Long duration exercise program in individuals with parkinson´s disease: effects on functional capacity

The aim of this study was to investigate the effects of long duration exercise program on physical fitness components of functional capacity in individuals with Parkinson disease (PD) and to evaluate ongoing effects of exercise after 8 to 10-week follow-up without exercise. Twenty-four individuals with PD were randomly assigned to two groups: generalized exercise program and stretching exercise program (control group). The generalized exercise program provided training in physical fitness components of functional capacity. The stretching exercise program was characterized by low intensity and volume, mainly with static exercises. Both groups were evaluated before (BI) and after the 4-month (AI) exercise program. In addition, the individuals of generalized exercise program were also evaluated after 8-month exercise program and after 8 to 10- week follow-up without exercise. The generalized exercise program improved flexibility (BI - 38.50±12.42 cm; AI - 44.00±12.74 cm) and agility (BI - 30.59±7.54 s; AI - 28.56±8.20 s) while the stretching exercise program worsened coordination (BI - 23.27±6.58 s; AI - 28.06±7.37 s) and aerobic resistance (BI- 13.64±3.76 min; AI - 17.27±5.15 min) and improved balance (BI - 44.00±7.79 pts; AI - 46.57±6.53 pts). Lower-limb strength and UPDRS-motor scale scores were better at 8 months (14.75±2.92 rep and 26.25±13.97 pts, respectively) compared to baseline (13.13±2.59 rep and 31.63±12.82 pts, respectively) and 4 months (13.50±1.93 rep and 30.38±14.52 pts, respectively) for generalized exercise program. However, the benefits of 8 months of exercise were lost after 8 to 10-week follow-up without exercise (lower-limb strength - 12.43±3.15 rep and UPDRS-motor scale - 32.57±14.05 pts). In conclusion, generalized exercise program improved the functional capacity in individuals with PD, differently of stretching exercise program. In addition, a long duration exercise program promoted benefits for functional capacity and disease progression in individuals with PD. However, benefits were lost after a short period without exercise.

Beneficial effects of exercise : shifting the focus from body weight to other markers of health

Background: Exercise is widely promoted as a method of weight management, while the other health benefits are often ignored. The purpose of this study was to examine whether exercise-induced improvements in health are influenced by changes in body weight. Methods: Fifty-eight sedentary overweight/obese men and women (BMI 31.8 (SD 4.5) kg/m2) participated in a 12-week supervised aerobic exercise intervention (70% heart rate max, five times a week, 500 kcal per session). Body composition, anthropometric parameters, aerobic capacity, blood pressure and acute psychological response to exercise were measured at weeks 0 and 12. Results: The mean reduction in body weight was −3.3 (3.63) kg (p<0.01). However, 26 of the 58 participants failed to attain the predicted weight loss estimated from individuals’ exercise-induced energy expenditure. Their mean weight loss was only −0.9 (1.8) kg (p<0.01). Despite attaining a lower-than-predicted weight reduction, these individuals experienced significant increases in aerobic capacity (6.3 (6.0) ml/kg/min; p<0.01), and a decreased systolic (−6.00 (11.5) mm Hg; p<0.05) and diastolic blood pressure (−3.9 (5.8) mm Hg; p<0.01), waist circumference (−3.7 (2.7) cm; p<0.01) and resting heart rate (−4.8 (8.9) bpm, p<0.001). In addition, these individuals experienced an acute exercise-induced increase in positive mood. Conclusions: These data demonstrate that significant and meaningful health benefits can be achieved even in the presence of lower-than-expected exercise-induced weight loss. A less successful reduction in body weight does not undermine the beneficial effects of aerobic exercise. From a public health perspective, exercise should be encouraged and the emphasis on weight loss reduced.

