Given Danziger’s Claims Essay Example for Free

Given Danziger’s Claims Essay Given Danziger’s claims about ‘methodomorphic theories’ and given what you know of quantitative and qualitative research methods and psychology in general, what do you think would be the obstacles to attempt to break free of the ‘methodological circle’? Research methods in modern psychology offer a variety of methodological options for researchers to utilise. However, there are issues associated with all methods. This essay will examine problems associated with the ‘methodological cycle’, such as the monopolisation of statistical methods in social sciences. These ‘issues’ continue to be common practice in psychological research and present obstacles to moving towards a less rigid, constrained method of working. This will be followed by exploring approaches that move forward, towards a more fluid and inclusive method of empirical psychology, such as Theoretical Sampling in Grounded Theory and Relational metatheory. Danziger coined the term ‘methodological circle’, asserting that many psychological researchers adopt methods based on certain assumptions about the subject matter, which in turn â€Å"only produce observations which must confirm these assumptions† (Danziger, 1998, p 1). These assumptions continue to be common practice in current psychological research, and pose as a barrier to moving away from the ‘methodological circle’. Psychology as Pure Science Kuhn (1962) described ordinary science as involving discussion of problematic truth claims and is carried out within the context of implicitly shared metatheoretical frameworks; on the other hand â€Å"paradigms† involve discussion that challenges these metatheoretical frameworks themselves. Psychology operates within both of these frameworks. ‘Ordinary science’, also known as Scientism, involves uncritically accepting that science is both highly distinct from, and superior to, common sense and methods for identifying cultural patterns. However, factors that a social scientist may wish to study do involve facets that are not static and are defined by the context in which these facets operate. An example of this could be trauma. Trauma is viewed by individuals in Western society as a concept which individuals or a collective may suffer after a disrupting or distressing event. However, in less developed societies, such as in Rwanda which suffered mass genocide, no instances of trauma are reported (Alexander et al, 2004). Such examples highlight the problems presented by adopting a purely scientific (positivist) approach to a social phenomenon. In addition to this, it must be remembered that even though research will always endeavour to be as objective as possible they will, ultimately, use their common-sense knowledge of how social phenomena operate in order to define and measure these variables for precise investigation (Silverman, 1993). Psychologists who work purely in line with Scientism make the error to totally remove itself from common sense, rather than acknowledging and working with it, adopting, say, a more constructivist approach e.g. Conversation Analysis. Kock (1973) sums this up assumption beautifully by saying â€Å"The entire subsequent history of psychology can be seen as a ritualistic endeavor to emulate the forms of science in order to sustain the delusion that it already is a science (Kock, 1973, p. 66). Dependence on statistics The use of statistical methods in psychology can be said to have become â€Å"institutionalized† (Danziger, 1998, p. 4). According to Danziger, such institutionalization presents 3 main problems: 1. It assumes that statistical conclusions are the only means of providing reliable and valid results for interpreting and developing theory; 2. It asserts that certain rules and models are constant, and cannot be amended or updated by new evidence; 3. it postulates that methodology must lead theory formation, and not the other way round. Such facets create a rigid environment, which restricts ways in which the social scientist can explore social phenomena which focuses on interactions between figures rather than meanings of interactions. The importance of the meaning behind words was acknowledged as far back as Freud, who stated â€Å"In medics you are accustomed to see things†¦in psychoanalysis, alas, everything is different†¦Words were originally magic and to this day words have retained much of their ancient power†¦Words provoke affects and are in general the means of mutual influence among men† (Freud, 1918, p.12). This statement emphasises the importance in not just, say, overt behaviour in the amount of words one uses (i.e. numerical data) in an interview, but also what one says and the meaning behind those words (i.e. qualitative data). Artificial settings to measure real life Psychology is the science of the real life, cannot be manipulated in artificial models. In its attempt to become a ‘pure’ science, psychological research methods tend to prefer to use controlled, experimental procedures, where one variable is directly manipulated by another variable, controlling for any other influencing factors. While such methods offer detailed and reliable statistical information, details of social, political, economic, and historical contexts can be overlooked (Waitzkin, 1990). The variety within psychology Psychology is a broad discipline with a variety of approaches such as Social and Cognitive Psychology. Social Psychology looks at qualitative interactions in the real world between people, whereas Cognitive Psychology examines the thought processes involved in individual reasoning. The former cannot be effectively manipulated in a controlled laboratory experiment, whereas the latter can be. If one attempts to artificially create and conduct a social experiment which uses solely statistics as a method of obtaining and interpreting results, one will miss the rich data that can be gained through qualitative measurement, looking at meanings and interpretations. A degree of flexibility is required in theory construction and method development, taking care to acknowledge how applied the science is and the vast array of methodological procedures to adopt. Top down vs. bottom up When conducting empirical investigation in psychology, the research question should lead the methodology, not the other way round. However, with the dominant quantitative method, researchers tend impose theories on data and see whether or not the data supports the theory. Upon these results, the researchers either accept or reject their hypotheses, rather than further exploring any discrepancies. Alternatively, researchers who adopt a qualitative method allow the data drive the theory and design models and theory from data. This is unpopular with many as it can oversimplifying complex social phenomena. As we can see, both designs appear to be poloarised, with little or no room for convergence. Deductive vs. Inductive Another assumption that perpetuates the ‘methodological circle’ is the belief that quantitative methods always must use a hypothetico-deductive approach and qualitative methods an inductive approach. Again, this restricts the way in which researchers can work with their subject matter, and rather than adopting an antithetical approach, researchers should endeavor to focus on the rationale of the study and the research question. Realism vs. Idealism In a similar vain to the short discussion above, there is the determinist assumption that all quantitative researchers are realists and qualitative researchers are idealist in their approach. This assumption enforces more restrictions on the way research would be carried out. Indeed quantitative research could do well to accept more subjective and individual attitudes, as qualitative methods could with more objective, measurable approaches. Moving forward Acknowledging the obstacles above, I will now explore ways in which psychology can move forward, away from the ‘methodological circle’ towards an approach that recognises and embraces both ‘quantitative’ and ‘qualitative’ virtues. Such an approach should not be concerned with paradigmatic purism but more concerned with identifying effective ways of conceptualising and discovering answers to the research questions. Grounded Theory -Theoretical saturation and sampling When using Grounded Theory, researchers use Theoretical sampling until they reach ‘Theoretical saturation’, where researchers collect data â€Å"until (a) no new or relevant data seem to emerge regarding a category, (b) the category is well developed in terms of its properties and dimensions demonstrating variation, and (c) the relations among categories are well established and validated.† (Strauss Corbin, 1998, p. 212). Such a fluid and flexible approach provides a useful means in theory construction because it builds the theory as it evolves from incoming data, offering an alternate perspective on how the results are interpreted than the restrictive positivist, deductive approaches. Relational metatheory Relational metatheory offers a relational dialectical perspective in which interpretation (a more quantitative, positivist approach) and observation (a more qualitative, construstivist approach) are both acknowledged and used (Overton, 1998; 2003). Relationism metatheory acknowledges that there is interconnection between the person, culture and biology (Hase, 2000), which is a much more fluid and explorative method then a split metatheory (using only quantitative or qualitative). This results in more complex, self creating, self organising, self regulating and adaptive systems that function and develop in relation with sociocultural constructs. In conclusion, there is a range of obstacles researchers encounter when attempting to break free of the ‘methodological circle’. These include both theoretical considerations such as theory construction and practical considerations such as the dependence on statistics. In order to move away from these imposed restrictions, researchers should consider adopting a more inclusive, flexible approach such as Grounded Theory and Relational Metatheory. As Danzgier concludes we must overcome these problems associated with the ‘methodological circle’ in psychological research; if not â€Å"theory testing in psychology will be a matter of choosing among different versions of a theoretical position, the fundamental features of which are in fact beyond dispute.† (Danziger, 1985, p.13). References Alexander, J. C., Eyerman, R., Giesen, B., Smelser, N. J., Sztompka, P. (2004) Cultural Trauma and Collective Identity, University of California Press, CA Danziger, K. (1985) The methodological imperative in psychology. Philosophy of the Social Sciences, 15, 1-13 Freud, S. (1918) The Complete Introductionary Lectures on Psychoanalsis, Alden Press, Oxford Hase, S. (2000) ‘Mixing methodologies in research’, NCVER conference, Coffs Harbour, April. Koch, S. (1963) Psychology: A Study Of a Science, (Koch, S. (Ed.). (1959-1963), McGraw-Hill, New York Kuhn, T. S. (1962) The structure of scientific revolutions. University of Chicago Press, Chicago Overton, W. F. (2012) Paradigms in Theory Construction, (Eds L’Abate, L.) Springer; US. Silverman, D. (1993) â€Å"Beginning Research†. Interpreting Qualitative Data. Methods for Analysing Talk, Text and Interaction, Sage Publications, Londres Strauss, A. L. Corbin, J. M. (1998) Basics of qualitative research: techniques and procedures for developing grounded theory, Sage Publications, US Waitzkin, H. (1990) On Studying the Discourse of Medical Encounters, Medical Care. 28:6, 473-487

Effects of Yoga on Life Satisfaction and Stress

