beneficial effect.In long run, the degradation of coir geotextile is expected, which results in a soil - fibre matrix. Hence, studies pertaining to strength and compressibility characteristics of soil - coir fibre composites were conducted. Experiments were done using coir fibres having different aspect ratios and in different proportions. The results revealed that the strength of the soil was increased by 150% to 200% when mixed with 2% of fibre having approximately 12mm length, at all compaction conditions. Also, the coefficient of consolidation increased and compression index decreased with the addition of coir fibre.Typical design charts were prepared for the design of coir geotextile reinforced unpaved roads. Some illustrative examples are also given. The results demonstrated that a considerable saving in subase / base thickness can he achieved with the use of eoir geotextiles, which in turn, would save large quantities of natural aggregates.

Análise experimental e numérica do comportamento de estruturas de solo reforçado com geossintéticos : solo granular versus fino

As estruturas de solo reforçado com geossintéticos são normalmente constituídas por solos granulares com boas propriedades físicas e mecânicas. O uso de apenas este tipo de solos pode proporcionar o aumento, por vezes insustentável, do custo da execução das estruturas e o aumento do seu impacto ambiental. Deste modo, as estruturas de solo reforçado perdem a sua vantagem competitiva em relação a outros tipos de estruturas (muros de betão, muros de gravidade, muros de gabiões, etc.). Para resolver este problema podem ser utilizados outros tipos de solos (solos locais, finos, com propriedades físicas e mecânicas piores mas, no entanto, mais baratos) para a execução deste tipo de estruturas. De forma geral, com este estudo pretendeu-se contribuir para o incremento do conhecimento sobre a utilização de solos finos para a construção de estruturas de solo reforçado (muros e taludes). Para tal avaliaram-se as diferenças no comportamento mecânico dos materiais compósitos (solo granular reforçado versus solo fino reforçado) e das estruturas de solo reforçado constituídas com os dois tipos de solos. Assim, os objetivos deste estudo foram avaliar: a influência de vários parâmetros nas propriedades mecânicas e na capacidade de carga dos solos reforçados com geossintéticos; a influência de vários parâmetros no dimensionamento das estruturas de solo reforçado; e o comportamento das estruturas dimensionadas (incluindo a estabilidade global e a influência do processo construtivo) recorrendo a uma ferramenta numérica (PLAXIS). Para cumprir os objetivos propostos foram realizadas análises experimentais em laboratório (análise do comportamento do solo reforçado através de ensaios triaxiais e de California Bearing Ratio) e análises numéricas (dimensionamento de estruturas de solo reforçado; modelação numérica do comportamento através de uma ferramenta numérica comercial com o método dos elementos finitos). Os resultados dos ensaios experimentais mostraram que o comportamento mecânico e a capacidade de carga do solo foram incrementados com a inclusão das camadas de geossintético. Este efeito variou com os diversos parâmetros analisados mas, de forma geral, foi mais importante no solo fino (solo com propriedades mecânicas piores). As análises numéricas mostraram que as estruturas de solo fino precisaram de maior densidade de reforços para serem estáveis. Além disso, as estruturas de solo fino foram mais deformáveis e o efeito do seu processo construtivo foi mais importante (principalmente para estruturas de solo fino saturado).

Durability/corrosion of soil reinforced structures /

"December 1990."

Natural fibers for soil reinforcement

The reinforcement of soil is defined as an effective and reliable technique to improve strength and stability. For this propose, the use of natural fibers has been commonly. Over the past years, a series of studies have been performed in order to investigate the influence of randomly oriented fibers, especially for compressible clayey soils. However, less attention has been given to the reinforcing of sandy materials, as well as the use of oriented fibers meshes in order to improve mechanical behaviour. The main aim of this study is to identify the influence that different percentages of fibers, as well as the use of meshes of oriented fibers, has on soil mechanical behaviour. For this purpose, unconfined compression tests with local strain measurements were performed on a silty sand reinforced with Sisal fibers and a comparative study between randomly oriented and 0° and 90° fibers is presented.