The effect of exercise intensity on fat oxidation and non-exercise activity thermogenesis in overweight/obese men

It is frequently reported that the actual weight loss achieved through exercise interventions is less than theoretically expected. Amongst other compensatory adjustments that accompany exercise training (e.g., increases in resting metabolic rate and energy intake), a possible cause of the less than expected weight loss is a failure to produce a marked increase in total daily energy expenditure due to a compensatory reduction in non-exercise activity thermogenesis (NEAT). Therefore, there is a need to understand how behaviour is modified in response to exercise interventions. The proposed benefits of exercise training are numerous, including changes to fat oxidation. Given that a diminished capacity to oxidise fat could be a factor in the aetiology of obesity, an exercise training intensity that optimises fat oxidation in overweight/obese individuals would improve impaired fat oxidation, and potentially reduce health risks that are associated with obesity. To improve our understanding of the effectiveness of exercise for weight management, it is important to ensure exercise intensity is appropriately prescribed, and to identify and monitor potential compensatory behavioural changes consequent to exercise training. In line with the gaps in the literature, three studies were performed. The aim of Study 1 was to determine the effect of acute bouts of moderate- and high-intensity walking exercise on NEAT in overweight and obese men. Sixteen participants performed a single bout of either moderate-intensity walking exercise (MIE) or high-intensity walking exercise (HIE) on two separate occasions. The MIE consisted of walking for 60-min on a motorised treadmill at 6 km.h-1. The 60-min HIE session consisted of walking in 5-min intervals at 6 km.h-1 and 10% grade followed by 5-min at 0% grade. NEAT was assessed by accelerometer three days before, on the day of, and three days after the exercise sessions. There was no significant difference in NEAT vector magnitude (counts.min-1) between the pre-exercise period (days 1-3) and the exercise day (day 4) for either protocol. In addition, there was no change in NEAT during the three days following the MIE session, however NEAT increased by 16% on day 7 (post-exercise) compared with the exercise day (P = 0.32). During the post-exercise period following the HIE session, NEAT was increased by 25% on day 7 compared with the exercise day (P = 0.08), and by 30-33% compared with the pre-exercise period (day 1, day 2 and day 3); P = 0.03, 0.03, 0.02, respectively. To conclude, a single bout of either MIE or HIE did not alter NEAT on the exercise day or on the first two days following the exercise session. However, extending the monitoring of NEAT allowed the detection of a 48 hour delay in increased NEAT after performing HIE. A longer-term intervention is needed to determine the effect of accumulated exercise sessions over a week on NEAT. In Study 2, there were two primary aims. The first aim was to test the reliability of a discontinuous incremental exercise protocol (DISCON-FATmax) to identify the workload at which fat oxidation is maximised (FATmax). Ten overweight and obese sedentary male men (mean BMI of 29.5 ¡Ó 4.5 kg/m2 and mean age of 28.0 ¡Ó 5.3 y) participated in this study and performed two identical DISCON-FATmax tests one week apart. Each test consisted of alternate 4-min exercise and 2-min rest intervals on a cycle ergometer. The starting work load of 28 W was increased every 4-min using 14 W increments followed by 2-min rest intervals. When the respiratory exchange ratio was consistently >1.0, the workload was increased by 14 W every 2-min until volitional exhaustion. Fat oxidation was measured by indirect calorimetry. The mean FATmax, ƒtV O2peak, %ƒtV O2peak and %Wmax at which FATmax occurred during the two tests were 0.23 ¡Ó 0.09 and 0.18 ¡Ó 0.08 (g.min-1); 29.7 ¡Ó 7.8 and 28.3 ¡Ó 7.5 (ml.kg-1.min-1); 42.3 ¡Ó 7.2 and 42.6 ¡Ó 10.2 (%ƒtV O2max) and 36.4 ¡Ó 8.5 and 35.4 ¡Ó 10.9 (%), respectively. A paired-samples T-test revealed a significant difference in FATmax (g.min-1) between the tests (t = 2.65, P = 0.03). The mean difference in FATmax was 0.05 (g.min-1) with the 95% confidence interval ranging from 0.01 to 0.18. Paired-samples T-test, however, revealed no significant difference in the workloads (i.e. W) between the tests, t (9) = 0.70, P = 0.4. The intra-class correlation coefficient for FATmax (g.min-1) between the tests was 0.84 (95% confidence interval: 0.36-0.96, P < 0.01). However, Bland-Altman analysis revealed a large disagreement in FATmax (g.min-1) related to W between the two tests; 11 ¡Ó 14 (W) (4.1 ¡Ó 5.3 ƒtV O2peak (%)).These data demonstrate two important phenomena associated