Effects of Yoga on Life Satisfaction and Stress Literature Review and  Results Chapters Contents (Jump to) Literature Review Results Discussion Conclusion Literature Review Carlson, Goodey, Patel and Speca (2003) studied the effects of mindful-based stress reduction on quality of life, mood and stress in those with breast and prostate cancer. The MBSR programme was found to be associated with enhanced quality of life and decreased stress with low cortisol levels (Carlson, Goodey, Patel and Speca, 2003). From the above study it was inferred that practice of yoga increased life satisfaction and reduced stress. Culpepper, Davis, Eisenberg, Phillips and Saper (2004) conducted the first U.S. national yoga survey on 15 million Americans who had practiced yoga at least once in their lifetime, in order to identify the relationship between yoga practice and life satisfaction. 3.8% of this population were in the age range of 18 to 55 years and had practiced yoga for over one year. These individuals were found to score higher on life satisfaction than those who had tried yoga only once (Culpepper, Davis, Eisenberg, Phillips and Saper, 2004). From the above study it was inferred that individuals who had practiced yoga for over a period of one year were significantly more satisfied with life than those who had practiced yoga only once. Lee (2004) studied the relationship between Hatha Yoga practice and subjective well-being between beginners who practiced yoga from one to ten months and advanced Hatha yoga practitioners who practiced yoga for at least two years. 107 adult Hatha yoga practitioners participated in the study that practiced yoga consistently, at least twice a week for an hour. Advanced Hatha yoga practitioners were found to have higher levels of subjective well-being on the Satisfaction With Life Scale (SWLS), Positive and Negative Affect Scale (PANAS) and the Spiritual Well-Being Scale than the beginners (Lee, 2004). From the above study it was inferred that regular practice of yoga led to higher life satisfaction, positive affect and spiritual well-being. Bijlani (2005) studied the effect of a yoga intervention on 98 subjects with chronic illnesses and high risk for cardiovascular diseases who practiced yoga for 3 to 4 hours for 8 days and were later tested on subjective well-being and anxiety scales. It was found that subjective well-being increased and anxiety decreased significantly after the practice of yoga (Bijlani, 2005 cited in Carson, King and Koenig, 2012). From the above study it was inferred that yoga practice increased life satisfaction and reduced anxiety. Daubenmier, Hirschman and Impett (2006) conducted a study to examine the potential of yoga to promote embodiment and well-being (life satisfaction) on 89 participants pursuing a 2 years yoga course. After the course and on completing a short survey assessing life satisfaction in many domains, it was found that women objectified their bodies less after participating in the programme. Also, men and women had increased body awareness, positive affect and higher satisfaction with life as well as decrease negative affect with more frequent yoga practice (Daubenmier, Hirschman Impett, 2006). From the above study it was inferred that the practice of yoga increased satisfaction with life along with an increase in positive affect and increased body awareness. Dehen, Flegal, Haas, Kishiyam, Okena and Zajdel (2006) in U.S.A. studied the effects of six months of Hatha Yoga intervention on cognition and quality of life of 135 healthy older people, aged 65 to 85 years who were randomly assigned to the yoga intervention group and the wait-listed control group. Results indicated that the yoga group had significant improvements on cognitive and quality of life measures than the wait-listed control group (Dehen, Flegal, Haas, Kishiyam, Okena and Zajdel, 2006). From the above study it was inferred that yoga practice increased quality of life as well as cognition functioning. Geher, Otte and West (2006) researched the effects of Hatha Yoga on stress and life satisfaction on a U.S. population of 168 individuals in the age range of 20 to 40 years. 94 yoga practitioners who had practiced yoga for more than a year were significantly more satisfied with life and had lower cortisol (stress hormone) levels than the 74 individuals had completed only three sessions of Hatha Yoga (Geher, Otte and West, 2006). From the above study it was inferred that long-term yoga practitioners were more satisfied with life on and had lower stress levels than beginners of yoga. Kirstein (2006) studied the effects of 10 weeks yoga intervention on postural control, spasticity, mobility and quality of life of 12 patients with Multiple Sclerosis aged 30–76 years who practiced yoga twice a week for 70 minutes. Significant differences between the pre and post intervention scores suggested that yoga was a valuable alternative to other exercises for Multiple Sclerosis patients because of the improved scores on all scales (Kirstein, 2006). From the above study it was inferred that yoga intervention increased postural control, mobility, quality of life and decreased spasticity. Vito (2007) evaluated the effects of Hatha Yoga in relieving the psychological and physical symptoms of 25 female breast cancer patients aged 25–60 years, who were alternatively assigned to a twice weekly, 8 week yoga group and a wait-list control group. Questionnaires were administered before and after the yoga intervention. The yoga participants showed significant improvements in all outcome measures with a decrease in fatigue and negative mood as compared to the wait-listed control group (Vito, 2007). From the above study it was inferred that yoga increased quality of life simultaneously decreasing symptoms of cancer. Bijlani, Gupta and Sharma (2008) studied the effect of an 8-day intensive yoga intervention on 77 subjects’ subjective well-being who were randomly assigned to the yoga group and the control group. Using the Subjective Well-Being Inventory (SUBI), the yoga group reported significant improvements in the areas of general well-being, expectation and achievement, confidence in coping, and mental mastery along with less worry and better abilities to cope with stress, and thus scored higher on subjective well-being than the control group (Bijlani, Gupta and Sharma, 2008). From the above study it was inferred that a yogic lifestyle increased subjective well-being. Duncan, Leis and Taylor-Brown (2008) evaluated the impact and outcomes of Iyengar Yoga in a Cancer Centre on 24 participants aged 38 to 57 years on measures of quality of life, spiritual well-being and mood disturbance. They were taught yoga and practiced it for 90 minutes per day for ten weeks. On comparing the World Health Organization Quality of Life scale (WHOQOL) before and after intervention scores, quality of life and spiritual well-being significantly improved with a reduction in mood disturbance (Duncan, Leis and Taylor-Brown, 2008). From the above study it was inferred that the practice of yoga increased quality of life and spiritual well-being, and regulated mood. Thomas (2008) examined the relationship between adopting a yogic lifestyle and subjective well-being on 152 Australian yoga students aged 30 to 50 years. Those who undertook an intensive Satyanand Yogic training (incorporation of Bhakti Yoga, Karma Yoga and Hatha Yoga) for two years scored higher on the Satisfaction With Life Scale and the Personal Wellbeing Index than those who only attended a weekly programme (Thomas, 2008). From the above study it was inferred that practice of yoga increased satisfaction with life. Havalappanavar and Jadhav (2009) studied the effect of yoga on subjective well-being and anxiety on 50 first year students from Naturopathy and Yogic Sciences Course aged 20 years and above. The Spielberger’s State Trait Anxiety Inventory and the Subjective Well-being Inventory were administered before and after one academic year with the practice of yoga. A significant decrease was found in both state and trait anxiety levels and positive changes in subjective well-being with an impressive ascend in life satisfaction scores after the yoga intervention (Havalappanavar and Jadhav, 2009). From the above study it was inferred that the yoga intervention reduced anxiety levels with an increase in life satisfaction. Maharana, Nagendra, Raghuram, Rakhshani and Venkatram (2010) studied the yoga effects on quality of life and interpersonal relationships on 102 pregnant women who were randomly assigned to two groups; 51 each to the integrated yoga group and the antenatal exercises (relief from back pain) (control) group, both for one hour, thrice a week. Results indicated that there were significant improvements in quality of life and interpersonal relationships in the integrated yoga group compared to the antenatal exercise group (Maharana, Nagendra, Raghuram, Rakhshani and Venkatram, 2010). From the above study it was inferred that integrated yoga effectively improved quality of life and interpersonal relationships. Moliver (2010) studied yogic effects on subjective wellness ad well as physical and psychological wellness in 393 women, including 211 yoginis (female yoga practitioners) who had more yogic experience than the rest aged 45 to 80 years. It was found those with more yoga experience scored higher on physical wellness, subjective vitality and life satisfaction scales than those with lesser yoga experience (Moliver, 2010). From the above study it was inferred that life satisfaction, physical well-being and subjective vitality increased with greater yoga experience. Ulger (2010) studied the effects of 8 hourly sessions of yoga on the quality of life in 22 breast cancer patients aged 30 to 50 years. The State-Trait Anxiety Inventory-I and State-Trait Anxiety Inventory-II to measure anxiety and its permanence respectively, and Visual Analog Scale to measure life satisfaction were administered before and after yoga training. Patients’ quality of life after yoga was found to be higher with decrease in stress than before training (Ulger, 2010). From the above study it was inferred that yoga training can diminish stress and increase quality of life. Choudhary and Rathore (2011) studied the impact of 6 months of yoga on emotional intelligence and life satisfaction on 60 individuals who were given the Emotional Intelligence Scale (EIS) and the Satisfaction With Life Scale (SWLS) before and after the completion of the yoga training. Results revealed that yoga increased life satisfaction and emotional intelligence before and after yoga intervention. Also, females had higher scores on both tests than males after practice of yoga (Choudhary and Rathore, 2011). From the above study it was inferred that consistent practice of yoga increased life satisfaction. Reis (2011) studied the effect of a 6-week prenatal yoga intervention in late pregnancy and its changes in optimism, power and well-being on 21 women. Tests were administered in the first week and after the yoga intervention. Optimism, power and well-being had significantly increased from the first to the sixth week of the yoga practice (Reis, 2011). From the above study it was inferred that practice of yoga promoted optimism and well-being. Woodyard (2011) explored the therapeutic effects of yoga to increase quality of life on 404 individuals aged 20 to 40 years who had newly enrolled for six months of yoga. Results showed that yoga enhanced individuals’ muscular strength and body flexibility, promoted and improved respiratory and cardiovascular function, promoted recovery from and treatment of addiction, reduced stress, anxiety, depression, and chronic pain, improved sleep patterns, and enhanced overall well-being and satisfaction with life than they previously experienced (Woodyard, 2011). From the above study it was inferred that satisfaction with life along with overall well-being increased with the practice of yoga. Seldin (2012) studied the effects of yoga on female body experience on factors such as self-objectification and self-acceptance on 7 American women aged 25-49 years who had consistently practiced yoga 4 times a week for 2-12 years. The self-objectification theory stated that expectations of physical and sexual body appeal resulted in poor body image. In 2004, Myers and Sinclair’s study established a link between poor body image and lower life satisfaction in adulthood among women. Using a semi-structured interview format, most women acknowledged decrease in body dissatisfaction and self-objectification after several years of yoga practice which was also directly related to higher marital, familial, occupational and other life satisfaction variables (Seldin, 2012). From the above study it was inferred that the practice of yoga increased self-acceptance and satisfaction with life with a reduced dissatisfaction with body image. Chartrand, Haussmann, Khalsa, Mika and Moliver (2013) studied the effect of yoga practice as a predictor of psychological well-being on 211 female yoga practitioners between 35 and 60 years of age. Some who had practiced yoga for 10 years had higher life satisfaction and positive health outcomes compared to those who had practiced for only 2 months. Increased yoga experience predicted increased psychological well-being for those who intended to practice yoga throughout their lifetime (Chartrand, Haussmann, Khalsa, Mika and Moliver, 2013). Subjective well-being reduces in midlife years and rise in old age. However, the practice of yoga has shown to increase emotional well-being and life satisfaction in both midlife years as well as old age despite material and social losses (George, 2010). From the above studies it was inferred that yoga increased life satisfaction with age due to prolonged practice. Lucia (2013) studied the effects of yoga on psychological and physical wellness, and subjective well-being on 372 individuals aged 18-85 years. The participants were divided into yoga practitioners group and the control group who engaged in non-yoga exercises. Results indicated that yoga participants had higher psychological wellness and subjective well-being than the control group with no significant differences in physical wellness (Lucia, 2013). From the above study it was inferred that yoga participants experienced higher levels of psychological wellness and subjective well-being than non-yoga participants. Margaret (2013) studied yogic effects on the quality of life and functional performance of older adults. 