Performance of Randomly Oriented, Fiber-Reinforced Roadway Soils, HR-211, 1982

Several primary techniques have been developed through which soil aggregate road material properties may be improved. Such techniques basically involve a mechanism of creating a continuous matrix system of soil and/or aggregate particles, interlocked through the use of some additive such as portland cement, lime, or bituminous products. Details by which soils are stabilized vary greatly, but they are dependent on the type of stabilizing agent and nature of the soil, though the overall approach to stabilization has the common feature that improvement is achieved by some mechanism(s) forcing individual particles to adhere to one another. This process creates a more rigid material, most often capable of resisting the influx of water during freezing, loss of strength due to high moisture content and particle dispersion during thawing, and loss of strength due to migration of fines and/or water by capillarity and pumping. The study reported herein, took a new and relatively different approach to strengthening of soils, i.e., improvement of roadway soils and/or soil-aggregate materials by structural reinforcement with randomly oriented fibers. The purpose of the study was to conduct a laboratory and field investigation into the potential of improving (a) soil-aggregate surfaced and subgrade materials, including those that are frost-prone and/or highly moisture susceptible, and (b) localized base course materials, by uniting such materials through fibrous reinforcement. The envisioned objective of the project was the development of a simple construction technique(s) that could be (a) applied on a selective basis to specific areas having a history of poor performance, or (b) used for improvement of potential base materials prior to surfacing. Little background information on such purpose and objective was available. Though the envisioned process had similarities to fibrous reinforced concrete, and to fibrous reinforced resin composites, the process was devoid of a cementitious binder matrix and thus highly dependent on the cohesive and frictional interlocking processes of a soil and/or aggregate with the fibrous reinforcement; a condition not unlike the introduction of reinforcing bars into a concrete sand/aggregate mixture without benefit of portland cement. Thus the study was also directed to answering some fundamental questions: (1) would the technique work; (2) what type or types of fibers are effective; (3) are workable fibers commercially available; and (4) can such fibers be effectively incorporated with conventional construction equipment, and employed in practical field applications? The approach to obtaining answers to these questions, was guided by the philosophy that an understanding of basic fundamentals was essential to developing a body of engineering knowledge, that would serve as the basis for eventual development of design procedures with fibrous products for the applications previously noted.

Reinforced Slope with Geogrids, HR-548, 1997

The objective of this research study is to evaluate the performance, maintenance requirements and cost effectiveness of constructing reinforced slope along a concrete bikeway overpass with a Geogrid system such as manufactured by Tensar Corporation or Reinforced Earth Company. This final report consists of two separate reports - construction and performance. An earlier design report and work plan was submitted to the Iowa DOT in 1989. From the Design Report, it was determined that the reinforced slope would be the most economical system for this particular bikeway project. Preliminary cost estimates for other design alternatives including concrete retaining walls, gabions and sheet pile walls ranged from $204/L.F. to $220/L.F. The actual final construction cost of the reinforced slope with GEDGRIDS was around $112/L.F. Although, since the reinforced slope system was not feasible next to the bridge overpass because of design constraints, a fair cost comparison should reflect costs of constructing a concrete retaining wall. Including the concrete retaining wall costs raises the per lineal foot cost to around $122/L.F. In addition to this initial construction cost effectiveness of the reinforced slope, there has been little or no maintenance needed for this reinforced slope. It was noted that some edge mowing or weed whacking could be done near the concrete bikeway slab to improve the visual quality of the slope, but no work has been assigned to city crews. It was added that this kind of weed whacking over such steep slope is more difficult and there could possibly be more potential for work related injury. The geogrid reinforced slope has performed really well once the vegetation took control and prevented soil washing across the bikeway slab. To that end, interim erosion control measures might need to be considered in future projects. Some construction observations were noted. First, there i s no specialized experience or equipment required for a contractor to successfully build a low-to-medium geogrid reinforced slope structure. Second, the adaptability of the reinforced earth structure enables the designer to best fit the shape of the structure to the environment and could enhance aesthetic quality. Finally, a reinforced slope can be built with relatively soft soils provided differential settlements between facing are limited to one or two percent.