with exercise-induced substrate oxidation; firstly, that maximal fat oxidation derived from a discontinuous FATmax protocol differed statistically between repeated tests, and secondly, there was large variability in the workload corresponding with FATmax. The second aim of Study 2 was to test the validity of a DISCON-FATmax protocol by comparing maximal fat oxidation (g.min-1) determined by DISCON-FATmax with fat oxidation (g.min-1) during a continuous exercise protocol using a constant load (CONEX). Ten overweight and obese sedentary males (BMI = 29.5 ¡Ó 4.5 kg/m2; age = 28.0 ¡Ó 4.5 y) with a ƒtV O2max of 29.1 ¡Ó 7.5 ml.kg-1.min-1 performed a DISCON-FATmax test consisting of alternate 4-min exercise and 2-min rest intervals on a cycle ergometer. The 1-h CONEX protocol used the workload from the DISCON-FATmax to determine FATmax. The mean FATmax, ƒtV O2max, %ƒtV O2max and workload at which FATmax occurred during the DISCON-FATmax were 0.23 ¡Ó 0.09 (g.min-1); 29.1 ¡Ó 7.5 (ml.kg-1.min-1); 43.8 ¡Ó 7.3 (%ƒtV O2max) and 58.8 ¡Ó 19.6 (W), respectively. The mean fat oxidation during the 1-h CONEX protocol was 0.19 ¡Ó 0.07 (g.min-1). A paired-samples T-test revealed no significant difference in fat oxidation (g.min-1) between DISCON-FATmax and CONEX, t (9) = 1.85, P = 0.097 (two-tailed). There was also no significant correlation in fat oxidation between the DISCON-FATmax and CONEX (R=0.51, P = 0.14). Bland- Altman analysis revealed a large disagreement in fat oxidation between the DISCONFATmax and CONEX; the upper limit of agreement was 0.13 (g.min-1) and the lower limit of agreement was ¡V0.03 (g.min-1). These data suggest that the CONEX and DISCONFATmax protocols did not elicit different rates of fat oxidation (g.min-1). However, the individual variability in fat oxidation was large, particularly in the DISCON-FATmax test. Further research is needed to ascertain the validity of graded exercise tests for predicting fat oxidation during constant load exercise sessions. The aim of Study 3 was to compare the impact of two different intensities of four weeks of exercise training on fat oxidation, NEAT, and appetite in overweight and obese men. Using a cross-over design 11 participants (BMI = 29 ¡Ó 4 kg/m2; age = 27 ¡Ó 4 y) participated in a training study and were randomly assigned initially to: [1] a lowintensity (45%ƒtV O2max) exercise (LIT) or [2] a high-intensity interval (alternate 30 s at 90%ƒtV O2max followed by 30 s rest) exercise (HIIT) 40-min duration, three times a week. Participants completed four weeks of supervised training and between cross-over had a two week washout period. At baseline and the end of each exercise intervention,ƒtV O2max, fat oxidation, and NEAT were measured. Fat oxidation was determined during a standard 30-min continuous exercise bout at 45%ƒtV O2max. During the steady state exercise expired gases were measured intermittently for 5-min periods and HR was monitored continuously. In each training period, NEAT was measured for seven consecutive days using an accelerometer (RT3) the week before, at week 3 and the week after training. Subjective appetite sensations and food preferences were measured immediately before and after the first exercise session every week for four weeks during both LIT and HIIT. The mean fat oxidation rate during the standard continuous exercise bout at baseline for both LIT and HIIT was 0.14 ¡Ó 0.08 (g.min-1). After four weeks of exercise training, the mean fat oxidation was 0.178 ¡Ó 0.04 and 0.183 ¡Ó 0.04 g.min-1 for LIT and HIIT, respectively. The mean NEAT (counts.min-1) was 45 ¡Ó 18 at baseline, 55 ¡Ó 22 and 44 ¡Ó 16 during training, and 51 ¡Ó 14 and 50 ¡Ó 21 after training for LIT and HIIT, respectively. There was no significant difference in fat oxidation between LIT and HIIT. Moreover, although not statistically significant, there was some evidence to suggest that LIT and HIIT tend to increase fat oxidation during exercise at 45% ƒtV O2max (P = 0.14 and 0.08, respectively). The order of training treatment did not significantly influence changes in fat oxidation, NEAT, and appetite. NEAT (counts.min-1) was not significantly different in the week following training for either LIT or HIIT. Although not statistically significant (P = 0.08), NEAT was 20% lower during week 3 of exercise training in HIIT compared with LIT. Examination of appetite sensations revealed differences in the intensity of hunger, with higher ratings after LIT compared with HIIT. No differences were found in preferences for high-fat sweet foods between LIT and HIIT. In conclusion, the results of this thesis suggest that while fat oxidation during steady state exercise was not affected by the level of exercise intensity, there is strong evidence to suggest that intense exercise could have a debilitative effect on NEAT.