135 individuals aged 60 years and above participated with 71 subjects in the intervention group and 64 in the control group. After 12 weeks of intervention, significant improvements were found in the quality of life and functional performance of the yoga participants. According to observations made in the study, the high attendance rate implied that yoga was preferred to medications (Margaret, 2013). From the above study it was inferred that aging individuals preferred yoga to medication, not only to increase functional performance and physical ability, but also to increase quality of life. Rai, Ramesham, Sathian and Sinu (2013) conducted a study on 280 married individuals, aged 30 to 55 years of which 164 individuals were Raja Yoga practitioners and 116 were non-yoga practitioners, to assess the effects of yoga on life satisfaction and happiness. It was found that yoga practitioners were happier and more satisfied with life than non-yoga practitioners. Also Rajayoga Meditation significantly increased life satisfaction and happiness in life further enhancing positive thinking (Rai, Ramesham, Sathian and Sinu, 2013). From the above study it was inferred that practice of yoga increased life satisfaction and enhanced positive thinking. Ivtzan and Papantoniou (2014) studied the effect of yoga on three dimensions of psychological wellbeing: gratitude, life satisfaction and meaning in life on 124 participants, aged 18 to 40 years, with equal number of individuals with and without yoga experience. The research findings stated yoga practitioners scored higher on all scales (Ivtzan and Papantoniou, 2014). From the above study it was inferred that practice of yoga increased meaningfulness of life, satisfaction with life and gratitude towards life. Sharma (1986) focused on the application of yoga to modify behaviour for achievement of self-actualization. The scheme of yoga fits the Hierarchy of Needs Model by Maslow where self-actualization is the final goal after satisfaction of psychological, safety, love and esteem needs. According to Sir Aurobindo, ego is the source of all conflicts, which if continues, leads to mental ill health and disorders (Sharma, 1986). In 1988, Hoffman stated that self-actualization is a continuous process of becoming satisfied with one’s life. According to Maslow, the desire for fulfilment in all aspects of life caters to becoming actualized. Diener and Tay tested Maslow’s theory in which 60,865 participants representing all continents of the world were surveyed from 2005 to 2010. They answered questions regarding six needs closely resembling those of Maslow’s needs to assess well-being across three measures, namely life evaluation also called life satisfaction, positive feeling s and negative feelings. It was found that satisfaction of the six needs rendered life satisfaction and positive feelings being greater than negative feelings (Diener and Tay, 2011). Positive psychologists Martin Seligman, Christopher Peterson and others have ascertained the fulfilment of these six needs to contribute to higher well-being and life satisfaction. They also stated that those who successfully fulfill these needs are capable of self-actualization (Coon and Mitterer, 2010). The above literature reviews have stated that the practice of yoga had significantly increased satisfaction with life. Greater experience of a yogic lifestyle increased life satisfaction as individuals grew older. CHAPTER 4 RESULTS AND DISCUSSION 4.1. INTRODUCTION This chapter comprises of the two sections namely, the statistical analysis of the data obtained and the discussion of the results. 4.2. RESULTS This section entails the statistical analysis of the obtained data for the two groups, yoga practitioners and non-yoga practitioners using Descriptive Statistics and Independent Samples T-test. Table 4.1. (a) showing Descriptive Statistics for Yoga Practitioners and Non Yoga Practitioners on the Satisfaction With Life Scale. From Table 4.1. (a) showing the descriptive statistics for the two comparative groups it was observed that the total sample (N) consisted of 200 individuals, 100 yoga practitioners and 100 non-yoga practitioners. For the group of non-yoga practitioners, the Mean was calculated to be 23.71 with a Standard Deviation of 3.19. For the group of yoga practitioners, the Mean was calculated to be 27.75 with a Standard Deviation of 2.98. Table 4.1. (b) showing Independent Sample T-test for the sample of Yoga Practitioners and Non-Yoga Practitioners on Life Satisfaction. Table 4.1. (b) shows the Independence Sample T-test for the two comparative groups, yoga practitioners and non-yoga practitioners on life satisfaction. In the Levenes Test for Equality of Variances, the F value obtained was 0.51 which was significant at the 0.47 level indicating that the homogeneity in the sample was maintained. Thus, equal variances were assumed. In the T-test for Equality of Means, the t value obtained was 9.22 with df value (degree of freedom) of 198 which was significant at the 0.000 level. The mean difference obtained was 4.04. The significant difference obtained between the two comparative groups thus indicated that yoga practitioners showed significantly higher life satisfaction compared to non-yoga practitioners. 4.3. DISCUSSION The present study is a comparative study of yoga practitioners and non-yoga practitioners on life satisfaction. From the above section, the t value of 9.22 was significant at the 0.000 level. Thus the hypothesis stating that ‘the scores on life satisfaction will be significantly higher for yoga practitioners than non-yoga practitioners’ was accepted because the statistical analysis of the obtained data showed a significant difference between the two groups. In congruence to the above findings, previous researches done on the practice of yoga and satisfaction with life are listed below. Gharote (1982) studied the psychophysiological effects of meditation (Pranayama) and yogasanas on personality and use of yoga in therapy over a period of one year on several individuals who enrolled at the College of Yoga and Cultural Synthesis at Kaivalyadhyama, Lonavala. On various testing grounds, meditation and yogasanas decreased neuroticism, increased extroversion and self-control, self-actualization, happiness and psychological well-being (Gharote, 1982). From the above study it was inferred that practice of yoga increased happiness and life satisfaction. Bhushan (1998) studied the effect of a 14 month yoga course on measures of psychological well-being. The Satisfaction With Life Scale and Spielberger’s State Trait Anxiety Inventory were administered before and after the yoga course to 139 employed individuals. When the pre and post intervention scores obtained for the two variables, life satisfaction and anxiety were compared, an interesting finding was seen. There was a significant decrease for those with initial high levels of anxiety, and life satisfaction had increased after the yoga course (Bhushan, 1998 cited in Thomas, 2008) From the above study it was inferred that yoga increased life satisfaction and reduced anxiety. Jhansi (2007) studied the impact of yoga training on self-ideal disparity (incongruence between real self and ideal self) and psychological well-being on an experimental sample of 19 adults who had completed a yoga training course for six months and a control sample of 19 adults who had newly enrolled for the same. The experimental sample was tested after their yoga course and the control sample was tested before it on self-ideal disparity and on a scale of psychological well-being. Results revealed that the experimental group showed higher congruence between real self and ideal self and higher psychological well-being than the control group (Jhansi, 2007). From the above study it was inferred that practice of yoga increased life satisfaction and reduced self-ideal disparity. Bakshi and Kumari (2009) studied the effect of practicing yoga on subjective well-being (SWB) and academic performance on 100 adolescents aged 14 to 16 years. After a year of yoga practice, the students had high scores on subjective well-being and showed a gradual increase in academic performance in school (Bakshi and Kumari, 2009). From the above study it was inferred that practice of yoga increased subjective well-being and ultimately improved their academic performance. Monk-Turner and Turner (2010) conducted a study on an adult sample of yoga practitioners and non-yoga practitioners to assess life satisfaction along with body, mind, spirit and happiness differences. It was found that yoga practitioners significantly reported more mental wellness, strong morals, healthy values, ability to express their feelings and consider those of others, a positive outlook towards life and high well-being with higher scores on life satisfaction as compared to non-yoga practitioners. Yoga practitioners were also more likely to experience happiness within themselves (Monk-Turner and Turner, 2010). From the above study it was inferred that satisfaction with life along with mental wellness, positive outlook and happiness increased with the practice of yoga. Malhotra and Nangia (2012) studied the influence of regular practice of yoga on cognitive skills and well-being on 19 regular yoga practitioners who were tested on outcome measures of attention, remote memory, mental balance, immediate and free recall, verbal and visual retention, and on a measure of well-being. Results indicated that the practitioners obtained high scores on all cognitive measures and well-being (Malhotra and Nangia, 2012). From the above study it was inferred that practice of yoga not only enhanced well-being but it also sharpened cognitive skills. Dubey (2012) studied the role of perceived control (a belief that individuals are capable of influencing the events in their lives to deal with stressors and their inner states) in continuing yoga for six months every day, and its effect on health and well-being on regular, irregular and non-yoga practitioners aged 22 to 60 years. Various tests were administered before the course and six months after it. Perceived control was a good predictor of life satisfaction and health in the regular yoga group and thus they were more satisfied with life and had better health scores than the irregular yoga and the non-yoga practitioners (Dubey, 2012). From the above study it was inferred that yoga practice increased life satisfaction and promoted better health outcomes. Bankar, Chaudhari and Chaudhari (2013) studied the impact of long-term yoga on sleep quality and quality of life on 65 adults aged 60 years and above. Scores of yoga practitioners on the Pittsburgh Sleep Quality Index (PSQI) and Quality Of Life Leiden-Padua (LEIPAD) Scale were compared with a non-yoga group of the same age. The yoga group was found to have higher life satisfaction with better sleep quality than the control group (Bankar, Chaudhari and Chaudhari, 2013). From the above study it was inferred that regular yoga exercises helped to improve sleep quality as well as quality of life. Basavaraddi, Gangadhar, Hariprasad, Koparde, Sivakumar, Thirthalli, Varambally and Varghese (2013) studied the effect on yoga on sleep, life satisfaction and quality of life on 220 individuals aged 40 to 55 years. 133 subjects in the yoga group attended a yoga intervention twice a week for six months. 87 individuals formed the non-yoga practitioner group. After the yoga group had completed the course, both groups were administered with tests. The yoga group had scored significantly higher on all the domains of quality of life, had higher satisfaction with life and better sleep quality after the intervention (Basavaraddi, Gangadhar, Hariprasad, Koparde, Sivakumar, Thirthalli, Varambally and Varghese, 2013). From the above study it was inferred that the practice of yoga increased life satisfaction as well as quality of sleep. Cramer, Dobos, Langhorst, Lauche and Paul (2013) conducted a comparative study on the quality of life, mental health and life satisfaction between yoga practitioners and non-yoga practitioners on 2486 individuals who were married and employed. Yoga practitio