Effect of body position on measurements of diffusion capacity after exercise

Background--Pulmonary diffusing capacity for carbon monoxide (Dlco), alveolar capillary membrane diffusing capacity (Dm), and pulmonary capillary blood volume (Vc) are all significantly reduced after exercise. Objective--To investigate whether measurement position affects this impaired gas transfer. Methods--Before and one, two, and four hours after incremental cycle ergometer exercise to fatigue, single breath Dlco, Dm, and Vc measurements were obtained in 10 healthy men in a randomly assigned supine and upright seated position. Results--After exercise, Dlco, Dm, and Vc were significantly depressed compared with baseline in both positions. The supine position produced significantly higher values over time for Dlco (5.22 (0.13) v 4.66 (0.15) ml/min/mm Hg/l, p = 0.022) and Dm (6.78 (0.19) v 6.03 (0.19) ml/min/mm Hg/l, p = 0.016), but there was no significant position effect for Vc. There was a similar pattern of change over time for Dlco, Dm, and Vc in the two positions. Conclusions--The change in Dlco after exercise appears to be primarily due to a decrease in Vc. Although the mechanism for the reduction in Vc cannot be determined from these data, passive relocation of blood to the periphery as the result of gravity can be discounted, suggesting that active vasoconstriction of the pulmonary vasculature and/or peripheral vasodilatation is occurring after exercise.

The effect of ß-alanine on buffering capacity and exercise performance during and following high-intensity exercise in healthy males