Finite Element Analysis And Analytical Method

Finite Element Analysis And Analytical Method Stone columns are widely used as a ground improvement technique especially in construction of shallow foundations. The main concern in the application of stone columns rely on how well it performs, which involves reducing the overall settlement of the stone column. This project mainly investigates the comparison and contrast between finite element analysis and analytical method in modelling stone columns, whereby settlements of the stone columns are checked whether it is consistent. Finite element analyses were carried out by axisymmetric modelling of the stone column using 15-noded triangular elements with the software package PLAXIS. A drained analysis was conducted using Mohr-Coulombs criterion for soft clay, stones and sand. Analytical data used to compare the settlement was found according to the design method published by Heinz J. Priebe (1995). Both methods were compared by varying parameters such as modulus of deformation of the column to sand ratio, area ratio, stress, diameter, and friction angle of stone column that signifies different soil conditions. It is challenging to find a site with acceptable ground conditions for construction of structures such as buildings, bridges, etc. Often the bearing capacity of the soil would not be sufficient to support the loads of the structures nor would it be in a workable condition for the employees to build the structure. The need for the use of such land with weak cohesive soil strata has been a challenge for design engineers. Although the design of piles foundation can meet all the design necessities, extensive lengths of piles needed eventually results in vast increase of cost of the overall project. Therefore, it is a necessity that the ground conditions must be improved to allow the buildings and heavy construction. A number of ground improvement techniques have been developed over the past fifty years. Main concern of these techniques includes creating stiff reinforcing elements to the soil mass, which results in a soil that has a higher bearing capacity. Out of the various techniques available for ground improvement, the stone column has been widely used. Stone columns (also known as granular columns, granular piles or sand columns) are used to improve soft ground by increasing the load bearing pressure of the soil and reducing settlement of the foundation of structures, embankments, etc. Although these structures are permissible for a relatively large settlement, it is necessary that the settlement be minimized for maximum safety. There have been several ways for installing stone columns depending on the design, local practice and availability of equipment. Among which, the most general methods are the vibro-replacement method and vibro-displacement or vibro-compaction methods. Vibro-replacement technique of stone column is a process whereby large sized columns of compacted coarse aggregates are installed through the weak soil by means of special in-depth vibrators. This can be carried out either with the dry or wet process. In the dry process, a hole of desired depth is drilled down in to the ground by jetting a vibroflot. Upon extraction of the vibroflot, the borehole must be able to stand open. The densification of the soil will be a result of the vibrator near the bottom of the vibroflot. In the wet process, the vibroflot will form a borehole that is of larger diameter than the vibrator and it requires continuous supply of water. As a result the uncased hole is flushed out and filled with granular soil. Th e main difference between wet and dry process is the absence of continuous jetting water during the initial formation of the borehole in the dry process. The performance of the stone columns is not measurable by simple investigations. However, analytically, the efficiency of this composite system that consists of stone column and soil interactions can be assessed by separate consideration of significant parameters as proposed by Priebe (1995) [1]. Stone column technique has proven successful in improving many applications. Such applications include slope stability of both natural slopes and embankments. Construction of such embankments can commence immediately after the installation of stone columns (Vibro Stone Columns, 2009) [2]. Other advantages include increasing bearing capacity of ground, reducing total and differential settlements, reducing the liquefaction potential of sands. The main disadvantage of the stone column technique is its ability to induce bulging failure on the upper part of the stone column. In-situ field tests (cone penetration test and full scale footing test) before construction and after construction of stone columns have shown significant improvements in the soil (J. T. Blackburn, J. K. Cavey, K. C. Wikar, and M. R. Demcsak., 2010) [3]. In a study of the behaviour of stone columns, (Mitchell J.K., and Huber T.K., 1985) [4], by using finite element analysis, had proved that the installation of stone columns leads to a 30-40% reduction in settlement of the values expected that of an untreated ground. 1.2 Objectives The main objective of this project is to show that the analytical method used to design stone columns and the finite element method used to model the stone column numerically, has comparable total and differential settlement. The analysis also provide the understanding of the influence on settlement by varying parameters such as modulus of deformation of the column to sand ratio (Ec/Es), Area ratio (Ac/A), stress à Ã†â€™0, diameter D, and friction angle of stone column ÃŽÂ ¦c, and finally comparing them against the Priebe analytical approach. The objectives of the project are to: study the existing analytical and numerical theories related to stone column modelling develop an axisymmetric simulation of the stone columns by using finite element method, and compare the settlement difference with the analytical results by altering various parameters related to settlement change. This project uses the finite element software package PLAXIS to simulate the stone column numerically and the design method proposed by Heinz J. Priebe (1995) [1] for the analytical results. 1.3 Organization of the research paper In addition to the abstract, list of figures and notation, acknowledgement, and table of contents, this dissertation is divided to six chapters: The first chapter consists of introduction and background of stone columns where it briefly summarizes the installation methods, some of the advantages and disadvantages of the stone columns. The second chapter describes the study of existing analytical and numerical theories regarding modelling stone columns. In this chapter, other than the main findings from the theories, the full procedure of Priebe (1995) method of modelling stone column has been reviewed. Third chapter describes how the stone column was modelled using the PLAXIS software, including the assumptions made and technical data used in different models. The fourth chapter shows the results obtained from the analysis compared to the analytical method proposed by Priebe (1995). The results are presented using necessary graphs and charts. The fifth chapter includes the conclusion of the project and provides recommendations for further studying. The final chapter lists out the references used in this project. The Appendix contains documents such as the Risk Assessment, Diary of the work progress, and the any additional tables and figures of the analysis. CHAPTER TWO 2. LITERATURE REVIEW Many researchers in this field have made their effortless contribution studying the behaviour of stone columns numerically and analytically. Most of the numerical analyses were conducted using finite element analysis, whereas analytical method is derived from a series of equations. Some of the main findings from researchers related to this study are reviewed below. 2.1 Analytical Models 2.1.1 Alamgir, Miura, Poorooshasb, and Madhav, (1996) Alamgir et al. (1995) proposed a simple theoretical approach to evaluate the deformation behaviour of uniformly loaded ground reinforced by columnar inclusions. The displacements of the soil and stone columns are obtained by considering the elastic deformation of both soil and column. A typical column-reinforced ground and column soil unit (Fig. 2.1) where the column is considered to be cylinder, of height H and diameter of dc (=2a where a is the radius) The deformation at a cross section within the column, wcz, is assumed to be constant throughout whereas the deformation of the surrounding soil, wrz, increases from the soil column surface towards the outer boundary of the unit cell (Fig. 2.2). This denotes that since the column soil interface is elastic and no slip occurs, the displacements of the soil and the column at interface can be assumed to be equal. The deformation of the surrounding ground, wrz, is assumed to follow: where wrz is the displacement of the soil element at a depth z and at a radial distance r, wcz is the displacement of the column element at a depth z, ÃŽÂ ±cz and ÃŽÂ ²c are the displacement parameters, a and b are the radii of column and unit cell, respectively, r is the radial distance measured from the center of the column. The column and the surrounding soil were discretized in to a number of elements as shown in Fig. 2.3. The interaction shear stresses and stresses on the column and the soil were obtained by using equilibrium of vertical forces within the medium (Fig. 2.4). Successively the displacement of the column and soil were obtained by solving equations by applying the linear deformation characteristics of the soil. Therefore, the deformation of the jth element of the column, Wcj was obtained as: where à ¢Ã‹â€ Ã¢â‚¬  H is the height of a single element, Es and Ec are the modulus of deformations of soil and column material respectively, vs is the Poissons ratio of the soil, and à Ã†â€™cj is the normal stress acting at the top of the jth element of the column. Due to the symmetry of load and geometry, the shear stress at the outside boundary of the unit cell is zero, which subsequently leads to an equation for ÃŽÂ ²c Furthermore, the compression of the soil element adjacent to the boundary of unit cell (N,jth element of the soil), wsNj was derived as: where à Ã†â€™sNj is the normal stress acting at the top of the element, n is the spacing ratio b/a, à ¢Ã‹â€ Ã¢â‚¬  R is à ¢Ã‹â€ Ã¢â‚¬  r/a and à ¢Ã‹â€ Ã¢â‚¬  r is (b-a)/n. By using the displacement compatibility and substituting r/a=n-à ¢Ã‹â€ Ã¢â‚¬  R/2, Eq. [2.1] can be written as: Finally, solving the equations 2.2, 2.3, 2.4, and 2.5 can lead to the displacement parameter The settlement profiles, the shear stress distribution, and the load sharing from the above mention method was compared against a simple finite element analysis as shown in Fig. 2.5, Fig. 2.6, and Fig. 2.7. It is seen that the results obtained shows a reasonable agreement between the two methods and can be used as a useful method to determine the settlement of the stone columns. 2.1.2 Priebe (1995) Priebe (1995) proposed a design method to assess the behaviour of stone columns that uses an improvement factor which stone columns improve the performance of the subsoil in comparisons to the state without columns. The above statement was best described using the following relationship: According to this improvement factor, the deformation modulus of the composite system is increased respectively settlements are reduced. A unit cell of area A is considered which consists of a single column with the cross section area Ac. Calculation of the improvement factor was done by assuming that: The stone column to be of incompressible material The stone column is installed within a rigid layer The bulk densities of the stone column and soil are also neglected. Hence, according to Priebes approach, column cannot fail in end bearing and any settlement of the load area results in a bulging of the column, which remains constant all over its length. The improvement of a soil achieved by the presence of stone columns is evaluated based on the assumption that the column material shears from the beginning whilst the surrounding soil reacts elastically. Additionally, the coefficient of earth pressure amounts to K=1 by assuming that the soil to be displaced already during the column installation to such a degree that its preliminary resistance corresponds to the liquid state. Using the above criterion the basic improvement factor n0 is expressed as: where = Improvement factor Ac = Area of the stone column A = Grid area of the single unit = Poissons ratio = Coefficient of active earth pressure for the stone column material = Friction angle of the stone column material Since a Poissons ratio of 1/3 is adequate for the state of final settlement in most cases, the results of the evaluation is expressed as basic improvement factor n0 and substituting 1/3 as Poissons ratio, which leads to the following equation. The relation between the improvement factor n0, the area ratio A/Ac and the friction angle of the backfill material is illustrated in figure 2.8 below. The compacted backfill material of the stone column is still compressible. Due to this reason, applied load of any amount will lead to settlements that are unconnected with bulging of the columns. Subsequently, compressibility of the column is integrated by adding up an additional area ratio (A/Ac) as a function of the constrained moduli of the columns and soil Dc/Ds and is provided in the Fig. 2.9. The improvement factor as a result of the consideration of the column compressibility is represented by n1, as shown in the equation: where and Furthermore, for =1/3 can be found using the equation below The additional loads due to the bulk densities of the soil and columns decrease the pressure difference asymptotically and reduce the bulging correspondingly. Subsequently, multiplying the basic improvement factor by a depth factor could incorporate the effect of the bulk density, which is given by: where, fd = Depth factor K0C = Coefficient of earth pressure at rest for stone column material = Bulk density of the soil = Layer thickness Pc = Pressure within the column along the depth Figure 2.10 shows the influence factor y as a function of the Area ratio A/Ac and can be used to approximate the depth factor. The figure considers the same bulk density for the columns and soil, which may not be true in most cases. Therefore as a safety measure, the lower value of the soil should be always considered. Using the above depth factor fd, a more enhanced improvement factor can be defined that considers the effects of the overburden pressure, and therefore is represented by n2 where it can be related by the following equation: The depth factor is limited so that the settlement of the columns resulting from their inherent compressibility does not exceed the settlement of the composite system. This is because as the depth increases, the support by the soil reaches such an extent that the column do not bulge anymore. The first compatibility control where the depth factor is limited is applied when the existing soil is stiff or dense and is given by: The second compatibility control is required since should not be considered even if it may result from the calculation. This second control relates to the maximum value of the improvement factor nmax and is applied when the existing soil is loose or soft. Both compatibility controls can be determined using figure 2.11 below. Finally, the total settlement of a single or a strip footing can be assessed using the above series of equations. The design results from the performance of an unlimited column grid below an unlimited load area. For the unimproved ground, the settlement can be found using the equation: where, sà ¢Ã‹â€ Ã… ¾ = Total settlement p = Pressure exerted by the above structure d = Depth of the stone column Ds = Constrained modulus of the soil Similarly, the total settlement of the improved ground, where the improvement factor is incorporated, can be found by dividing the settlement by n2, which is shown below: This method is one of the most common and well-known method of designing stone columns and has been widely used all over the world because of its simplicity. Moreover, in comparison with the other methods, it shows a much wider behaviour of the stone column by assuming the stone column and surrounding soil as a composite system. 2.2 Numerical Models 2.2.1 A.P. Ambily and Shailesh R. Gandhi (2007) Ambily and Shailesh (2007) studied the behaviour of stone columns by comparing experimental and Finite Element analysis on a single stone column and a group of 7 columns. Laboratory experiments were carried out on a stone column of 100mm diameter surrounded by soft clay in cylindrical tanks of 500mm high with diameter varying from 210 to 420 mm for a single column test and from 210 835 mm for a group of 7 columns. This represents the required unit cell area of soft clay around each stone column. Pressure cells attached to the loading plate were used to measure the stress intensity of the column and the soil as shown in figures 2.12 and 2.13. Furthermore, it is also assumed the stone columns are installed in a triangular pattern. The load deformation behaviour of the column/treated soil was studied by applying vertical load for both cases; column only loading and entire area loading, and observed for equal intervals of settlements until failure occurs. After a series of procedure, the shapes of the tested columns are obtained. It is clearly seen in Fig. 2.14 that bulging mode of failure only occurs in the case of column alone loaded, and not in the case of entire area loaded. Finite Element analysis was conducted using 15-noded triangular elements with the software package PLAXIS, to compare the load-settlement behaviour with the model test and the laboratory experiment. The analysis was carried out using a stone column of diameter 25 mm and 225 mm high, which was made at the center of the clay bed and loaded with a plate of diameter two times the diameter of the stone column. The axisymmetric finite element mesh to represent the single stone column and the group of stone columns are shown in Fig. 2.15 and Fig. 2.16 respectively. Likewise the laboratory experiment, finite element analyses were done for column alone loaded and entire area loaded case for s/d=3. The results of these simulations (Fig. 2.17) shows that failure by bulging occurs in column alone loaded case, which also agrees with the results from laboratory experiment. The comparison of the experimental results and finite element analysis data shows significant consistency in both methods. The comparisons made by A.P. Ambily and Shailesh R. Gandhi include the effect of shear strength, Cu (Fig. 2.18) and the effect of s/d (Fig. 2.19) on the behaviour of stone columns. Additionally, the effect of surcharge on stress settlement behaviour (Fig. 2.20) and effect of s/d and ÃŽÂ ¦ on the stiffness improvement factor (Fig. 2.21) was compared between both methods. These tests have also shown similar behaviour. The stiffness improvement factor (ÃŽÂ ²) was calculated as the ratio of the stiffness of treated and untreated ground, and beyond s/d = 3, it shows no significant improvement. The analysis was extended to study the effect of the angle of internal friction of stones by varying the ÃŽÂ ¦ as 35, 40, 43, and 45o for varying values of s/d ranging from 1.5 4. From the results shown in Fig. 2.22, it is confirmed that this relationship is valid for any shear strength values of surrounding soil. Furthermore, the comparisons between a single column and group of 7 columns were found as in Fig. 2.23. Both experimental and finite element method results reveal comparable behaviour regarding the ultimate load and load deformation relationship. To ensure that this proposed design method agrees with the existing theories, this study was compared with the existing theories as shown in Fig. 2.24 and Fig. 2.25. The result shows a slightly higher stiffness improvement factor (ÃŽÂ ²) for an area ratio more than 4 and a lower value for an area ratio less than 4 compared to Priebe (1995). 2.3 Summary The studies mentioned above show comparable results and have been adopted by many engineers and contractors. However, not many researchers had compared Priebes analytical model with finite element method. Therefore, the finite element analysis carried out in this project will be compared to the design method proposed by Priebe (1995), since it gives a much broader overview of the composite system consisting of the stone column and soil interactions and moreover it is the most common and improved analytical method used by the design engineers around the globe. CHAPTER THREE 3. METHODOLOGY 3.1 Introduction Different methods of modelling stone columns numerically have been implemented in the past. Among those, the most simplest and common type of numerical modelling is using finite element method. In fact, studies have shown that the settlements predicted from the finite element analysis shows comparable results that of the values gained from actual field tests (Kirsch, F. 2009). Numerical calculations are usually complex and most of the time is impossible to conduct without means of dedicated software. Likewise, in this research project, PLAXIS software is used to carry out the finite element analyses. 3.2 PLAXIS software The main computer software used in this investigative project is PLAXIS Professional Version 8.2. PLAXIS is a comprehensive package for finite element analyses for geotechnical applications. It allows simulating the soil behaviour by using soil models. The software employs a graphical user interface that makes it simple to use and also provide the ability to input the necessary parameters such as different soil layers, structural elements, variety of loadings, and boundary conditions through CAD drawing procedures. It allows discretizing the soil component into either 6-noded or 15-noded triangular elements whereby 15-noded triangles provides high stress results for complex problems. The software also allows automatic generation of 2D finite element meshes that can be further refined according to the choice of analysis. In addition to that, the software comes with a very useful feature named Staged Construction. This feature allows the models to be simulated at different stages by ac tivating and deactivating clusters of elements, application of loads, etc. One of the advantages of this software is the ability to generate the results quickly with minimum errors. The output results include values for stresses, strains, settlements, and structural forces together with the plots of different curves such as, load-displacement curve, stress-strain diagrams, and time-settlement curve. 3.3 Finite Element Modelling Finite element analysis was conducted to compare the load-settlement behaviour of the stone column. A two dimensional axisymmetric analysis was carried out since the investigation concerns a single unit of stone column using Mohr-Coulombs criterion for clay and stone column. 15-noded discretization was used for more precise results. The initial vertical stress due to gravity has been considered in this analysis. Similarly, the stress due to column installation, which often depends on the method of construction, is also considered in this analysis. Assumptions made in the finite element modelling: The soil is assumed to be homogenous, infinite and behaves as Mohr-Coulomb model. The ground water table is at the same level as the stone column and clay layer, meaning the stone column and clay layer is submerged in the water. Hence, effect of ground water condition should be taken into account. The base of the clay layer is rigid, i.e., full fixity at the base of the geometry (ux=0, uy=0) and roller conditions at the vertical sides (ux=0, uy=free) boundary conditions are shown in Figure 3.1(a). Assumed that deformation of the column is mainly by radial bulging and no significant shear is possible. Therefore, interface element between stone column and clay has not been used. Mitchell, J. K., and Huber, T. R. (1985) also carried out similar type of finite element analysis without the inclusion of the interface element. 3.4 Geometrical Parameters The dimensions of the PLAXIS model are shown in Figure 3.1(b). H is the height of the column, which varies between 10m, 20m, and 30m. D is the diameter of the stone column, which has a typical value of 1m, in all the models except for the model to check the influence of diameter and spacing. Equivalent diameter De depends on the spacing between stone columns as well as the arrangement pattern of the columns. The value of De was calculated by considering the following Influence Area methods. 3.4.1 Influence Area Methods There are several methods for calculating the equivalent diameter around the stone column, which depends greatly on the spacing, diameter, and pattern of installation of the stone column. Two methods were considered in this investigation. 3.4.1.1 Equivalent Area method The equivalent area method simply equates the area of the grid spacing with that of the cross sectional area of column to find the influence area around the stone column. The following example gives a better understanding of the above statement. Example: Grid spacing of the column = 1.5 X 1.5 meters (square grid) Therefore, Diameter of stone column = Finally, Where, De is the equivalent diameter around the stone column. 