Introduction Intense exercise induced acidosis occurs from the accumulation of hydrogen ions as by-products of anaerobic metabolism. Oral ingestion of ß-alanine, a limiting precursor of the intracellular physiochemical buffer carnosine in skeletal muscle, may counteract any detrimental effect of acidosis and benefit performance. The aim of this study was to investigate the effect of ß-alanine as an ergogenic aid during high intensity exercise performance in healthy males. Methods Five males ingested either ß-alanine (BAl) (4.8 g.d-1 for 4wk, then 6.4 g.d-1 for 2wk) or placebo (Pl) (CaCO3) in a crossover design with 6 wk washout between. Following supplementation, participants performed two different intense exercise protocols over consecutive days. On the first day a repeated sprint ability (RSA) test of 5 x 6s, with 24s rest periods, was performed. On the second day a cycling capacity test measuring the time to exhaustion (TTE) was performed at 110% of their max workload achieved in a pre supplementation max test (CCT110%). Non-invasive quantification of carnosine, prior to, and following each supplementation, with magnetic resonance spectrometry was performed in the soleus and gastrocnemius. Time to fatigue (CCT110%), peak and mean power (RSA), blood pH, and plasma lactate were measured. Results Muscle carnosine concentration was not different prior to ß-alanine supplementation and increased 18% in the soleus and 26% in the gastrocnemius, respectively with 6 wk supplementation. There was no difference in the measured performance variables during the RSA test (peak and average power output). TTE during the CCT110% was significantly enhanced following the ingestion of BAl (155s ± 19.03) compared to Pl (134s ± 26.16). No changes were observed in blood pH during either exercise protocol and during the recovery from exercise. Plasma lactate in the BAl condition was significantly higher than Pl only from the 15th minute following exercise during the CCT110%. FIG. 1: Changes in carnosine concentration in the gastrocnemius prior and post 6 week chronic supplementation of placebo and β-alanine. Values expressed as mean.* p<0.05 from Pl at 6 weeks, # p<0.05 from pre supplementation. Conclusion/Discussion Greater muscle carnosine content following 6wk supplementation of ß-alanine enhanced the potential for intracellular buffering capacity. However, this only translated into enhanced performance during the CCT110% high intensity cycling exercise protocol, with no change observed during the RSA test. No differences in post exercise and recovery plasma lactates and blood pH, indicates that 6wks ß-alanine supplementation has no effect on anaerobic metabolism during multiple bout high intensity exercise. Changes in plasma lactate during recovery supports that ß-alanine supplementation may affect anaerobic metabolism however during single bout high intensity.

The effect of ß-alanine on buffering capacity and exercise performance during and following high-intensity exercise in healthy males

Intense exercise induced acidosis occurs after accumulation of hydrogen ions as by-products of anaerobic metabolism. Oral ingestion of ß-alanine, a limiting precursor of the intracellular physiochemical buffer carnosine in skeletal muscle, may counteract detrimental effects of acidosis and benefit performance. This study aimed to investigate the effect of ß-alanine as an ergogenic aid during high intensity exercise performance. Five healthy males ingested either ß-alanine or placebo (Pl) (CaCO3) in a crossover design with 6 wk washout between. Participants performed two different intense exercise protocols over consecutive days. On the first day a repeated sprint ability (RSA) test was performed. On the second day a cycling capacity test measuring the time to exhaustion (TTE) was performed at 110% of maximum workload achieved in a pre supplementation max test (CCT110%). Non-invasive quantification of carnosine, prior to, and following each supplementation, with in vivo magnetic resonance spectrometry was performed in the soleus and gastrocnemius muscle. Time to fatigue (CCT110%), peak and mean power (RSA), blood pH, and plasma lactate were measured. Muscle carnosine concentration was not different prior to ß-alanine supplementation and increased 18% in the soleus and 26% in the gastrocnemius, respectively after supplementation. There was no difference in the measured performance variables during the RSA test (peak and average power output). TTE during the CCT110% was significantly enhanced following the ingestion of BAl (155s ± 19.03) compared to Pl (134s ± 26.16). No changes were observed in blood pH during either exercise protocol and during the recovery from exercise. Plasma lactate after BAI was significantly higher than Pl only from the 15th minute following exercise during the CCT110%. Greater muscle carnosine content following 6wk supplementation of ß-alanine enhanced the potential for intracellular buffering capacity. This translated into enhanced performance during the CCT110% high intensity cycling exercise protocol but not during the RSA test. The lack of change in plasma lactate or blood pH indicates that 6wks ß-alanine supplementation has no effect on anaerobic metabolism during multiple-bout high-intensity exercise. Changes measured in plasma lactate during recovery support the hypothesis that ß-alanine supplementation may affect anaerobic metabolism particularly during single bout high intensity.