3.4.1.2 Unit cell method (Balaam Booker, 1981) Unit cell consists of the column and the surrounding soil within the zone of influence of the column. The unit cell has the same area as the actual domain and its perimeter is shear free and undergoes no lateral displacement. Balaam Booker (1981) relates the diameter of the unit cell to the spacing of the columns as: where, De is the equivalent diameter (for square grid) S is the spacing of the stone column Similarly the different geometrical patterns due to column arrangements are shown in the Figure 3.2. Both methods reviewed above gives relatively similar magnitudes. However, Priebes analytical method concerns more on unit cell area. Hence, for this investigation Equivalent Area method is used to model the influence are in PLAXIS. 3.5 Mesh Refinement Test Mesh generation has a great influence in the accuracy of the model. Generally, the finer the mesh the more accurate the result would be. However, this is not true for every case. Therefore a simple test using PLAXIS was conducted to check the effect of mesh refinement. Initially, mesh generation was set to coarse (around 100 elements), utilized as global coarseness of model. The test was carried out by comparing it with the refined mesh (around 500 elements). Moreover, the mesh is further refined which in PLAXIS is set to very fined (around 1000 elements). The generated meshes are shown in Figure 3.3. followed by the time-displacement graph showing the comparison between coarse, medium, fine and very fine mesh refinements. (Figure 3.4) From the above graph it can be seen that the four curves gives comparable results. However, the coarse, medium, and fine meshes give very similar results compared to the very fine mesh refinement. The objective here was to get the lowest value for the displacement since the improved ground due to the installation of stone column would eventually lead to a reduced settlement. Therefore, the finest mesh refinement gives the most precise result. Even though it takes a substantial amount of time to simulate using the most finest meshing, for this investigation, models had been simulated using the very fine mesh option. 3.6 Input Parameters Varying the soil parameters can alter soil characteristics. Most important outcome by altering these parameters is deformation that leads to settlement. Such parameters that have major impact on settlement includes, material type, spacing of stone columns, diameter of influence area, diameter of stone column, elastic modulus of both column and soil, depth of the soil layer, Poissons ratio for both column material and soil, Unit weights of the materials, cohesion, friction angle, etc. Soil and material properties are shown in Table 3.1. Note that the effective stress cohesion, c of the stone column is given a small nonzero value to avoid numerical complications. The majority of the above parameters are considered for only one type of test model and are varied for different model tests. The varied parameters such as elastic modulus of soil and column, friction angle, spacing between columns and influence area around the stone column are reviewed in the following section. 3.7 Test Models The main objective of this project is comparing both analytical and numerical method using Priebes analytical approach and finite element analysis as numerical solution. This can only be achieved by developing multiple models and simulations to obtain a range of values to compare with, which would lead to a more solid conclusion. Three constitutive models were considered for the representation of the following three cases. A clay layer of 30 m, which has a stone column of height 10 m installed. A clay layer of 30 m, which has a stone column of height 20 m installed. A clay layer of 30 m, which has a stone column of height 30 m installed. Note that 1 and 2 are floating columns that are not extended to bedrock or hard layer, which in stone column installation is a rare case, yet installed occasionally. Each of the above tests was carried out by varying the spacing between columns, which would alter the s/d relationship together with the Ac/A ratio. Further tests were carried out to check the influence of stress à Ã†â€™0, diameter D, modulus of deformation of the column to sand ratio Ec/Es and friction angle of stone column ÃŽÂ ¦c using the third case and compared them against the Priebe analytical approach. The summary of test models is given in the Tables 3.2. All the tests were carried out in 3 stages. Install the stone column: Just after the stone column is installed Apply Load: Just after the load is applied to the column Consolidation: After the consolidation process completed to a minimum pore pressure of 1kPa In the all cases the materials were idealized as the Mohr-Coulomb model with the characteristic linear-elastic-perfectly plastic behaviour and the failure criteria defined by the strength parameters given in tables below. Table 3.2 Summary of Model tests Model Test Description Constants Variables 1 Influence of column height on settlement (case 1, 2, and 3) à Ã†â€™0 = 100 kPa Ac/A = 0.2 ÃŽÂ ¦c = 40o Ec/Es = 20 Heigh

Losing Weight the Correct Way Essay example -- Health Exercise Weight

Losing Weight the Correct Way Though many Americans are in the diet and weight-loss craze, the population as a whole is still considered overweight (Lemonick). This may be due to many factors, such as lack of nutrition in food and having a slothful lifestyle. Also, as people pursue other interests, such as careers and family life, they ignore keeping themselves healthy and fit. To maintain health and life span, one must exercise, eat moderately, and eat foods that have nutritional value. If one follows this plan, one can successfully lose weight and be healthy.   Ã‚  Ã‚  Ã‚  Ã‚  Exercise and having an active lifestyle is an important component to maintain in order to lose weight. Some people may think that if they skip a few meals a day and cut down on snacks, that they will lose weight without having to exercise. However, this is an incorrect assumption. To lose weight in a way that doesn’t damage one’s body, one has to make time to exercise. Skipping breakfast and ignoring when your body tells you it needs energy from food is not the way to safely lose weight. When one exercises, he slowly burns off fat, which helps the body function smoothly and effectively. Though, nowadays, people don’t have time to go to the gym or take aerobics classes, simply taking the stairs instead of the elevator is a way of keeping oneself active and can make a huge difference in one’s health.   Ã‚  Ã‚  Ã‚  Ã‚  People must learn to eat moderately to effectively lose weight. It seems as if as the American popu...

My Educational Philosophy :: Philosophy of Education Teaching

My Educational Philosophy When I become a teacher I will strive to better my student’s life not only intellectually, but also socially and emotionally. I will strive to learn from them as much as I teach them; in hopes to become a better teacher to my future pupils. I was inspired to do this by a special teacher who is also my ideal teacher. Mr. Bishop, my junior high teacher, was a big role model to me; he is a teacher whom I model myself after. He is a teacher who always had an answer to everything. Sometimes, I think that he must be the wisest man I know. If you ever needed help he was there for you. Mr. Bishop is a teacher to this day that I trust in and talk to, and I think that’s the way every teacher should be. I hope that after I graduate and become a teacher that I will be someone’s role model or someone a student can come and talk to when they may have a problem and can trust in. As an educator I want to motivate my students to learn. I hope to build their confidence and self-esteem to overcome fears of failure and strive to reach their goals and dreams. There are many reasons why I want to become a teacher, but the main reason would be that I love the feeling of helping someone be the best person they can be. When I think that I would have a part in this process it makes all my efforts worth everything. Teachers play a very vital role in today’s society. Without teachers there would be no doctors, lawyers, or any other professions. Every skilled working person in America can attribute some of his or her abilities or skills to a teacher. A good teacher does not only teach curriculum, but he or she also teaches children about life. A classroom should make children feel emotionally fit, because not all of them have that stability at home. A good teacher laughs with their students, but knows when to be serious. Children need good teachers, and I intend to become one. When I become a teacher, my classroom will consist of many different colors to give the children a sense of a fun atmosphere.

The Kite Tunner

In The Kite Runner, even though Hassan remains loyal, forgiving, and good natured, he is still the character who suffers the most. Hassan is a character who is discriminated against from the start of the book, till the very end. He is a part of a poor ethnic group called Hazaras whom are considered victims in the Afghan society. Amir and Hassan are half brothers, but because Hassan was a Hazara, he grew up in a hut as a servant working for his own father. Hassan understands his inferiority and accepts it, which causes other people to take advantage of him by betraying him. For example, even though Hassan always stood up for Amir, Amir left Hassan to get raped. Hassan was too scared to stand up for his best friend and believed that Hassan is sacrificing himself for Amir. Not only was the rape an attack physically, but it is also an attack on the victim’s emotions and dignity. In the Kite Runner, Hassan suffers the most pain both physically and mentally by living his life being betrayed, discriminated and losing his family. To start off, Hassan is a poor ethnic Hazara, he is considered inferior to the Afghan society, and therefore is discriminated throughout the whole novel. For example, Hassan and Amir both have the same rich father, but because Hassan was illegitimate and was a Hazara, he grew up as a servant in his father’s hut. With this in mind, Hassan is discriminated by everyone even his own family even the ones who Hassam didn’t even know was his family. Discrimination is so significant in his life that he has accepted the fact that he was born to be hated for his appearance. Hassan’s biological father Baba lies to Hassan and doesn’t even tell him that he is his real father. Despite the fact that Hassan gets discriminated upon, he still remains loyal and forgiving. Another example would be when the Taliban wanted Baba’s house and when they found out that Hassan and his wife were kuvubg u but alone, they wouldn’t listen to him when he tried to explain that Rahim Khan was the owner and they were waiting his return. The Taliban of course shot Hassan and his wife leaving Sohrab alone. The Taliban who show Hassan and his Wife were dismissed from their trial because they said it was self defence. They were dismissed because they have no proof that the Hazaras attacked the Taliban because no one would stand up for Hazaras. With this in mind, Hassan has died In addition, despite the fact that everyone knows that Hassan is good natured, he still is betrayed many times in the story mostly by his best friend Amir. In detail, Amir treats Hassan unfairly even thought he knows that Hassan will be good about it. For example, Amir left Hassan to get raped by Assef in the alley Hassan taught him incorrect meaning of words. Even after Amir betrays Amir, Hassan continues to serve him. and abandoning him even though Hassan saved him countless amounts of time. Amir only does this because When Assef asked Amir why he’s friends with a Hazara, Amir said that he’s his servant and nothing more. Amir didn’t know that Hassan was his half brother, which leads Amir to take advantage of Hassan. Rape is one of the events in the story that happens to Hassan that makes him suffer the most. In this story, rape is not just physically violent, but it is also an attack on the victim’s emotions and dignity. The fact that Hassan didn’t resist just proves his role in society and how he accepts punishment that is given upon him. The rape proves that he doesn’t care about his own suffering Lastly, Hassan suffers by losing the people who were once family to him. Hassan suffers because his half brother Amir is the reason why Hassan and Ali left the house. In fact, Hassan has it tougher than Amir from the beginning. Not only did he lose his mother, his mother rejected him at birth. Sanaubar had taken one glance at the baby in Ali's arms, seen the cleft lip, and barked a bitter laughter. [†¦ ]. She had refused to even hold Hassan, and just five days later she was gone. (29). This event has left Hassan motherless ever since birth. He is separated from his beloved Amir and Baba whom he spent his whole life with. Another example would be when his mother left and rejected him at birth