Testing the effectiveness of a self-efficacy based exercise intervention for adults with venous leg ulcers : protocol of a randomised controlled trial

Background: Exercise and adequate self-management capacity may be important strategies in the management of venous leg ulcers. However, it remains unclear if exercise improves the healing rates of venous leg ulcers and if a self-management exercise program based on self-efficacy theory is well adhered to. Method/Design: This is a randomised controlled in adults with venous leg ulcers to determine the effectiveness of a self-efficacy based exercise intervention. Participants with venous leg ulcers are recruited from 3 clinical sites in Australia. After collection of baseline data, participants are randomised to either an intervention group or control group. The control group receive usual care, as recommended by evidence based guidelines. The intervention group receive an individualised program of calf muscle exercises and walking. The twelve week exercise program integrates multiple elements, including up to six telephone delivered behavioural coaching and goal setting sessions, supported by written materials, a pedometer and two follow-up booster calls if required. Participants are encouraged to seek social support among their friends, self-monitor their weekly steps and lower limb exercises. The control group are supported by a generic information sheet that the intervention group also receive encouraging lower limb exercises, a pedometer for self-management and phone calls at the same time points as the intervention group. The primary outcome is the healing rates of venous leg ulcers which are assessed at fortnightly clinic appointments. Secondary outcomes, assessed at baseline and 12 weeks: functional ability (range of ankle motion and Tinetti gait and balance score), quality of life and self-management scores. Discussion: This study seeks to address a significant gap in current wound management practice by providing evidence for the effectiveness of a home-based exercise program for adults with venous leg ulcers. Theory-driven, evidence-based strategies that can improve an individual’s exercise self-efficacy and self-management capacity could have a significant impact in improving the management of people with venous leg ulcers. Information gained from this study will provide much needed information on management of this chronic disease to promote health and independence in this population. Trial registration: Australian New Zealand Clinical Trials Registry ACTRN12612000475842 Trial status: Current follow up

The effect of β-alanine and NaHCO3 co-ingestion on buffering capacity and exercise performance with high-intensity exercise in healthy males

Introduction β-alanine (BAl) and NaHCO3 (SB) ingestion may provide performance benefits by enhancing concentrations of their respective physiochemical buffer counterparts, muscle carnosine and blood bicarbonate, counteracting acidosis during intense exercise. This study examined the effect of BAl and SB co-supplementation as an ergogenic strategy during high-intensity exercise. Methods Eight healthy males ingested either BAl (4.8 g day−1 for 4 weeks, increased to 6.4 g day−1 for 2 weeks) or placebo (Pl) (CaCO3) for 6 weeks, in a crossover design (6-week washout between supplements). After each chronic supplementation period participants performed two trials, each consisting of two intense exercise tests performed over consecutive days. Trials were separated by 1 week and consisted of a repeated sprint ability (RSA) test and cycling capacity test at 110 % Wmax (CCT110 %). Placebo (Pl) or SB (300 mg kgbw−1) was ingested prior to exercise in a crossover design to creating four supplement conditions (BAl-Pl, BAl-SB, Pl–Pl, Pl-SB). Results Carnosine increased in the gastrocnemius (n = 5) (p = 0.03) and soleus (n = 5) (p = 0.02) following BAl supplementation, and Pl-SB and BAl-SB ingestion elevated blood HCO3 − concentrations (p < 0.01). Although buffering capacity was elevated following both BAl and SB ingestion, performance improvement was only observed with BAl-Pl and BAl-SB increasing time to exhaustion of the CCT110 % test 14 and 16 %, respectively, compared to Pl–Pl (p < 0.01). Conclusion Supplementation of BAl and SB elevated buffering potential by increasing muscle carnosine and blood bicarbonate levels, respectively. BAl ingestion improved performance during the CCT110 %, with no aggregating effect of SB supplementation (p > 0.05). Performance was not different between treatments during the RSA test.

Bearing capacity of interfering multiple strip footings by using lower bound finite elements limit analysis

The ultimate bearing capacity of a number of multiple strip footings, identically spaced and equally loaded to failure at the same time,is computed by using the lower bound limit analysis in combination with finite elements. The efficiency factor due to the component of soil unit weight, is computed with respect to changes in the clear spacing (xi(gamma)) between the footings. It is noted that the failure load for a footing in the group becomes always greater than that of a single isolated footing. The values of xi(gamma) for the smooth footings are found to be always lower than the rough footings. The values ofxi(gamma) are found to increase continuously with a decrease in the spacing between footings. As compared to the available theoretical and experimental results reported in literature, the present analysis provides generally a little lower values of xi(gamma). (C) 2010 Elsevier Ltd. All rights reserved.

Bearing capacity factors of circular foundations for a general c-phi soil using lower bound finite elements limit analysis

By using the lower bound limit analysis in conjunction with finite elements and linear programming, the bearing capacity factors due to cohesion, surcharge and unit weight, respectively, have been computed for a circular footing with different values of phi. The recent axisymmetric formulation proposed by the authors under phi = 0 condition, which is based on the concept that the magnitude of the hoop stress (sigma(theta)) remains closer to the least compressive normal stress (sigma(3)), is extended for a general c-phi soil. The computational results are found to compare quite well with the available numerical results from literature. It is expected that the study will be useful for solving various axisymmetric geotechnical stability problems. Copyright (C) 2010 John Wiley & Sons, Ltd.

Bearing capacity of two interfering strip footings from lower bound finite elements limit analysis

A rigorous lower bound solution, with the usage of the finite elements limit analysis, has been obtained for finding the ultimate bearing capacity of two interfering strip footings placed on a sandy medium. Smooth as well as rough footingsoil interfaces are considered in the analysis. The failure load for an interfering footing becomes always greater than that for a single isolated footing. The effect of the interference on the failure load (i) for rough footings becomes greater than that for smooth footings, (ii) increases with an increase in phi, and (iii) becomes almost negligible beyond S/B>3. Compared with various theoretical and experimental results reported in literature, the present analysis generally provides the lowest magnitude of the collapse load. Copyright (c) 2011 John Wiley & Sons, Ltd.

Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis

The ultimate bearing capacity of a circular footing, placed over rock mass, is evaluated by using the lower bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization. The generalized Hoek-Brown (HB) failure criterion, but by keeping a constant value of the exponent, alpha = 0.5, was used. The failure criterion was smoothened both in the meridian and pi planes. The nonlinear optimization was carried out by employing an interior point method based on the logarithmic barrier function. The results for the obtained bearing capacity were presented in a non-dimensional form for different values of GSI, m(i), sigma(ci)/(gamma b) and q/sigma(ci). Failure patterns were also examined for a few cases. For validating the results, computations were also performed for a strip footing as well. The results obtained from the analysis compare well with the data reported in literature. Since the equilibrium conditions are precisely satisfied only at the centroids of the elements, not everywhere in the domain, the obtained lower bound solution will be approximate not true. (C) 2015 Elsevier Ltd. All rights reserved.

Bearing capacity factors for a conical footing using lower- and upper-bound finite elements limit analysis

Bearing capacity factors, N-c, N-q, and N-gamma, for a conical footing are determined by using the lower and upper bound axisymmetric formulation of the limit analysis in combination with finite elements and optimization. These factors are obtained in a bound form for a wide range of the values of cone apex angle (beta) and phi with delta = 0, 0.5 phi, and phi. The bearing capacity factors for a perfectly rough (delta = phi) conical footing generally increase with a decrease in beta. On the contrary, for delta = 0 degrees, the factors N-c and N-q reduce gradually with a decrease in beta. For delta = 0 degrees, the factor N-gamma for phi >= 35 degrees becomes a minimum for beta approximate to 90 degrees. For delta = 0 degrees, N-gamma for phi <= 30 degrees, as in the case of delta = phi, generally reduces with an increase in beta. The failure and nodal velocity patterns are also examined. The results compare well with different numerical solutions and centrifuge tests' data available from the literature.

Reply to Discussion on ``Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis'' Comput. Geotech. 70 (2015) 138-149]

A discussion has been provided for the comments raised by the discusser (Clausen, 2015)1] on the article recently published by the authors (Chakraborty and Kumar, 2015). The effect of exponent alpha for values of GSI approximately smaller than 30 becomes more critical. On the other hand, for greater values of GSI, the results obtained by the authors earlier remain primarily independent of alpha and can be easily used. (C) 2015 Elsevier Ltd. All rights reserved.