Digital Fortress Chapter 100-106

Chapter 100 Hulohot took the Giralda stairs three at a time. The only light in the spiral passage was from small open-air windows every 180 degrees. He's trapped! David Becker will die! Hulohot circled upward, gun drawn. He kept to the outside wall in case Becker decided to attack from above. The iron candle poles on each landing would make good weapons if Becker decided to use one. But by staying wide, Hulohot would be able to spot him in time. Hulohot's gun had a range significantly longer than a five-foot candle pole. Hulohot moved quickly but carefully. The stairs were steep; tourists had died here. This was not America-no safety signs, no handrails, no insurance disclaimers. This was Spain. If you were stupid enough to fall, it was your own damn fault, regardless of who built the stairs. Hulohot paused at one of the shoulder-high openings and glanced out. He was on the north face and, from the looks of things, about halfway up. The opening to the viewing platform was visible around the corner. The staircase to the top was empty. David Becker had not challenged him. Hulohot realized maybe Becker had not seen him enter the tower. That meant the element of surprise was on Hulohot's side as well-not that he'd need it. Hulohot held all the cards. Even the layout of the tower was in his favor; the staircase met the viewing platform in the southwest corner-Hulohot would have a clear line of fire to every point of the cell with no possibility that Becker could get behind him. And to top things off, Hulohot would be moving out of the dark into the light. A killing box, he mused. Hulohot measured the distance to the doorway. Seven steps. He practiced the kill in his mind. If he stayed right as he approached the opening, he would be able to see the leftmost corner of the platform before he reached it. If Becker was there, Hulohot would fire. If not, he would shift inside and enter moving east, facing the right corner, the only place remaining that Becker could be. He smiled. SUBJECT: DAVID BECKER-TERMINATED The time had come. He checked his weapon. With a violent surge, Hulohot dashed up. The platform swung into view. The left corner was empty. As rehearsed, Hulohot shifted inside and burst through the opening facing right. He fired into the corner. The bullet ricocheted back off the bare wall and barely missed him. Hulohot wheeled wildly and let out a muted scream. There was no one there. David Becker had vanished. Three flights below, suspended 325 feet over the Jardin de los Naranjos, David Becker hung on the outside of the Giralda like a man doing chin-ups on a window ledge. As Hulohot had been racing up the staircase, Becker had descended three flights and lowered himself out one of the openings. He'd dropped out of sight just in time. The killer had run right by him. He'd been in too much of a hurry to notice the white knuckles grasping the window ledge. Hanging outside the window, Becker thanked God that his daily squash routine involved twenty minutes on the Nautilus machine to develop his biceps for a harder overhead serve. Unfortunately, despite his strong arms, Becker was now having trouble pulling himself back in. His shoulders burned. His side felt as if it were tearing open. The rough-cut stone ledge provided little grip, grating into his fingertips like broken glass. Becker knew it was only a matter of seconds before his assailant would come running down from above. From the higher ground, the killer would undoubtedly see Becker's fingers on the ledge. Becker closed his eyes and pulled. He knew he would need a miracle to escape death. His fingers were losing their leverage. He glanced down, past his dangling legs. The drop was the length of a football field to the orange trees below. Unsurvivable. The pain in his side was getting worse. Footsteps now thundered above him, loud leaping footsteps rushing down the stairs. Becker closed his eyes. It was now or never. He gritted his teeth and pulled. The stone tore against the skin on his wrists as he yanked himself upward. The footsteps were coming fast. Becker grappled at the inside of the opening, trying to secure his hold. He kicked his feet. His body felt like lead, as if someone had a rope tied to his legs and were pulling him down. He fought it. He surged up onto his elbows. He was in plain view now, his head half through the window like a man in a guillotine. He wriggled his legs, kicking himself into the opening. He was halfway through. His torso now hung into the stairwell. The footsteps were close. Becker grabbed the sides of the opening and in a single motion launched his body through. He hit the staircase hard. Hulohot sensed Becker's body hit the floor just below him. He leapt forward, gun leveled. A window spun into view. This is it! Hulohot moved to the outside wall and aimed down the staircase. Becker's legs dashed out of sight just around the curve. Hulohot fired in frustration. The bullet ricocheted down the stairwell. As Hulohot dashed down the stairs after his prey, he kept to the outside wall for the widest angle view. As the staircase revolved into view before him, it seemed Becker was always 180 degrees ahead of him, just out of sight. Becker had taken the inside track, cutting off the angle and leaping four or five stairs at a time. Hulohot stayed with him. It would take only a single shot. Hulohot was gaining. He knew that even if Becker made the bottom, there was nowhere to run; Hulohot could shoot him in the back as he crossed the open patio. The desperate race spiraled downward. Hulohot moved inside to the faster track. He sensed he was gaining. He could see Becker's shadow every time they passed an opening. Down. Down. Spiraling. It seemed that Becker was always just around the corner. Hulohot kept one eye on his shadow and one eye on the stairs. Suddenly it appeared to Hulohot that Becker's shadow had stumbled. It made an erratic lurch left and then seemed to spin in midair and sail back toward the center of the stairwell. Hulohot leapt forward. I've got him! On the stairs in front of Hulohot, there was a flash of steel. It jabbed into the air from around the corner. It thrust forward like a fencer's foil at ankle level. Hulohot tried to shift left, but it was too late. The object was between his ankles. His back foot came forward, caught it hard, and the post slammed across his shin. Hulohot's arms went out for support but found only empty air. He was abruptly airborne, turning on his side. As Hulohot sailed downward, he passed over David Becker, prone on his stomach, arms outstretched. The candle pole in his hands was now caught up in Hulohot's legs as he spun downward. Hulohot crashed into the outside wall before he hit the staircase. When he finally found the floor, he was tumbling. His gun clattered to the floor. Hulohot's body kept going, head over heels. He spiraled five complete 360-degree rotations before he rolled to a stop. Twelve more steps, and he would have tumbled out onto the patio. Chapter 101 David Becker had never held a gun, but he was holding one now. Hulohot's body was twisted and mangled in the darkness of the Giralda staircase. Becker pressed the barrel of the gun against his assailant's temple and carefully knelt down. One twitch and Becker would fire. But there was no twitch. Hulohot was dead. Becker dropped the gun and collapsed on the stairs. For the first time in ages he felt tears well up. He fought them. He knew there would be time for emotion later; now it was time to go home. Becker tried to stand, but he was too tired to move. He sat a long while, exhausted, on the stone staircase. Absently, he studied the twisted body before him. The killer's eyes began to glaze over, gazing out at nothing in particular. Somehow, his glasses were still intact. They were odd glasses, Becker thought, with a wire protruding from behind the earpiece and leading to a pack of some sort on his belt. Becker was too exhausted to be curious. As he sat alone in the staircase and collected his thoughts, Becker shifted his gaze to the ring on his finger. His vision had cleared somewhat, and he could finally read the inscription. As he had suspected, it was not English. He stared at the engraving along moment and then frowned. This is worth killing for? The morning sun was blinding when Becker finally stepped out of the Giralda onto the patio. The pain in his side had subsided, and his vision was returning to normal. He stood a moment, in a daze, enjoying the fragrance of the orange blossoms. Then he began moving slowly across the patio. As Becker strode away from the tower, a van skidded to a stop nearby. Two men jumped out. They were young and dressed in military fatigues. They advanced on Becker with the stiff precision of well-tuned machines. â€Å"David Becker?† one demanded. Becker stopped short, amazed they knew his name. â€Å"Who†¦ who are you?† â€Å"Come with us, please. Right away.† There was something unreal about the encounter-something that made Becker's nerve endings start to tingle again. He found himself backing away from them. The shorter man gave Becker an icy stare. â€Å"This way, Mr. Becker. Right now.† Becker turned to run. But he only took one step. One of the men drew a weapon. There was a shot. A searing lance of pain erupted in Becker's chest. It rocketed to his skull. His fingers went stiff, and Becker fell. An instant later, there was nothing but blackness. Chapter 102 Strathmore reached the TRANSLTR floor and stepped off the catwalk into an inch of water. The giant computer shuddered beside him. Huge droplets of water fell like rain through the swirling mist. The warning horns sounded like thunder. The commander looked across at the failed main generators. Phil Chartrukian was there, his charred remains splayed across a set of coolant fins. The scene looked like some sort of perverse Halloween display. Although Strathmore regretted the man's death, there was no doubt it had been â€Å"a warranted casualty.† Phil Chartrukian had left Strathmore no choice. When the Sys-Sec came racing up from the depths, screaming about a virus, Strathmore met him on the landing and tried to talk sense to him. But Chartrukian was beyond reason. We've got a virus! I'm calling Jabba! When he tried to push past, the commander blocked his way. The landing was narrow. They struggled. The railing was low. It was ironic, Strathmore thought, that Chartrukian had been right about the virus all along. The man's plunge had been chilling-a momentary howl of terror and then silence. But it was not half as chilling as the next thing Commander Strathmore saw. Greg Hale was staring up at him from the shadows below, a look of utter horror on his face. It was then that Strathmore knew Greg Hale would die. TRANSLTR crackled, and Strathmore turned his attention back to the task at hand. Kill power. The circuit breaker was on the other side of the freon pumps to the left of the body. Strathmore could see it clearly. All he had to do was pull a lever and the remaining power in Crypto would die. Then, after a few seconds, he could restart the main generators; all doorways and functions would comeback on-line; the freon would start flowing again, and TRANSLTR would be safe. But as Strathmore slogged toward the breaker, he realized there was one final obstacle: Chartrukian's body was still on the main generator's cooling fins. Killing and then restarting the main generator would only cause another power failure. The body had to be moved. Strathmore eyed the grotesque remains and made his way over. Reaching up, he grabbed a wrist. The flesh was like Styrofoam. The tissue had been fried. The whole body was devoid of moisture. The commander closed his eyes, tightened his grip around the wrist, and pulled. The body slid an inch or two. Strathmore pulled harder. The body slid again. The commander braced himself and pulled with all his might. Suddenly he was tumbling backward. He landed hard on his backside up against a power casement. Struggling to sit up in the rising water, Strathmore stared down in horror at the object in his fist. It was Chartrukian's forearm. It had broken off at the elbow. Upstairs, Susan continued her wait. She sat on the Node 3 couch feeling paralyzed. Hale lay at her feet. She couldn't imagine what was taking the commander so long. Minutes passed. She tried to push David from her thoughts, but it was no use. With every blast of the horns, Hale's words echoed inside her head: I'm truly sorry about David Becker. Susan thought she would lose her mind. She was about to jump up and race onto the Crypto floor when finally it happened. Strathmore had thrown the switch and killed all power. The silence that engulfed Crypto was instantaneous. The horns choked off mid blare, and the Node 3 monitors flickered to black. Greg Hale's corpse disappeared into the darkness, and Susan instinctively yanked her legs up onto the couch. She wrapped Strathmore's suit coat around her. Darkness. Silence. She had never heard such quiet in Crypto. There'd always been the low hum of the generators. But now there was nothing, only the great beast heaving and sighing in relief. Crackling, hissing, slowly cooling down. Susan closed her eyes and prayed for David. Her prayer was a simple one-that God protect the man she loved. Not being a religious woman, Susan had never expected to hear a response to her prayer. But when there was a sudden shuddering against her chest, she jolted upright. She clutched her chest. A moment later she understood. The vibrations she felt were not the hand of God at all-they were coming from the commander's jacket pocket. He had set the vibrating silent-ring feature on his SkyPager. Someone was sending Commander Strathmore a message. Six stories below, Strathmore stood at the circuit breaker. The sublevels of Crypto were now as dark as the deepest night. He stood a moment enjoying the blackness. The water poured down from above. It was a midnight storm. Strathmore tilted his head back and let the warm droplets wash away his guilt. I'm a survivor. He knelt and washed the last of Chartrukian's flesh from his hands. His dreams for Digital Fortress had failed. He could accept that. Susan was all that mattered now. For the first time in decades, he truly understood that there was more to life than country and honor. I sacrificed the best years of my life for country and honor. But what about love? He had deprived himself for far too long. And for what? To watch some young professor steal away his dreams? Strathmore had nurtured Susan. He had protected her. He had earned her. And now, at last, he would have her. Susan would seek shelter in his arms when there was nowhere else to turn. She would come to him helpless, wounded by loss, and in time, he would show her that love heals all. Honor. Country. Love. David Becker was about to die for all three. Chapter 103 The Commander rose through the trapdoor like Lazarus back from the dead. Despite his soggy clothes, his step was light. He strode toward Node 3-toward Susan. Toward his future. The Crypto floor was again bathed in light. Freon was flowing downward through the smoldering TRANSLTR like oxygenated blood. Strathmore knew it would take a few minutes for the coolant to reach the bottom of the hull and prevent the lowest processors from igniting, but he was certain he'd acted in time. He exhaled in victory, never suspecting the truth-that it was already too late. I'm a survivor, he thought. Ignoring the gaping hole in the Node 3 wall, he strode to the electronic doors. They hissed open. He stepped inside. Susan was standing before him, damp and tousled in his blazer. She looked like a freshman coed who'd been caught in the rain. He felt like the senior who'd lent her his varsity sweater. For the first time in years, he felt young. His dream was coming true. But as Strathmore moved closer, he felt he was staring into the eyes of a woman he did not recognize. Her gaze was like ice. The softness was gone. Susan Fletcher stood rigid, like an immovable statue. The only perceptible motion were the tears welling in her eyes. â€Å"Susan?† A single tear rolled down her quivering cheek. â€Å"What is it?† the commander pleaded. The puddle of blood beneath Hale's body had spread across the carpet like an oil spill. Strathmore glanced uneasily at the corpse, then back at Susan. Could she possibly know? There was no way. Strathmore knew he had covered every base. â€Å"Susan?† he said, stepping closer. â€Å"What is it?† Susan did not move. â€Å"Are you worried about David?† There was a slight quiver in her upper lip. Strathmore stepped closer. He was going to reach for her, but he hesitated. The sound of David's name had apparently cracked the dam of grief. Slowly at first-a quiver, a tremble. And then a thundering wave of misery seemed to course through her veins. Barely able to control her shuddering lips, Susan opened her mouth to speak. Nothing came. Without ever breaking the icy gaze she'd locked on Strathmore, she took her hand from the pocket of his blazer. In her hand was an object. She held it out, shaking. Strathmore half expected to look down and see the Beretta leveled at his gut. But the gun was still on the floor, propped safely in Hale's hand. The object Susan was holding was smaller. Strathmore stared down at it, and an instant later, he understood. As Strathmore stared, reality warped, and time slowed to a crawl. He could hear the sound of his own heart. The man who had triumphed over giants for so many years had been outdone in an instant. Slain by love-by his own foolishness. In a simple act of chivalry, he had given Susan his jacket. And with it, his SkyPager. Now it was Strathmore who went rigid. Susan's hand was shaking. The pager fell at Hale's feet. With a look of astonishment and betrayal that Strathmore would never forget, Susan Fletcher raced past him out of Node 3. The commander let her go. In slow motion, he bent and retrieved the pager. There were no new messages-Susan had read them all. Strathmore scrolled desperately through the list. SUBJECT: ENSEI TANKADO-TERMINATED SUBJECT: PIERRE CLOUCHARDE-TERMINATED SUBJECT: HANS HUBER-TERMINATED SUBJECT: ROCIO EVA GRANADA-TERMINATED†¦ The list went on. Strathmore felt a wave of horror. I can explain! She will understand! Honor! Country! But there was one message he had not yet seen-one message he could never explain. Trembling, he scrolled to the final transmission. SUBJECT: DAVID BECKER-TERMINATED Strathmore hung his head. His dream was over. Chapter 104 Susan staggered out of Node 3. SUBJECT: DAVID BECKER-TERMINATED As if in a dream, she moved toward Crypto's main exit. Greg Hale's voice echoed in her mind: Susan, Strathmore's going to kill me! Susan, the commander's in love with you! Susan reached the enormous circular portal and began stabbing desperately at the keypad. The door did not move. She tried again, but the enormous slab refused to rotate. Susan let out a muted scream-apparently the power outage had deleted the exit codes. She was still trapped. Without warning, two arms closed around her from behind, grasping her half-numb body. The touch was familiar yet repulsive. It lacked the brute strength of Greg Hale, but there was a desperate roughness to it, an inner determination like steel. Susan turned. The man restraining her was desolate, frightened. It was a face she had never seen. â€Å"Susan,† Strathmore begged, holding her. â€Å"I can explain.† She tried to pull away. The commander held fast. Susan tried to scream, but she had no voice. She tried to run, but strong hands restrained her, pulling her backward. â€Å"I love you,† the voice was whispering. â€Å"I've loved you forever.† Susan's stomach turned over and over. â€Å"Stay with me.† Susan's mind whirled with grisly images-David's bright-green eyes, slowly closing for the last time; Greg Hale's corpse seeping blood onto the carpet; Phil Chartrukian's burned and broken on the generators. â€Å"The pain will pass,† the voice said. â€Å"You'll love again.† Susan heard nothing. â€Å"Stay with me,† the voice pleaded. â€Å"I'll heal your wounds.† She struggled, helpless. â€Å"I did it for us. We're made for each other. Susan, I love you.† The words flowed as if he had waited a decade to speak them. â€Å"I love you! I love you!† In that instant, thirty yards away, as if rebutting Strathmore's vile confession, TRANSLTR let out a savage, pitiless hiss. The sound was an entirely new one-a distant, ominous sizzling that seemed to grow like a serpent in the depths of the silo. The freon, it appeared, had not reached its mark in time. The commander let go of Susan and turned toward the $2 billion computer. His eyes went wide with dread. â€Å"No!† He grabbed his head. â€Å"No!† The six-story rocket began to tremble. Strathmore staggered a faltering step toward the thundering hull. Then he fell to his knees, a sinner before an angry god. It was no use. At the base of the silo, TRANSLTR's titanium-strontium processors had just ignited. Chapter 105 A fireball racing upward through three million silicon chips makes a unique sound. The crackling of a forest fire, the howling of a tornado, the steaming gush of a geyser†¦ all trapped within a reverberant hull. It was the devil's breath, pouring through a sealed cavern, looking for escape. Strathmore knelt transfixed by the horrific noise rising toward them. The world's most expensive computer was about to become an eight-story inferno. In slow motion, Strathmore turned back toward Susan. She stood paralyzed beside the Crypto door. Strathmore stared at her tear-streaked face. She seemed to shimmer in the fluorescent light. She's an angel, he thought. He searched her eyes for heaven, but all he could see was death. It was the death of trust. Love and honor were gone. The fantasy that had kept him going all these years was dead. He would never have Susan Fletcher. Never. The sudden emptiness that gripped him was overwhelming. Susan gazed vaguely toward TRANSLTR. She knew that trapped within the ceramic shell, a fireball was racing toward them. She sensed it rising faster and faster, feeding on the oxygen released by the burning chips. In moments the Crypto dome would be a blazing inferno. Susan's mind told her to run, but David's dead weight pressed down all around her. She thought she heard his voice calling to her, telling her to escape, but there was nowhere to go. Crypto was a sealed tomb. It didn't matter; the thought of death did not frighten her. Death would stop the pain. She would be with David. The Crypto floor began to tremble, as if below it an angry sea monster were rising out of the depths. David's voice seemed to be calling. Run, Susan! Run! Strathmore was moving toward her now, his face a distant memory. His cool gray eyes were lifeless. The patriot who had lived in her mind a hero had died-a murderer. His arms were suddenly around her again, clutching desperately. He kissed her cheeks. â€Å"Forgive me,† he begged. Susan tried to pull away, but Strathmore held on. TRANSLTR began vibrating like a missile preparing to launch. The Crypto floor began to shake. Strathmore held tighter. â€Å"Hold me, Susan. I need you.† A violent surge of fury filled Susan's limbs. David's voice called out again. I love you! Escape! In a sudden burst of energy, Susan tore free. The roar from TRANSLTR became deafening. The fire was at the silo's peak. TRANSLTR groaned, straining at its seams. David's voice seemed to lift Susan, guide her. She dashed across the Crypto floor and started up Strathmore's catwalk stairs. Behind her, TRANSLTR let out a deafening roar. As the last of the silicon chips disintegrated, a tremendous updraft of heat tore through the upper casing of the silo and sent shards of ceramic thirty feet into the air. Instantly the oxygen-rich air of Crypto rushed in to fill the enormous vacuum. Susan reached the upper landing and grabbed the banister when the tremendous rush of wind ripped at her body. It spun her around in time to see the deputy director of operations, far below, staring up at her from beside TRANSLTR. There was a storm raging all around him, and yet there was peace in his eyes. His lips parted, and he mouthed his final word. â€Å"Susan.† The air rushing into TRANSLTR ignited on contact. In a brilliant flash of light, Commander Trevor Strathmore passed from man, to silhouette, to legend. When the blast hit Susan, it blew her back fifteen feet into Strathmore's office. All she remembered was a searing heat. Chapter 106 In the window of the Director's conference room, high above the Crypto dome, three faces appeared, breathless. The explosion had shaken the entire NSA complex. Leland Fontaine, Chad Brinkerhoff, and Midge Milken all stared out in silent horror. Seventy feet below, the Crypto dome was blazing. The polycarbonate roof was still intact, but beneath the transparent shell, a fire raged. Black smoke swirled like fog inside the dome. The three stared down without a word. The spectacle had an eerie grandeur to it. Fontaine stood a long moment. He finally spoke, his voice faint but unwavering. â€Å"Midge, get a crew down there†¦ now.† Across the suite, Fontaine's phone began to ring. It was Jabba.